Package 'metaConvert'

Title: An Automatic Suite for Estimation of Various Effect Size Measures
Description: Automatically estimate 11 effect size measures from a well-formatted dataset. Various other functions can help, for example, removing dependency between several effect sizes, or identifying differences between two datasets. This package is mainly designed to assist in conducting a systematic review with a meta-analysis but can be useful to any researcher interested in estimating an effect size.
Authors: Corentin J. Gosling [aut, cre], Samuele Cortese [aut], Marco Solmi [aut], Belen Haza [aut], Eduard Vieta [aut], Richard Delorme [aut], Paolo Fusar-Poli [aut], Joaquim Radua [aut]
Maintainer: Corentin J. Gosling <[email protected]>
License: GPL (>= 3)
Version: 1.0.1
Built: 2024-10-27 12:34:43 UTC
Source: CRAN

Help Index


metaConvert: An R Package Dedicated to Automated Effect Size Calculations

Description

The metaConvert package automatically estimates 11 effect size measures from a well-formatted dataframe. Various other functions can help, for example, removing dependency between several effect sizes, or identifying differences between two dataframes. This package is mainly designed to assist in conducting a systematic review with a meta-analysis, but it can be useful to any researcher interested in estimating an effect size.

Overview of the package

To visualize all the types of input data that can be used to estimate the 11 effect size measures available in metaConvert, you can use the see_input_data() function.

Estimate effect sizes

To automatically estimate effect sizes directly from a dataset, you can use the convert_df() function.

Aggregate dependent effect sizes

To automatically aggregate dependent effect sizes using Borenstein's formulas, you can use the aggregate_df() function. This function can handle dependent effect sizes from multiple subgroups, or dependent effect sizes from the same participants.

Flag differences between two datasets

If pairs of data extractors have generated similar datasets that should be compared, you can use the compare_df() function.

Prepare a dataset extraction sheet

If you have not started data extraction yet, you can use the data_extraction_sheet() function to obtain a perfectly formatted data extraction sheet.

Well-formatted dataset

One of the specificities of the metaConvert package is that its core function (convert_df) does not have arguments to specify the names of the variables contained in the dataset. While this allow using a convenient automatic process in the calculations, this requires that the datasets passed to this function respect a very precise formatting (which we will refer to as well-formatted dataset).

Rather than a long description of all column names, we built several tools that help you find required information.

  1. You can use the data_extraction_sheet() function that generates an excel/csv/txt file containing all the column names available, as well as a description of the information it should contain.

  2. You can use the see_input_data() function that generates a list of all available types of input data as well as their estimated/converted effect size measures. This function also points out to the corresponding helper tables available in https://metaconvert.org

Effect size measures available

Eleven effect size measures are accepted:

  • "d": standardized mean difference (i.e., Cohen's d)

  • "g": Hedges' g

  • "md": mean difference

  • "r": Correlation coefficient

  • "z": Fisher's r-to-z correlation

  • "or" or "logor": odds ratio or its logarithm

  • "rr" or "logrr": risk ratio or its logarithm

  • "irr" or "logirr": incidence rate ratio or its logarithm

  • "nnt": number needed to treat

  • "logcvr": log coefficient of variation

  • "logvr": log variability ratio

Output

All the functions of the metaConvert package that are dedicated to effect size calculations (i.e., all the functions named es_from_*) return a dataframe that contain, depending on the function - some of the following columns:

info_used input data used to generate the effect size.
md value of the mean difference.
md_se standard error of the mean difference.
md_ci_lo lower bound of the 95% CI of the mean difference.
md_ci_up upper bound of the 95% CI of the mean difference.
d value of the Cohen's d.
d_se standard error of the Cohen's d.
d_ci_lo lower bound of the 95% CI of the Cohen's d.
d_ci_up upper bound of the 95% CI of the Cohen's d.
g value of the Hedges' g.
g_se standard error of the Hedges' g.
g_ci_lo lower bound of the 95% CI of the Hedges' g.
g_ci_up upper bound of the 95% CI of the Hedges' g.
r value of the correlation coefficient.
r_se standard error of the correlation coefficient.
r_ci_lo lower bound of the 95% CI of the correlation coefficient.
r_ci_up upper bound of the 95% CI of the correlation coefficient.
z value of the r-to-z transformed correlation coefficient.
z_se standard error of the r-to-z transformed correlation coefficient.
z_ci_lo lower bound of the 95% CI of the r-to-z transformed correlation coefficient.
z_ci_up upper bound of the 95% CI of the r-to-z transformed correlation coefficient.
logor value of the log odds ratio.
logor_se standard error of the log odds ratio.
logor_ci_lo lower bound of the 95% CI of the log odds ratio.
logor_ci_up upper bound of the 95% CI of the log odds ratio.
logrr value of the log risk ratio.
logrr_se standard error of the log risk ratio.
logrr_ci_lo lower bound of the 95% CI of the log risk ratio.
logrr_ci_up upper bound of the 95% CI of the log risk ratio.
logirr value of the log incidence rate ratio.
logirr_se standard error of the log incidence rate ratio.
logirr_ci_lo lower bound of the 95% CI of the log incidence rate ratio.
logirr_ci_up upper bound of the 95% CI of the log incidence rate ratio.
logvr value of the log variability ratio.
logvr_se standard error of the log variability ratio.
logvr_ci_lo lower bound of the 95% CI of the log variability ratio.
logvr_ci_up upper bound of the 95% CI of the log variability ratio.
logcvr value of the log coefficient of variation.
logcvr_se standard error of the log coefficient of variation.
logcvr_ci_lo lower bound of the 95% CI of the log coefficient of variation.
logcvr_ci_up upper bound of the 95% CI of the log coefficient of variation.
nnt number needed to treat.

Aggregate a dataframe containing dependent effect sizes

Description

Aggregate a dataframe containing dependent effect sizes

Usage

aggregate_df(
  x,
  dependence = "outcomes",
  cor_unit = 0.8,
  agg_fact,
  es = "es",
  se = "se",
  col_mean = NA,
  col_weighted_mean = NA,
  weights = NA,
  col_sum = NA,
  col_min = NA,
  col_max = NA,
  col_fact = NA,
  na.rm = TRUE
)

Arguments

x

a dataframe that should be aggregated (must contain effect size values and standard errors).

dependence

The type of dependence in your dataframe (can be either "outcomes" or "subgroups"). See details.

cor_unit

The correlation between effect sizes coming from the same clustering unit (only used when dependence = "times" or dependence = "outcomes").

agg_fact

A character string identifying the column name that contains the clustering units (all rows with the same agg_fact value will be aggregated together).

es

A character string identifying the column name containing the effect size values. Default is "es".

se

A character string identifying the column name containing the standard errors of the effect size. Default is "se".

col_mean

a vector of character strings identifying the column names for which the dependent values are summarized by taking their mean.

col_weighted_mean

a vector of character strings identifying the column names for which the dependent values are summarized by taking their weighted mean.

weights

The weights that will be used to estimated the weighted means.

col_sum

a vector of character strings identifying the column names for which the dependent values are summarized by taking their sum.

col_min

a vector of character strings identifying the column names for which the dependent values are summarized by taking their minimum.

col_max

a vector of character strings identifying the column names for which the dependent values are summarized by taking their maximum.

col_fact

a vector of character strings identifying the column names that are factors (different values will be separated by a "/" character).

na.rm

a logical vector indicating whether missing values should be ignored in the calculations for the col_mean, col_weighted_mean, col_sum, col_min and col_max arguments.

Details

  1. In the dependence argument, you should indicate "outcomes" if the dependence within the same clustering unit (e.g., study) is due to the presence of multiple effect sizes produced from the same participants at the same time-point (e.g., multiple outcome measures)

  2. In the dependence argument, you should indicate "times" if the dependence within the same clustering unit (e.g., study) is due to the presence of multiple effect sizes produced from the same participants at the different time-points (e.g., an RCT with several follow-up waves).

  3. In the dependence argument, you should indicate "subgroups" if the dependence within the same clustering unit (e.g., study) is due to the presence of multiple effect sizes produced by independent subgroups (e.g., one effect size for boys, and one for girls).

If you are working with ratio measures, make sure that the information on the effect size estimates (i.e., the column passed to the es argument of the function) is presented on the log scale.

Value

The object returned by the aggregate_df contains, is a dataframe containing at the very least, the aggregating factor, and the aggregated effect size values and standard errors. All columns indicated in the col_* arguments will also be included in this dataframe.

row_id the row number in the original dataset.
es the aggregated effect size value.
se the standard error of the aggregated effect size.
... any columns indicated in the col_* arguments.

Examples

res <- summary(convert_df(df.haza, measure = "d"))
aggregate_df(res, dependence = "outcomes", cor_unit = 0.8,
             agg_fact = "study_id", es = "es_crude", se = "se_crude",
             col_fact = c("outcome", "type_publication"))

Flag the differences between two dataframes.

Description

Flag the differences between two dataframes.

Usage

compare_df(
  df_extractor_1,
  df_extractor_2,
  ordering_columns = NULL,
  tolerance = 0,
  tolerance_type = "ratio",
  output = "html",
  file_name = "comparison.xlsx"
)

Arguments

df_extractor_1

a first dataset. Differences with the second dataset will be flagged in green.

df_extractor_2

a second dataset. Differences with the first dataset will be flagged in red.

ordering_columns

column names that should be used to re-order the two datasets before running the comparisons

tolerance

the cut-off value used to flag differences between two numeric values

tolerance_type

must be either 'difference' or 'ratio'

output

type of object returned by the function (see 'Value' section). Must be either 'wide', 'long', 'html', 'html2' or 'xlsx'.

file_name

the name of the generated file (only used when output="xlsx")

Details

This function aims to facilitate the comparison of two datasets created by blind data extractors during a systematic review. It is a wrapper of several functions from the 'compareDF' package.

Value

This function returns a dataframe composed of the rows that include a difference (all identical rows are removed). Several outputs can be requested :

  1. setting output="xlsx" returns an excel file. A message indicates the location of the generated file on your computer.

  2. setting output="html" returns an html file

  3. setting output="html2" returns an html file (only useful when the "html" command did not make the html pane appear in R studio).

  4. setting output="wide" a wide dataframe

  5. setting output="long" a long dataframe

References

Alex Joseph (2022). compareDF: Do a Git Style Diff of the Rows Between Two Dataframes with Similar Structure. R package version 2.3.3. https://CRAN.R-project.org/package=compareDF

Examples

df.compare1 = df.compare1[order(df.compare1$author), ]
df.compare2 = df.compare2[order(df.compare2$year), ]

compare_df(
  df_extractor_1 = df.compare1,
  df_extractor_2 = df.compare2,
  ordering_columns = c("author", "year")
)

Automatically compute effect sizes from a well formatted dataset

Description

Automatically compute effect sizes from a well formatted dataset

Usage

convert_df(
  x,
  measure = c("d", "g", "md", "logor", "logrr", "logirr", "nnt", "r", "z", "logvr",
    "logcvr"),
  main_es = TRUE,
  es_selected = c("auto", "hierarchy", "minimum", "maximum"),
  selection_auto = c("crude", "paired", "adjusted"),
  split_adjusted = TRUE,
  format_adjusted = c("wide", "long"),
  verbose = TRUE,
  max_asymmetry = 10,
  hierarchy = "means_sd > means_se > means_ci",
  table_2x2_to_cor = "tetrachoric",
  rr_to_or = "metaumbrella",
  or_to_rr = "metaumbrella_cases",
  or_to_cor = "bonett",
  smd_to_cor = "viechtbauer",
  pre_post_to_smd = "bonett",
  r_pre_post = 0.5,
  cor_to_smd = "viechtbauer",
  unit_type = "raw_scale",
  yates_chisq = FALSE
)

Arguments

x

a well formatted dataset

measure

the effect size measure that will be estimated from the information stored in the dataset. See details.

main_es

a logical variable indicating whether a main effect size should be selected when overlapping data are present. See details.

es_selected

the method used to select the main effect size when several information allows to estimate an effect size for the same association/comparison. Must be either "minimum" (the smallest effect size will be selected), "maximum" (the largest effect size will be selected) or "hierarchy" (the effect size computed from the information specified highest in the hierarchy will be selected). See details.

selection_auto

a character string giving details on the best "auto" hierarchy to use (only useful when hierarchy="auto" and measure= "d", "g" or "md"). See details.

split_adjusted

a logical value indicating whether crude and adjusted effect sizes should be presented separately. See details.

format_adjusted

presentation format of the adjusted effect sizes. See details.

verbose

a logical variable indicating whether text outputs and messages should be generated. We recommend turning this option to FALSE only after having carefully read all the generated messages.

max_asymmetry

A percentage indicating the tolerance before detecting asymmetry in the 95% CI bounds.

hierarchy

a character string indicating the hierarchy in the information to be prioritized for the effect size calculations. See details.

table_2x2_to_cor

formula used to obtain a correlation coefficient from the contingency table. For now only 'tetrachoric' is available.

rr_to_or

formula used to convert the rr value into an odds ratio.

or_to_rr

formula used to convert the or value into a risk ratio.

or_to_cor

formula used to convert the or value into a correlation coefficient.

smd_to_cor

formula used to convert the cohen_d value into a coefficient correlation.

pre_post_to_smd

formula used to obtain a SMD from pre/post means and SD of two independent groups.

r_pre_post

pre-post correlation across the two groups (use this argument only if the precise correlation in each group is unknown)

cor_to_smd

formula used to convert a correlation coefficient value into a SMD.

unit_type

the type of unit for the unit_increase_iv argument. Must be either "sd" or "value" (see es_from_pearson_r).

yates_chisq

a logical value indicating whether the Chi square has been performed using Yate's correction for continuity.

Details

This function automatically computes or converts between 11 effect sizes measures from any relevant type of input data stored in the dataset you pass to this function.

Effect size measures

Possible effect size measures are:

  1. Cohen's d ("d")

  2. Hedges' g ("g")

  3. mean difference ("md")

  4. (log) odds ratio ("or" and "logor")

  5. (log) risk ratio ("rr" and "logrr")

  6. (log) incidence rate ratio ("irr" and "logirr")

  7. correlation coefficient ("r")

  8. transformed r-to-z correlation coefficient ("z")

  9. log variability ratio ("logvr")

  10. log coefficient of variation ("logcvr")

  11. number needed to treat ("nnt")

Computation of a main effect size

If you enter multiple types of input data (e.g., means/sd of two groups and a student t-test value) for the same comparison i.e., for the same row of the dataset, the convert_df() function can have two behaviours. If you set:

  • main_es = FALSE the function will estimate all possible effect sizes from all types of input data (which implies that if a comparison has several types of input data, it will result in multiple rows in the dataframe returned by the function)

  • main_es = TRUE the function will select one effect size per comparison (which implies that if a comparison has several types of input data, it will result in a unique row in the dataframe returned by the function)

Selection of input data for the computation of the main effect size

If you choose to estimate one main effect size (i.e., by setting main_es = TRUE), you have several options to select this main effect size. If you set:

  • es_selected = "auto": the main effect size will be automatically selected, by prioritizing specific types of input data over other (see next section "Hierarchy").

  • es_selected = "hierarchy": the main effect size will be selected, by prioritizing specific types of input data over other (see next section "Hierarchy").

  • es_selected = "minimum": the main effect size will be selected, by selecting the lowest effect size available.

  • es_selected = "maximum": the main effect size will be selected, by selecting the highest effect size available.

Hierarchy

More than 70 different combinations of input data can be used to estimate an effect size. You can retrieve the effect size measures estimated by each combination of input data in the see_input_data() function and online https://metaconvert.org/input.html.

You have two options to use a hierarchy in the types of input data.

  • an automatic way (es_selected = "auto")

  • an manual way (es_selected = "hierarchy")

Automatic

If you select an automatic hierarchy, here are the types of input data that will be prioritized.

Crude SMD or MD (measure=c("d", "g", "md") and selection_auto="crude")
  1. User's input effect size value

  2. SMD value

  3. Means at post-test

  4. ANOVA/Student's t-test/point biserial correlation statistics

  5. Linear regression estimates

  6. Mean difference values

  7. Quartiles/median/maximum values

  8. Post-test means extracted from a plot

  9. Pre-test+post-test means or mean change

  10. Paired ANOVA/t-test statistics

  11. Odds ratio value

  12. Contingency table

  13. Correlation coefficients

  14. Phi/chi-square value

Paired SMD or MD (measure=c("d", "g", "md") and selection_auto="paired")
  1. User's input effect size value

  2. Paired SMD value

  3. Pre-test+post-test means or mean change

  4. Paired ANOVA/t-test statistics

  5. Means at post-test

  6. ANOVA/Student's t-test/point biserial correlation

  7. Linear regression estimates

  8. Mean difference values

  9. Quartiles/median/maximum values

  10. Odds ratio value

  11. Contingency table

  12. Correlation coefficients

  13. Phi/chi-square value

Adjusted SMD or MD (measure=c("d", "g", "md") and selection_auto="adjusted")
  1. User's input adjusted effect size value

  2. Adjusted SMD value

  3. Estimated marginal means from ANCOVA

  4. F- or t-test value from ANCOVA

  5. Adjusted mean difference from ANCOVA

  6. Estimated marginal means from ANCOVA extracted from a plot

Odds Ratio (measure=c("or"))
  1. User's input effect size value

  2. Odds ratio value

  3. Contingency table

  4. Risk ratio values

  5. Phi/chi-square value

  6. Correlation coefficients

  7. (Then hierarchy as for "d" or "g" option crude)

Risk Ratio (measure=c("rr"))
  1. User's input effect size value

  2. Risk ratio values

  3. Contingency table

  4. Odds ratio values

  5. Phi/chi-square value

Incidence rate ratio (measure=c("irr"))
  1. User's input effect size value

  2. Number of cases and time of disease free observation time

Correlation (measure=c("r", "z"))
  1. User's input effect size value

  2. Correlation coefficients

  3. Contingency table

  4. Odds ratio value

  5. Phi/chi-square value

  6. SMD value

  7. Means at post-test

  8. ANOVA/Student's t-test/point biserial correlation

  9. Linear regression estimates

  10. Mean difference values 11 Quartiles/median/maximum values

  11. Post-test means extracted from a plot

  12. Pre-test+post-test means or mean change

  13. Paired ANOVA/t-test

Variability ratios (measure=c("vr", "cvr"))
  1. User's input effect size value

  2. means/variability indices at post-test

  3. means/variability indices at post-test extracted from a plot

Number needed to treat (measure=c("nnt"))
  1. User's input effect size value

  2. Contingency table

  3. Odds ratio values

  4. Risk ratio values

  5. Phi/chi-square value

Manual

If you select a manual hierarchy, you can specify the order in which you want to use each type of input data. You can prioritize some types of input data by placing them at the begining of the hierarchy argument, and you must separate all input data with a ">" separator. For example, if you set:

  • hierarchy = "means_sd > means_se > student_t", the convert_df function will prioritize the means + SD, then the means + SE, then the Student's t-test to estimate the main effect size.

  • hierarchy = "2x2 > or_se > phi", the convert_df function will prioritize the contigency table, then the odds ratio value + SE, then the phi coefficient to estimate the main effect size.

Importantly, if none of the types of input data indicated in the hierarchy argument can be used to estimate the target effect size measure, the convert_df() function will automatically try to use other types of input data to estimate an effect size.

Adjusted effect sizes

Some datasets will be composed of crude (i.e., non-adjusted) types of input data (such as standard means + SD, Student's t-test, etc.) and adjusted types of input data (such as means + SE from an ANCOVA model, a t-test from an ANCOVA, etc.).

In these situations, you can decide to:

  • treat crude and adjusted input data the same way split_adjusted = FALSE

  • split calculations for crude and adjusted types of input data split_adjusted = TRUE

If you want to split the calculations, you can decide to present the final dataset:

  • in a long format (i.e., crude and adjusted effect sizes presented in separate rows format_adjusted = "long")

  • in a wide format (i.e., crude and adjusted effect sizes presented in separate columns format_adjusted = "wide")

Value

The convert_df() function returns a list of more than 70 dataframes (one for each function automatically applied to the dataset). These dataframes systematically contain the columns described in metaConvert-package. The list of dataframes can be easily converted to a single, calculations-ready dataframe using the summary function (see summary.metaConvert).

Examples

res <- convert_df(df.haza,
  measure = "g",
  split_adjusted = TRUE,
  es_selected = "minimum",
  format_adjusted = "long"
)
summary(res)

Data extraction sheet generator

Description

Data extraction sheet generator

Usage

data_extraction_sheet(
  measure = c("d", "g", "md", "or", "rr", "nnt", "r", "z", "logvr", "logcvr", "irr"),
  type_of_measure = c("natural", "natural+converted"),
  name = "mcv_data_extraction",
  extension = c("data.frame", ".txt", ".csv", ".xlsx"),
  verbose = TRUE
)

Arguments

measure

Target effect size measure (one of the 11 available in metaConvert). Default is "all".

type_of_measure

One of "natural+converted" or "natural" (see details).

name

Name of the file created

extension

Extension of the file created. Most common are ".xlsx", ".csv" or ".txt". It is also possible to generate an R dataframe object by using the "data.frame" extension.

verbose

logical variable indicating whether some information should be printed (e.g., the location where the sheet is created when using ".xlsx", ".csv" or ".txt" extensions)

Details

This function generates, on your computer, a data extraction sheet that contains the name of columns that can be used by our tools to estimate various effect size measures.

If you select a specific measure (e.g., measure = "g"), you will be presented only with most common information allowing to estimate this measure (e.g., you will not be provided with columns for contigency tables if you request a data extraction sheet for measure = "g").

Measure

You can specify a specific effect size measures (among those available in the metaConvert-package). Doing this, the data extraction sheet will contain only the columns of the input data allowing a natural estimation of the effect size measure. For example, if you request measure="d" the data extraction sheet will not contain the columns for the contingency table since, although the convert_df function allows you to convert a contingency table into a "d", this requires to convert the "OR" that is naturally estimated from the contingency table into a "d".

This table is designed to be used in combination with tables showing the combination of input data leading to estimate each of the effect size measures (https://metaconvert.org/html/input.html)

Extension

You can export a file in various formats outside R (by indicating, for example, ".txt", ".xlsx", or ".csv") in the extension argument. You can also visualise this dataset directly in R by setting extension = "data.frame".

Value

This function returns a data extraction sheet that contains all the information necessary to estimate any effect size using the metaConvert tools.

Examples

data_extraction_sheet(measure = "md", extension = "data.frame")

Fictitious dataset 1

Description

First fictitious dataset aiming to understand how the compare_df function works. Slightly different from df.compare1

Usage

df.compare1

Format

An object of class data.frame with 5 rows and 7 columns.


Fictitious dataset 2

Description

First fictitious dataset aiming to understand how the compare_df function works. Slightly different from df.compare2

Usage

df.compare2

Format

An object of class data.frame with 6 rows and 7 columns.


Meta-analytic dataset inspired from Haza and colleagues (2024)

Description

Dataset of a meta-analysis exploring the specificity of social functioning of children with ADHD (compared to healthy controls) in case-control studies. This dataset contains: 1. several information coming from the same participants (due to the completion of multiple outcomes). 1. several information coming from the same study (due to the presence of multiple subgroups). 1. overlapping information for the same comparison 1. several information types from which a standardized mean difference can be estimated/converted

Usage

df.haza

Format

An object of class data.frame with 170 rows and 106 columns.

Source

Haza B, Gosling CJ, Conty L & Pinabiaux C (2024). Social Functioning in Children and Adolescents with ADHD: A Meta-analysis. Journal of Child Psychology and Psychiatry and Allied Disciplines.


Short version of the df.haza dataset

Description

This dataset is a shoter version of the df.haza dataset.

Usage

df.short

Format

An object of class grouped_df (inherits from tbl_df, tbl, data.frame) with 37 rows and 109 columns.

Source

Haza B, Gosling CJ, Conty L & Pinabiaux C (2024). Social Functioning in Children and Adolescents with ADHD: A Meta-analysis. Journal of Child Psychology and Psychiatry and Allied Disciplines.


Convert a 2x2 table into several effect size measures

Description

Convert a 2x2 table into several effect size measures

Usage

es_from_2x2(
  n_cases_exp,
  n_cases_nexp,
  n_controls_exp,
  n_controls_nexp,
  table_2x2_to_cor = "tetrachoric",
  reverse_2x2
)

Arguments

n_cases_exp

number of cases/events in the exposed group

n_cases_nexp

number of cases/events in the non exposed group

n_controls_exp

number of controls/no-event in the exposed group

n_controls_nexp

number of controls/no-event in the non exposed group

table_2x2_to_cor

formula used to obtain a correlation coefficient from the contingency table (see details).

reverse_2x2

a logical value indicating whether the direction of generated effect sizes should be flipped.

Details

This function first computes (log) odds ratio (OR), (log) risk ratio (RR) and number needed to treat (NNT) from the 2x2 table. Note that if a cell is equal to 0, we applied the typical adjustment (add 0.5) to all cells. Cohen's d (D), Hedges' g (G) and correlation coefficients (R/Z) are then estimated from the OR.

To estimate an OR, the formulas used (Box 6.4.a in the Cochrane Handbook) are:

logor=log(n_cases_exp/n_cases_nexpn_controls_exp/n_controls_nexp)logor = log(\frac{n\_cases\_exp / n\_cases\_nexp}{n\_controls\_exp / n\_controls\_nexp})

logor_se=1n_cases_exp+1n_cases_nexp+1n_controls_exp+1n_controls_nexplogor\_se = \sqrt{\frac{1}{n\_cases\_exp} + \frac{1}{n\_cases\_nexp} + \frac{1}{n\_controls\_exp} + \frac{1}{n\_controls\_nexp}}

To estimate an RR, the formulas used (Box 6.4.a in the Cochrane Handbook) are:

logrr=log(n_cases_exp/n_expn_cases_nexp/n_nexp)logrr = log(\frac{n\_cases\_exp / n\_exp}{n\_cases\_nexp / n\_nexp})

logrr_se=1n_cases_exp1n_exp+1n_cases_nexp1n_nexplogrr\_se = \sqrt{\frac{1}{n\_cases\_exp} - \frac{1}{n\_exp} + \frac{1}{n\_cases\_nexp} - \frac{1}{n\_nexp}}

To estimate a NNT, the formulas used are (Sedwick, 2013) :

pt=n_cases_expn_cases_exp+n_controls_exppt = \frac{n\_cases\_exp}{n\_cases\_exp + n\_controls\_exp}

pc=n_cases_nexpn_cases_nexp+n_controls_nexppc = \frac{n\_cases\_nexp}{n\_cases\_nexp + n\_controls\_nexp}

AAR=pcptAAR = pc - pt

nnt=1AARnnt = \frac{1}{AAR}

To convert the 2x2 table into a SMD, the function estimates an OR value from the 2x2 table (formula above) that is then converted to a SMD (see formula in es_from_or_se()).

To convert the 2x2 table into a correlation coefficient, For now, only the tetrachoric correlation is currently proposed

  • table_2x2_to_cor = "tetrachoric". Given the heavy calculations required for this effect size measure, we relied on the implementation of the formulas of the 'metafor' package. More information can be retrieved here (https://wviechtb.github.io/metafor/reference/escalc.html#-b-measures-for-two-dichotomous-variables).

Value

This function estimates and converts between several effect size measures.

natural effect size measure OR + RR + NNT
converted effect size measure D + G + R + Z
required input data See 'Section 7. Contingency (2x2) table or proportions'
https://metaconvert.org/input.html

References

Cooper, H., Hedges, L.V., & Valentine, J.C. (Eds.). (2019). The handbook of research synthesis and meta-analysis. Russell Sage Foundation.

Higgins JPT, Thomas J, Chandler J, Cumpston M, Li T, Page MJ, Welch VA (editors). Cochrane Handbook for Systematic Reviews of Interventions version 6.3 (updated February 2022). Available from www.training.cochrane.org/handbook.

Lipsey, M. W., & Wilson, D. B. (2001). Practical meta-analysis. Sage Publications, Inc.

Sedgwick, P. (2013). What is number needed to treat (NNT)? Bmj, 347.

Examples

es_from_2x2(n_cases_exp = 467, n_cases_nexp = 22087, n_controls_exp = 261, n_controls_nexp = 8761)

Convert the proportion of occurrence of a binary event in two independent groups into several effect size measures

Description

Convert the proportion of occurrence of a binary event in two independent groups into several effect size measures

Usage

es_from_2x2_prop(
  prop_cases_exp,
  prop_cases_nexp,
  n_exp,
  n_nexp,
  table_2x2_to_cor = "tetrachoric",
  reverse_prop
)

Arguments

prop_cases_exp

proportion of cases/events in the exposed group (ranging from 0 to 1)

prop_cases_nexp

proportion of cases/events in the non-exposed group (ranging from 0 to 1)

n_exp

total number of participants in the exposed group

n_nexp

total number of participants in the non exposed group

table_2x2_to_cor

formula used to obtain a correlation coefficient from the contigency table (see details).

reverse_prop

a logical value indicating whether the direction of generated effect sizes should be flipped.

Details

This function uses the proportions and sample size to recreate the 2x2 table, and then relies on the calculations of the es_from_2x2_sum() function.

The formulas used is to obtain the 2x2 table are

n_cases_exp=prop_cases_expn_expn\_cases\_exp = prop\_cases\_exp * n\_exp

n_cases_nexp=prop_cases_nexpn_nexpn\_cases\_nexp = prop\_cases\_nexp * n\_nexp

n_controls_exp=(1prop_cases_exp)n_expn\_controls\_exp = (1 - prop\_cases\_exp) * n\_exp

n_controls_nexp=(1prop_cases_nexp)n_nexpn\_controls\_nexp = (1 - prop\_cases\_nexp) * n\_nexp

Value

This function estimates and converts between several effect size measures.

natural effect size measure OR + RR + NNT
converted effect size measure D + G + R + Z
required input data See 'Section 7. Contingency (2x2) table or proportions'
https://metaconvert.org/input.html

Examples

es_from_2x2_prop(prop_cases_exp = 0.80, prop_cases_nexp = 0.60, n_exp = 10, n_nexp = 20)

Convert a table with the number of cases and row marginal sums into several effect size measures

Description

Convert a table with the number of cases and row marginal sums into several effect size measures

Usage

es_from_2x2_sum(
  n_cases_exp,
  n_exp,
  n_cases_nexp,
  n_nexp,
  table_2x2_to_cor = "tetrachoric",
  reverse_2x2
)

Arguments

n_cases_exp

number of cases/events in the exposed group

n_exp

total number of participants in the exposed group

n_cases_nexp

number of cases/events in the non exposed group

n_nexp

total number of participants in the non exposed group

table_2x2_to_cor

formula used to obtain a correlation coefficient from the contigency table (see details).

reverse_2x2

a logical value indicating whether the direction of generated effect sizes should be flipped.

Details

This function uses the number of cases in both the exposed and non-exposed groups and the total number of participants exposed and non-exposed to recreate a 2x2 table. Then relies on the calculations of the es_from_2x2 function.

n_controls_exp=n_expn_cases_expn\_controls\_exp = n\_exp - n\_cases\_exp

n_controls_nexp=n_nexpn_cases_nexpn\_controls\_nexp = n\_nexp - n\_cases\_nexp

Value

This function estimates and converts between several effect size measures.

natural effect size measure OR + RR + NNT
converted effect size measure D + G + R + Z
required input data See 'Section 7. Contingency (2x2) table or proportions'
https://metaconvert.org/input.html

Examples

es_from_2x2_sum(n_cases_exp = 10, n_exp = 40, n_cases_nexp = 25, n_nexp = 47)

Convert a F-statistic obtained from an ANCOVA model into several effect size measures.

Description

Convert a F-statistic obtained from an ANCOVA model into several effect size measures.

Usage

es_from_ancova_f(
  ancova_f,
  cov_outcome_r,
  n_cov_ancova,
  n_exp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  reverse_ancova_f
)

Arguments

ancova_f

a F-statistic from an ANCOVA (binary predictor)

cov_outcome_r

correlation between the outcome and covariate(s) (multiple correlation when multiple covariates are included in the ANCOVA model).

n_cov_ancova

number of covariates in the ANCOVA model.

n_exp

number of participants in the experimental/exposed group.

n_nexp

number of participants in the non-experimental/non-exposed group.

smd_to_cor

formula used to convert the adjusted cohen_d value into a coefficient correlation (see details).

reverse_ancova_f

a logical value indicating whether the direction of the generated effect sizes should be flipped.

Details

This function first computes an "adjusted" Cohen's d (D), and Hedges' g (G) from the F-value of an ANCOVA (binary predictor). Odds ratio (OR) and correlation coefficients (R/Z) are then converted from the Cohen's d.

To estimate a Cohen's d the formula used is (table 12.3 in Cooper):

cohen_d=ancova_f(n_exp+n_nexp)n_expn_nexp1cov_out_cor2cohen\_d = \sqrt{ancova\_f * \frac{(n\_exp+n\_nexp)}{n\_exp*n\_nexp}} * \sqrt{1 - cov\_out\_cor^2}

To estimate other effect size measures, Calculations of the es_from_cohen_d_adj() are applied.

Value

This function estimates and converts between several effect size measures.

natural effect size measure D + G
converted effect size measure OR + R + Z
required input data See 'Section 18. Adjusted: ANCOVA statistics, eta-squared'
https://metaconvert.org/input.html

References

Cooper, H., Hedges, L. V., & Valentine, J. C. (Eds.). (2019). The handbook of research synthesis and meta-analysis. Russell Sage Foundation.

Examples

es_from_ancova_f(ancova_f = 4, cov_outcome_r = 0.2, n_cov_ancova = 3, n_exp = 20, n_nexp = 20)

Convert a two-tailed p-value of an ANCOVA t-test into several effect size measures.

Description

Convert a two-tailed p-value of an ANCOVA t-test into several effect size measures.

Usage

es_from_ancova_f_pval(
  ancova_f_pval,
  cov_outcome_r,
  n_cov_ancova,
  n_exp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  reverse_ancova_f_pval
)

Arguments

ancova_f_pval

a two-tailed p-value of an F-test in an ANCOVA (binary predictor)

cov_outcome_r

correlation between the outcome and covariate(s) (multiple correlation when multiple covariates are included in the ANCOVA model).

n_cov_ancova

number of covariates in the ANCOVA model.

n_exp

number of participants in the experimental/exposed group.

n_nexp

number of participants in the non-experimental/non-exposed group.

smd_to_cor

formula used to convert the adjusted cohen_d value into a coefficient correlation (see details).

reverse_ancova_f_pval

a logical value indicating whether the direction of the generated effect sizes should be flipped.

Details

This function converts the p-value of an ANCOVA (binary predictor) into a t value, and then relies on the calculations of the es_from_ancova_t() function.

To convert the p-value into a t-value, the following formula is used (table 12.3 in Cooper):

df=n_exp+n_nexp+n_exp2n_cov_ancovadf = n\_exp + n\_nexp + n\_exp - 2 - n\_cov\_ancova

t=pt(ancova_f_pval/2,df=df)t = | pt(ancova\_f\_pval/2, df = df) |

Then, calculations of the es_from_ancova_t() are applied.

Value

This function estimates and converts between several effect size measures.

natural effect size measure D + G
converted effect size measure OR + R + Z
required input data See 'Section 18. Adjusted: ANCOVA statistics, eta-squared'
https://metaconvert.org/input.html

References

Cooper, H., Hedges, L.V., & Valentine, J.C. (Eds.). (2019). The handbook of research synthesis and meta-analysis. Russell Sage Foundation.

Examples

es_from_ancova_f_pval(
  ancova_f_pval = 0.05, cov_outcome_r = 0.2,
  n_cov_ancova = 3, n_exp = 20, n_nexp = 20
)

Convert an adjusted mean difference and adjusted standard deviation between two independent groups obtained from an ANCOVA model into several effect size measures

Description

Convert an adjusted mean difference and adjusted standard deviation between two independent groups obtained from an ANCOVA model into several effect size measures

Usage

es_from_ancova_md_ci(
  ancova_md,
  ancova_md_ci_lo,
  ancova_md_ci_up,
  cov_outcome_r,
  n_cov_ancova,
  n_exp,
  n_nexp,
  max_asymmetry = 10,
  smd_to_cor = "viechtbauer",
  reverse_ancova_md
)

Arguments

ancova_md

adjusted mean difference between two independent groups

ancova_md_ci_lo

lower bound of the covariate-adjusted 95% CI of the mean difference

ancova_md_ci_up

upper bound of the covariate-adjusted 95% CI of the mean difference

cov_outcome_r

correlation between the outcome and covariate (multiple correlation when multiple covariates are included in the ANCOVA model).

n_cov_ancova

number of covariates in the ANCOVA model.

n_exp

number of participants in the experimental/exposed group.

n_nexp

number of participants in the non-experimental/non-exposed group.

max_asymmetry

A percentage indicating the tolerance before detecting asymmetry in the 95% CI bounds.

smd_to_cor

formula used to convert the cohen_d value into a coefficient correlation (see details).

reverse_ancova_md

a logical value indicating whether the direction of generated effect sizes should be flipped.

Details

This function converts the mean difference (MD) 95% CI into a standard error, and then relies on the calculations of the es_from_ancova_md_se function.

To convert the 95% CI into a standard error, the following formula is used (table 12.3 in Cooper):

md_se=ancova_md_ci_upancova_md_ci_lo(2qt(0.975,n_exp+n_nexp2n_cov_ancova))md\_se = \frac{ancova\_md\_ci\_up - ancova\_md\_ci\_lo}{(2 * qt(0.975, n\_exp + n\_nexp - 2 - n\_cov\_ancova))}

Calculations of the es_from_ancova_md_se() are then applied.

Value

This function estimates and converts between several effect size measures.

natural effect size measure MD + D + G
converted effect size measure OR + R + Z
required input data See 'Section 20. Adjusted: Mean difference and dispersion'
https://metaconvert.org/input.html

Examples

es_from_ancova_md_ci(
  ancova_md = 4, ancova_md_ci_lo = 2,
  ancova_md_ci_up = 6,
  cov_outcome_r = 0.5, n_cov_ancova = 5,
  n_exp = 20, n_nexp = 22
)

Convert an adjusted mean difference and adjusted standard deviation between two independent groups obtained from an ANCOVA model into several effect size measures

Description

Convert an adjusted mean difference and adjusted standard deviation between two independent groups obtained from an ANCOVA model into several effect size measures

Usage

es_from_ancova_md_pval(
  ancova_md,
  ancova_md_pval,
  cov_outcome_r,
  n_cov_ancova,
  n_exp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  reverse_ancova_md
)

Arguments

ancova_md

adjusted mean difference between two independent groups

ancova_md_pval

p-value (two-tailed) of the adjusted mean difference

cov_outcome_r

correlation between the outcome and covariate (multiple correlation when multiple covariates are included in the ANCOVA model).

n_cov_ancova

number of covariates in the ANCOVA model.

n_exp

number of participants in the experimental/exposed group.

n_nexp

number of participants in the non-experimental/non-exposed group.

smd_to_cor

formula used to convert the cohen_d value into a coefficient correlation (see details).

reverse_ancova_md

a logical value indicating whether the direction of generated effect sizes should be flipped.

Details

This function converts the mean difference (MD) p-value into a standard error, and then relies on the calculations of the es_from_ancova_md_se() function.

To convert the p-value into a standard error, the following formula is used (table 12.3 in Cooper):

t=qt(p=ancova_md_pval2,df=n_exp+n_nexp2n_cov_ancova)t = qt(p = \frac{ancova\_md\_pval}{2}, df = n\_exp + n\_nexp - 2 - n\_cov\_ancova)

ancova_md_se=ancova_mdtancova\_md\_se = | \frac{ancova\_md}{t} |

Calculations of the es_from_ancova_md_se() are then applied.

Value

This function estimates and converts between several effect size measures.

natural effect size measure MD + D + G
converted effect size measure OR + R + Z
required input data See 'Section 20. Adjusted: Mean difference and dispersion'
https://metaconvert.org/input.html

Examples

es_from_ancova_md_pval(
  ancova_md = 4, ancova_md_pval = 0.05,
  cov_outcome_r = 0.5, n_cov_ancova = 5,
  n_exp = 20, n_nexp = 22
)

Convert an adjusted mean difference and adjusted standard deviation between two independent groups obtained from an ANCOVA model into several effect size measures

Description

Convert an adjusted mean difference and adjusted standard deviation between two independent groups obtained from an ANCOVA model into several effect size measures

Usage

es_from_ancova_md_sd(
  ancova_md,
  ancova_md_sd,
  cov_outcome_r,
  n_cov_ancova,
  n_exp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  reverse_ancova_md
)

Arguments

ancova_md

adjusted mean difference between two independent groups

ancova_md_sd

covariate-adjusted standard deviation of the mean difference

cov_outcome_r

correlation between the outcome and covariate (multiple correlation when multiple covariates are included in the ANCOVA model).

n_cov_ancova

number of covariates in the ANCOVA model.

n_exp

number of participants in the experimental/exposed group.

n_nexp

number of participants in the non-experimental/non-exposed group.

smd_to_cor

formula used to convert the cohen_d value into a coefficient correlation (see details).

reverse_ancova_md

a logical value indicating whether the direction of generated effect sizes should be flipped.

Details

This function first computes an "adjusted" Cohen's d (D), Hedges' g (G) from the adjusted mean difference (MD). Odds ratio (OR) and correlation coefficients (R/Z) are then converted from the Cohen's d.

To estimate the unadjusted variance of MD (table 12.3 in Cooper):

md_sd=ancova_md_sd1cor_outcome_r2md\_sd = \frac{ancova\_md\_sd}{\sqrt{1 - cor\_outcome\_r^2}}

md_se=md_sd1n_exp+1n_nexpmd\_se = md\_sd * \sqrt{\frac{1}{n\_exp} + \frac{1}{n\_nexp}}

md_lo=mdmd_seqt(.975,n_exp+n_nexp2n_cov_ancova)md\_lo = md - md\_se * qt(.975, n\_exp + n\_nexp-2-n\_cov\_ancova)

md_up=md+md_seqt(.975,n_exp+n_nexp2n_cov_ancova)md\_up = md + md\_se * qt(.975, n\_exp + n\_nexp-2-n\_cov\_ancova)

To estimate the Cohen's d (table 12.3 in Cooper):

d=ancova_mdmd_sdd = \frac{ancova\_md}{md\_sd}

To estimate other effect size measures, Calculations of the es_from_cohen_d_adj() are applied.

Value

This function estimates and converts between several effect size measures.

natural effect size measure MD + D + G
converted effect size measure OR + R + Z
required input data See 'Section 20. Adjusted: Mean difference and dispersion'
https://metaconvert.org/input.html

Examples

es_from_ancova_md_sd(
  ancova_md = 4, ancova_md_sd = 2,
  cov_outcome_r = 0.5, n_cov_ancova = 5,
  n_exp = 20, n_nexp = 22
)

Convert an adjusted mean difference and standard error between two independent groups obtained from an ANCOVA model into several effect size measures

Description

Convert an adjusted mean difference and standard error between two independent groups obtained from an ANCOVA model into several effect size measures

Usage

es_from_ancova_md_se(
  ancova_md,
  ancova_md_se,
  cov_outcome_r,
  n_cov_ancova,
  n_exp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  reverse_ancova_md
)

Arguments

ancova_md

adjusted mean difference between two independent groups

ancova_md_se

covariate-adjusted standard error of the mean difference

cov_outcome_r

correlation between the outcome and covariate (multiple correlation when multiple covariates are included in the ANCOVA model).

n_cov_ancova

number of covariates in the ANCOVA model.

n_exp

number of participants in the experimental/exposed group.

n_nexp

number of participants in the non-experimental/non-exposed group.

smd_to_cor

formula used to convert the cohen_d value into a coefficient correlation (see details).

reverse_ancova_md

a logical value indicating whether the direction of generated effect sizes should be flipped.

Details

This function converts the mean difference (MD) standard error into a standard deviation, and then relies on the calculations of the es_from_ancova_md_sd function.

To convert the standard error into a standard deviation, the following formula is used.

ancova_md_sd=ancova_md_se1/nexp+1/nnexpancova\_md\_sd = \frac{ancova\_md\_se}{\sqrt{1 / n_exp + 1 / n_nexp}}

Calculations of the es_from_ancova_md_sd() are then applied.

Value

This function estimates and converts between several effect size measures.

natural effect size measure MD + D + G
converted effect size measure OR + R + Z
required input data See 'Section 20. Adjusted: Mean difference and dispersion'
https://metaconvert.org/input.html

Examples

es_from_ancova_md_se(
  ancova_md = 4, ancova_md_se = 2,
  cov_outcome_r = 0.5, n_cov_ancova = 5,
  n_exp = 20, n_nexp = 22
)

Convert means and 95% CIs of two independent groups obtained from an ANCOVA model into several effect size measures

Description

Convert means and 95% CIs of two independent groups obtained from an ANCOVA model into several effect size measures

Usage

es_from_ancova_means_ci(
  n_exp,
  n_nexp,
  ancova_mean_exp,
  ancova_mean_ci_lo_exp,
  ancova_mean_ci_up_exp,
  ancova_mean_nexp,
  ancova_mean_ci_lo_nexp,
  ancova_mean_ci_up_nexp,
  cov_outcome_r,
  n_cov_ancova,
  max_asymmetry = 10,
  smd_to_cor = "viechtbauer",
  reverse_ancova_means
)

Arguments

n_exp

number of participants in the experimental/exposed group.

n_nexp

number of participants in the non-experimental/non-exposed group.

ancova_mean_exp

adjusted mean of participants in the experimental/exposed group.

ancova_mean_ci_lo_exp

lower bound of the adjusted 95% CI of the mean of the experimental/exposed group

ancova_mean_ci_up_exp

upper bound of the adjusted 95% CI of the mean of the experimental/exposed group

ancova_mean_nexp

adjusted mean of participants in the non-experimental/non-exposed group.

ancova_mean_ci_lo_nexp

lower bound of the adjusted 95% CI of the mean of the non-experimental/non-exposed group.

ancova_mean_ci_up_nexp

upper bound of the adjusted 95% CI of the mean of the non-experimental/non-exposed group.

cov_outcome_r

correlation between the outcome and covariate(s) (multiple correlation when multiple covariates are included in the ANCOVA model).

n_cov_ancova

number of covariates in the ANCOVA model.

max_asymmetry

A percentage indicating the tolerance before detecting asymmetry in the 95% CI bounds.

smd_to_cor

formula used to convert the adjusted cohen_d value into a coefficient correlation (see details).

reverse_ancova_means

a logical value indicating whether the direction of the generated effect sizes should be flipped.

Details

This function converts the adjusted means 95% CI of two independent groups into a standard error, and then relies on the calculations of the es_from_ancova_means_se() function.

To convert the 95% CIs into standard errors, the following formula is used (table 12.3 in Cooper):

ancova_mean_se_exp=ancova_mean_ci_up_expancova_mean_ci_lo_exp2qt(0.975,df=n_exp1)ancova\_mean\_se\_exp = \frac{ancova\_mean\_ci\_up\_exp - ancova\_mean\_ci\_lo\_exp}{2 * qt(0.975, df = n\_exp - 1)}

ancova_mean_se_nexp=ancova_mean_ci_up_nexpancova_mean_ci_lo_nexp2qt(0.975,df=n_nexp1)ancova\_mean\_se\_nexp = \frac{ancova\_mean\_ci\_up\_nexp - ancova\_mean\_ci\_lo\_nexp}{2 * qt(0.975, df = n\_nexp - 1)}

Calculations of the es_from_ancova_means_se() are then applied.

Value

This function estimates and converts between several effect size measures.

natural effect size measure MD + D + G
converted effect size measure OR + R + Z
required input data See 'Section 19. Adjusted: Means and dispersion'
https://metaconvert.org/input.html

References

Cooper, H., Hedges, L.V., & Valentine, J.C. (Eds.). (2019). The handbook of research synthesis and meta-analysis. Russell Sage Foundation.

Examples

es_from_ancova_means_ci(
  n_exp = 55, n_nexp = 55, cov_outcome_r = 0.5, n_cov_ancova = 4,
  ancova_mean_exp = 25, ancova_mean_ci_lo_exp = 15, ancova_mean_ci_up_exp = 35,
  ancova_mean_nexp = 18, ancova_mean_ci_lo_nexp = 12, ancova_mean_ci_up_nexp = 24
)

Convert means and standard deviations of two independent groups obtained from an ANCOVA model into several effect size measures

Description

Convert means and standard deviations of two independent groups obtained from an ANCOVA model into several effect size measures

Usage

es_from_ancova_means_sd(
  n_exp,
  n_nexp,
  ancova_mean_exp,
  ancova_mean_nexp,
  ancova_mean_sd_exp,
  ancova_mean_sd_nexp,
  cov_outcome_r,
  n_cov_ancova,
  smd_to_cor = "viechtbauer",
  reverse_ancova_means
)

Arguments

n_exp

number of participants in the experimental/exposed group.

n_nexp

number of participants in the non-experimental/non-exposed group.

ancova_mean_exp

adjusted mean of participants in the experimental/exposed group.

ancova_mean_nexp

adjusted mean of participants in the non-experimental/non-exposed group.

ancova_mean_sd_exp

adjusted standard deviation of participants in the experimental/exposed group.

ancova_mean_sd_nexp

adjusted standard deviation of participants in the non-experimental/non-exposed group.

cov_outcome_r

correlation between the outcome and covariate(s) (multiple correlation when multiple covariates are included in the ANCOVA model).

n_cov_ancova

number of covariates in the ANCOVA model.

smd_to_cor

formula used to convert the adjusted cohen_d value into a coefficient correlation (see details).

reverse_ancova_means

a logical value indicating whether the direction of the generated effect sizes should be flipped.

Details

This function first computes an "adjusted" mean difference (MD), Cohen's d (D) and Hedges' g (G) from the adjusted means and standard deviations. Odds ratio (OR) and correlation coefficients (R/Z) are then converted from the Cohen's d.

This function start by estimating the non-adjusted standard deviation of the two groups (formula 12.24 in Cooper);

mean_sd_exp=ancova_mean_sd_exp1cov_outcome_r2mean\_sd\_exp = \frac{ancova\_mean\_sd\_exp}{\sqrt{1 - cov\_outcome\_r^2}}

mean_sd_nexp=ancova_mean_sd_nexp1cov_outcome_r2mean\_sd\_nexp = \frac{ancova\_mean\_sd\_nexp}{\sqrt{1 - cov\_outcome\_r^2}}

To obtain the mean difference, the following formulas are used (authors calculations):

md=ancova_mean_expancova_mean_nexpmd = ancova\_mean\_exp - ancova\_mean\_nexp

md_se=mean_sd_exp2n_exp+mean_sd_nexp2n_nexpmd\_se = \sqrt{\frac{mean\_sd\_exp^2}{n\_exp} + \frac{mean\_sd\_nexp^2}{n\_nexp}}

md_ci_lo=mdmd_seqt(.975,n_exp+n_nexp2n_cov_ancova)md\_ci\_lo = md - md\_se * qt(.975, n\_exp+n\_nexp-2-n\_cov\_ancova)

md_ci_up=md+md_seqt(.975,n_exp+n_nexp2n_cov_ancova)md\_ci\_up = md + md\_se * qt(.975, n\_exp+n\_nexp-2-n\_cov\_ancova)

To obtain the Cohen's d, the following formulas are used (table 12.3 in Cooper):

mean_sd_pooled=(n_exp1)ancova_mean_exp2+(n_nexp1)ancova_mean_nexp2n_exp+n_nexp2mean\_sd\_pooled = \sqrt{\frac{(n\_exp - 1) * ancova\_mean\_exp^2 + (n\_nexp - 1) * ancova\_mean\_nexp^2}{n\_exp+n\_nexp-2}}

cohen_d=ancova_mean_expancova_mean_nexpmean_sd_pooledcohen\_d = \frac{ancova\_mean\_exp - ancova\_mean\_nexp}{mean\_sd\_pooled}

cohen_d_se=(n_exp+n_nexp)(1cov_outcome_r2)n_expn_nexp+cohen_d22(n_exp+n_nexp)cohen\_d\_se = \frac{(n\_exp+n\_nexp)*(1-cov\_outcome\_r^2)}{n\_exp*n\_nexp} + \frac{cohen\_d^2}{2(n\_exp+n\_nexp)}

cohen_d_ci_lo=cohen_dcohen_d_seqt(.975,n_exp+n_nexp2n_cov_ancova)cohen\_d\_ci\_lo = cohen\_d - cohen\_d\_se * qt(.975, n\_exp + n\_nexp - 2 - n\_cov\_ancova)

cohen_d_ci_up=cohen_d+cohen_d_seqt(.975,n_exp+n_nexp2n_cov_ancova)cohen\_d\_ci\_up = cohen\_d + cohen\_d\_se * qt(.975, n\_exp + n\_nexp - 2 - n\_cov\_ancova)

To estimate other effect size measures, Calculations of the es_from_cohen_d_adj() are applied.

Value

This function estimates and converts between several effect size measures.

natural effect size measure MD + D + G
converted effect size measure OR + R + Z
required input data See 'Section 19. Adjusted: Means and dispersion'
https://metaconvert.org/input.html

References

Cooper, H., Hedges, L.V., & Valentine, J.C. (Eds.). (2019). The handbook of research synthesis and meta-analysis. Russell Sage Foundation.

Examples

es_from_ancova_means_sd(
  n_exp = 55, n_nexp = 55,
  ancova_mean_exp = 2.3, ancova_mean_sd_exp = 1.2,
  ancova_mean_nexp = 1.9, ancova_mean_sd_nexp = 0.9,
  cov_outcome_r = 0.2, n_cov_ancova = 3
)

Convert means and adjusted pooled standard deviation of two independent groups obtained from an ANCOVA model into several effect size measures

Description

Convert means and adjusted pooled standard deviation of two independent groups obtained from an ANCOVA model into several effect size measures

Usage

es_from_ancova_means_sd_pooled_adj(
  ancova_mean_exp,
  ancova_mean_nexp,
  ancova_mean_sd_pooled,
  cov_outcome_r,
  n_cov_ancova,
  n_exp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  reverse_ancova_means
)

Arguments

ancova_mean_exp

adjusted mean of participants in the experimental/exposed group.

ancova_mean_nexp

adjusted mean of participants in the non-experimental/non-exposed group.

ancova_mean_sd_pooled

adjusted pooled standard deviation.

cov_outcome_r

correlation between the outcome and covariate(s) (multiple correlation when multiple covariates are included in the ANCOVA model).

n_cov_ancova

number of covariates in the ANCOVA model.

n_exp

number of participants in the experimental/exposed group.

n_nexp

number of participants in the non-experimental/non-exposed group.

smd_to_cor

formula used to convert the adjusted cohen_d value into a coefficient correlation (see details).

reverse_ancova_means

a logical value indicating whether the direction of the generated effect sizes should be flipped.

Details

This function converts the adjusted pooled standard deviations of two independent groups into a crude pooled standard deviation. and then relies on the calculations of the es_from_ancova_means_sd_pooled_crude() function.

To convert the adjusted pooled SD into a crude pooled SD (table 12.3 in Cooper):

mean_sd_pooled=ancova_mean_sd_pooled1cov_outcome_r2mean\_sd\_pooled = \frac{ancova\_mean\_sd\_pooled}{\sqrt{1 - cov\_outcome\_r^2}}

Calculations of the es_from_ancova_means_sd_pooled_crude() are then applied.

Value

This function estimates and converts between several effect size measures.

natural effect size measure MD + D + G
converted effect size measure OR + R + Z
required input data See 'Section 19. Adjusted: Means and dispersion'
https://metaconvert.org/input.html

References

Cooper, H., Hedges, L.V., & Valentine, J.C. (Eds.). (2019). The handbook of research synthesis and meta-analysis. Russell Sage Foundation.

Examples

es_from_ancova_means_sd_pooled_adj(
  ancova_mean_exp = 98, ancova_mean_nexp = 87,
  ancova_mean_sd_pooled = 17, cov_outcome_r = 0.2,
  n_cov_ancova = 3, n_exp = 20, n_nexp = 20
)

Convert adjusted means obtained from an ANCOVA model and crude pooled standard deviation of two independent groups into several effect size measures

Description

Convert adjusted means obtained from an ANCOVA model and crude pooled standard deviation of two independent groups into several effect size measures

Usage

es_from_ancova_means_sd_pooled_crude(
  ancova_mean_exp,
  ancova_mean_nexp,
  mean_sd_pooled,
  cov_outcome_r,
  n_cov_ancova,
  n_exp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  reverse_ancova_means
)

Arguments

ancova_mean_exp

adjusted mean of participants in the experimental/exposed group.

ancova_mean_nexp

adjusted mean of participants in the non-experimental/non-exposed group.

mean_sd_pooled

crude pooled standard deviation.

cov_outcome_r

correlation between the outcome and covariate(s) (multiple correlation when multiple covariates are included in the ANCOVA model).

n_cov_ancova

number of covariates in the ANCOVA model.

n_exp

number of participants in the experimental/exposed group.

n_nexp

number of participants in the non-experimental/non-exposed group.

smd_to_cor

formula used to convert the adjusted cohen_d value into a coefficient correlation (see details).

reverse_ancova_means

a logical value indicating whether the direction of the generated effect sizes should be flipped.

Details

This function first computes an "adjusted" mean difference (MD) and Cohen's d (D) from the adjusted means and crude pooled standard deviation of two independent groups. Odds ratio (OR) and correlation coefficients (R/Z) are then converted from the Cohen's d.

To estimate the Cohen's d:

d=ancova_mean_expancova_mean_nexp_adjmean_sd_pooledd = \frac{ancova\_mean\_exp - ancova\_mean\_nexp\_adj}{mean\_sd\_pooled}

To estimate the mean difference:

md=ancova_mean_expancova_mean_nexp_adjmd = ancova\_mean\_exp - ancova\_mean\_nexp\_adj

md_se=n_exp+n_nexpn_expn_nexp(1cov_outcome_r2)mean_sd_pooled2md\_se = \sqrt{\frac{n\_exp + n\_nexp}{n\_exp * n\_nexp} * (1 - cov\_outcome\_r^2) * mean\_sd\_pooled^2}

Then, calculations of the es_from_ancova_means_sd() and es_from_cohen_d_adj() are applied.

Value

This function estimates and converts between several effect size measures.

natural effect size measure MD + D + G
converted effect size measure OR + R + Z
required input data See 'Section 19. Adjusted: Means and dispersion'
https://metaconvert.org/input.html

References

Cooper, H., Hedges, L.V., & Valentine, J.C. (Eds.). (2019). The handbook of research synthesis and meta-analysis. Russell Sage Foundation.

Examples

es_from_ancova_means_sd_pooled_crude(
  ancova_mean_exp = 29, ancova_mean_nexp = 34,
  mean_sd_pooled = 7, cov_outcome_r = 0.2,
  n_cov_ancova = 3, n_exp = 20, n_nexp = 20
)

Convert means and standard errors of two independent groups obtained from an ANCOVA model into several effect size measures

Description

Convert means and standard errors of two independent groups obtained from an ANCOVA model into several effect size measures

Usage

es_from_ancova_means_se(
  n_exp,
  n_nexp,
  ancova_mean_exp,
  ancova_mean_nexp,
  ancova_mean_se_exp,
  ancova_mean_se_nexp,
  cov_outcome_r,
  n_cov_ancova,
  smd_to_cor = "viechtbauer",
  reverse_ancova_means
)

Arguments

n_exp

number of participants in the experimental/exposed group.

n_nexp

number of participants in the non-experimental/non-exposed group.

ancova_mean_exp

adjusted mean of participants in the experimental/exposed group.

ancova_mean_nexp

adjusted mean of participants in the non-experimental/non-exposed group.

ancova_mean_se_exp

adjusted standard error of participants in the experimental/exposed group.

ancova_mean_se_nexp

adjusted standard error of participants in the non-experimental/non-exposed group.

cov_outcome_r

correlation between the outcome and covariate(s) (multiple correlation when multiple covariates are included in the ANCOVA model).

n_cov_ancova

number of covariates in the ANCOVA model.

smd_to_cor

formula used to convert the adjusted cohen_d value into a coefficient correlation (see details).

reverse_ancova_means

a logical value indicating whether the direction of the generated effect sizes should be flipped.

Details

This function converts the adjusted means standard errors of two independent groups into standard deviations, and then relies on the calculations of the es_from_ancova_means_sd function.

To convert the standard errors into standard deviations, the following formula is used.

ancova_mean_sd_exp=ancova_mean_se_expn_expancova\_mean\_sd\_exp = ancova\_mean\_se\_exp * \sqrt{n\_exp}

ancova_mean_sd_nexp=ancova_mean_se_nexpn_nexpancova\_mean\_sd\_nexp = ancova\_mean\_se\_nexp * \sqrt{n\_nexp}

Calculations of the es_from_ancova_means_sd() are then applied.

Value

This function estimates and converts between several effect size measures.

natural effect size measure MD + D + G
converted effect size measure OR + R + Z
required input data See 'Section 19. Adjusted: Means and dispersion'
https://metaconvert.org/input.html

References

Higgins JPT, Li T, Deeks JJ (editors). Chapter 6: Choosing effect size measures and computing estimates of effect. In: Higgins JPT, Thomas J, Chandler J, Cumpston M, Li T, Page MJ, Welch VA (editors). Cochrane Handbook for Systematic Reviews of Interventions version 6.3 (updated February 2022). Cochrane, 2022. Available from www.training.cochrane.org/handbook.

Examples

es_from_ancova_means_se(
  n_exp = 55, n_nexp = 55,
  ancova_mean_exp = 2.3, ancova_mean_se_exp = 1.2,
  ancova_mean_nexp = 1.9, ancova_mean_se_nexp = 0.9,
  cov_outcome_r = 0.2, n_cov_ancova = 3
)

Convert a t-statistic obtained from an ANCOVA model into several effect size measures.

Description

Convert a t-statistic obtained from an ANCOVA model into several effect size measures.

Usage

es_from_ancova_t(
  ancova_t,
  cov_outcome_r,
  n_cov_ancova,
  n_exp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  reverse_ancova_t
)

Arguments

ancova_t

a t-statistic from an ANCOVA (binary predictor)

cov_outcome_r

correlation between the outcome and covariate(s) (multiple correlation when multiple covariates are included in the ANCOVA model).

n_cov_ancova

number of covariates in the ANCOVA model.

n_exp

number of participants in the experimental/exposed group.

n_nexp

number of participants in the non-experimental/non-exposed group.

smd_to_cor

formula used to convert the adjusted cohen_d value into a coefficient correlation (see details).

reverse_ancova_t

a logical value indicating whether the direction of the generated effect sizes should be flipped.

Details

This function first computes an "adjusted" Cohen's d (D), and Hedges' g (G) from the t-value of an ANCOVA (binary predictor). Odds ratio (OR) and correlation coefficients (R/Z) are then converted from the Cohen's d.

To estimate a Cohen's d the formula used is (table 12.3 in Cooper):

cohen_d=ancova_t(n_exp+n_nexp)n_expn_nexp1cov_out_cor2cohen\_d = ancova\_t* \sqrt{\frac{(n\_exp+n\_nexp)}{n\_exp*n\_nexp}}\sqrt{1 - cov\_out\_cor^2}

To estimate other effect size measures, Calculations of the es_from_cohen_d_adj() are applied.

Value

This function estimates and converts between several effect size measures.

natural effect size measure D + G
converted effect size measure OR + R + Z
required input data See 'Section 18. Adjusted: ANCOVA statistics, eta-squared'
https://metaconvert.org/input.html

References

Cooper, H., Hedges, L. V., & Valentine, J. C. (Eds.). (2019). The handbook of research synthesis and meta-analysis. Russell Sage Foundation.

Examples

es_from_ancova_t(ancova_t = 2, cov_outcome_r = 0.2, n_cov_ancova = 3, n_exp = 20, n_nexp = 20)

Convert a two-tailed p-value of an ANCOVA t-test into several effect size measures.

Description

Convert a two-tailed p-value of an ANCOVA t-test into several effect size measures.

Usage

es_from_ancova_t_pval(
  ancova_t_pval,
  cov_outcome_r,
  n_cov_ancova,
  n_exp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  reverse_ancova_t_pval
)

Arguments

ancova_t_pval

a two-tailed p-value of a t-test in an ANCOVA (binary predictor)

cov_outcome_r

correlation between the outcome and covariate(s) (multiple correlation when multiple covariates are included in the ANCOVA model).

n_cov_ancova

number of covariates in the ANCOVA model.

n_exp

number of participants in the experimental/exposed group.

n_nexp

number of participants in the non-experimental/non-exposed group.

smd_to_cor

formula used to convert the adjusted cohen_d value into a coefficient correlation (see details).

reverse_ancova_t_pval

a logical value indicating whether the direction of the generated effect sizes should be flipped.

Details

This function converts the p-value of an ANCOVA (binary predictor) into a t value, and then relies on the calculations of the es_from_ancova_t() function.

To convert the p-value into a t-value, the following formula is used (table 12.3 in Cooper):

df=n_exp+n_nexp+n_exp2n_cov_ancovadf = n\_exp + n\_nexp + n\_exp - 2 - n\_cov\_ancova

t=pt(ancova_f_pval/2,df=df)t = | pt(ancova\_f\_pval/2, df = df) |

Then, calculations of the es_from_ancova_t() are applied.

Value

This function estimates and converts between several effect size measures.

natural effect size measure D + G
converted effect size measure OR + R + Z
required input data See 'Section 18. Adjusted: ANCOVA statistics, eta-squared'
https://metaconvert.org/input.html

References

Cooper, H., Hedges, L.V., & Valentine, J.C. (Eds.). (2019). The handbook of research synthesis and meta-analysis. Russell Sage Foundation.

Examples

es_from_ancova_t_pval(
  ancova_t_pval = 0.05, cov_outcome_r = 0.2,
  n_cov_ancova = 3, n_exp = 20, n_nexp = 20
)

Convert a one-way independent ANOVA F-value to several effect size measures

Description

Convert a one-way independent ANOVA F-value to several effect size measures

Usage

es_from_anova_f(
  anova_f,
  n_exp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  reverse_anova_f
)

Arguments

anova_f

ANOVA F-value (one-way, binary predictor).

n_exp

number of participants in the experimental/exposed group.

n_nexp

number of participants in the non-experimental/non-exposed group.

smd_to_cor

formula used to convert the anova_f value into a coefficient correlation (see details).

reverse_anova_f

a logical value indicating whether the direction of generated effect sizes should be flipped.

Details

This function converts the F-value (one-way, binary predictor) into a t-value, and then relies on the calculations of the es_from_student_t() function.

To convert the F-value into a t-value, the following formula is used (table 12.1 in Cooper):

student_t=anova_fstudent\_t = \sqrt{anova\_f}

Then, calculations of the es_from_student_t() are applied.

Value

This function estimates and converts between several effect size measures.

natural effect size measure D + G
converted effect size measure OR + R + Z
required input data See 'Section 11. ANOVA statistics, Student's t-test, or point-bis correlation'
https://metaconvert.org/html/input.html

References

Cooper, H., Hedges, L.V., & Valentine, J.C. (Eds.). (2019). The handbook of research synthesis and meta-analysis. Russell Sage Foundation.

Examples

es_from_anova_f(anova_f = 2.01, n_exp = 20, n_nexp = 22)

Convert a p-value from a one-way independent ANOVA to several effect size measures

Description

Convert a p-value from a one-way independent ANOVA to several effect size measures

Usage

es_from_anova_pval(
  anova_f_pval,
  n_exp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  reverse_anova_f_pval
)

Arguments

anova_f_pval

p-value (two-tailed) from an ANOVA (binary predictor). If your p-value is one-tailed, simply multiply it by two.

n_exp

number of participants in the experimental/exposed group.

n_nexp

number of participants in the non-experimental/non-exposed group.

smd_to_cor

formula used to convert the anova_f_pval value into a coefficient correlation (see details).

reverse_anova_f_pval

a logical value indicating whether the direction of generated effect sizes should be flipped.

Details

This function converts the p-value from the F-value of an ANOVA (one-way, binary predictor) into a t-value, and then relies on the calculations of the es_from_student_t() function.

To convert the p-value into a t-value, the following formula is used (table 12.1 in Cooper):

student_t=qt(anova_f_pval2,df=n_exp+n_nexp2)student\_t = qt(\frac{anova\_f\_pval}{2}, df = n\_exp + n\_nexp - 2)

Then, calculations of the es_from_student_t() are applied.

Value

This function estimates and converts between several effect size measures.

natural effect size measure D + G
converted effect size measure OR + R + Z
required input data See 'Section 11. ANOVA statistics, Student's t-test, or point-bis correlation'
https://metaconvert.org/html/input.html

References

Cooper, H., Hedges, L.V., & Valentine, J.C. (Eds.). (2019). The handbook of research synthesis and meta-analysis. Russell Sage Foundation.

Examples

es_from_anova_pval(anova_f_pval = 0.0012, n_exp = 20, n_nexp = 22)

Convert a standardized regression coefficient and the standard deviation of the dependent variable into several effect size measures

Description

Convert a standardized regression coefficient and the standard deviation of the dependent variable into several effect size measures

Usage

es_from_beta_std(
  beta_std,
  sd_dv,
  n_exp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  reverse_beta_std
)

Arguments

beta_std

a standardized regression coefficient value (binary predictor, no other covariables in the model)

sd_dv

standard deviation of the dependent variable

n_exp

number of participants in the experimental/exposed group.

n_nexp

number of participants in the non-experimental/non-exposed group.

smd_to_cor

formula used to convert the cohen_d value into a coefficient correlation (see details).

reverse_beta_std

a logical value indicating whether the direction of the generated effect sizes should be flipped.

Details

This function converts a standardized linear regression coefficient (coming from a model with only one binary predictor), into an unstandardized linear regression coefficient.

sd_dummy=nexp(nexp2/(nexp+nnexp))(nexp+nnexp1)sd\_dummy = \sqrt{\frac{n_exp - (n_exp^2 / (n_exp + n_nexp))}{(n_exp + n_nexp - 1)}}

unstd_beta=beta_stdsd_dvsd_dummyunstd\_beta = beta\_std * \frac{sd\_dv}{sd\_dummy}

Calculations of the es_from_beta_unstd functions are then used.

Value

This function estimates and converts between several effect size measures.

natural effect size measure D + G
converted effect size measure OR + R + Z
required input data See 'Section 13. (Un-)Standardized regression coefficient'
https://metaconvert.org/input.html

References

Lipsey, M. W., & Wilson, D. B. (2001). Practical meta-analysis. Sage Publications, Inc.

Examples

es_from_beta_std(beta_std = 2.1, sd_dv = 0.98, n_exp = 20, n_nexp = 22)

Convert an unstandardized regression coefficient and the standard deviation of the dependent variable into several effect size measures

Description

Convert an unstandardized regression coefficient and the standard deviation of the dependent variable into several effect size measures

Usage

es_from_beta_unstd(
  beta_unstd,
  sd_dv,
  n_exp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  reverse_beta_unstd
)

Arguments

beta_unstd

an unstandardized regression coefficient value (binary predictor, no other covariables in the model)

sd_dv

standard deviation of the dependent variable

n_exp

number of participants in the experimental/exposed group.

n_nexp

number of participants in the non-experimental/non-exposed group.

smd_to_cor

formula used to convert the cohen_d value into a coefficient correlation (see details).

reverse_beta_unstd

a logical value indicating whether the direction of the generated effect sizes should be flipped.

Details

This function estimates a Cohen's d (D) and Hedges' g (G) from an unstandardized linear regression coefficient (coming from a model with only one binary predictor), and the standard deviation of the dependent variable. Odds ratio (OR) and correlation coefficients (R/Z) are then converted from the Cohen's d.

The formula used to obtain the Cohen's d is:

N=n_exp+n_nexpN = n\_exp + n\_nexp

sd_pooled=sd_dv2(N1)unstd_beta2n_expn_nexpNN2sd\_pooled = \sqrt{\frac{sd\_dv^2 * (N - 1) - unstd\_beta^2 * \frac{n\_exp * n\_nexp}{N}}{N - 2}}

cohen_d=unstd_betasd_pooledcohen\_d = \frac{unstd\_beta}{sd\_pooled}

To estimate other effect size measures, calculations of the es_from_cohen_d() are applied.

Value

This function estimates and converts between several effect size measures.

natural effect size measure D + G
converted effect size measure OR + R + Z
required input data See 'Section 13. (Un-)Standardized regression coefficient'
https://metaconvert.org/input.html

References

Lipsey, M. W., & Wilson, D. B. (2001). Practical meta-analysis. Sage Publications, Inc.

Examples

es_from_beta_unstd(beta_unstd = 2.1, sd_dv = 0.98, n_exp = 20, n_nexp = 22)

Convert the number of cases and the person-time of disease-free observation in two independent groups into an incidence rate ratio (IRR)

Description

Convert the number of cases and the person-time of disease-free observation in two independent groups into an incidence rate ratio (IRR)

Usage

es_from_cases_time(n_cases_exp, n_cases_nexp, time_exp, time_nexp, reverse_irr)

Arguments

n_cases_exp

number of cases in the exposed group

n_cases_nexp

number of cases in the non-exposed group

time_exp

person-time of disease-free observation in the exposed group

time_nexp

person-time of disease-free observation in the non-exposed group

reverse_irr

a logical value indicating whether the direction of the generated effect sizes should be flipped.

Details

This function estimates the incidence rate ratio from the number of cases and the person-time of disease-free observation in two independent groups.

The formula used to obtain the IRR and its standard error are (Cochrane Handbook (section 6.7.1):

logirr=log(n_cases_exp/time_expn_cases_nexp/time_nexp)logirr = log(\frac{n\_cases\_exp / time\_exp}{n\_cases\_nexp / time\_nexp)}

logirr_se=1n_cases_exp+1n_cases_nexplogirr\_se = \sqrt{\frac{1}{n\_cases\_exp} + \frac{1}{n\_cases\_nexp}}

Value

This function estimates IRR.

natural effect size measure IRR
converted effect size measure N/A
required input data See 'Section 5. Incidence Ratio Ratio'
https://metaconvert.org/input.html

References

Higgins JPT, Thomas J, Chandler J, Cumpston M, Li T, Page MJ, Welch VA (editors). Cochrane Handbook for Systematic Reviews of Interventions version 6.3 (updated February 2022). Cochrane, 2022. Available from www.training.cochrane.org/handbook.

Examples

es_from_cases_time(
  n_cases_exp = 241, n_cases_nexp = 554,
  time_exp = 12.764, time_nexp = 19.743
)

Convert a chi-square value to several effect size measures

Description

Convert a chi-square value to several effect size measures

Usage

es_from_chisq(
  chisq,
  n_sample,
  n_cases,
  n_exp,
  yates_chisq = FALSE,
  reverse_chisq
)

Arguments

chisq

value of the chi-squared

n_sample

total number of participants in the sample

n_cases

total number of cases/events

n_exp

total number of participants in the exposed group

yates_chisq

a logical value indicating whether the Chi square has been performed using Yate's correction for continuity.

reverse_chisq

a logical value indicating whether the direction of generated effect sizes should be flipped.

Details

This function converts a chi-square value (with one degree of freedom) into a phi coefficient (Lipsey et al. 2001):

phi=chisq2n_samplephi = \sqrt{\frac{chisq^2}{n\_sample}}

.

Note that if yates_chisq = "TRUE", a small correction is added.

Then, the phi coefficient is converted to other effect size measures (see es_from_phi).

Value

This function estimates and converts between several effect size measures.

natural effect size measure OR + RR + NNT
converted effect size measure D + G + R + Z
required input data See 'Section 8. Phi or chi-square'
https://metaconvert.org/input.html

References

Lipsey, M. W., & Wilson, D. B. (2001). Practical meta-analysis. Sage Publications, Inc.

Examples

es_from_chisq(chisq = 4.21, n_sample = 78, n_cases = 51, n_exp = 50)

Convert a p-value of a chi-square to several effect size measures

Description

Convert a p-value of a chi-square to several effect size measures

Usage

es_from_chisq_pval(
  chisq_pval,
  n_sample,
  n_cases,
  n_exp,
  yates_chisq = FALSE,
  reverse_chisq_pval
)

Arguments

chisq_pval

p-value of a chi-square coefficient

n_sample

total number of participants in the sample

n_cases

total number of cases/events

n_exp

total number of participants in the exposed group

yates_chisq

a logical value indicating whether the Chi square has been performed using Yate's correction for continuity.

reverse_chisq_pval

a logical value indicating whether the direction of generated effect sizes should be flipped.

Details

This function converts a chi-square value (with one degree of freedom) into a chi-square coefficient (Section 3.12 in Lipsey et al., 2001):

chisq=qchisq(chisq_pval,df=1,lower.tail=FALSE)chisq = qchisq(chisq\_pval, df = 1, lower.tail = FALSE)

Note that if yates_chisq = "TRUE", a small correction is added.

Then, the chisq coefficient is converted to other effect size measures (see es_from_chisq).

Value

This function estimates and converts between several effect size measures.

natural effect size measure OR + RR + NNT
converted effect size measure D + G + R + Z
required input data See 'Section 8. Phi or chi-square'
https://metaconvert.org/input.html

References

Lipsey, M. W., & Wilson, D. B. (2001). Practical meta-analysis. Sage Publications, Inc.

Examples

es_from_chisq_pval(chisq_pval = 0.2, n_sample = 42, n_exp = 25, n_cases = 13)

Convert a Cohen's d value to several effect size measures

Description

Convert a Cohen's d value to several effect size measures

Usage

es_from_cohen_d(cohen_d, n_exp, n_nexp, smd_to_cor = "viechtbauer", reverse_d)

Arguments

cohen_d

Cohen's d (i.e., standardized mean difference) value.

n_exp

number of participants in the experimental/exposed group.

n_nexp

number of participants in the non-experimental/non-exposed group.

smd_to_cor

formula used to convert the cohen_d value into a coefficient correlation (see details).

reverse_d

a logical value indicating whether the direction of generated effect sizes should be flipped.

Details

This function estimates the standard error of a Cohen's d value and computes a Hedges' g (G). Odds ratio (OR) and correlation coefficients (R/Z) are then converted from the Cohen's d.

To estimate the standard error of Cohen's d, the following formula is used (formula 12.13 in Cooper):

cohen_d_se=n_exp+n_nexpn_expn_nexp+cohen_d22(n_exp+n_nexp)cohen\_d\_se = \sqrt{\frac{n\_exp+n\_nexp}{n\_exp*n\_nexp} + \frac{cohen\_d^2}{2*(n\_exp+n\_nexp)}}

cohen_d_ci_lo=cohen_dcohen_d_seqt(.975,df=n_exp+n_nexp2)cohen\_d\_ci\_lo = cohen\_d - cohen\_d\_se * qt(.975, df = n\_exp+n\_nexp-2)

cohen_d_ci_up=cohen_d+cohen_d_seqt(.975,df=n_exp+n_nexp2)cohen\_d\_ci\_up = cohen\_d + cohen\_d\_se * qt(.975, df = n\_exp+n\_nexp-2)

To estimate the Hedges' g and its standard error, the following formulas are used (Hedges, 1981):

df=n_exp+n_nexp2df = n\_exp + n\_nexp - 2

J=exp(loggamma(df2)0.5log(df2)loggamma(df12))J = exp(\log_{gamma}(\frac{df}{2}) - 0.5 * \log(\frac{df}{2}) - \log_{gamma}(\frac{df - 1}{2}))

hedges_g=cohen_dJhedges\_g = cohen\_d * J

hedges_g_se=cohen_d_se2J2hedges\_g\_se = \sqrt{cohen\_d\_se^2 * J^2}

hedges_g_ci_lo=hedges_ghedges_g_seqt(.975,df=n_exp+n_nexp2)hedges\_g\_ci\_lo = hedges\_g - hedges\_g\_se * qt(.975, df = n\_exp+n\_nexp-2)

hedges_g_ci_up=hedges_g+hedges_g_seqt(.975,df=n_exp+n_nexp2)hedges\_g\_ci\_up = hedges\_g + hedges\_g\_se * qt(.975, df = n\_exp+n\_nexp-2)

To estimate the log odds ratio and its standard error, the following formulas are used (formulas 12.34-12.35 in Cooper):

logor=cohen_dπ3logor = \frac{cohen\_d * \pi}{\sqrt{3}}

logor_se=cohen_d_se2π23logor\_se = \sqrt{\frac{cohen\_d\_se^2 * \pi^2}{3}}

logor_lo=logorlogor_seqnorm(.975)logor\_lo = logor - logor\_se * qnorm(.975)

logor_up=logor+logor_seqnorm(.975)logor\_up = logor + logor\_se * qnorm(.975)

Note that this conversion assumes that responses within the two groups follow logistic distributions.

To estimate the correlation coefficient and its standard error, various formulas can be used.

A. To estimate the 'biserial' correlation (smd_to_cor="viechtbauer"), the following formulas are used (formulas 5, 8, 13, 17, 18, 19 in Viechtbauer):

h=n_exp+n_nexpn_exp+n_exp+n_nexpn_nexph = \frac{n\_exp + n\_nexp}{n\_exp} + \frac{n\_exp + n\_nexp}{n\_nexp}

r.pb=cohen_dcohen_d2+hr.pb = \frac{cohen\_d}{\sqrt{cohen\_d^2 + h}}

p=n_expn_exp+n_nexpp = \frac{n\_exp}{n\_exp + n\_nexp}

q=1pq = 1 - p

R=pqdnorm(qnorm(1p))r.pbR = \frac{\sqrt{p*q}}{dnorm(qnorm(1-p)) * r.pb}

R_var=1n_exp+n_nexp1(pqdnorm(qnorm(1p))R2)2R\_var = \frac{1}{n\_exp + n\_nexp - 1} * (\frac{\sqrt{p*q}}{dnorm(qnorm(1-p))} - R^2)^2

R_se=R_varR\_se = \sqrt{R\_var}

a=dnorm(qnorm(1p))(pq)14a = \frac{\sqrt{dnorm(qnorm(1-p))}}{(p*q)^\frac{1}{4}}

Z=a2log(1+aR1aR)Z = \frac{a}{2} * \log(\frac{1+a*R}{1-a*R})

Z_var=1n1Z\_var = \frac{1}{n - 1}

Z_se=Z_varZ\_se = \sqrt{Z\_var}

Z_ci_lo=Zqnorm(.975)Z_seZ\_ci\_lo = Z - qnorm(.975) * Z\_se

Z_ci_up=Z+qnorm(.975)Z_seZ\_ci\_up = Z + qnorm(.975) * Z\_se

R_ci_lo=tanh(Z_lo)R\_ci\_lo = tanh(Z\_lo)

R_ci_up=tanh(Z_up)R\_ci\_up = tanh(Z\_up)

B. To estimate the correlation coefficient according to Cooper et al. (2019) (formulas 12.40-42) and Borenstein et al. (2009) (formulas 54-56), the following formulas are used (smd_to_cor="lipsey_cooper"):

p=n_expn_exp+n_nexpp = \frac{n\_exp}{n\_exp + n\_nexp}

R=cohen_dcohen_d2+1/(p(1p))R = \frac{cohen\_d}{\sqrt{cohen\_d^2 + 1 / (p * (1 - p))}}

a=(n_exp+n_nexp)2(n_expn_nexp)a = \frac{(n\_exp + n\_nexp)^2}{(n\_exp*n\_nexp)}

var_R=a2cohen_d_se2(cohen_d2+a)3var\_R = \frac{a^2 * cohen\_d\_se^2}{(cohen\_d^2 + a)^3}

R_se=R_varR\_se = \sqrt{R\_var}

R_ci_lo=Rqt(.975,n_exp+n_nexp2)R_seR\_ci\_lo = R - qt(.975, n\_exp+n\_nexp- 2) * R\_se

R_ci_up=R+qt(.975,n_exp+n_nexp2)R_seR\_ci\_up = R + qt(.975, n\_exp+n\_nexp- 2) * R\_se

Z=atanh(R)Z = atanh(R)

Z_var=cohen_d_se2cohen_d_se2+(1/p(1p))Z\_var = \frac{cohen\_d\_se^2}{cohen\_d\_se^2 + (1 / p*(1-p))}

Z_se=Z_varZ\_se = \sqrt{Z\_var}

Z_ci_lo=Zqnorm(.975)Z_seZ\_ci\_lo = Z - qnorm(.975) * Z\_se

Z_ci_up=Z+qnorm(.975)Z_seZ\_ci\_up = Z + qnorm(.975) * Z\_se

Value

This function estimates and converts between several effect size measures.

natural effect size measure D + G
converted effect size measure OR + R + Z
required input data See 'Section 1. Cohen's d or Hedges' g'
https://metaconvert.org/input.html

References

Cooper, H., Hedges, L.V., & Valentine, J.C. (Eds.). (2019). The handbook of research synthesis and meta-analysis. Russell Sage Foundation.

Borenstein, M., Hedges, L. V., Higgins, J. P., & Rothstein, H. R. (2021). Introduction to meta-analysis. John Wiley & Sons.

Hedges LV (1981): Distribution theory for Glass’s estimator of effect size and related estimators. Journal of Educational and Behavioral Statistics, 6, 107–28

Jacobs, P., & Viechtbauer, W. (2017). Estimation of the biserial correlation and its sampling variance for use in meta-analysis. Research synthesis methods, 8(2), 161–180.

Examples

es_from_cohen_d(cohen_d = 1, n_exp = 20, n_nexp = 20)

Convert an adjusted Cohen's d value to several effect size measures

Description

Convert an adjusted Cohen's d value to several effect size measures

Usage

es_from_cohen_d_adj(
  cohen_d_adj,
  n_cov_ancova,
  cov_outcome_r,
  n_exp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  reverse_d
)

Arguments

cohen_d_adj

Adjusted Cohen's d (i.e., standardized mean difference) value.

n_cov_ancova

number of covariates

cov_outcome_r

covariate-outcome correlation (in case of multiple covariates, the multiple correlation)

n_exp

number of participants in the experimental/exposed group.

n_nexp

number of participants in the non-experimental/non-exposed group.

smd_to_cor

formula used to convert the cohen_d value into a coefficient correlation (see details).

reverse_d

a logical value indicating whether the direction of generated effect sizes should be flipped.

Details

This function estimates the standard error of an adjusted Cohen's d value and Hedges' g (G), and converts an odds ratio (OR) and correlation coefficients (R/Z).

To estimate the standard error of Cohen's d, the following formula is used (table 12.3 in Cooper):

d_se=n_exp+n_nexpn_expn_nexp(1cov_outcome_r2)+cohen_d_adj22(n_exp+n_nexp)d\_se = \sqrt{\frac{n\_exp+n\_nexp}{n\_exp*n\_nexp} * (1 - cov\_outcome\_r^2) + \frac{cohen\_d\_adj^2}{2*(n\_exp+n\_nexp)}}

To estimate other effect size measures, calculations of the es_from_cohen_d() function are used (with the exception of the degree of freedom that is estimated as df = n_exp + n_nexp - 2 - n_cov_ancova).

Value

This function estimates and converts between several effect size measures.

natural effect size measure D + G
converted effect size measure OR + R + Z
required input data See 'Section 1. Cohen's d or Hedges' g'
https://metaconvert.org/input.html

References

Cooper, H., Hedges, L.V., & Valentine, J.C. (Eds.). (2019). The handbook of research synthesis and meta-analysis. Russell Sage Foundation.

Examples

es_from_cohen_d_adj(cohen_d_adj = 1, n_cov_ancova = 4, cov_outcome_r = .30, n_exp = 20, n_nexp = 20)

Convert an eta-squared value to various effect size measures

Description

Convert an eta-squared value to various effect size measures

Usage

es_from_etasq(etasq, n_exp, n_nexp, smd_to_cor = "viechtbauer", reverse_etasq)

Arguments

etasq

an eta-squared value (binary predictor, ANOVA model))

n_exp

number of participants in the experimental/exposed group.

n_nexp

number of participants in the non-experimental/non-exposed group.

smd_to_cor

formula used to convert the cohen_d value into a coefficient correlation.

reverse_etasq

a logical value indicating whether the direction of generated effect sizes should be flipped.

Details

This function first computes a Cohen's d (D) and Hedges' g (G) from the eta squared of a binary predictor (ANOVA model). Odds ratio (OR) and correlation coefficients (R/Z) are then converted from the Cohen's d.

To estimate a Cohen's d the following formula is used (Cohen, 1988):

d=2etasq1etasqd = 2 * \sqrt{\frac{etasq}{1 - etasq}}

To estimate other effect size measures, calculations of the es_from_cohen_d() are applied.

Value

This function estimates and converts between several effect size measures.

natural effect size measure D + G
converted effect size measure OR + R + Z
required input data See 'Section 11. ANOVA statistics, Student's t-test, or point-bis correlation'
https://metaconvert.org/input.html

References

Cohen, J. (1988). Statistical power analysis for the behavioral sciences. Routledge.

Examples

es_from_etasq(etasq = 0.28, n_exp = 20, n_nexp = 22)

Convert an adjusted eta-squared value (i.e., from an ANCOVA) to various effect size measures

Description

Convert an adjusted eta-squared value (i.e., from an ANCOVA) to various effect size measures

Usage

es_from_etasq_adj(
  etasq_adj,
  n_exp,
  n_nexp,
  n_cov_ancova,
  cov_outcome_r,
  smd_to_cor = "viechtbauer",
  reverse_etasq
)

Arguments

etasq_adj

an adjusted eta-squared value (i.e., obtained from an ANCOVA model)

n_exp

number of participants in the experimental/exposed group.

n_nexp

number of participants in the non-experimental/non-exposed group.

n_cov_ancova

number of covariates in the ANCOVA model.

cov_outcome_r

correlation between the outcome and covariate (multiple correlation when multiple covariates are included in the ANCOVA model).

smd_to_cor

formula used to convert the cohen_d value into a coefficient correlation (see details).

reverse_etasq

a logical value indicating whether the direction of generated effect sizes should be flipped.

Details

This function first computes an adjusted Cohen's d (D) and Hedges' g (G) from the adjusted eta squared of a binary predictor (ANCOVA model). Odds ratio (OR) and correlation coefficients (R/Z) are then converted from the Cohen's d.

To estimate a Cohen's d the following formula is used (Cohen, 1988):

d_adj=2etasq_adj1etasq_adjd\_adj = 2 * \sqrt{\frac{etasq\_adj}{1 - etasq\_adj}}

To estimate other effect size measures, calculations of the es_from_cohen_d_adj() are applied.

Value

This function estimates and converts between several effect size measures.

natural effect size measure D + G
converted effect size measure OR + R + Z
required input data See 'Section 18. Adjusted: ANCOVA statistics, eta-squared'
https://metaconvert.org/input.html

References

Cohen, J. (1988). Statistical power analysis for the behavioral sciences. Routledge.

Examples

es_from_etasq_adj(etasq = 0.28, n_cov_ancova = 3, cov_outcome_r = 0.2, n_exp = 20, n_nexp = 22)

Convert a Fisher's z (r-to-z transformation) to several effect size measures

Description

Convert a Fisher's z (r-to-z transformation) to several effect size measures

Usage

es_from_fisher_z(
  fisher_z,
  n_sample,
  unit_type = "raw_scale",
  n_exp,
  n_nexp,
  cor_to_smd = "viechtbauer",
  sd_iv,
  unit_increase_iv,
  reverse_fisher_z
)

Arguments

fisher_z

a Fisher's r-to-z transformed correlation coefficient

n_sample

the total number of participants

unit_type

the type of unit for the unit_increase_iv argument. Must be either "sd" or "value"

n_exp

number of the experimental/exposed group

n_nexp

number of the non-experimental/non-exposed group

cor_to_smd

formula used to convert a pearson_r or fisher_z value into a SMD.

sd_iv

the standard deviation of the independent variable

unit_increase_iv

a value of the independent variable that will be used to estimate the Cohen's d (see details).

reverse_fisher_z

a logical value indicating whether the direction of the generated effect sizes should be flipped.

Details

This function converts estimates the standard error of the Fisher's z and performs the z-to-r Fisher's transformation.

Last, it converts this r value into a Cohen's d and OR (see details in es_from_pearson_r()).

Value

This function estimates and converts between several effect size measures.

natural effect size measure R + Z
converted effect size measure D + G + OR
required input data See 'Section 4. Pearson's r or Fisher's z'
https://metaconvert.org/input.html

References

Cooper, H., Hedges, L.V., & Valentine, J.C. (Eds.). (2019). The handbook of research synthesis and meta-analysis. Russell Sage Foundation.

Mathur, M. B., & VanderWeele, T. J. (2020). A Simple, Interpretable Conversion from Pearson's Correlation to Cohen's for d Continuous Exposures. Epidemiology (Cambridge, Mass.), 31(2), e16–e18. https://doi.org/10.1097/EDE.0000000000001105

Viechtbauer W (2010). “Conducting meta-analyses in R with the metafor package.” Journal of Statistical Software, 36(3), 1–48. doi:10.18637/jss.v036.i03.

Examples

es_from_fisher_z(
  fisher_z = .21, n_sample = 44,
)

Convert a Hedges' g value to other effect size measures (G, OR, COR)

Description

Convert a Hedges' g value to other effect size measures (G, OR, COR)

Usage

es_from_hedges_g(
  hedges_g,
  n_exp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  reverse_g
)

Arguments

hedges_g

Hedges' g value

n_exp

number of participants in the experimental/exposed group.

n_nexp

number of participants in the non-experimental/non-exposed group.

smd_to_cor

formula used to convert the hedges_g value into a coefficient correlation (see details).

reverse_g

a logical value indicating whether the direction of the hedges_g value should be flipped.

Details

This function estimates the standard error of the Hedges' g and the Cohen's d (D). Odds ratio (OR) and correlation coefficients (R/Z) are then converted from the Cohen's d.

To estimate standard error of Hedges'g, the following formula is used (Hedges, 1981):

df=n_exp+n_nexp2df = n\_exp + n\_nexp - 2

hedges_g_se=cohen_d_se2J2hedges\_g\_se = \sqrt{cohen\_d\_se^2 * J^2}

hedges_g_ci_lo=hedges_ghedges_g_seqt(.975,df=n_exp+n_nexp2)hedges\_g\_ci\_lo = hedges\_g - hedges\_g\_se * qt(.975, df = n\_exp+n\_nexp-2)

hedges_g_ci_up=hedges_g+hedges_g_seqt(.975,df=n_exp+n_nexp2)hedges\_g\_ci\_up = hedges\_g + hedges\_g\_se * qt(.975, df = n\_exp+n\_nexp-2)

To estimate the Cohen's d value, the following formula is used (Hedges, 1981):

J=exp(loggamma(df2)0.5log(df2)loggamma(df12))J = exp(\log_{gamma}(\frac{df}{2}) - 0.5 * \log(\frac{df}{2}) - \log_{gamma}(\frac{df - 1}{2}))

cohen_d=hedges_gJcohen\_d = \frac{hedges\_g}{J}

cohen_d_se=(n_exp+n_nexpn_expn_nexp+cohen_d22(n_exp+n_nexp))cohen\_d\_se = \sqrt{(\frac{n\_exp+n\_nexp}{n\_exp*n\_nexp} + \frac{cohen\_d^2}{2*(n\_exp+n\_nexp)})}

To estimate other effect size measures, calculations of the es_from_cohen_d() are applied.

Value

This function estimates and converts between several effect size measures.

natural effect size measure D + G
converted effect size measure OR + R + Z
required input data See 'Section 1. Cohen's d or Hedges' g'
https://metaconvert.org/input.html

References

Hedges LV (1981): Distribution theory for Glass’s estimator of effect size and related estimators. Journal of Educational and Behavioral Statistics, 6, 107–28

Examples

es_from_hedges_g(hedges_g = 0.243, n_exp = 20, n_nexp = 20)

Convert a mean difference between two independent groups and 95% CI into several effect size measures

Description

Convert a mean difference between two independent groups and 95% CI into several effect size measures

Usage

es_from_md_ci(
  md,
  md_ci_lo,
  md_ci_up,
  n_exp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  max_asymmetry = 10,
  reverse_md
)

Arguments

md

mean difference between two independent groups

md_ci_lo

lower bound of the 95% CI of the mean difference

md_ci_up

upper bound of the 95% CI of the mean difference

n_exp

number of participants in the experimental/exposed group.

n_nexp

number of participants in the non-experimental/non-exposed group.

smd_to_cor

formula used to convert the cohen_d value into a coefficient correlation (see details).

max_asymmetry

A percentage indicating the tolerance before detecting asymmetry in the 95% CI bounds.

reverse_md

a logical value indicating whether the direction of generated effect sizes should be flipped.

Details

This function converts 95% CI of a mean difference into a standard error (Cochrane Handbook section 6.5.2.3):

md_se=md_ci_upmd_ci_lo2qt(0.975,df=n_exp+n_nexp2)md\_se = \frac{md\_ci\_up - md\_ci\_lo}{2 * qt(0.975, df = n\_exp + n\_nexp - 2)}

Calculations of the es_from_md_se() function are then used to estimate the Cohen's d and other effect size measures.

Value

This function estimates and converts between several effect size measures.

natural effect size measure MD + D + G
converted effect size measure OR + R + Z
required input data See 'Section 10. Mean difference and dispersion (crude)'
https://metaconvert.org/input.html

References

Higgins JPT, Li T, Deeks JJ (editors). Chapter 6: Choosing effect size measures and computing estimates of effect. In: Higgins JPT, Thomas J, Chandler J, Cumpston M, Li T, Page MJ, Welch VA (editors). Cochrane Handbook for Systematic Reviews of Interventions version 6.3 (updated February 2022). Cochrane, 2022. Available from www.training.cochrane.org/handbook.

Examples

es_from_md_ci(md = 4, md_ci_lo = 2, md_ci_up = 6, n_exp = 20, n_nexp = 22)

Convert a mean difference between two independent groups and its p-value into several effect size measures

Description

Convert a mean difference between two independent groups and its p-value into several effect size measures

Usage

es_from_md_pval(
  md,
  md_pval,
  n_exp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  reverse_md
)

Arguments

md

mean difference between two independent groups

md_pval

p-value of the mean difference

n_exp

number of participants in the experimental/exposed group.

n_nexp

number of participants in the non-experimental/non-exposed group.

smd_to_cor

formula used to convert the cohen_d value into a coefficient correlation (see details).

reverse_md

a logical value indicating whether the direction of generated effect sizes should be flipped.

Details

This function converts the p-value of a mean difference into a standard error (Cochrane Handbook section 6.5.2.3):

t=qt(md_pval2,df=n_exp+n_nexp2)t = qt(\frac{md\_pval}{2}, df = n\_exp + n\_nexp - 2)

md_se=mdtmd\_se = |\frac{md}{t}|

Calculations of the es_from_md_se function are then used to estimate the Cohen's d and other effect size measures.

Value

This function estimates and converts between several effect size measures.

natural effect size measure MD + D + G
converted effect size measure OR + R + Z
required input data See 'Section 10. Mean difference and dispersion (crude)'
https://metaconvert.org/input.html

References

Higgins JPT, Thomas J, Chandler J, Cumpston M, Li T, Page MJ, Welch VA (editors). Cochrane Handbook for Systematic Reviews of Interventions version 6.3 (updated February 2022). Cochrane, 2022. Available from www.training.cochrane.org/handbook.

Examples

es_from_md_pval(md = 4, md_pval = 0.024, n_exp = 20, n_nexp = 22)

Convert a mean difference between two independent groups and standard deviation into several effect size measures

Description

Convert a mean difference between two independent groups and standard deviation into several effect size measures

Usage

es_from_md_sd(md, md_sd, n_exp, n_nexp, smd_to_cor = "viechtbauer", reverse_md)

Arguments

md

mean difference between two independent groups

md_sd

standard deviation of the mean difference

n_exp

number of participants in the experimental/exposed group.

n_nexp

number of participants in the non-experimental/non-exposed group.

smd_to_cor

formula used to convert the cohen_d value into a coefficient correlation (see details).

reverse_md

a logical value indicating whether the direction of generated effect sizes should be flipped.

Details

This function converts the mean difference and 95% CI into a Cohen's d (D) and Hedges' g (G). Odds ratio (OR) and correlation coefficients (R/Z) are then converted from the Cohen's d.

The formula used to obtain the Cohen's d is:

d=mdmd_sdd = \frac{md}{md\_sd}

Note that this formula is perfectly accurate only if the md_sd has been estimated by assuming that the variance of the two groups is equal.

To estimate other effect size measures, calculations of the es_from_cohen_d() are applied.

Value

This function estimates and converts between several effect size measures.

natural effect size measure MD + D + G
converted effect size measure OR + R + Z
required input data See 'Section 10. Mean difference and dispersion (crude)'
https://metaconvert.org/input.html

Examples

es_from_md_sd(md = 4, md_sd = 2, n_exp = 20, n_nexp = 22)

Convert a mean difference between two independent groups and its standard error into several effect size measures

Description

Convert a mean difference between two independent groups and its standard error into several effect size measures

Usage

es_from_md_se(md, md_se, n_exp, n_nexp, smd_to_cor = "viechtbauer", reverse_md)

Arguments

md

mean difference between two independent groups

md_se

standard error of the mean difference

n_exp

number of participants in the experimental/exposed group.

n_nexp

number of participants in the non-experimental/non-exposed group.

smd_to_cor

formula used to convert the cohen_d value into a coefficient correlation (see details).

reverse_md

a logical value indicating whether the direction of generated effect sizes should be flipped.

Details

This function the standard error of a mean difference into a standard deviation:

inv_n=1n_exp+1n_nexpinv\_n = \frac{1}{n\_exp} + \frac{1}{n\_nexp}

md_sd=md_seinv_nmd\_sd = \frac{md\_se}{\sqrt{inv\_n}}

Calculations of the es_from_md_sd function are then used to estimate the Cohen's d and other effect size measures.

Value

This function estimates and converts between several effect size measures.

natural effect size measure MD + D + G
converted effect size measure OR + R + Z
required input data See 'Section 10. Mean difference and dispersion (crude)'
https://metaconvert.org/input.html

References

Higgins JPT, Li T, Deeks JJ (editors). Chapter 6: Choosing effect size measures and computing estimates of effect. In: Higgins JPT, Thomas J, Chandler J, Cumpston M, Li T, Page MJ, Welch VA (editors). Cochrane Handbook for Systematic Reviews of Interventions version 6.3 (updated February 2022). Cochrane, 2022. Available from www.training.cochrane.org/handbook.

Examples

es_from_md_se(md = 4, md_se = 2, n_exp = 20, n_nexp = 22)

Convert mean changes and standard deviations of two independent groups into standard effect size measures

Description

Convert mean changes and standard deviations of two independent groups into standard effect size measures

Usage

es_from_mean_change_ci(
  mean_change_exp,
  mean_change_ci_lo_exp,
  mean_change_ci_up_exp,
  mean_change_nexp,
  mean_change_ci_lo_nexp,
  mean_change_ci_up_nexp,
  r_pre_post_exp,
  r_pre_post_nexp,
  n_exp,
  n_nexp,
  max_asymmetry = 10,
  smd_to_cor = "viechtbauer",
  reverse_mean_change
)

Arguments

mean_change_exp

mean change of participants in the experimental/exposed group.

mean_change_ci_lo_exp

lower bound of the 95% CI around the mean change of the experimental/exposed group.

mean_change_ci_up_exp

upper bound of the 95% CI around the mean change of the experimental/exposed group.

mean_change_nexp

mean change of participants in the non-experimental/non-exposed group.

mean_change_ci_lo_nexp

lower bound of the 95% CI around the mean change of the non-experimental/non-exposed group.

mean_change_ci_up_nexp

upper bound of the 95% CI around the mean change of the non-experimental/non-exposed group.

r_pre_post_exp

pre-post correlation in the experimental/exposed group

r_pre_post_nexp

pre-post correlation in the non-experimental/non-exposed group

n_exp

number of participants in the experimental/exposed group.

n_nexp

number of participants in the non-experimental/non-exposed group.

max_asymmetry

A percentage indicating the tolerance before detecting asymmetry in the 95% CI bounds.

smd_to_cor

formula used to convert the cohen_d value into a coefficient correlation (see details).

reverse_mean_change

a logical value indicating whether the direction of generated effect sizes should be flipped.

Details

This function converts the mean change and 95% CI of two independent groups into a Cohen's d. The Cohen's d is then converted to other effect size measures.

This function simply internally calls the es_from_means_ci_pre_post function but setting:

mean_pre_exp=mean_change_expmean\_pre\_exp = mean\_change\_exp

mean_pre_ci_lo_exp=mean_change_ci_lo_expmean\_pre\_ci\_lo\_exp = mean\_change\_ci\_lo\_exp

mean_pre_ci_up_exp=mean_change_ci_up_expmean\_pre\_ci\_up\_exp = mean\_change\_ci\_up\_exp

mean_exp=0mean\_exp = 0

mean_ci_lo_exp=0mean\_ci\_lo\_exp = 0

mean_ci_up_exp=0mean\_ci\_up\_exp = 0

mean_pre_nexp=mean_change_nexpmean\_pre\_nexp = mean\_change\_nexp

mean_pre_ci_lo_nexp=mean_change_ci_lo_nexpmean\_pre\_ci\_lo\_nexp = mean\_change\_ci\_lo\_nexp

mean_pre_ci_up_nexp=mean_change_ci_up_nexpmean\_pre\_ci\_up\_nexp = mean\_change\_ci\_up\_nexp

mean_nexp=0mean\_nexp = 0

mean_ci_lo_nexp=0mean\_ci\_lo\_nexp = 0

mean_ci_up_nexp=0mean\_ci\_up\_nexp = 0

To know more about the calculations, see es_from_means_sd_pre_post function.

Value

This function estimates and converts between several effect size measures.

natural effect size measure MD + D + G
converted effect size measure OR + R + Z
required input data See 'Section 14. Paired: mean change, and dispersion'
https://metaconvert.org/input.html

References

Bonett, S. B. (2008). Estimating effect sizes from pretest-posttest-control group designs. Organizational Research Methods, 11(2), 364–386. https://doi.org/10.1177/1094428106291059

Cooper, H., Hedges, L.V., & Valentine, J.C. (Eds.). (2019). The handbook of research synthesis and meta-analysis. Russell Sage Foundation.

Examples

es_from_mean_change_ci(
  n_exp = 36, n_nexp = 35,
  mean_change_exp = 8.4,
  mean_change_ci_lo_exp = 6.4, mean_change_ci_up_exp = 10.4,
  mean_change_nexp = 2.43,
  mean_change_ci_lo_nexp = 1.43, mean_change_ci_up_nexp = 3.43,
  r_pre_post_exp = 0.2, r_pre_post_nexp = 0.2
)

Convert mean changes and standard deviations of two independent groups into standard effect size measures

Description

Convert mean changes and standard deviations of two independent groups into standard effect size measures

Usage

es_from_mean_change_pval(
  mean_change_exp,
  mean_change_pval_exp,
  mean_change_nexp,
  mean_change_pval_nexp,
  r_pre_post_exp,
  r_pre_post_nexp,
  n_exp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  reverse_mean_change
)

Arguments

mean_change_exp

mean change of participants in the experimental/exposed group.

mean_change_pval_exp

p-value of the mean change for participants in the experimental/exposed group.

mean_change_nexp

mean change of participants in the non-experimental/non-exposed group.

mean_change_pval_nexp

p-value of the mean change for participants in the non-experimental/non-exposed group.

r_pre_post_exp

pre-post correlation in the experimental/exposed group

r_pre_post_nexp

pre-post correlation in the non-experimental/non-exposed group

n_exp

number of participants in the experimental/exposed group.

n_nexp

number of participants in the non-experimental/non-exposed group.

smd_to_cor

formula used to convert the cohen_d value into a coefficient correlation (see details).

reverse_mean_change

a logical value indicating whether the direction of generated effect sizes should be flipped.

Details

This function converts the mean change and associated p-values of two independent groups into a Cohen's d. The Cohen's d is then converted to other effect size measures.

To start, this function estimates the mean change standard errors from the p-values:

t_exp<qt(p=mean_change_pval_exp/2,df=n_exp1,lower.tail=FALSE)t\_exp <- qt(p = mean\_change\_pval\_exp / 2, df = n\_exp - 1, lower.tail = FALSE)

t_nexp<qt(p=mean_change_pval_nexp/2,df=n_nexp1,lower.tail=FALSE)t\_nexp <- qt(p = mean\_change\_pval\_nexp / 2, df = n\_nexp - 1, lower.tail = FALSE)

mean_change_se_exp<mean_change_expt_expmean\_change\_se\_exp <- |\frac{mean\_change\_exp}{t\_exp}|

mean_change_se_nexp<mean_change_nexpt_nexpmean\_change\_se\_nexp <- |\frac{mean\_change\_nexp}{t\_nexp}|

Then, this function simply internally calls the es_from_means_se_pre_post function but setting:

mean_pre_exp=mean_change_expmean\_pre\_exp = mean\_change\_exp

mean_pre_se_exp=mean_change_se_expmean\_pre\_se\_exp = mean\_change\_se\_exp

mean_exp=0mean\_exp = 0

mean_se_exp=0mean\_se\_exp = 0

mean_pre_nexp=mean_change_nexpmean\_pre\_nexp = mean\_change\_nexp

mean_pre_se_nexp=mean_change_se_nexpmean\_pre\_se\_nexp = mean\_change\_se\_nexp

mean_nexp=0mean\_nexp = 0

mean_se_nexp=0mean\_se\_nexp = 0

To know more about other calculations, see es_from_means_sd_pre_post function.

Value

This function estimates and converts between several effect size measures.

natural effect size measure MD + D + G
converted effect size measure OR + R + Z
required input data See 'Section 14. Paired: mean change, and dispersion'
https://metaconvert.org/input.html

References

Bonett, S. B. (2008). Estimating effect sizes from pretest-posttest-control group designs. Organizational Research Methods, 11(2), 364–386. https://doi.org/10.1177/1094428106291059

Cooper, H., Hedges, L.V., & Valentine, J.C. (Eds.). (2019). The handbook of research synthesis and meta-analysis. Russell Sage Foundation.

Examples

es_from_mean_change_pval(
  n_exp = 36, n_nexp = 35,
  mean_change_exp = 8.4, mean_change_pval_exp = 0.13,
  mean_change_nexp = 2.43, mean_change_pval_nexp = 0.61,
  r_pre_post_exp = 0.8, r_pre_post_nexp = 0.8
)

Convert mean changes and standard deviations of two independent groups into standard effect size measures

Description

Convert mean changes and standard deviations of two independent groups into standard effect size measures

Usage

es_from_mean_change_sd(
  mean_change_exp,
  mean_change_sd_exp,
  mean_change_nexp,
  mean_change_sd_nexp,
  r_pre_post_exp,
  r_pre_post_nexp,
  n_exp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  reverse_mean_change
)

Arguments

mean_change_exp

mean change of participants in the experimental/exposed group.

mean_change_sd_exp

standard deviation of the mean change for participants in the experimental/exposed group.

mean_change_nexp

mean change of participants in the non-experimental/non-exposed group.

mean_change_sd_nexp

standard deviation of the mean change for participants in the non-experimental/non-exposed group.

r_pre_post_exp

pre-post correlation in the experimental/exposed group

r_pre_post_nexp

pre-post correlation in the non-experimental/non-exposed group

n_exp

number of participants in the experimental/exposed group.

n_nexp

number of participants in the non-experimental/non-exposed group.

smd_to_cor

formula used to convert the cohen_d value into a coefficient correlation (see details).

reverse_mean_change

a logical value indicating whether the direction of generated effect sizes should be flipped.

Details

This function first computes a Cohen's d (D), Hedges' g (G) from the mean change (MC) and standard deviations of two independent groups. Odds ratio (OR) and correlation coefficients (R/Z) are then converted from the Cohen's d.

This function simply internally calls the es_from_means_sd_pre_post function but setting:

mean_pre_exp=mean_change_expmean\_pre\_exp = mean\_change\_exp

mean_pre_sd_exp=mean_change_sd_expmean\_pre\_sd\_exp = mean\_change\_sd\_exp

mean_exp=0mean\_exp = 0

mean_sd_exp=0mean\_sd\_exp = 0

mean_pre_nexp=mean_change_nexpmean\_pre\_nexp = mean\_change\_nexp

mean_pre_sd_nexp=mean_change_sd_nexpmean\_pre\_sd\_nexp = mean\_change\_sd\_nexp

mean_nexp=0mean\_nexp = 0

mean_sd_nexp=0mean\_sd\_nexp = 0

To know more about the calculations, see es_from_means_sd_pre_post function.

Value

This function estimates and converts between several effect size measures.

natural effect size measure MD + D + G
converted effect size measure OR + R + Z
required input data See 'Section 14. Paired: mean change, and dispersion'
https://metaconvert.org/input.html

References

Bonett, S. B. (2008). Estimating effect sizes from pretest-posttest-control group designs. Organizational Research Methods, 11(2), 364–386. https://doi.org/10.1177/1094428106291059

Cooper, H., Hedges, L.V., & Valentine, J.C. (Eds.). (2019). The handbook of research synthesis and meta-analysis. Russell Sage Foundation.

Examples

es_from_mean_change_sd(
  n_exp = 36, n_nexp = 35,
  mean_change_exp = 8.4, mean_change_sd_exp = 9.13,
  mean_change_nexp = 2.43, mean_change_sd_nexp = 6.61,
  r_pre_post_exp = 0.2, r_pre_post_nexp = 0.2
)

Convert mean changes and standard errors of two independent groups into standard effect size measures

Description

Convert mean changes and standard errors of two independent groups into standard effect size measures

Usage

es_from_mean_change_se(
  mean_change_exp,
  mean_change_se_exp,
  mean_change_nexp,
  mean_change_se_nexp,
  r_pre_post_exp,
  r_pre_post_nexp,
  n_exp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  reverse_mean_change
)

Arguments

mean_change_exp

mean change of participants in the experimental/exposed group.

mean_change_se_exp

standard error of the mean change for participants in the experimental/exposed group.

mean_change_nexp

mean change of participants in the non-experimental/non-exposed group.

mean_change_se_nexp

standard error of the mean change for participants in the non-experimental/non-exposed group.

r_pre_post_exp

pre-post correlation in the experimental/exposed group

r_pre_post_nexp

pre-post correlation in the non-experimental/non-exposed group

n_exp

number of participants in the experimental/exposed group.

n_nexp

number of participants in the non-experimental/non-exposed group.

smd_to_cor

formula used to convert the cohen_d value into a coefficient correlation (see details).

reverse_mean_change

a logical value indicating whether the direction of generated effect sizes should be flipped.

Details

This function converts the mean change and standard errors of two independent groups into a Cohen's d. The Cohen's d is then converted to other effect size measures.

This function simply internally calls the es_from_means_se_pre_post function but setting:

mean_pre_exp=mean_change_expmean\_pre\_exp = mean\_change\_exp

mean_pre_se_exp=mean_change_se_expmean\_pre\_se\_exp = mean\_change\_se\_exp

mean_exp=0mean\_exp = 0

mean_se_exp=0mean\_se\_exp = 0

mean_pre_nexp=mean_change_nexpmean\_pre\_nexp = mean\_change\_nexp

mean_pre_se_nexp=mean_change_se_nexpmean\_pre\_se\_nexp = mean\_change\_se\_nexp

mean_nexp=0mean\_nexp = 0

mean_se_nexp=0mean\_se\_nexp = 0

To know more about the calculations, see es_from_means_se_pre_post function.

Value

This function estimates and converts between several effect size measures.

natural effect size measure MD + D + G
converted effect size measure OR + R + Z
required input data See 'Section 14. Paired: mean change, and dispersion'
https://metaconvert.org/input.html

References

Bonett, S. B. (2008). Estimating effect sizes from pretest-posttest-control group designs. Organizational Research Methods, 11(2), 364–386. https://doi.org/10.1177/1094428106291059

Cooper, H., Hedges, L.V., & Valentine, J.C. (Eds.). (2019). The handbook of research synthesis and meta-analysis. Russell Sage Foundation.

Examples

es_from_mean_change_se(
  n_exp = 36, n_nexp = 35,
  mean_change_exp = 8.4, mean_change_se_exp = 9.13,
  mean_change_nexp = 2.43, mean_change_se_nexp = 6.61,
  r_pre_post_exp = 0.2, r_pre_post_nexp = 0.2
)

Convert means and 95% CI of two independent groups several effect size measures

Description

Convert means and 95% CI of two independent groups several effect size measures

Usage

es_from_means_ci(
  mean_exp,
  mean_ci_lo_exp,
  mean_ci_up_exp,
  mean_nexp,
  mean_ci_lo_nexp,
  mean_ci_up_nexp,
  n_exp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  max_asymmetry = 10,
  reverse_means
)

Arguments

mean_exp

mean of participants in the experimental/exposed group.

mean_ci_lo_exp

lower bound of the 95% CI of the mean of the experimental/exposed group

mean_ci_up_exp

upper bound of the 95% CI of the mean of the experimental/exposed group

mean_nexp

mean of participants in the non-experimental/non-exposed group.

mean_ci_lo_nexp

lower bound of the 95% CI of the mean of the non-experimental/non-exposed group.

mean_ci_up_nexp

upper bound of the 95% CI of the mean of the non-experimental/non-exposed group.

n_exp

number of participants in the experimental/exposed group.

n_nexp

number of participants in the non-experimental/non-exposed group.

smd_to_cor

formula used to convert the cohen_d value into a coefficient correlation (see details).

max_asymmetry

A percentage indicating the tolerance before detecting asymmetry in the 95% CI bounds.

reverse_means

a logical value indicating whether the direction of the generated effect sizes should be flipped.

Details

This function converts the 95% CI of two independent groups into a standard error, and then relies on the calculations of the es_from_means_se() function.

To convert the 95% CIs into standard errors, the following formula is used (table 12.3 in Cooper):

mean_se_exp=mean_ci_up_expmean_ci_lo_exp2qt(0.975,df=n_exp1)mean\_se\_exp = \frac{mean\_ci\_up\_exp - mean\_ci\_lo\_exp}{2 * qt{(0.975, df = n\_exp - 1)}}

mean_se_nexp=mean_ci_up_nexpmean_ci_lo_nexp2qt(0.975,df=n_nexp1)mean\_se\_nexp = \frac{mean\_ci\_up\_nexp - mean\_ci\_lo\_nexp}{2 * qt{(0.975, df = n\_nexp - 1)}}

Calculations of the es_from_means_se() are then applied.

Value

This function estimates and converts between several effect size measures.

natural effect size measure MD + D + G
converted effect size measure OR + R + Z
required input data See 'Section 9. Means and dispersion (crude)'
https://metaconvert.org/input.html

References

Higgins JPT, Li T, Deeks JJ (editors). Chapter 6: Choosing effect size measures and computing estimates of effect. In: Higgins JPT, Thomas J, Chandler J, Cumpston M, Li T, Page MJ, Welch VA (editors). Cochrane Handbook for Systematic Reviews of Interventions version 6.3 (updated February 2022). Cochrane, 2022. Available from www.training.cochrane.org/handbook.

Examples

es_from_means_ci(
  n_exp = 55, n_nexp = 55,
  mean_exp = 25, mean_ci_lo_exp = 15, mean_ci_up_exp = 35,
  mean_nexp = 18, mean_ci_lo_nexp = 12, mean_ci_up_nexp = 24
)

Convert pre-post means of two independent groups into various effect size measures

Description

Convert pre-post means of two independent groups into various effect size measures

Usage

es_from_means_ci_pre_post(
  mean_pre_exp,
  mean_exp,
  mean_pre_ci_lo_exp,
  mean_pre_ci_up_exp,
  mean_ci_lo_exp,
  mean_ci_up_exp,
  mean_pre_nexp,
  mean_nexp,
  mean_pre_ci_lo_nexp,
  mean_pre_ci_up_nexp,
  mean_ci_lo_nexp,
  mean_ci_up_nexp,
  n_exp,
  n_nexp,
  r_pre_post_exp,
  r_pre_post_nexp,
  smd_to_cor = "viechtbauer",
  pre_post_to_smd = "bonett",
  max_asymmetry = 10,
  reverse_means_pre_post
)

Arguments

mean_pre_exp

mean of the experimental/exposed group at baseline

mean_exp

mean of the experimental/exposed group at follow up

mean_pre_ci_lo_exp

lower bound of the 95% CI of the mean of the experimental/exposed group at baseline

mean_pre_ci_up_exp

upper bound of the 95% CI of the mean of the experimental/exposed group at baseline

mean_ci_lo_exp

lower bound of the 95% CI of the mean of the experimental/exposed group at follow up

mean_ci_up_exp

upper bound of the 95% CI of the mean of the experimental/exposed group at follow up

mean_pre_nexp

mean of the non-experimental/non-exposed group at baseline

mean_nexp

mean of the non-experimental/non-exposed group at follow up

mean_pre_ci_lo_nexp

lower bound of the 95% CI of the mean of the non-experimental/non-exposed group at baseline

mean_pre_ci_up_nexp

upper bound of the 95% CI of the mean of the non-experimental/non-exposed group at baseline

mean_ci_lo_nexp

lower bound of the 95% CI of the mean of the non-experimental/non-exposed group at follow up

mean_ci_up_nexp

upper bound of the 95% CI of the mean of the non-experimental/non-exposed group at follow up

n_exp

number of the experimental/exposed group

n_nexp

number of the non-experimental/non-exposed group

r_pre_post_exp

pre-post correlation in the experimental/exposed group

r_pre_post_nexp

pre-post correlation in the non-experimental/non-exposed group

smd_to_cor

formula used to convert the cohen_d value into a coefficient correlation (see details).

pre_post_to_smd

formula used to convert the pre and post means/SD into a SMD (see details).

max_asymmetry

A percentage indicating the tolerance before detecting asymmetry in the 95% CI bounds.

reverse_means_pre_post

a logical value indicating whether the direction of generated effect sizes should be flipped.

Details

This function converts the bounds of the 95% CI of the pre/post means of two independent groups into standard errors (Section 6.3.1 in the Cochrane Handbook).

mean_pre_se_exp=mean_pre_ci_up_expmean_pre_ci_lo_exp2qt(0.975,df=n_exp1)mean\_pre\_se\_exp = \frac{mean\_pre\_ci\_up\_exp - mean\_pre\_ci\_lo\_exp}{2 * qt{(0.975, df = n\_exp - 1)}}

mean_pre_se_nexp=mean_pre_ci_up_nexpmean_pre_ci_lo_nexp2qt(0.975,df=n_nexp1)mean\_pre\_se\_nexp = \frac{mean\_pre\_ci\_up\_nexp - mean\_pre\_ci\_lo\_nexp}{2 * qt{(0.975, df = n\_nexp - 1)}}

mean_se_exp=mean_ci_up_expmean_ci_lo_exp2qt(0.975,df=n_exp1)mean\_se\_exp = \frac{mean\_ci\_up\_exp - mean\_ci\_lo\_exp}{2 * qt{(0.975, df = n\_exp - 1)}}

mean_se_nexp=mean_ci_up_nexpmean_ci_lo_nexp2qt(0.975,df=n_nexp1)mean\_se\_nexp = \frac{mean\_ci\_up\_nexp - mean\_ci\_lo\_nexp}{2 * qt{(0.975, df = n\_nexp - 1)}}

Then, calculations of the es_from_means_se_pre_post are applied.

Value

This function estimates and converts between several effect size measures.

natural effect size measure MD + D + G
converted effect size measure OR + R + Z
required input data See 'Section 15. Paired: pre-post means and dispersion'
https://metaconvert.org/input.html

References

Higgins JPT, Li T, Deeks JJ (editors). Chapter 6: Choosing effect size measures and computing estimates of effect. In: Higgins JPT, Thomas J, Chandler J, Cumpston M, Li T, Page MJ, Welch VA (editors). Cochrane Handbook for Systematic Reviews of Interventions version 6.3 (updated February 2022). Cochrane, 2022. Available from www.training.cochrane.org/handbook.

Examples

es_from_means_ci_pre_post(
  n_exp = 36, n_nexp = 35,
  mean_pre_exp = 98,
  mean_pre_ci_lo_exp = 88,
  mean_pre_ci_up_exp = 108,
  mean_exp = 102,
  mean_ci_lo_exp = 92,
  mean_ci_up_exp = 112,
  mean_pre_nexp = 96,
  mean_pre_ci_lo_nexp = 86,
  mean_pre_ci_up_nexp = 106,
  mean_nexp = 102,
  mean_ci_lo_nexp = 92,
  mean_ci_up_nexp = 112,
  r_pre_post_exp = 0.8, r_pre_post_nexp = 0.8
)

Convert means and standard deviations of two independent groups into several effect size measures

Description

Convert means and standard deviations of two independent groups into several effect size measures

Usage

es_from_means_sd(
  mean_exp,
  mean_sd_exp,
  mean_nexp,
  mean_sd_nexp,
  n_exp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  reverse_means
)

Arguments

mean_exp

mean of participants in the experimental/exposed group.

mean_sd_exp

standard deviation of participants in the experimental/exposed group.

mean_nexp

mean of participants in the non-experimental/non-exposed group.

mean_sd_nexp

standard deviation of participants in the non-experimental/non-exposed group.

n_exp

number of participants in the experimental/exposed group.

n_nexp

number of participants in the non-experimental/non-exposed group.

smd_to_cor

formula used to convert the generated cohen_d value into a coefficient correlation (see details).

reverse_means

a logical value indicating whether the direction of the generated effect sizes should be flipped.

Details

This function first computes a Cohen's d (D), Hedges' g (G) and mean difference (MD) from the means and standard deviations of two independent groups. Odds ratio (OR) and correlation coefficients (R/Z) are then converted from the Cohen's d.

To estimate a mean difference (formulas 12.1-12.6 in Cooper):

md=mean_expmean_nexpmd = mean\_exp - mean\_nexp

md_se=mean_sd_exp2n_exp+mean_sd_nexp2n_nexpmd\_se = \sqrt{\frac{mean\_sd\_exp^2}{n\_exp} + \frac{mean\_sd\_nexp^2}{n\_nexp}}

md_ci_lo=mdmd_seqt(.975,df=n_exp+n_nexp2)md\_ci\_lo = md - md\_se * qt(.975, df = n\_exp + n\_nexp - 2)

md_ci_up=md+md_seqt(.975,df=n_exp+n_nexp2)md\_ci\_up = md + md\_se * qt(.975, df = n\_exp + n\_nexp - 2)

To estimate a Cohen's d the following formulas are used (formulas 12.10-12.18 in Cooper):

mean_sd_pooled=(n_exp1)sd_exp2+(n_nexp1)sd_nexp2n_exp+n_nexp2mean\_sd\_pooled = \sqrt{\frac{(n\_exp - 1) * sd\_exp^2 + (n\_nexp - 1) * sd\_nexp^2}{n\_exp+n\_nexp-2}}

cohen_d=mean_expmean_nexpmean_sd_pooledcohen\_d = \frac{mean\_exp - mean\_nexp}{mean\_sd\_pooled}

cohen_d_se=(n_exp+n_nexp)n_expn_nexp+cohen_d22(n_exp+n_nexp)cohen\_d\_se = \frac{(n\_exp+n\_nexp)}{n\_exp*n\_nexp} + \frac{cohen\_d^2}{2(n\_exp+n\_nexp)}

cohen_d_ci_lo=cohen_dcohen_d_seqt(.975,df=n_exp+n_nexp2)cohen\_d\_ci\_lo = cohen\_d - cohen\_d\_se * qt(.975, df = n\_exp + n\_nexp - 2)

cohen_d_ci_up=cohen_d+cohen_d_seqt(.975,df=n_exp+n_nexp2)cohen\_d\_ci\_up = cohen\_d + cohen\_d\_se * qt(.975, df = n\_exp + n\_nexp - 2)

To estimate other effect size measures, calculations of the es_from_cohen_d() are applied.

Value

This function estimates and converts between several effect size measures.

natural effect size measure MD + D + G
converted effect size measure OR + R + Z
required input data See 'Section 9. Means and dispersion (crude)'
https://metaconvert.org/input.html

References

Cooper, H., Hedges, L.V., & Valentine, J.C. (Eds.). (2019). The handbook of research synthesis and meta-analysis. Russell Sage Foundation.

Examples

es_from_means_sd(
  n_exp = 55, n_nexp = 55,
  mean_exp = 2.3, mean_sd_exp = 1.2,
  mean_nexp = 1.9, mean_sd_nexp = 0.9
)

Convert means of two groups and the pooled standard deviation into several effect size measures

Description

Convert means of two groups and the pooled standard deviation into several effect size measures

Usage

es_from_means_sd_pooled(
  mean_exp,
  mean_nexp,
  mean_sd_pooled,
  n_exp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  reverse_means
)

Arguments

mean_exp

mean of participants in the experimental/exposed group.

mean_nexp

mean of participants in the non-experimental/non-exposed group.

mean_sd_pooled

pooled standard deviation across both groups.

n_exp

number of participants in the experimental/exposed group.

n_nexp

number of participants in the non-experimental/non-exposed group.

smd_to_cor

formula used to convert the cohen_d value into a coefficient correlation (see details).

reverse_means

a logical value indicating whether the direction of the generated effect sizes should be flipped.

Details

This function first computes a Cohen's d (D), Hedges' g (G) and mean difference (MD) from the means of two independent groups and the pooled standard deviation across the groups. Odds ratio (OR) and correlation coefficients (R/Z) are then converted from the Cohen's d.

To estimate a mean difference (formulas 12.1-12.6 in Cooper):

md=mean_expmean_nexpmd = mean\_exp - mean\_nexp

md_se=nexp+nnexpnexpnnexpmeansdpooled2md\_se = \sqrt{\frac{n_exp+n_nexp}{n_exp*n_nexp} * mean_sd_pooled^2}

md_ci_lo=mdmd_seqt(.975,df=n_exp+n_nexp2)md\_ci\_lo = md - md\_se * qt(.975, df = n\_exp + n\_nexp - 2)

md_ci_up=md+md_seqt(.975,df=n_exp+n_nexp2)md\_ci\_up = md + md\_se * qt(.975, df = n\_exp + n\_nexp - 2)

To estimate a Cohen's d the following formulas are used (formulas 12.10-12.18 in Cooper):

cohen_d=mean_expmean_nexpmeans_sd_pooledcohen\_d = \frac{mean\_exp - mean\_nexp}{means\_sd\_pooled}

cohen_d_se=(n_exp+n_nexp)n_expn_nexp+cohen_d22(n_exp+n_nexp)cohen\_d\_se = \frac{(n\_exp+n\_nexp)}{n\_exp*n\_nexp} + \frac{cohen\_d^2}{2(n\_exp+n\_nexp)}

cohen_d_ci_lo=cohen_dcohen_d_seqt(.975,df=n_exp+n_nexp2)cohen\_d\_ci\_lo = cohen\_d - cohen\_d\_se * qt(.975, df = n\_exp + n\_nexp - 2)

cohen_d_ci_up=cohen_d+cohen_d_seqt(.975,df=n_exp+n_nexp2)cohen\_d\_ci\_up = cohen\_d + cohen\_d\_se * qt(.975, df = n\_exp + n\_nexp - 2)

To estimate other effect size measures, calculations of the es_from_cohen_d() are applied.

Value

This function estimates and converts between several effect size measures.

natural effect size measure MD + D + G
converted effect size measure OR + R + Z
required input data See 'Section 9. Means and dispersion (crude)'
https://metaconvert.org/input.html

References

Cooper, H., Hedges, L.V., & Valentine, J.C. (Eds.). (2019). The handbook of research synthesis and meta-analysis. Russell Sage Foundation.

Examples

es_from_means_sd_pooled(
  n_exp = 55, n_nexp = 55,
  mean_exp = 2.3, mean_nexp = 1.9,
  mean_sd_pooled = 0.9
)

Convert pre-post means of two independent groups into various effect size measures

Description

Convert pre-post means of two independent groups into various effect size measures

Usage

es_from_means_sd_pre_post(
  mean_pre_exp,
  mean_exp,
  mean_pre_sd_exp,
  mean_sd_exp,
  mean_pre_nexp,
  mean_nexp,
  mean_pre_sd_nexp,
  mean_sd_nexp,
  n_exp,
  n_nexp,
  r_pre_post_exp,
  r_pre_post_nexp,
  smd_to_cor = "viechtbauer",
  pre_post_to_smd = "bonett",
  reverse_means_pre_post
)

Arguments

mean_pre_exp

mean of the experimental/exposed group at baseline

mean_exp

mean of the experimental/exposed group at follow up

mean_pre_sd_exp

standard deviation of the experimental/exposed group at baseline

mean_sd_exp

standard deviation of the experimental/exposed group at follow up

mean_pre_nexp

mean of the non-experimental/non-exposed group at baseline

mean_nexp

mean of the non-experimental/non-exposed group at follow up

mean_pre_sd_nexp

standard deviation of the non-experimental/non-exposed group at baseline

mean_sd_nexp

standard deviation of the non-experimental/non-exposed group at follow up

n_exp

number of the experimental/exposed group

n_nexp

number of the non-experimental/non-exposed group

r_pre_post_exp

pre-post correlation in the experimental/exposed group

r_pre_post_nexp

pre-post correlation in the non-experimental/non-exposed group

smd_to_cor

formula used to convert the cohen_d value into a coefficient correlation (see details).

pre_post_to_smd

formula used to convert the pre and post means/SD into a SMD (see details).

reverse_means_pre_post

a logical value indicating whether the direction of generated effect sizes should be flipped.

Details

This function converts pre-post means of two independent groups into a Cohen's d (D) and Hedges' g (G). Odds ratio (OR) and correlation coefficients (R/Z) are then converted from the Cohen's d.

Two approaches can be used to compute the Cohen's d.

In these two approaches, the standard deviation of the difference within each group first needs to be obtained:

adj_exp=2r_pre_post_expmean_pre_sd_expmean_sd_expadj\_exp = 2*r\_pre\_post\_exp*mean\_pre\_sd\_exp*mean\_sd\_exp

sd_change_exp=mean_pre_sd_exp2+mean_sd_exp2adj_expsd\_change\_exp = \sqrt{mean\_pre\_sd\_exp^2 + mean\_sd\_exp^2 - adj\_exp}

adj_nexp=2r_pre_post_nexpmean_pre_sd_nexpmean_sd_nexpadj\_nexp = 2*r\_pre\_post\_nexp*mean\_pre\_sd\_nexp*mean\_sd\_nexp

sd_change_nexp=mean_pre_sd_nexp2+mean_sd_nexp2adj_nexpsd\_change\_nexp = \sqrt{mean\_pre\_sd\_nexp^2 + mean\_sd\_nexp^2 - adj\_nexp}

  1. In the approach described by Bonett (pre_post_to_smd = "bonett"), one Cohen's d per group is obtained by standardizing the pre-post mean difference by the standard deviation at baseline (Bonett, 2008):

    cohen_d_exp=mean_pre_expmean_expmean_pre_sd_expcohen\_d\_exp = \frac{mean\_pre\_exp - mean\_exp}{mean\_pre\_sd\_exp}

    cohen_d_nexp=mean_pre_nexpmean_nexpmean_pre_sd_nexpcohen\_d\_nexp = \frac{mean\_pre\_nexp - mean\_nexp}{mean\_pre\_sd\_nexp}

    cohen_d_se_exp=sd_change_exp2mean_pre_sd_exp2(n_exp1)+g_exp2/(2(n_exp1))cohen\_d\_se\_exp = \sqrt{\frac{sd\_change\_exp^2}{mean\_pre\_sd\_exp^2 * (n\_exp - 1) + g\_exp^2 / (2 * (n\_exp - 1))}}

    cohen_d_se_nexp=sd_change_nexp2mean_pre_sd_nexp2(n_nexp1)+g_nexp2/(2(n_nexp1))cohen\_d\_se\_nexp = \sqrt{\frac{sd\_change\_nexp^2}{mean\_pre\_sd\_nexp^2 * (n\_nexp - 1) + g\_nexp^2 / (2 * (n\_nexp - 1))}}

  2. In the approach described by Cooper (pre_post_to_smd = "cooper"), the following formulas are used:

    cohen_d_exp=mean_pre_expmean_expsd_change_exp2(1r_pre_post_exp)cohen\_d\_exp = \frac{mean\_pre\_exp - mean\_exp}{sd\_change\_exp} * \sqrt{2 * (1 - r\_pre\_post\_exp)}

    cohen_d_nexp=mean_pre_nexpmean_nexpsd_change_nexp2(1r_pre_post_nexp)cohen\_d\_nexp = \frac{mean\_pre\_nexp - mean\_nexp}{sd\_change\_nexp} * \sqrt{2 * (1 - r\_pre\_post\_nexp)}

    cohen_d_se_exp=2(1r_pre_post_exp)n_exp+cohen_d_exp22n_expcohen\_d\_se\_exp = \frac{2 * (1 - r\_pre\_post\_exp)}{n\_exp} + \frac{cohen\_d\_exp^2}{2 * n\_exp}

    cohen_d_se_nexp=2(1r_pre_post_nexp)n_nexp+cohen_d_nexp22n_nexpcohen\_d\_se\_nexp = \frac{2 * (1 - r\_pre\_post\_nexp)}{n\_nexp} + \frac{cohen\_d\_nexp^2}{2 * n\_nexp}

Last, the Cohen's d reflecting the within-group change from baseline to follow-up are combined into one Cohen's d:

cohen_d=d_expd_nexpcohen\_d = d\_exp - d\_nexp

cohen_d_se=cohen_d_se_exp2+cohen_d_se_nexp2cohen\_d\_se = \sqrt{cohen\_d\_se\_exp^2 + cohen\_d\_se\_nexp^2}

To estimate other effect size measures, calculations of the es_from_cohen_d() are applied.

Value

This function estimates and converts between several effect size measures.

natural effect size measure MD + D + G
converted effect size measure OR + R + Z
required input data See 'Section 15. Paired: pre-post means and dispersion'
https://metaconvert.org/input.html

References

Bonett, S. B. (2008). Estimating effect sizes from pretest-posttest-control group designs. Organizational Research Methods, 11(2), 364–386. https://doi.org/10.1177/1094428106291059

Cooper, H., Hedges, L.V., & Valentine, J.C. (Eds.). (2019). The handbook of research synthesis and meta-analysis. Russell Sage Foundation.

Examples

es_from_means_sd_pre_post(
  n_exp = 36, n_nexp = 35,
  mean_pre_exp = 98, mean_exp = 102,
  mean_pre_sd_exp = 16, mean_sd_exp = 17,
  mean_pre_nexp = 96, mean_nexp = 102,
  mean_pre_sd_nexp = 14, mean_sd_nexp = 15,
  r_pre_post_exp = 0.8, r_pre_post_nexp = 0.8
)

Convert means and standard errors of two independent groups several effect size measures

Description

Convert means and standard errors of two independent groups several effect size measures

Usage

es_from_means_se(
  mean_exp,
  mean_se_exp,
  mean_nexp,
  mean_se_nexp,
  n_exp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  reverse_means
)

Arguments

mean_exp

mean of participants in the experimental/exposed group.

mean_se_exp

standard error of participants in the experimental/exposed group.

mean_nexp

mean of participants in the non-experimental/non-exposed group.

mean_se_nexp

standard error of participants in the non-experimental/non-exposed group.

n_exp

number of participants in the experimental/exposed group.

n_nexp

number of participants in the non-experimental/non-exposed group.

smd_to_cor

formula used to convert the cohen_d value into a coefficient correlation (see details).

reverse_means

a logical value indicating whether the direction of the generated effect sizes should be flipped.

Details

This function converts the standard errors of two independent groups into standard deviations, and then relies on the calculations of the es_from_means_sd() function.

To convert the standard errors into standard deviations, the following formula is used.

mean_sd_exp=mean_se_expn_expmean\_sd\_exp = mean\_se\_exp * \sqrt{n\_exp}

mean_sd_nexp=mean_se_nexpn_nexpmean\_sd\_nexp = mean\_se\_nexp * \sqrt{n\_nexp}

Then, calculations of the es_from_means_sd() are applied.

To estimate other effect size measures, calculations of the es_from_cohen_d() are applied.

Value

This function estimates and converts between several effect size measures.

natural effect size measure MD + D + G
converted effect size measure OR + R + Z
required input data See 'Section 9. Means and dispersion (crude)'
https://metaconvert.org/input.html

References

Higgins JPT, Li T, Deeks JJ (editors). Chapter 6: Choosing effect size measures and computing estimates of effect. In: Higgins JPT, Thomas J, Chandler J, Cumpston M, Li T, Page MJ, Welch VA (editors). Cochrane Handbook for Systematic Reviews of Interventions version 6.3 (updated February 2022). Cochrane, 2022. Available from www.training.cochrane.org/handbook.

Examples

es_from_means_se(
  mean_exp = 42, mean_se_exp = 11,
  mean_nexp = 42, mean_se_nexp = 15,
  n_exp = 43, n_nexp = 34
)

Convert pre-post means of two independent groups into various effect size measures

Description

Convert pre-post means of two independent groups into various effect size measures

Usage

es_from_means_se_pre_post(
  mean_pre_exp,
  mean_exp,
  mean_pre_se_exp,
  mean_se_exp,
  mean_pre_nexp,
  mean_nexp,
  mean_pre_se_nexp,
  mean_se_nexp,
  n_exp,
  n_nexp,
  r_pre_post_exp,
  r_pre_post_nexp,
  smd_to_cor = "viechtbauer",
  pre_post_to_smd = "bonett",
  reverse_means_pre_post
)

Arguments

mean_pre_exp

mean of the experimental/exposed group at baseline

mean_exp

mean of the experimental/exposed group at follow up

mean_pre_se_exp

standard error of the experimental/exposed group at baseline

mean_se_exp

standard error of the experimental/exposed group at follow up

mean_pre_nexp

mean of the non-experimental/non-exposed group at baseline

mean_nexp

mean of the non-experimental/non-exposed group at follow up

mean_pre_se_nexp

standard error of the non-experimental/non-exposed group at baseline

mean_se_nexp

standard error of the non-experimental/non-exposed group at follow up

n_exp

number of the experimental/exposed group

n_nexp

number of the non-experimental/non-exposed group

r_pre_post_exp

pre-post correlation in the experimental/exposed group

r_pre_post_nexp

pre-post correlation in the non-experimental/non-exposed group

smd_to_cor

formula used to convert the cohen_d value into a coefficient correlation (see details).

pre_post_to_smd

formula used to convert the pre and post means/SD into a SMD (see details).

reverse_means_pre_post

a logical value indicating whether the direction of generated effect sizes should be flipped.

Details

This function converts the pre/post standard errors of two independent groups into standard deviations (Section 6.5.2.2 in the Cochrane Handbook).

mean_pre_sd_exp=mean_pre_se_expn_expmean\_pre\_sd\_exp = mean\_pre\_se\_exp * \sqrt{n\_exp}

mean_pre_sd_nexp=mean_pre_se_nexpn_nexpmean\_pre\_sd\_nexp = mean\_pre\_se\_nexp * \sqrt{n\_nexp}

mean_sd_exp=mean_se_expn_expmean\_sd\_exp = mean\_se\_exp * \sqrt{n\_exp}

mean_sd_nexp=mean_se_nexpn_nexpmean\_sd\_nexp = mean\_se\_nexp * \sqrt{n\_nexp}

Then, calculations of the es_from_means_sd_pre_post() are applied.

Value

This function estimates and converts between several effect size measures.

natural effect size measure MD + D + G
converted effect size measure OR + R + Z
required input data See 'Section 15. Paired: pre-post means and dispersion'
https://metaconvert.org/input.html

References

Higgins JPT, Li T, Deeks JJ (editors). Chapter 6: Choosing effect size measures and computing estimates of effect. In: Higgins JPT, Thomas J, Chandler J, Cumpston M, Li T, Page MJ, Welch VA (editors). Cochrane Handbook for Systematic Reviews of Interventions version 6.3 (updated February 2022). Cochrane, 2022. Available from www.training.cochrane.org/handbook.

Examples

es_from_means_sd_pre_post(
  n_exp = 36, n_nexp = 35,
  mean_pre_exp = 98, mean_exp = 102,
  mean_pre_sd_exp = 16, mean_sd_exp = 17,
  mean_pre_nexp = 96, mean_nexp = 102,
  mean_pre_sd_nexp = 14, mean_sd_nexp = 15,
  r_pre_post_exp = 0.8, r_pre_post_nexp = 0.8
)

Convert median, quartiles, and range of two independent groups into several effect size measures

Description

Convert median, quartiles, and range of two independent groups into several effect size measures

Usage

es_from_med_min_max(
  min_exp,
  med_exp,
  max_exp,
  n_exp,
  min_nexp,
  med_nexp,
  max_nexp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  reverse_med
)

Arguments

min_exp

minimum value of the experimental/exposed group.

med_exp

median value of the experimental/exposed group.

max_exp

maximum value of the experimental/exposed group.

n_exp

number of participants in the experimental/exposed group.

min_nexp

minimum value of the non-experimental/non-exposed group.

med_nexp

median value of the non-experimental/non-exposed group.

max_nexp

maximum value of the non-experimental/non-exposed group.

n_nexp

number of participants in the non-experimental/non-exposed group.

smd_to_cor

formula used to convert the generated cohen_d value into a coefficient correlation (see details).

reverse_med

a logical value indicating whether the direction of generated effect sizes should be flipped.

Details

This function first converts a Cohen's d (D), Hedges' g (G) and mean difference (MD) from the medians and ranges of two independent groups. Odds ratio (OR) and correlation coefficients (R/Z) are then converted from the Cohen's d.

This function recreates means+SD of the two groups (Wan et al., 2014):

mean_exp=min_exp+2med_exp+max_exp4mean\_exp = \frac{min\_exp + 2*med\_exp + max\_exp}{4}

mean_nexp=min_nexp+2med_nexp+max_nexp4mean\_nexp = \frac{min\_nexp + 2*med\_nexp + max\_nexp}{4}

mean_sd_exp=max_expmin_exp2qnorm((n_exp0.375)/(n_exp+0.25))mean\_sd\_exp = \frac{max\_exp - min\_exp}{2*qnorm((n\_exp-0.375) / (n\_exp+0.25))}

mean_sd_nexp=max_nexpmin_nexp2qnorm((n_nexp0.375)/(n_nexp+0.25))mean\_sd\_nexp = \frac{max\_nexp - min\_nexp}{2*qnorm((n\_nexp-0.375) / (n\_nexp+0.25))}

Note that if the group sample size is inferior to 50, a correction is applied to estimate the standard deviation.

From these means+SD, the function computes MD, D and G using formulas described in es_from_means_sd().

To estimate other effect size measures, calculations of the es_from_cohen_d() are applied.

Importantly,, authors of the Cochrane Handbook stated "As a general rule, we recommend that ranges should not be used to estimate SDs." (see section 6.5.2.6). It is thus a good practice to explore the consequences of the use of this conversion in sensitivity analyses.

Value

This function estimates and converts between several effect size measures.

natural effect size measure
converted effect size measure MD + D + G
OR + R + Z
required input data See 'Section 12. Median, range and/or interquartile range'
https://metaconvert.org/input.html

This function estimates and converts between several effect size measures.

natural effect size measure
converted effect size measure MD + D + G
OR + R + Z
required input data See 'Section 12. Median, range and/or interquartile range'
https://metaconvert.org/input.html

References

Wan, X., Wang, W., Liu, J. et al. Estimating the sample mean and standard deviation from the sample size, median, range and/or interquartile range. BMC Med Res Methodol 14, 135 (2014). https://doi.org/10.1186/1471-2288-14-135

Higgins JPT, Li T, Deeks JJ (editors). Chapter 6: Choosing effect size measures and computing estimates of effect. In: Higgins JPT, Thomas J, Chandler J, Cumpston M, Li T, Page MJ, Welch VA (editors). Cochrane Handbook for Systematic Reviews of Interventions version 6.3 (updated February 2022). Cochrane, 2022. Available from www.training.cochrane.org/handbook.

Examples

es_from_med_min_max(
  min_exp = 1335, med_exp = 1400,
  max_nexp = 1765, n_exp = 40,
  min_nexp = 1481, med_nexp = 1625,
  max_exp = 1800, n_nexp = 40
)

Convert median, range and interquartile range of two independent groups into several effect size measures

Description

Convert median, range and interquartile range of two independent groups into several effect size measures

Usage

es_from_med_min_max_quarts(
  q1_exp,
  med_exp,
  q3_exp,
  min_exp,
  max_exp,
  n_exp,
  q1_nexp,
  med_nexp,
  q3_nexp,
  min_nexp,
  max_nexp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  reverse_med
)

Arguments

q1_exp

first quartile of the experimental/exposed group.

med_exp

median value of the experimental/exposed group.

q3_exp

third quartile of the experimental/exposed group.

min_exp

minimum value of the experimental/exposed group.

max_exp

maximum value of the experimental/exposed group.

n_exp

number of participants in the experimental/exposed group.

q1_nexp

first quartile of the non-experimental/non-exposed group.

med_nexp

median value of the non-experimental/non-exposed group.

q3_nexp

third quartile of the non-experimental/non-exposed group.

min_nexp

minimum value of the non-experimental/non-exposed group.

max_nexp

maximum value of the non-experimental/non-exposed group.

n_nexp

number of participants in the non-experimental/non-exposed group.

smd_to_cor

formula used to convert the generated cohen_d value into a coefficient correlation (see details).

reverse_med

a logical value indicating whether the direction of generated effect sizes should be flipped.

Details

This function first converts a Cohen's d (D), Hedges' g (G) and mean difference (MD) from the medians, ranges, and interquartile ranges of two independent groups. Odds ratio (OR) and correlation coefficients (R/Z) are then converted from the Cohen's d.

This function recreates means+SD of the two groups (Wan et al., 2014):

mean_exp=min_exp+2q1_exp+2med_exp+2q3_exp+max_exp8mean\_exp = \frac{min\_exp + 2*q1\_exp + 2*med\_exp + 2*q3\_exp + max\_exp}{8}

mean_nexp=min_nexp+2q1_nexp+2med_nexp+2q3_nexp+max_nexp8mean\_nexp = \frac{min\_nexp + 2*q1\_nexp + 2*med\_nexp + 2*q3\_nexp + max\_nexp}{8}

mean_sd_exp=max_expmin_exp4qnorm(n_exp0.375n_exp+0.25)+q3_expq1_exp4qnorm(0.75n_exp0.125n_exp+0.25)mean\_sd\_exp = \frac{max\_exp - min\_exp}{4*qnorm(\frac{n\_exp-0.375}{n\_exp+0.25})} + \frac{q3\_exp-q1\_exp}{4*qnorm(\frac{0.75*n\_exp-0.125}{n\_exp+0.25})}

mean_sd_nexp=max_nexpmin_nexp4qnorm(n_nexp0.375n_nexp+0.25)+q3_nexpq1_nexp4qnorm(0.75n_nexp0.125n_nexp+0.25)mean\_sd\_nexp = \frac{max\_nexp - min\_nexp}{4*qnorm(\frac{n\_nexp-0.375}{n\_nexp+0.25})} + \frac{q3\_nexp-q1\_nexp}{4*qnorm(\frac{0.75*n\_nexp-0.125}{n\_nexp+0.25})}

Note that if the group sample size is inferior to 50, a correction is applied to estimate the standard deviation.

From these means+SD, the function computes MD, D and G using formulas described in es_from_means_sd().

To estimate other effect size measures, calculations of the es_from_cohen_d() are applied.

Value

This function estimates and converts between several effect size measures.

natural effect size measure
converted effect size measure MD + D + G
OR + R + Z
required input data See 'Section 12. Median, range and/or interquartile range'
https://metaconvert.org/input.html

References

Wan, X., Wang, W., Liu, J. et al. Estimating the sample mean and standard deviation from the sample size, median, range and/or interquartile range. BMC Med Res Methodol 14, 135 (2014). https://doi.org/10.1186/1471-2288-14-135

Examples

es_from_med_min_max_quarts(
  min_exp = 1102, q1_exp = 1335,
  med_exp = 1400, q3_exp = 1765,
  max_exp = 1899, n_exp = 40,
  min_nexp = 1181, q1_nexp = 1481,
  med_nexp = 1625, q3_nexp = 1800,
  max_nexp = 1910, n_nexp = 40
)

Convert median and interquartile range of two independent groups into several effect size measures

Description

Convert median and interquartile range of two independent groups into several effect size measures

Usage

es_from_med_quarts(
  q1_exp,
  med_exp,
  q3_exp,
  n_exp,
  q1_nexp,
  med_nexp,
  q3_nexp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  reverse_med
)

Arguments

q1_exp

first quartile of the experimental/exposed group.

med_exp

median value of the experimental/exposed group.

q3_exp

third quartile of the experimental/exposed group.

n_exp

number of participants in the experimental/exposed group.

q1_nexp

first quartile of the non-experimental/non-exposed group.

med_nexp

median value of the non-experimental/non-exposed group.

q3_nexp

third quartile of the non-experimental/non-exposed group.

n_nexp

number of participants in the non-experimental/non-exposed group.

smd_to_cor

formula used to convert the generated cohen_d value into a coefficient correlation (see details).

reverse_med

a logical value indicating whether the direction of generated effect sizes should be flipped.

Details

This function first converts a Cohen's d (D), Hedges' g (G) and mean difference (MD) from the medians and interquartile ranges of two independent groups. Odds ratio (OR) and correlation coefficients (R/Z) are then converted from the Cohen's d.

This function recreates means+SD of the two groups (Wan et al., 2014):

mean_exp=q1_exp+med_exp+q3_exp3mean\_exp = \frac{q1\_exp + med\_exp + q3\_exp}{3}

mean_nexp=q1_nexp+med_nexp+q3_nexp3mean\_nexp = \frac{q1\_nexp + med\_nexp + q3\_nexp}{3}

mean_sd_exp=q3_expq1_exp2qnorm(0.75n_exp0.125n_exp+0.25)mean\_sd\_exp = \frac{q3\_exp - q1\_exp}{2*qnorm(\frac{0.75*n\_exp - 0.125}{n\_exp+0.25})}

mean_sd_nexp=q3_nexpq1_nexp2qnorm(0.75n_nexp0.125n_nexp+0.25)mean\_sd\_nexp = \frac{q3\_nexp - q1\_nexp}{2*qnorm(\frac{0.75*n\_nexp - 0.125}{n\_nexp+0.25})}

Note that if the group sample size is inferior to 50, a correction is applied to estimate the standard deviation.

From these means+SD, the function computes MD, D and G using formulas described in es_from_means_sd().

To estimate other effect size measures, calculations of the es_from_cohen_d() are applied.

Value

This function estimates and converts between several effect size measures.

References

Wan, X., Wang, W., Liu, J. et al. Estimating the sample mean and standard deviation from the sample size, median, range and/or interquartile range. BMC Med Res Methodol 14, 135 (2014). https://doi.org/10.1186/1471-2288-14-135

Examples

es_from_med_quarts(
  q1_exp = 1335, med_exp = 1400,
  q3_exp = 1765, n_exp = 40,
  q1_nexp = 1481, med_nexp = 1625,
  q3_nexp = 1800, n_nexp = 40
)

Convert an odds ratio value to several effect size measures

Description

Convert an odds ratio value to several effect size measures

Usage

es_from_or(
  or,
  logor,
  n_cases,
  n_controls,
  n_sample,
  small_margin_prop,
  baseline_risk,
  n_exp,
  n_nexp,
  or_to_cor = "bonett",
  or_to_rr = "metaumbrella_cases",
  reverse_or
)

Arguments

or

odds ratio value

logor

log odds ratio value

n_cases

number of cases/events

n_controls

number of controls/no-event

n_sample

total number of participants in the sample

small_margin_prop

smallest margin proportion of the underlying 2x2 table

baseline_risk

proportion of cases in the non-exposed group

n_exp

number of participants in the exposed group

n_nexp

number of participants in the non-exposed group

or_to_cor

formula used to convert the or value into a correlation coefficient (see details).

or_to_rr

formula used to convert the or value into a risk ratio (see details).

reverse_or

a logical value indicating whether the direction of the generated effect sizes should be flipped.

Details

This function computes the standard error of the log odds ratio. Risk ratio (RR), Cohen's d (D), Hedges' g (G) and correlation coefficients (R/Z), are converted from the odds ratio value.

Estimation of the standard error of the log OR. This function generates the standard error of an odds ratio (OR) based on the OR value and the number of cases and controls. More precisely, this function simulates all combinations of the possible number of cases and controls in the exposed and non-exposed groups compatible with the reported OR value and with the overall number of cases and controls. Then, our function assumes that the variance of the OR is equal to the mean of the standard error of all possible situations. This estimation thus necessarily comes with some imprecision and should not be used before having requested the value (or raw data) to authors of the original report.

Conversion of other effect size measures. Calculations of es_from_or_se() are then applied to estimate the other effect size measures

Value

This function estimates and converts between several effect size measures.

natural effect size measure N/A
converted effect size measure OR + RR + NNT
D + G + R + Z
required input data See 'Section 2. Odds Ratio'
https://metaconvert.org/input.html

References

Gosling, C. J., Solanes, A., Fusar-Poli, P., & Radua, J. (2023). metaumbrella: the first comprehensive suite to perform data analysis in umbrella reviews with stratification of the evidence. BMJ mental health, 26(1), e300534. https://doi.org/10.1136/bmjment-2022-300534

Examples

es_or_guess <- es_from_or(or = 0.5, n_cases = 210, n_controls = 220)
es_or <- es_from_or_se(or = 0.5, logor_se = 0.4, n_cases = 210, n_controls = 220)
round(es_or_guess$logor_se, 0.10) == round(es_or$logor_se, 0.10)

Convert an odds ratio value and its 95% confidence interval to several effect size measures

Description

Convert an odds ratio value and its 95% confidence interval to several effect size measures

Usage

es_from_or_ci(
  or,
  or_ci_lo,
  or_ci_up,
  logor,
  logor_ci_lo,
  logor_ci_up,
  baseline_risk,
  small_margin_prop,
  n_exp,
  n_nexp,
  n_cases,
  n_controls,
  n_sample,
  max_asymmetry = 10,
  or_to_cor = "bonett",
  or_to_rr = "metaumbrella_cases",
  reverse_or
)

Arguments

or

odds ratio value

or_ci_lo

lower bound of the 95% CI around the odds ratio value

or_ci_up

upper bound of the 95% CI around the odds ratio value

logor

log odds ratio value

logor_ci_lo

lower bound of the 95% CI around the log odds ratio value

logor_ci_up

upper bound of the 95% CI around the log odds ratio value

baseline_risk

proportion of cases in the non-exposed group (only required for the or_to_rr = "grant" argument).

small_margin_prop

smallest margin proportion of the underlying 2x2 table

n_exp

number of participants in the exposed group (only required for the or_to_rr = "grant", and or_to_rr = "metaumbrella_exp" arguments)

n_nexp

number of participants in the non-exposed group (only required for the or_to_rr = "grant", and or_to_rr = "metaumbrella_exp" arguments)

n_cases

number of cases/events

n_controls

number of controls/no-event

n_sample

total number of participants in the sample

max_asymmetry

A percentage indicating the tolerance before detecting asymmetry in the 95% CI bounds.

or_to_cor

formula used to convert the or value into a correlation coefficient (see details).

or_to_rr

formula used to convert the or value into a risk ratio (see details).

reverse_or

a logical value indicating whether the direction of the generated effect sizes should be flipped.

Details

This function computes the standard error of the (log) odds ratio into a standard error (Section 6.5.2.2 in the Cochrane Handbook).

logor_se=logor_ci_uplogor_ci_lo2qnorm(.975)logor\_se = \frac{\log{or\_ci\_up} - \log{or\_ci\_lo}}{2 * qnorm(.975)}

Then, calculations of es_from_or_se are applied.

Value

This function estimates and converts between several effect size measures.

natural effect size measure OR
converted effect size measure RR + NNT
D + G + R + Z
required input data See 'Section 2. Odds Ratio'
https://metaconvert.org/input.html

References

Higgins JPT, Li T, Deeks JJ (editors). Chapter 6: Choosing effect size measures and computing estimates of effect. In: Higgins JPT, Thomas J, Chandler J, Cumpston M, Li T, Page MJ, Welch VA (editors). Cochrane Handbook for Systematic Reviews of Interventions version 6.3 (updated February 2022). Cochrane, 2022. Available from www.training.cochrane.org/handbook.

Examples

es_or <- es_from_or_ci(
  or = 1, or_ci_lo = 0.5, or_ci_up = 2,
  n_cases = 42, n_controls = 38, baseline_risk = 0.08,
  or_to_rr = "grant"
)

Convert an odds ratio value and its standard error to several effect size measures

Description

Convert an odds ratio value and its standard error to several effect size measures

Usage

es_from_or_pval(
  or,
  logor,
  or_pval,
  baseline_risk,
  small_margin_prop,
  n_exp,
  n_nexp,
  n_cases,
  n_controls,
  n_sample,
  or_to_rr = "metaumbrella_cases",
  or_to_cor = "bonett",
  reverse_or_pval
)

Arguments

or

odds ratio value

logor

log odds ratio value

or_pval

p-value of the (log) odds ratio

baseline_risk

proportion of cases in the non-exposed group (only required for the or_to_rr = "grant" argument).

small_margin_prop

smallest margin proportion of the underlying 2x2 table

n_exp

number of participants in the exposed group (only required for the or_to_rr = "grant", and or_to_rr = "metaumbrella_exp" arguments)

n_nexp

number of participants in the non-exposed group (only required for the or_to_rr = "grant", and or_to_rr = "metaumbrella_exp" arguments)

n_cases

number of cases/events

n_controls

number of controls/no-event

n_sample

total number of participants in the sample

or_to_rr

formula used to convert the or value into a risk ratio (see details).

or_to_cor

formula used to convert the or value into a correlation coefficient (see details).

reverse_or_pval

a logical value indicating whether the direction of the generated effect sizes should be flipped.

Details

This function computes the standard error of the (log) odds ratio into from a p-value (Section 6.3.2 in the Cochrane Handbook).

logor_z=qnorm(orpval/2,lower.tail=FALSE)logor\_z = qnorm(or_pval/2, lower.tail=FALSE)

logor_se=log(or)logor_zlogor\_se = |\frac{\log(or)}{logor\_z}|

Then, calculations of es_from_or_se() are applied.

Value

This function estimates and converts between several effect size measures.

natural effect size measure OR
converted effect size measure RR + NNT
D + G + R + Z
required input data See 'Section 2. Odds Ratio'
https://metaconvert.org/input.html

References

Higgins, J. P., Thomas, J., Chandler, J., Cumpston, M., Li, T., Page, M. J., & Welch, V. A. (Eds.). (2019). Cochrane handbook for systematic reviews of interventions. John Wiley & Sons.

Examples

es_or <- es_from_or_pval(
  or = 3.51, or_pval = 0.001,
  n_cases = 12, n_controls = 68
)

Convert an odds ratio value and its standard error into several effect size measures

Description

Convert an odds ratio value and its standard error into several effect size measures

Usage

es_from_or_se(
  or,
  logor,
  logor_se,
  baseline_risk,
  small_margin_prop,
  n_exp,
  n_nexp,
  n_cases,
  n_controls,
  n_sample,
  or_to_rr = "metaumbrella_cases",
  or_to_cor = "pearson",
  reverse_or
)

Arguments

or

odds ratio value

logor

log odds ratio value

logor_se

the standard error of the log odds ratio

baseline_risk

proportion of cases in the non-exposed group

small_margin_prop

smallest margin proportion of cases/events in the underlying 2x2 table

n_exp

number of participants in the exposed group

n_nexp

number of participants in the non-exposed group

n_cases

number of cases/events across exposed/non-exposed groups

n_controls

number of controls/no-event across exposed/non-exposed groups

n_sample

total number of participants in the sample

or_to_rr

formula used to convert the or value into a risk ratio (see details).

or_to_cor

formula used to convert the or value into a correlation coefficient (see details).

reverse_or

a logical value indicating whether the direction of the generated effect sizes should be flipped.

Details

This function converts the log odds ratio into a Risk ratio (RR), Cohen's d (D), Hedges' g (G) and correlation coefficients (R/Z).

To estimate the Cohen's d value and its standard error The following formulas are used (Cooper et al., 2019):

d=log(or)3πd = \log(or) * \frac{\sqrt{3}}{\pi}

d_se=logor_se23π2d\_se = \sqrt{\frac{logor\_se^2 * 3}{\pi^2}}

To estimate the risk ratio and its standard error, various formulas can be used.

A. First, the approach described in Grant (2014) can be used. However, in the paper, only the formula to convert an OR value to a RR value is described. To derive the variance, we used this formula to convert the bounds of the 95% CI, which were then used to obtain the variance.

This argument requires (or + baseline_risk + or_ci_lo + or_ci_up) to generate a RR. The following formulas are used (br = baseline_risk):

rr=or1br+brorrr = \frac{or}{1 - br + br*or}

rr_ci_lo=or_ci_lo1br+bror_ci_lorr\_ci\_lo = \frac{or\_ci\_lo}{1 - br + br*or\_ci\_lo}

rr_ci_up=or_ci_up1br+bror_ci_uprr\_ci\_up = \frac{or\_ci\_up}{1 - br + br*or\_ci\_up}

logrr_se=log(rr_ci_up)log(rr_ci_lo)2qnorm(.975)logrr\_se = \frac{log(rr\_ci\_up) - log(rr\_ci\_lo)}{2 * qnorm(.975)}

B. Second, the formulas implemented in the metaumbrella package can be used (or_to_rr = "metaumbrella_cases" or or_to_rr = "metaumbrella_exp"). This argument requires (or + logor_se + n_cases + n_controls) or (or + logor_se + n_exp + n_nexp) to generate a RR. More precisely, when the OR value and its standard error, plus either (i) the number of cases and controls or (ii) the number of participants in the exposed and non-exposed groups, are available, we previously developed functions that simulate all combinations of the possible number of cases and controls in the exposed and non-exposed groups compatible with the actual value of the OR. Then, the functions select the contingency table whose standard error coincides best with the standard error reported. The RR value and its standard are obtained from this estimated contingency table.

C. Third, it is possible to transpose the RR to a OR (or_to_rr = "transpose"). This argument requires (or + logor_se) to generate a OR. It is known that OR and RR are similar when the baseline risk is small. Therefore, users can request to simply transpose the OR value & standard error into a RR value & standard error.

rr=orrr = or

logrr_se=logor_selogrr\_se = logor\_se

D. Fourth, it is possible to recreate the 2x2 table using the dipietrantonj's formulas (or_to_rr = "dipietrantonj"). This argument requires (or + logor_ci_lo + logor_ci_lo) to generate a RR. Information on this approach can be retrieved in Di Pietrantonj (2006).

To estimate the NNT, the formulas used are :

(1br(1or))(1br)(br(1or))\frac{(1 - br * (1 - or))}{(1 - br) * (br * (1 - or))}

To estimate a correlation coefficient, various formulas can be used.

A. First, the approach described in Pearson (1900) can be used (or_to_cor = "pearson"). This argument requires (or + logor_se) to generate a R/Z. It converts the OR value and its standard error to a tetrachoric correlation. Note that the formula assumes that each cell of the 2x2 used to estimate the OR has been added 1/2 before estimating the OR value and its standard error. If it is not the case, formulas can produce slightly less accurate results.

c=12c = \frac{1}{2}

r=cosπ1+orcr = \cos{\frac{\pi}{1+or^c}}

r_se=logor_se((πcorc)sin(π/(1+orc))1+orc)2r\_se = logor\_se * ((\pi * c * or^c) * \frac{\sin(\pi / (1+or^c))}{1+or^c})^2

or_ci_lo=exp(log(or)qnorm(.975)logor_se)or\_ci\_lo = exp(log(or) - qnorm(.975)*logor\_se)

or_ci_up=exp(log(or)+qnorm(.975)logor_se)or\_ci\_up = exp(log(or) + qnorm(.975)*logor\_se)

r_ci_lo=cos(π1+or_ci_loc)r\_ci\_lo = cos(\frac{\pi}{1 + or\_ci\_lo^c})

r_ci_up=cos(π1+or_ci_upc)r\_ci\_up = cos(\frac{\pi}{1 + or\_ci\_up^c})

z=atanh(r)z = atanh(r)

z_se=r_se2(1r2)2z\_se = \sqrt{\frac{r\_se^2}{(1 - r^2)^2}}

z_ci_lo=atanh(r_lo)z\_ci\_lo = atanh(r\_lo)

z_ci_up=atanh(r_up)z\_ci\_up = atanh(r\_up)

B. Second, the approach described in Digby (1983) can be used (or_to_cor = "digby"). This argument requires (or + logor_se) to generate a R/Z. It converts the OR value and its standard error to a tetrachoric correlation. Note that the formula assumes that each cell of the 2x2 used to estimate the OR has been added 1/2 before estimating the OR value and its standard error. If it is not the case, formulas can produce slightly less accurate results.

c=34c = \frac{3}{4}

r=orc1orc+1r = \frac{or^c - 1}{or^c + 1}

r_se=c24(1r2)2logor_ser\_se = \sqrt{\frac{c^2}{4} * (1 - r^2)^2 * logor\_se}

z=atanh(r)z = atanh(r)

z_se=r_se2(1r2)2z\_se = \sqrt{\frac{r\_se^2}{(1 - r^2)^2}}

z_ci_lo=zqnorm(.975)c24logor_sez\_ci\_lo = z - qnorm(.975)*\sqrt{\frac{c^2}{4} * logor\_se}

z_ci_up=z+qnorm(.975)c24logor_sez\_ci\_up = z + qnorm(.975)*\sqrt{\frac{c^2}{4} * logor\_se}

r_ci_lo=tanh(z_lo)r\_ci\_lo = tanh(z\_lo)

r_ci_up=tanh(z_up)r\_ci\_up = tanh(z\_up)

C. Third, the approach described in Bonett (2005) can be used (or_to_cor = "bonett"). This argument requires (or + logor_se + n_cases + n_exp + small_margin_prop) to generate a R/Z. Note that the formula assumes that each cell of the 2x2 used to estimate the OR has been added 1/2 before estimating the OR value and its standard error. If it is not the case, formulas can produce slightly less accurate results.

c=1n_expn_cases5(0.5small_margin_prop)22c = \frac{\frac{1 - |n\_exp - n\_cases|}{5} - (0.5 - small\_margin\_prop)^2}{2}

r=cosπ1+orcr = \cos{\frac{\pi}{1+or^c}}

r_se=logor_se((πcorc)sin(π1+orc)1+orc)2r\_se = logor\_se * ((\pi * c * or^c) * \frac{\sin(\frac{\pi}{1+or^c})}{1+or^c})^2

or_ci_lo=exp(log(or)qnorm(.975)logor_se)or\_ci\_lo = exp(log(or) - qnorm(.975)*logor\_se)

or_ci_up=exp(log(or)+qnorm(.975)logor_se)or\_ci\_up = exp(log(or) + qnorm(.975)*logor\_se)

r_ci_lo=cos(π1+or_ci_loc)r\_ci\_lo = cos(\frac{\pi}{1 + or\_ci\_lo^c})

r_ci_up=cos(π1+or_ci_upc)r\_ci\_up = cos(\frac{\pi}{1 + or\_ci\_up^c})

z=atanh(r)z = atanh(r)

z_se=r_se2(1r2)2z\_se = \sqrt{\frac{r\_se^2}{(1 - r^2)^2}}

z_ci_lo=atanh(r_lo)z\_ci\_lo = atanh(r\_lo)

z_ci_up=atanh(r_up)z\_ci\_up = atanh(r\_up)

D. Last, the approach described in Cooper et al. (2019) can be used (or_to_cor = "lipsey_cooper"). This argument requires (or + logor_se + n_exp + n_nexp) to generate a R/Z. As shown above, the function starts to estimate a SMD from the OR. Then, as described in es_from_cohen_d, it converts this Cohen's d value into a correlation coefficient using the "lipsey_cooper" formulas.

Value

This function estimates and converts between several effect size measures.

natural effect size measure OR
converted effect size measure RR + NNT
D + G + R + Z
required input data See 'Section 2. Odds Ratio'
https://metaconvert.org/input.html

References

Bonett, Douglas G. and Robert M. Price. (2005). Inferential Methods for the Tetrachoric Correlation Coefficient. Journal of Educational and Behavioral Statistics 30:213-25.

Bonett, D. G., & Price, R. M. (2007). Statistical inference for generalized Yule coefficients in 2× 2 contingency tables. Sociological methods & research, 35(3), 429-446.

Cooper, H., Hedges, L. V., & Valentine, J. C. (Eds.). (2019). The handbook of research synthesis and meta-analysis. Russell Sage Foundation.

Di Pietrantonj C. (2006). Four-fold table cell frequencies imputation in meta analysis. Statistics in medicine, 25(13), 2299–2322. https://doi.org/10.1002/sim.2287

Digby, Peter G. N. (1983). Approximating the Tetrachoric Correlation Coefficient. Biometrics 39:753-7.

Gosling, C. J., Solanes, A., Fusar-Poli, P., & Radua, J. (2023). metaumbrella: the first comprehensive suite to perform data analysis in umbrella reviews with stratification of the evidence. BMJ mental health, 26(1), e300534. https://doi.org/10.1136/bmjment-2022-300534

Grant R. L. (2014). Converting an odds ratio to a range of plausible relative risks for better communication of research findings. BMJ (Clinical research ed.), 348, f7450. https://doi.org/10.1136/bmj.f7450

Pearson, K. (1900). Mathematical Contributions to the Theory of Evolution. VII: On the Correlation of Characters Not Quantitatively Measurable. Philosophical Transactions of the Royal Statistical Society of London, Series A 19:1-47

Veroniki, A. A., Pavlides, M., Patsopoulos, N. A., & Salanti, G. (2013). Reconstructing 2x2 contingency tables from odds ratios using the Di Pietrantonj method: difficulties, constraints and impact in meta-analysis results. Research synthesis methods, 4(1), 78–94. https://doi.org/10.1002/jrsm.1061

Examples

es_from_or_se(or = 2.12, logor_se = 0.242, n_exp = 120, n_nexp = 44)

Convert two paired ANOVA f value of two independent groups into several effect size measures

Description

Convert two paired ANOVA f value of two independent groups into several effect size measures

Usage

es_from_paired_f(
  paired_f_exp,
  paired_f_nexp,
  n_exp,
  n_nexp,
  r_pre_post_exp,
  r_pre_post_nexp,
  smd_to_cor = "viechtbauer",
  reverse_paired_f
)

Arguments

paired_f_exp

Paired ANOVA F value of the experimental/exposed group.

paired_f_nexp

Paired ANOVA F value of the non-experimental/non-exposed group.

n_exp

number of participants in the experimental/exposed group.

n_nexp

number of participants in the non-experimental/non-exposed group.

r_pre_post_exp

pre-post correlation in the experimental/exposed group

r_pre_post_nexp

pre-post correlation in the non-experimental/non-exposed group

smd_to_cor

formula used to convert the cohen_d value into a coefficient correlation (see details).

reverse_paired_f

a logical value indicating whether the direction of generated effect sizes should be flipped.

Details

This function converts the paired F-test obtained from two independent groups value into a Cohen's d (D) and Hedges' g (G) (table 12.2 in Cooper). Odds ratio (OR) and correlation coefficients (R/Z) are then converted from the Cohen's d.

To estimate the Cohen's d, the following formulas are used (Cooper et al., 2019): This function converts a Student's t-test value into a Cohen's d (table 12.2 in Cooper).

paired_t_exp=paired_f_exppaired\_t\_exp = \sqrt{paired\_f\_exp}

paired_t_nexp=paired_f_nexppaired\_t\_nexp = \sqrt{paired\_f\_nexp}

To estimate other effect size measures, calculations of the es_from_paired_t() are applied.

Value

This function estimates and converts between several effect size measures.

natural effect size measure D + G
converted effect size measure OR + R + Z
required input data See 'Section 16. Paired: Paired F- or t-test'
https://metaconvert.org/input.html

References

Cooper, H., Hedges, L.V., & Valentine, J.C. (Eds.). (2019). The handbook of research synthesis and meta-analysis. Russell Sage Foundation.

Examples

es_from_paired_f(paired_f_exp = 2.1, paired_f_nexp = 4.2, n_exp = 20, n_nexp = 22)

Convert two paired ANOVA f p-value of two independent groups into several effect size measures

Description

Convert two paired ANOVA f p-value of two independent groups into several effect size measures

Usage

es_from_paired_f_pval(
  paired_f_pval_exp,
  paired_f_pval_nexp,
  n_exp,
  n_nexp,
  r_pre_post_exp,
  r_pre_post_nexp,
  smd_to_cor = "viechtbauer",
  reverse_paired_f_pval
)

Arguments

paired_f_pval_exp

P-value of the paired ANOVA F of the experimental/exposed group.

paired_f_pval_nexp

P-value of the paired ANOVA F of the non-experimental/non-exposed group.

n_exp

number of participants in the experimental/exposed group.

n_nexp

number of participants in the non-experimental/non-exposed group.

r_pre_post_exp

pre-post correlation in the experimental/exposed group

r_pre_post_nexp

pre-post correlation in the non-experimental/non-exposed group

smd_to_cor

formula used to convert the cohen_d value into a coefficient correlation (see details).

reverse_paired_f_pval

a logical value indicating whether the direction of generated effect sizes should be flipped.

Details

This function converts the p-values of two paired F-test obtained from two independent groups value into a Cohen's d (D) and Hedges' g (G) (table 12.2 in Cooper). Odds ratio (OR) and correlation coefficients (R/Z) are then converted from the Cohen's d.

To estimate the Cohen's d, the following formulas are used (Cooper et al., 2019): This function converts a Student's t-test value into a Cohen's d (table 12.2 in Cooper).

paired_t_exp=qt(paired_f_pval_exp2,df=n_exp1)2(1rprepostexp)nexppaired\_t\_exp = qt(\frac{paired\_f\_pval\_exp}{2}, df = n\_exp - 1) * \sqrt{\frac{2 * (1 - r_pre_post_exp)}{n_exp}}

paired_t_nexp=qt(paired_f_pval_nexp2,df=n_nexp1)2(1rprepostnexp)nnexppaired\_t\_nexp = qt(\frac{paired\_f\_pval\_nexp}{2}, df = n\_nexp - 1) * \sqrt{\frac{2 * (1 - r_pre_post_nexp)}{n_nexp}}

To estimate other effect size measures, calculations of the es_from_paired_t() are applied.

Value

This function estimates and converts between several effect size measures.

natural effect size measure D + G
converted effect size measure OR + R + Z
required input data See 'Section 16. Paired: Paired F- or t-test'
https://metaconvert.org/input.html

References

Cooper, H., Hedges, L.V., & Valentine, J.C. (Eds.). (2019). The handbook of research synthesis and meta-analysis. Russell Sage Foundation.

Examples

es_from_paired_f_pval(paired_f_pval_exp = 0.4, paired_f_pval_nexp = 0.01, n_exp = 19, n_nexp = 22)

Convert two paired t-test value of two independent groups into several effect size measures

Description

Convert two paired t-test value of two independent groups into several effect size measures

Usage

es_from_paired_t(
  paired_t_exp,
  paired_t_nexp,
  n_exp,
  n_nexp,
  r_pre_post_exp,
  r_pre_post_nexp,
  smd_to_cor = "viechtbauer",
  reverse_paired_t
)

Arguments

paired_t_exp

Paired t-test value of the experimental/exposed group.

paired_t_nexp

Paired t-test value of the non-experimental/non-exposed group.

n_exp

number of participants in the experimental/exposed group.

n_nexp

number of participants in the non-experimental/non-exposed group.

r_pre_post_exp

pre-post correlation in the experimental/exposed group

r_pre_post_nexp

pre-post correlation in the non-experimental/non-exposed group

smd_to_cor

formula used to convert the cohen_d value into a coefficient correlation (see details).

reverse_paired_t

a logical value indicating whether the direction of generated effect sizes should be flipped.

Details

This function converts paired t-tests of two independent groups value into a Cohen's d (D) and Hedges' g (G) (table 12.2 in Cooper). Odds ratio (OR) and correlation coefficients (R/Z) are then converted from the Cohen's d.

To estimate the Cohen's d, the following formulas are used (Cooper et al., 2019):

cohen_d_exp=paired_t_exp2(1r_pre_post_exp)n_expcohen\_d\_exp = paired\_t\_exp * \sqrt{\frac{2 * (1 - r\_pre\_post\_exp)}{n\_exp}}

cohen_d_nexp=paired_t_nexp2(1r_pre_post_nexp)n_nexpcohen\_d\_nexp = paired\_t\_nexp * \sqrt{\frac{2 * (1 - r\_pre\_post\_nexp)}{n\_nexp}}

cohen_d_se_exp=2(1r_pre_post_exp)n_exp+d_exp22n_expcohen\_d\_se\_exp = \sqrt{\frac{2 * (1 - r\_pre\_post\_exp)}{n\_exp} + \frac{d\_exp^2}{2 * n\_exp}}

cohen_d_se_nexp=2(1r_pre_post_nexp)n_nexp+d_nexp22n_nexpcohen\_d\_se\_nexp = \sqrt{\frac{2 * (1 - r\_pre\_post\_nexp)}{n\_nexp} + \frac{d\_nexp^2}{2 * n\_nexp}}

cohen_d=d_expd_nexpcohen\_d = d\_exp - d\_nexp

d_se=cohen_d_se_exp2+cohen_d_se_nexp2d\_se = \sqrt{cohen\_d\_se\_exp^2 + cohen\_d\_se\_nexp^2}

To estimate other effect size measures, calculations of the es_from_cohen_d() are applied.

Value

This function estimates and converts between several effect size measures.

natural effect size measure D + G
converted effect size measure OR + R + Z
required input data See 'Section 16. Paired: Paired F- or t-test'
https://metaconvert.org/input.html

References

Cooper, H., Hedges, L.V., & Valentine, J.C. (Eds.). (2019). The handbook of research synthesis and meta-analysis. Russell Sage Foundation.

Examples

es_from_paired_t(paired_t_exp = 2.1, paired_t_nexp = 4.2, n_exp = 20, n_nexp = 22)

Convert two paired t-test p-value obtained from two independent groups into several effect size measures

Description

Convert two paired t-test p-value obtained from two independent groups into several effect size measures

Usage

es_from_paired_t_pval(
  paired_t_pval_exp,
  paired_t_pval_nexp,
  n_exp,
  n_nexp,
  r_pre_post_exp,
  r_pre_post_nexp,
  smd_to_cor = "viechtbauer",
  reverse_paired_t_pval
)

Arguments

paired_t_pval_exp

P-value of the paired t-test value of the experimental/exposed group.

paired_t_pval_nexp

P-value of the paired t-test value of the non-experimental/non-exposed group.

n_exp

number of participants in the experimental/exposed group.

n_nexp

number of participants in the non-experimental/non-exposed group.

r_pre_post_exp

pre-post correlation in the experimental/exposed group

r_pre_post_nexp

pre-post correlation in the non-experimental/non-exposed group

smd_to_cor

formula used to convert the cohen_d value into a coefficient correlation (see details).

reverse_paired_t_pval

a logical value indicating whether the direction of generated effect sizes should be flipped.

Details

This function converts the p-values of two paired t-test obtained from two independent groups value into a Cohen's d (D) and Hedges' g (G) (table 12.2 in Cooper). Odds ratio (OR) and correlation coefficients (R/Z) are then converted from the Cohen's d.

To estimate the Cohen's d, the following formulas are used (Cooper et al., 2019): This function converts a Student's t-test value into a Cohen's d (table 12.2 in Cooper).

paired_t_exp=qt(paired_t_pval_exp2,df=n_exp1)2(1r_pre_post_exp)n_exppaired\_t\_exp = qt(\frac{paired\_t\_pval\_exp}{2}, df = n\_exp - 1) * \sqrt{\frac{2 * (1 - r\_pre\_post\_exp)}{n\_exp}}

paired_t_nexp=qt(paired_t_pval_nexp2,df=n_nexp1)2(1r_pre_post_nexp)n_nexppaired\_t\_nexp = qt(\frac{paired\_t\_pval\_nexp}{2}, df = n\_nexp - 1) * \sqrt{\frac{2 * (1 - r\_pre\_post\_nexp)}{n\_nexp}}

To estimate other effect size measures, calculations of the es_from_cohen_d() are applied.

Value

This function estimates and converts between several effect size measures.

natural effect size measure D + G
converted effect size measure OR + R + Z
required input data See 'Section 16. Paired: Paired F- or t-test'
https://metaconvert.org/input.html

References

Cooper, H., Hedges, L.V., & Valentine, J.C. (Eds.). (2019). The handbook of research synthesis and meta-analysis. Russell Sage Foundation.

Examples

es_from_paired_t_pval(paired_t_pval_exp = 0.4, paired_t_pval_nexp = 0.01, n_exp = 19, n_nexp = 22)

Convert a Pearson's correlation coefficient to several effect size measures

Description

Convert a Pearson's correlation coefficient to several effect size measures

Usage

es_from_pearson_r(
  pearson_r,
  sd_iv,
  n_sample,
  n_exp,
  n_nexp,
  cor_to_smd = "viechtbauer",
  unit_increase_iv,
  unit_type = "raw_scale",
  reverse_pearson_r
)

Arguments

pearson_r

a Pearson's correlation coefficient value

sd_iv

the standard deviation of the independent variable

n_sample

the total number of participants

n_exp

number of the experimental/exposed group

n_nexp

number of the non-experimental/non-exposed group

cor_to_smd

formula used to convert a pearson_r or fisher_z value into a SMD.

unit_increase_iv

a value of the independent variable that will be used to estimate the Cohen's d (see details).

unit_type

the type of unit for the unit_increase_iv argument. Must be either "sd" or "value"

reverse_pearson_r

a logical value indicating whether the direction of the generated effect sizes should be flipped.

Details

This function estimates the variance of a Pearson's correlation coefficient, and computes the Fisher's r-to-z transformation. Cohen's d (D), Hedges' g (G) are converted from the Pearson's r, and odds ratio (OR) are converted from the Cohen's d.

  1. The formula used to estimate the standard error of the Pearson's correlation coefficient and 95% CI are (Formula 12.27 in Cooper):

    R_se=(1pearson_r2)2n_sample1R\_se = \sqrt{\frac{(1 - pearson\_r^2)^2}{n\_sample - 1}}

    R_lo=pearson_rqt(.975,n_sample2)R_seR\_lo = pearson\_r - qt(.975, n\_sample - 2) * R\_se

    R_up=pearson_r+qt(.975,n_sample2)R_seR\_up = pearson\_r + qt(.975, n\_sample - 2) * R\_se

  2. The formula used to estimate the Fisher's z are (Formula 12.28 & 12.29 in Cooper):

    Z=atanh(r)Z = atanh(r)

    Z_se=1n_sample3Z\_se = \frac{1}{n\_sample - 3}

    Z_ci_lo=Zqnorm(.975)Z_seZ\_ci\_lo = Z - qnorm(.975) * Z\_se

    Z_ci_up=Z+qnorm(.975)Z_seZ\_ci\_up = Z + qnorm(.975) * Z\_se

  3. Several approaches can be used to convert a correlation coefficient to a SMD.

A. Mathur proposes to use this formula (Formula 1.2 in Mathur, cor_to_smd = "mathur"):

increase=ifelse(unittype=="sd",unit_increase_ivsd_dv,unit_increase_iv)increase = ifelse(unit_type == "sd", unit\_increase\_iv * sd\_dv, unit\_increase\_iv)

d=rincreasesdiv1r2d = \frac{r * increase}{sd_iv * \sqrt{1 - r^2}}

d_se=abs(d)1r2(n_sample3)+12(n_sample1))d\_se = abs(d) * \sqrt{\frac{1}{r^2 * (n\_sample - 3)} + \frac{1}{2*(n\_sample - 1))}}

The resulting Cohen's d is the average increase in the dependent variable associated with an increase of x units in the independent variable (with x = unit_increase_iv).

B. Viechtbauer proposes to use the delta method to derive a Cohen's d from a correlation coefficient (Viechtbauer, 2023, cor_to_smd = "viechtbauer")

C. Cooper proposes to use this formula (Formula 12.38 & 12.39 in Cooper, cor_to_smd = cooper):

increase=ifelse(unittype=="sd",unit_increase_ivsd_dv,unit_increase_iv)increase = ifelse(unit_type == "sd", unit\_increase\_iv * sd\_dv, unit\_increase\_iv)

d=rincreasesd_iv1r2d = \frac{r * increase}{sd\_iv * \sqrt{1 - r^2}}

d_se=abs(d)1r2(n_sample3)+12(n_sample1))d\_se = abs(d) * \sqrt{\frac{1}{r^2 * (n\_sample - 3)} + \frac{1}{2*(n\_sample - 1))}}

Note that this formula was initially proposed for converting a point-biserial correlation to Cohen's d. It will thus produce similar results to the cor_to_smd = "mathur" option only when unit_type = "sd" and unit_increase_iv = 2.

To know how the Cohen's d value is converted to other effect measures (G/OR), see details of the es_from_cohen_d function.

Value

This function estimates and converts between several effect size measures.

natural effect size measure R + Z
converted effect size measure D + G + OR
required input data See 'Section 4. Pearson's r or Fisher's z'
https://metaconvert.org/input.html

References

Cooper, H., Hedges, L.V., & Valentine, J.C. (Eds.). (2019). The handbook of research synthesis and meta-analysis. Russell Sage Foundation.

Mathur, M. B., & VanderWeele, T. J. (2020). A Simple, Interpretable Conversion from Pearson's Correlation to Cohen's for d Continuous Exposures. Epidemiology (Cambridge, Mass.), 31(2), e16–e18. https://doi.org/10.1097/EDE.0000000000001105

Viechtbauer W (2010). “Conducting meta-analyses in R with the metafor package.” Journal of Statistical Software, 36(3), 1–48. doi:10.18637/jss.v036.i03.

Examples

es_from_pearson_r(
  pearson_r = .51, sd_iv = 0.24, n_sample = 214,
  unit_increase_iv = 1, unit_type = "sd"
)

Convert a phi value to several effect size measures

Description

Convert a phi value to several effect size measures

Usage

es_from_phi(phi, n_cases, n_exp, n_sample, reverse_phi)

Arguments

phi

phi value

n_cases

total number of cases/events

n_exp

total number of participants in the exposed group

n_sample

total number of participants in the sample

reverse_phi

a logical value indicating whether the direction of generated effect sizes should be flipped.

Details

The functions computes an odds ratio (OR), risk ratio (RR), and number needed to treat (NNT) from the the phi coefficient, the total number of participants, the total number of cases and the total number of people exposed. Cohen's d (D) and Hedges' g (G) are tried to be obtained from the OR, or are converted using the approach by Lipsey et al. (2001). The correlation coefficients (R/Z) are converted by assuming that the phi coefficient is equal to a R, and the variances of R and Z are obtained using the approach proposed by Lipsey et al. (2001) as well as by our own calculations.

To estimate the OR, RR, NNT,, this function reconstructs a 2x2 table (using the approach proposed by Viechtbauer, 2023).

Then, the calculations of the es_from_2x2() function are applied.

To estimate the Cohen's d (D) and Hedges' g (G), the function first tries to convert it from the OR obtained using the approach described above. If not possible (e.g., the number of cases and exposed are missing) the function converts the Cohen's d from the Phi coefficient using the approach proposed by Lipsey et al. (2001):

d=2phi1phi2d = \frac{2 * phi}{\sqrt{1 - phi^2}}

d_se=dphi2n_sampled\_se = \sqrt{\frac{d}{phi^2 * n\_sample}}

To estimate the correlation coefficients (R/Z), this function assumes that the phi coefficient is equal to a correlation coefficient, and then obtains the variance using the formula proposed by Lipsey et al. (2001):

r=phir = phi

z=atanh(r)z = atanh(r)

z_se=z2phi2n_samplez\_se = \frac{z^2}{phi^2 * n\_sample}

effective_n=1z_se+3effective\_n = \frac{1}{z\_se + 3}

r_se=(1r2)2effective_n1r\_se = \sqrt{\frac{(1 - r^2)^2}{effective\_n - 1}}

Note that the approach to determine the standard error of R was developed by our team.

Value

This function estimates and converts between several effect size measures.

natural effect size measure OR + RR + NNT
converted effect size measure D + G + R + Z
required input data See 'Section 8. Phi or chi-square'
https://metaconvert.org/input.html

References

Viechtbauer (2023). Accessed at https://wviechtb.github.io/metafor/reference/conv.2x2.html. Lipsey, M. W., & Wilson, D. B. (2001). Practical meta-analysis. Sage Publications, Inc.

Examples

es_from_phi(phi = 0.3, n_sample = 120, n_cases = 20, n_exp = 40)

Converts the means and bounds of an error bar (generally extracted from a plot) into four effect measures (SMD, MD, OR, COR)

Description

Converts the means and bounds of an error bar (generally extracted from a plot) into four effect measures (SMD, MD, OR, COR)

Usage

es_from_plot_ancova_means(
  n_exp,
  n_nexp,
  plot_ancova_mean_exp,
  plot_ancova_mean_nexp,
  plot_ancova_mean_sd_lo_exp,
  plot_ancova_mean_sd_lo_nexp,
  plot_ancova_mean_sd_up_exp,
  plot_ancova_mean_sd_up_nexp,
  plot_ancova_mean_se_lo_exp,
  plot_ancova_mean_se_lo_nexp,
  plot_ancova_mean_se_up_exp,
  plot_ancova_mean_se_up_nexp,
  plot_ancova_mean_ci_lo_exp,
  plot_ancova_mean_ci_lo_nexp,
  plot_ancova_mean_ci_up_exp,
  plot_ancova_mean_ci_up_nexp,
  cov_outcome_r,
  n_cov_ancova,
  smd_to_cor = "viechtbauer",
  reverse_plot_ancova_means
)

Arguments

n_exp

number of participants in the experimental/exposed group.

n_nexp

number of participants in the non-experimental/non-exposed group.

plot_ancova_mean_exp

ancova_mean of participants in the experimental/exposed group (extracted from a plot).

plot_ancova_mean_nexp

ancova_mean of participants in the non-experimental/non-exposed group (extracted from a plot).

plot_ancova_mean_sd_lo_exp

lower bound of an error bar depicting -1 SD from the ancova_mean of the experimental/exposed group (extracted from a plot).

plot_ancova_mean_sd_lo_nexp

lower bound of an error bar depicting -1 SD from the ancova_mean of the non-experimental/non-exposed group (extracted from a plot).

plot_ancova_mean_sd_up_exp

upper bound of an error bar depicting +1 SD from the ancova_mean of the experimental/exposed group (extracted from a plot).

plot_ancova_mean_sd_up_nexp

upper bound of an error bar depicting +1 SD from the ancova_mean of the non-experimental/non-exposed group (extracted from a plot).

plot_ancova_mean_se_lo_exp

lower bound of an error bar depicting -1 SE from the ancova_mean of the experimental/exposed group (extracted from a plot).

plot_ancova_mean_se_lo_nexp

lower bound of an error bar depicting -1 SE from the ancova_mean of the non-experimental/non-exposed group (extracted from a plot).

plot_ancova_mean_se_up_exp

upper bound of an error bar depicting +1 SE from the ancova_mean of the experimental/exposed group (extracted from a plot).

plot_ancova_mean_se_up_nexp

upper bound of an error bar depicting +1 SE from the ancova_mean of the non-experimental/non-exposed group (extracted from a plot).

plot_ancova_mean_ci_lo_exp

lower bound of an error bar depicting the 95% CI of the ancova_mean of the experimental/exposed group (extracted from a plot).

plot_ancova_mean_ci_lo_nexp

lower bound of an error bar depicting the 95% CI of the ancova_mean of the non-experimental/non-exposed group (extracted from a plot).

plot_ancova_mean_ci_up_exp

upper bound of an error bar depicting the 95% CI of the ancova_mean of the experimental/exposed group (extracted from a plot).

plot_ancova_mean_ci_up_nexp

upper bound of an error bar depicting the 95% CI of the ancova_mean of the non-experimental/non-exposed group (extracted from a plot).

cov_outcome_r

correlation between the outcome and covariate (multiple correlation when multiple covariates are included in the ANCOVA model).

n_cov_ancova

number of covariates in the ANCOVA model.

smd_to_cor

formula used to convert the cohen_d value into a coefficient correlation (see details).

reverse_plot_ancova_means

a logical value indicating whether the direction of the generated effect sizes should be flipped.

Details

This function uses the bounds of an error bar of a mean obtained from a plot into a standard deviation. Then, a mean difference (MD), Cohen's d (D), and Hedges' g (G) are estimated. Odds ratio (OR), risk ratio (RR) and correlation coefficients (R/Z) are converted from the Cohen's d value.

To convert the bound of an error bar into a standard deviation, this function always prioritizes information from the plot_ancova_mean_sd_* arguments, then those from the plot_ancova_mean_se_* arguments, then those from the plot_ancova_mean_ci_* arguments.

  1. If the bounds of the standard deviations are provided, the following formulas are used:

    ancova_mean_sd_lo_exp=plot_ancova_mean_expplot_ancova_mean_sd_lo_expancova\_mean\_sd\_lo\_exp = plot\_ancova\_mean\_exp - plot\_ancova\_mean\_sd\_lo\_exp

    ancova_mean_sd_up_exp=plot_ancova_mean_sd_up_expplot_ancova_mean_expancova\_mean\_sd\_up\_exp = plot\_ancova\_mean\_sd\_up\_exp - plot\_ancova\_mean\_exp

    ancova_mean_sd_exp=ancova_mean_sd_lo_exp+ancova_mean_sd_up_exp2ancova\_mean\_sd\_exp = \frac{ancova\_mean\_sd\_lo\_exp + ancova\_mean\_sd\_up\_exp}{2}

mean_sd_lo_nexp=plot_ancova_mean_nexpplot_ancova_mean_sd_lo_nexpmean\_sd\_lo\_nexp = plot\_ancova\_mean\_nexp - plot\_ancova\_mean\_sd\_lo\_nexp

mean_sd_up_nexp=plot_ancova_mean_sd_up_nexpplot_ancova_mean_nexpmean\_sd\_up\_nexp = plot\_ancova\_mean\_sd\_up\_nexp - plot\_ancova\_mean\_nexp

mean_sd_nexp=mean_sd_lo_nexp+mean_sd_up_nexp2mean\_sd\_nexp = \frac{mean\_sd\_lo\_nexp + mean\_sd\_up\_nexp}{2}

Then, calculations of the es_from_ancova_means_sd are used.

  1. If the bounds of the standard errors are provided, the following formulas are used:

    ancova_mean_se_lo_exp=plot_ancova_mean_expplot_ancova_mean_se_lo_expancova\_mean\_se\_lo\_exp = plot\_ancova\_mean\_exp - plot\_ancova\_mean\_se\_lo\_exp

    ancova_mean_se_up_exp=plot_ancova_mean_se_up_expplot_ancova_mean_expancova\_mean\_se\_up\_exp = plot\_ancova\_mean\_se\_up\_exp - plot\_ancova\_mean\_exp

    ancova_mean_se_exp=ancova_mean_se_lo_exp+ancova_mean_se_up_exp2ancova\_mean\_se\_exp = \frac{ancova\_mean\_se\_lo\_exp + ancova\_mean\_se\_up\_exp}{2}

mean_se_lo_nexp=plot_ancova_mean_nexpplot_ancova_mean_se_lo_nexpmean\_se\_lo\_nexp = plot\_ancova\_mean\_nexp - plot\_ancova\_mean\_se\_lo\_nexp

mean_se_up_nexp=plot_ancova_mean_se_up_nexpplot_ancova_mean_nexpmean\_se\_up\_nexp = plot\_ancova\_mean\_se\_up\_nexp - plot\_ancova\_mean\_nexp

mean_se_nexp=mean_se_lo_nexp+mean_se_up_nexp2mean\_se\_nexp = \frac{mean\_se\_lo\_nexp + mean\_se\_up\_nexp}{2}

Then, calculations of the es_from_ancova_means_se are used.

  1. If the bounds of the 95% confidence intervals are provided, the calculations of the es_from_ancova_means_ci() are used.

Value

This function estimates and converts between several effect size measures.

natural effect size measure MD + D + G
converted effect size measure OR + R + Z
required input data See 'Section 22. From plot: adjusted means and dispersion (adjusted)'
https://metaconvert.org/input.html

Examples

es_from_plot_ancova_means(
  n_exp = 35, n_nexp = 35,
  cov_outcome_r = 0.2, n_cov_ancova = 4,
  plot_ancova_mean_exp = 89, plot_ancova_mean_nexp = 104,
  plot_ancova_mean_sd_lo_exp = 69, plot_ancova_mean_sd_lo_nexp = 83,
  plot_ancova_mean_sd_up_exp = 109, plot_ancova_mean_sd_up_nexp = 125
)

Converts the means and bounds of an error bar (generally extracted from a plot) into four effect measures (SMD, MD, OR, COR)

Description

Converts the means and bounds of an error bar (generally extracted from a plot) into four effect measures (SMD, MD, OR, COR)

Usage

es_from_plot_means(
  n_exp,
  n_nexp,
  plot_mean_exp,
  plot_mean_nexp,
  plot_mean_sd_lo_exp,
  plot_mean_sd_lo_nexp,
  plot_mean_sd_up_exp,
  plot_mean_sd_up_nexp,
  plot_mean_se_lo_exp,
  plot_mean_se_lo_nexp,
  plot_mean_se_up_exp,
  plot_mean_se_up_nexp,
  plot_mean_ci_lo_exp,
  plot_mean_ci_lo_nexp,
  plot_mean_ci_up_exp,
  plot_mean_ci_up_nexp,
  smd_to_cor = "viechtbauer",
  reverse_plot_means
)

Arguments

n_exp

number of participants in the experimental/exposed group.

n_nexp

number of participants in the non-experimental/non-exposed group.

plot_mean_exp

mean of participants in the experimental/exposed group (extracted from a plot).

plot_mean_nexp

mean of participants in the non-experimental/non-exposed group (extracted from a plot).

plot_mean_sd_lo_exp

lower bound of an error bar depicting -1 SD from the mean of the experimental/exposed group (extracted from a plot).

plot_mean_sd_lo_nexp

lower bound of an error bar depicting -1 SD from the mean of the non-experimental/non-exposed group (extracted from a plot).

plot_mean_sd_up_exp

upper bound of an error bar depicting +1 SD from the mean of the experimental/exposed group (extracted from a plot).

plot_mean_sd_up_nexp

upper bound of an error bar depicting +1 SD from the mean of the non-experimental/non-exposed group (extracted from a plot).

plot_mean_se_lo_exp

lower bound of an error bar depicting -1 SE from the mean of the experimental/exposed group (extracted from a plot).

plot_mean_se_lo_nexp

lower bound of an error bar depicting -1 SE from the mean of the non-experimental/non-exposed group (extracted from a plot).

plot_mean_se_up_exp

upper bound of an error bar depicting +1 SE from the mean of the experimental/exposed group (extracted from a plot).

plot_mean_se_up_nexp

upper bound of an error bar depicting +1 SE from the mean of the non-experimental/non-exposed group (extracted from a plot).

plot_mean_ci_lo_exp

lower bound of an error bar depicting the 95% CI of the mean of the experimental/exposed group (extracted from a plot).

plot_mean_ci_lo_nexp

lower bound of an error bar depicting the 95% CI of the mean of the non-experimental/non-exposed group (extracted from a plot).

plot_mean_ci_up_exp

upper bound of an error bar depicting the 95% CI of the mean of the experimental/exposed group (extracted from a plot).

plot_mean_ci_up_nexp

upper bound of an error bar depicting the 95% CI of the mean of the non-experimental/non-exposed group (extracted from a plot).

smd_to_cor

formula used to convert the cohen_d value into a coefficient correlation (see details).

reverse_plot_means

a logical value indicating whether the direction of the generated effect sizes should be flipped.

Details

This function uses the bounds of an error bar of a mean obtained from a plot into a standard deviation. Then, a mean difference (MD), Cohen's d (D), and Hedges' g (G) are estimated. Odds ratio (OR), risk ratio (RR) and correlation coefficients (R/Z) are converted from the Cohen's d value.

To convert the bound of an error bar into a standard deviation, this function always prioritizes information from the plot_mean_sd_* arguments, then those from the plot_mean_se_* arguments, then those from the plot_mean_ci_* arguments.

  1. If the bounds of the standard deviations are provided, the following formulas are used:

    mean_sd_lo_exp=plot_mean_expplot_mean_sd_lo_expmean\_sd\_lo\_exp = plot\_mean\_exp - plot\_mean\_sd\_lo\_exp

    mean_sd_up_exp=plot_mean_sd_up_expplot_mean_expmean\_sd\_up\_exp = plot\_mean\_sd\_up\_exp - plot\_mean\_exp

    mean_sd_exp=mean_sd_lo_exp+mean_sd_up_exp2mean\_sd\_exp = \frac{mean\_sd\_lo\_exp + mean\_sd\_up\_exp}{2}

mean_sd_lo_nexp=plot_mean_nexpplot_mean_sd_lo_nexpmean\_sd\_lo\_nexp = plot\_mean\_nexp - plot\_mean\_sd\_lo\_nexp

mean_sd_up_nexp=plot_mean_sd_up_nexpplot_mean_nexpmean\_sd\_up\_nexp = plot\_mean\_sd\_up\_nexp - plot\_mean\_nexp

mean_sd_nexp=mean_sd_lo_nexp+mean_sd_up_nexp2mean\_sd\_nexp = \frac{mean\_sd\_lo\_nexp + mean\_sd\_up\_nexp}{2}

Note that if only one bound (e.g., the upper bound) is provided, it will be the only information used to estimate the standard deviation value.

Then, calculations of the es_from_means_sd are used.

  1. If the bounds of the standard errors are provided, the following formulas are used:

    mean_se_lo_exp=plot_mean_expplot_mean_se_lo_expmean\_se\_lo\_exp = plot\_mean\_exp - plot\_mean\_se\_lo\_exp

    mean_se_up_exp=plot_mean_se_up_expplot_mean_expmean\_se\_up\_exp = plot\_mean\_se\_up\_exp - plot\_mean\_exp

    mean_se_exp=mean_se_lo_exp+mean_se_up_exp2mean\_se\_exp = \frac{mean\_se\_lo\_exp + mean\_se\_up\_exp}{2}

mean_se_lo_nexp=plot_mean_nexpplot_mean_se_lo_nexpmean\_se\_lo\_nexp = plot\_mean\_nexp - plot\_mean\_se\_lo\_nexp

mean_se_up_nexp=plot_mean_se_up_nexpplot_mean_nexpmean\_se\_up\_nexp = plot\_mean\_se\_up\_nexp - plot\_mean\_nexp

mean_se_nexp=mean_se_lo_nexp+mean_se_up_nexp2mean\_se\_nexp = \frac{mean\_se\_lo\_nexp + mean\_se\_up\_nexp}{2}

Note that if only one bound (e.g., the upper bound) is provided, it will be the only information used to estimate the standard error value.

Then, calculations of the es_from_means_se() are used.

  1. If the bounds of the 95% confidence intervals are provided, the calculations of the es_from_means_ci are used.

Value

This function estimates and converts between several effect size measures.

natural effect size measure MD + D + G
converted effect size measure OR + R + Z
required input data See 'Section 21. From plot: means and dispersion (crude)'
https://metaconvert.org/input.html

Examples

es_from_plot_means(
  n_exp = 35, n_nexp = 35,
  plot_mean_exp = 89, plot_mean_nexp = 104,
  plot_mean_sd_lo_exp = 69, plot_mean_sd_lo_nexp = 83,
  plot_mean_sd_up_exp = 109, plot_mean_sd_up_nexp = 125
)

Convert a point-biserial correlation coefficient into several effect size measures

Description

Convert a point-biserial correlation coefficient into several effect size measures

Usage

es_from_pt_bis_r(
  pt_bis_r,
  n_exp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  reverse_pt_bis_r
)

Arguments

pt_bis_r

value of a point-biserial correlation coefficient

n_exp

total number of participants in the exposed group

n_nexp

total number of participants in the non exposed group

smd_to_cor

formula used to convert the pt_bis_r value into a coefficient correlation.

reverse_pt_bis_r

a logical value indicating whether the direction of the generated effect sizes should be flipped.

Details

This function uses a point-biserial correlation coefficient to estimate a Cohen's d (D) and Hedges' g (G). Odds ratio (OR) and correlation coefficients (R/Z) are then converted from the Cohen's d.

The formula used to obtain the Cohen's d are (Viechtbauer, 2021):

m=n_exp+n_nexp2m = n\_exp + n\_nexp - 2

h=mn_exp+mn_nexph = \frac{m}{n\_exp} + \frac{m}{n\_nexp}

d=pt_bis_rh1pt_bis_r2d = \frac{pt\_bis\_r * \sqrt{h}}{\sqrt{1 - pt\_bis\_r^2}}

To estimate other effect size measures, calculations of the es_from_cohen_d() are applied.

Value

This function estimates and converts between several effect size measures.

natural effect size measure D + G
converted effect size measure OR + R + Z
required input data See 'Section 11. ANOVA statistics, Student's t-test, or point-bis correlation'
https://metaconvert.org/input.html

References

Viechtbauer (2021). Accessed at: https://stats.stackexchange.com/questions/526789/convert-correlation-r-to-cohens-d-unequal-groups-of-known-size

Examples

es_from_pt_bis_r(pt_bis_r = 0.2, n_exp = 121, n_nexp = 121)

Convert a p-value of a point-biserial correlation coefficient into several effect size measures

Description

Convert a p-value of a point-biserial correlation coefficient into several effect size measures

Usage

es_from_pt_bis_r_pval(
  pt_bis_r_pval,
  n_exp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  reverse_pt_bis_r_pval
)

Arguments

pt_bis_r_pval

p-value of a point-biserial correlation coefficient

n_exp

total number of participants in the exposed group

n_nexp

total number of participants in the non exposed group

smd_to_cor

formula used to convert the pt_bis_r_pval value into a coefficient correlation.

reverse_pt_bis_r_pval

a logical value indicating whether the direction of the generated effect sizes should be flipped.

Details

This function converts the p-value of a point biserial correlation into a Student's t-value.

The formula used to obtain this Student's t-value is:

t=pt(pt_bis_r_pval2,df=n_exp+n_nexp2)t = pt(\frac{pt\_bis\_r\_pval}{2}, df = n\_exp + n\_nexp - 2)

Calculations of the es_from_student_t function are then applied.

Value

This function estimates and converts between several effect size measures.

natural effect size measure D + G
converted effect size measure OR + R + Z
required input data See 'Section 11. ANOVA statistics, Student's t-test, or point-bis correlation'
https://metaconvert.org/input.html

References

Lipsey, M. W., & Wilson, D. B. (2001). Practical meta-analysis. Sage Publications, Inc.

Examples

es_from_pt_bis_r_pval(pt_bis_r_pval = 0.2, n_exp = 121, n_nexp = 121)

Convert a risk ratio value and 95% confidence interval to various effect size measures

Description

Convert a risk ratio value and 95% confidence interval to various effect size measures

Usage

es_from_rr_ci(
  rr,
  rr_ci_lo,
  rr_ci_up,
  logrr,
  logrr_ci_lo,
  logrr_ci_up,
  baseline_risk,
  n_exp,
  n_nexp,
  n_cases,
  n_controls,
  rr_to_or = "metaumbrella",
  smd_to_cor = "viechtbauer",
  max_asymmetry = 10,
  reverse_rr
)

Arguments

rr

risk ratio value

rr_ci_lo

lower bound of the 95% CI around the risk ratio value

rr_ci_up

upper bound of the 95% CI around the risk ratio value

logrr

log risk ratio value

logrr_ci_lo

lower bound of the 95% CI around the log risk ratio value

logrr_ci_up

upper bound of the 95% CI around the log risk ratio value

baseline_risk

proportion of cases in the non-exposed group (only required for the rr_to_or = "grant_CI" and rr_to_or = "grant_2x2" arguments).

n_exp

number of participants in the exposed group (only required for the rr_to_or = "grant_CI", rr_to_or = "grant_2x2" arguments).

n_nexp

number of participants in the non-exposed group (only required for the rr_to_or = "grant_CI", rr_to_or = "grant_2x2" arguments).

n_cases

number of cases/events

n_controls

number of controls/no-event

rr_to_or

formula used to convert the rr value into an odds ratio (see details).

smd_to_cor

formula used to convert the SMD value (converted from RR) into a coefficient correlation (see es_from_cohen_d).

max_asymmetry

A percentage indicating the tolerance before detecting asymmetry in the 95% CI bounds.

reverse_rr

a logical value indicating whether the direction of the generated effect sizes should be flipped.

Details

This function uses the 95% CI of the (log) risk ratio to obtain the standard error (Section 6.5.2.2 in the Cochrane Handbook).

logrr_se=logrr_ci_uplogrr_ci_lo2qnorm(.975)logrr\_se = \frac{\log{rr\_ci\_up} - \log{rr\_ci\_lo}}{2 * qnorm(.975)}

Then, calculations of the es_from_rr_se() are applied.

Value

This function estimates and converts between several effect size measures.

natural effect size measure RR
converted effect size measure OR + NNT
required input data See 'Section 3. Risk Ratio'
https://metaconvert.org/input.html

References

Higgins JPT, Li T, Deeks JJ (editors). Chapter 6: Choosing effect size measures and computing estimates of effect. In: Higgins JPT, Thomas J, Chandler J, Cumpston M, Li T, Page MJ, Welch VA (editors). Cochrane Handbook for Systematic Reviews of Interventions version 6.3 (updated February 2022). Cochrane, 2022. Available from www.training.cochrane.org/handbook.

Examples

es_from_rr_ci(
  rr = 1, rr_ci_lo = 0.5, rr_ci_up = 2,
  n_cases = 42, n_controls = 38, baseline_risk = 0.08
)

Convert a risk ratio value and its p-value to various effect size measures

Description

Convert a risk ratio value and its p-value to various effect size measures

Usage

es_from_rr_pval(
  rr,
  logrr,
  rr_pval,
  baseline_risk,
  n_exp,
  n_nexp,
  n_cases,
  n_controls,
  rr_to_or = "metaumbrella",
  smd_to_cor = "viechtbauer",
  reverse_rr_pval
)

Arguments

rr

risk ratio value

logrr

log risk ratio value

rr_pval

p-value of the risk ratio

baseline_risk

proportion of cases in the non-exposed group (only required for the rr_to_or = "grant_CI" and rr_to_or = "grant_2x2" arguments).

n_exp

number of participants in the exposed group (only required for the rr_to_or = "grant_CI", rr_to_or = "grant_2x2" arguments).

n_nexp

number of participants in the non-exposed group (only required for the rr_to_or = "grant_CI", rr_to_or = "grant_2x2" arguments).

n_cases

number of cases/events

n_controls

number of controls/no-event

rr_to_or

formula used to convert the rr value into an odds ratio (see details).

smd_to_cor

formula used to convert the SMD value (converted from RR) into a coefficient correlation (see es_from_cohen_d).

reverse_rr_pval

a logical value indicating whether the direction of the generated effect sizes should be flipped.

Details

This function uses the p-value of the (log) risk ratio to obtain the standard error (Section 6.3.2 in the Cochrane Handbook).

logrr_z=qnorm(rrpval/2,lower.tail=FALSE)logrr\_z = qnorm(rr_pval/2, lower.tail=FALSE)

logrr_se=log(rr)logrr_zlogrr\_se = |\frac{\log(rr)}{logrr\_z}|

Then, calculations of es_from_rr_se are applied.

Value

This function estimates and converts between several effect size measures.

natural effect size measure RR
converted effect size measure OR + NNT
required input data See 'Section 3. Risk Ratio'
https://metaconvert.org/input.html

References

Higgins, J. P., Thomas, J., Chandler, J., Cumpston, M., Li, T., Page, M. J., & Welch, V. A. (Eds.). (2019). Cochrane handbook for systematic reviews of interventions. John Wiley & Sons.

Examples

es_rr <- es_from_rr_pval(
  rr = 3.51, rr_pval = 0.001,
  n_cases = 12, n_controls = 68
)

Convert a risk ratio value and standard error to various effect size measures

Description

Convert a risk ratio value and standard error to various effect size measures

Usage

es_from_rr_se(
  rr,
  logrr,
  logrr_se,
  baseline_risk,
  n_exp,
  n_nexp,
  n_cases,
  n_controls,
  smd_to_cor = "viechtbauer",
  rr_to_or = "metaumbrella",
  reverse_rr
)

Arguments

rr

risk ratio value

logrr

log risk ratio value

logrr_se

standard error of the log risk ratio

baseline_risk

proportion of cases in the non-exposed group

n_exp

number of participants in the exposed group

n_nexp

number of participants in the non-exposed group

n_cases

number of cases/events

n_controls

number of controls/no-event

smd_to_cor

formula used to convert the SMD value (converted from RR) into a coefficient correlation (see es_from_cohen_d).

rr_to_or

formula used to convert the rr value into an odds ratio (see details).

reverse_rr

a logical value indicating whether the direction of the generated effect sizes should be flipped.

Details

This function converts the (log) risk ratio (RR) value and its standard error to odds ratio (OR) and number needed to treat.

To estimate the odds ratio and its standard error, various formulas can be used.

A. First, the approach described in Grant (2014) can be used. However, in the paper, only the formula to convert an RR value to a OR value is described. To derive the variance, we used this formula to convert the bounds of the 95% CI, which were then used to obtain the variance.

This argument requires (rr + baseline_risk + rr_ci_lo + rr_ci_up) to generate a RR. The following formulas are used (br = baseline_risk):

or=rr(1br)1rrbror = \frac{rr * (1 - br)}{1 - rr * br}

or_ci_lo=rr_ci_lo1br+brrr_ci_loor\_ci\_lo = \frac{rr\_ci\_lo}{1 - br + br*rr\_ci\_lo}

or_ci_up=rr_ci_up1br+brrr_ci_upor\_ci\_up = \frac{rr\_ci\_up}{1 - br + br*rr\_ci\_up}

logor_se=log(or_ci_up)log(or_ci_lo)2qnorm(.975)logor\_se = \frac{log(or\_ci\_up) - log(or\_ci\_lo)}{2 * qnorm(.975)}

B. Second, the formulas implemented in the metaumbrella package can be used (or_to_rr = "metaumbrella_exp"). This argument requires (rr + logrr_se + n_exp + n_nexp) to generate a OR. More precisely, we previously developed functions that simulate all combinations of the possible number of cases and controls in the exposed and non-exposed groups compatible with the actual value of the RR. Then, the functions select the contingency table whose standard error coincides best with the standard error reported. The RR value and its standard are obtained from this estimated contingency table.

C. Third, it is possible to transpose the RR to a OR (rr_to_or = "transpose"). This argument requires (rr + logrr_se) to generate a OR. It is known that OR and RR are similar when the baseline risk is small. Therefore, users can request to simply transpose the RR value & standard error into a OR value & standard error.

or=rror = rr

logor_se=logrr_selogor\_se = logrr\_se

D. Fourth, it is possible to recreate the 2x2 table using the dipietrantonj's formulas (rr_to_or = "dipietrantonj"). This argument requires (rr + logrr_ci_lo + logrr_ci_lo) to generate a OR. Information on this approach can be retrieved in Di Pietrantonj (2006).

To estimate the NNT, the formulas used are :

nnt=1br(1rr)nnt = \frac{1}{br * (1 - rr)}

Value

This function estimates and converts between several effect size measures.

natural effect size measure RR
converted effect size measure OR + NNT
required input data See 'Section 3. Risk Ratio'
https://metaconvert.org/input.html

References

Di Pietrantonj C. (2006). Four-fold table cell frequencies imputation in meta analysis. Statistics in medicine, 25(13), 2299–2322. https://doi.org/10.1002/sim.2287

Gosling, C. J., Solanes, A., Fusar-Poli, P., & Radua, J. (2023). metaumbrella: the first comprehensive suite to perform data analysis in umbrella reviews with stratification of the evidence. BMJ mental health, 26(1), e300534. https://doi.org/10.1136/bmjment-2022-300534

Grant R. L. (2014). Converting an odds ratio to a range of plausible relative risks for better communication of research findings. BMJ (Clinical research ed.), 348, f7450. https://doi.org/10.1136/bmj.f7450

Veroniki, A. A., Pavlides, M., Patsopoulos, N. A., & Salanti, G. (2013). Reconstructing 2x2 contingency tables from odds ratios using the Di Pietrantonj method: difficulties, constraints and impact in meta-analysis results. Research synthesis methods, 4(1), 78–94. https://doi.org/10.1002/jrsm.1061

Examples

es_from_rr_se(rr = 2.12, logrr_se = 0.242, n_exp = 120, n_nexp = 44)

Convert a Student's t-test value to several effect size measures

Description

Convert a Student's t-test value to several effect size measures

Usage

es_from_student_t(
  student_t,
  n_exp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  reverse_student_t
)

Arguments

student_t

Student's t-test value.

n_exp

number of participants in the experimental/exposed group.

n_nexp

number of participants in the non-experimental/non-exposed group.

smd_to_cor

formula used to convert the student_t value into a coefficient correlation (see details).

reverse_student_t

a logical value indicating whether the direction of generated effect sizes should be flipped.

Details

This function converts the Student's t-test value into a Cohen's d (D) and Hedges' g (G), Odds ratio (OR) and correlation coefficients (R/Z) are then converted from the Cohen's d.

To estimate a Cohen's d the formula used is (table 12.1 in Cooper):

cohen_d=student_t(n_exp+n_nexp)n_expn_nexpcohen\_d = student\_t * \sqrt{\frac{(n\_exp+n\_nexp)}{n\_exp*n\_nexp}}

To estimate other effect size measures, calculations of the es_from_cohen_d() are applied.

Value

This function estimates and converts between several effect size measures.

natural effect size measure D + G
converted effect size measure OR + R + Z
required input data See 'Section 11. ANOVA statistics, Student's t-test, or point-bis correlation'
https://metaconvert.org/html/input.html

References

Cooper, H., Hedges, L.V., & Valentine, J.C. (Eds.). (2019). The handbook of research synthesis and meta-analysis. Russell Sage Foundation.

Examples

es_from_student_t(student_t = 2.1, n_exp = 20, n_nexp = 22)

Convert a Student's t-test p-value to several effect size measures

Description

Convert a Student's t-test p-value to several effect size measures

Usage

es_from_student_t_pval(
  student_t_pval,
  n_exp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  reverse_student_t_pval
)

Arguments

student_t_pval

p-value (two-tailed) from a Student's t-test. If your p-value is one-tailed, simply multiply it by two.

n_exp

number of participants in the experimental/exposed group.

n_nexp

number of participants in the non-experimental/non-exposed group.

smd_to_cor

formula used to convert the student_t_pval value into a coefficient correlation (see details).

reverse_student_t_pval

a logical value indicating whether the direction of generated effect sizes should be flipped.

Details

This function converts the Student's t-test p-value into a t-value, and then relies on the calculations of the es_from_student_t() function.

To convert the p-value into a t-value, the following formula is used (table 12.1 in Cooper):

student_t=qt(student_t_pval2,df=n_exp+n_nexp2)student\_t = qt(\frac{student\_t\_pval}{2}, df = n\_exp + n\_nexp - 2)

Then, calculations of the es_from_student_t() are applied.

Value

This function estimates and converts between several effect size measures.

natural effect size measure D + G
converted effect size measure OR + R + Z
required input data See 'Section 11. ANOVA statistics, Student's t-test, or point-bis correlation'
https://metaconvert.org/html/input.html

References

Cooper, H., Hedges, L.V., & Valentine, J.C. (Eds.). (2019). The handbook of research synthesis and meta-analysis. Russell Sage Foundation.

Examples

es_from_student_t_pval(student_t_pval = 0.24, n_exp = 20, n_nexp = 22)

Directly input an adjusted value + variance of an effect size measure

Description

Directly input an adjusted value + variance of an effect size measure

Usage

es_from_user_adj(
  measure,
  user_es_measure_adj,
  user_es_adj,
  user_se_adj,
  user_ci_lo_adj,
  user_ci_up_adj,
  max_asymmetry = 10
)

Arguments

measure

the effect size measure used in calculations (must be one of the 11 effect size measures available in metaConvert)

user_es_measure_adj

the name of the effect size measure that will appear when this function is called by the convert_df function (can be any character string)

user_es_adj

adjusted effect size value

user_se_adj

adjusted standard error of the effect size

user_ci_lo_adj

adjusted lower bound of the 95% CI around the effect size value

user_ci_up_adj

adjusted upper bound of the 95% CI around the effect size value

max_asymmetry

A percentage indicating the tolerance before detecting asymmetry in the 95% CI bounds.

Details

This function is a generic function allowing to include any adjusted effect size measure value + variance. Importantly, with this function, no conversions are performed (i.e., the effect size value + variance you enter is the value + variance exported by this function).

Value

This function allows to directly input any of the 11 effect size measures

natural effect size measure Any of the 11 available measures
converted effect size measure No conversion performed
required input data See 'Section 24. User's input (adjusted)'
https://metaconvert.org/input.html

Examples

dat = data.frame(measure = "OR", user_es_measure_adj = "adjusted OR",
                 user_es_adj = -0.04, user_se_adj = 0.2)
summary(convert_df(dat, measure="logor"))

Directly input a value + variance of an effect size measure

Description

Directly input a value + variance of an effect size measure

Usage

es_from_user_crude(
  measure,
  user_es_measure_crude,
  user_es_crude,
  user_se_crude,
  user_ci_lo_crude,
  user_ci_up_crude,
  max_asymmetry = 10
)

Arguments

measure

the effect size measure used in calculations (must be one of the 11 effect size measures available in metaConvert)

user_es_measure_crude

the name of the effect size measure that will appear when this function is called by the convert_df function (can be any character string)

user_es_crude

effect size value

user_se_crude

standard error of the effect size

user_ci_lo_crude

lower bound of the 95% CI around the effect size value

user_ci_up_crude

upper bound of the 95% CI around the effect size value

max_asymmetry

A percentage indicating the tolerance before detecting asymmetry in the 95% CI bounds.

Details

This function is a generic function allowing to include any crude effect size measure value + variance. Importantly, with this function, no conversions are performed (i.e., the effect size value + variance you enter is the value + variance exported by this function).

Value

This function allows to directly input any of the 11 effect size measures

natural effect size measure Any of the 11 available measures
converted effect size measure No conversion performed
required input data See 'Section 23. User's input (crude)'
https://metaconvert.org/input.html

Examples

dat = data.frame(measure = "OR", user_es_measure_crude = "mortality rate ratio",
                 user_es_crude = -0.04, user_se_crude = 0.2)
summary(convert_df(dat, measure="logor"))

Title

Description

Title

Usage

es_variab_from_means_ci(
  mean_exp,
  mean_nexp,
  mean_ci_lo_exp,
  mean_ci_up_exp,
  mean_ci_lo_nexp,
  mean_ci_up_nexp,
  n_exp,
  n_nexp,
  reverse_means_variability
)

Arguments

mean_exp

mean of participants in the experimental/exposed group.

mean_nexp

mean of participants in the non-experimental/non-exposed group.

mean_ci_lo_exp

lower bound of the 95% CI of the mean of the experimental/exposed group

mean_ci_up_exp

upper bound of the 95% CI of the mean of the experimental/exposed group

mean_ci_lo_nexp

lower bound of the 95% CI of the mean of the non-experimental/non-exposed group.

mean_ci_up_nexp

upper bound of the 95% CI of the mean of the non-experimental/non-exposed group.

n_exp

number of participants in the experimental/exposed group.

n_nexp

number of participants in the non-experimental/non-exposed group.

reverse_means_variability

a logical value indicating whether the direction of the generated effect sizes should be flipped.

Details

This function converts the bounds of the 95% CI of the means of two independent groups into standard errors.

mean_se_exp=mean_ci_up_expmean_ci_lo_exp2qt(0.975,df=n_exp1)mean\_se\_exp = \frac{mean\_ci\_up\_exp - mean\_ci\_lo\_exp}{2 * qt{(0.975, df = n\_exp - 1)}}

mean_se_nexp=mean_ci_up_nexpmean_ci_lo_nexp2qt(0.975,df=n_nexp1)mean\_se\_nexp = \frac{mean\_ci\_up\_nexp - mean\_ci\_lo\_nexp}{2 * qt{(0.975, df = n\_nexp - 1)}}

Then, calculations of the es_variab_from_means_se are applied.

Value

This function estimates VR and CVR

natural effect size measure VR + CVR
converted effect size measure No conversion performed
required input data See 'Section 23. User's input (crude)'
https://metaconvert.org/html/input.html

References

Senior, A. M., Viechtbauer, W., & Nakagawa, S. (2020). Revisiting and expanding the meta-analysis of variation: The log coefficient of variation ratio. Research Synthesis Methods, 11(4), 553-567. https://doi.org/10.1002/jrsm.1423

Examples

es_variab_from_means_ci(
  mean_exp = 42, mean_ci_lo_exp = 32, mean_ci_up_exp = 52,
  mean_nexp = 42, mean_ci_lo_nexp = 37, mean_ci_up_nexp = 47,
  n_exp = 43, n_nexp = 34
)

Convert means and/or standard deviations of two independent groups into two effect measures (VR/CVR)

Description

Convert means and/or standard deviations of two independent groups into two effect measures (VR/CVR)

Usage

es_variab_from_means_sd(
  mean_exp,
  mean_nexp,
  mean_sd_exp,
  mean_sd_nexp,
  n_exp,
  n_nexp,
  reverse_means_variability
)

Arguments

mean_exp

mean of participants in the experimental/exposed group.

mean_nexp

mean of participants in the non-experimental/non-exposed group.

mean_sd_exp

standard deviation of participants in the experimental/exposed group.

mean_sd_nexp

standard deviation of participants in the non-experimental/non-exposed group.

n_exp

number of participants in the experimental/exposed group.

n_nexp

number of participants in the non-experimental/non-exposed group.

reverse_means_variability

a logical value indicating whether the direction of the generated effect sizes should be flipped.

Details

This function converts the means and standard deviations of two independent groups into a log variability ratio (VR) and a log coefficient of variation ratio (CVR).

The formulas used to obtain the log VR are (formulas 5 and 15, Senior et al. 2020):

logvr=log(mean_sd_expmean_sd_nexp)+12(n_exp1)12(n_nexp1)logvr = log(\frac{mean\_sd\_exp}{mean\_sd\_nexp}) + \frac{1}{2 * (n\_exp - 1)} - \frac{1}{2 * (n\_nexp - 1)}

logvr_se=12(n_nexp(n_nexp1)2+n_exp(n_exp1)2)logvr\_se = \sqrt{\frac{1}{2} * (\frac{n\_nexp}{(n\_nexp - 1)^2} + \frac{n\_exp}{(n\_exp - 1)^2})}

logvr_ci_lo=logvrqnorm(.975)logvr_selogvr\_ci\_lo = logvr - qnorm(.975) * logvr\_se

logvr_ci_up=logvr+qnorm(.975)logvr_selogvr\_ci\_up = logvr + qnorm(.975) * logvr\_se

The formulas used to obtain the log CVR are (formulas 6 and 16, Senior et al. 2020):

cvt=mean_sd_exp/mean_expcvt = mean\_sd\_exp / mean\_exp

cvc=mean_sd_nexp/mean_nexpcvc = mean\_sd\_nexp / mean\_nexp

logcvr=log(cvtcvc)+12(1n_exp11n_nexp1)+12(mean_sd_nexp2n_nexpmean_nexp2mean_sd_exp2n_expmean_exp2)logcvr = log(\frac{cvt}{cvc}) + \frac{1}{2} * (\frac{1}{n\_exp - 1} - \frac{1}{n\_nexp - 1}) + \frac{1}{2} * (\frac{mean\_sd\_nexp^2}{n\_nexp * mean\_nexp^2} - \frac{mean\_sd\_exp^2}{n\_exp * mean\_exp^2})

vt_exp=mean_sd_exp2n_expmean_exp2+mean_sd_exp42n_exp2mean_exp4+n_exp(n_exp1)2vt\_exp = \frac{mean\_sd\_exp^2}{n\_exp * mean\_exp^2} + \frac{mean\_sd\_exp^4}{2 * n\_exp^2 * mean\_exp^4} + \frac{n\_exp}{(n\_exp - 1)^2}

vt_nexp=mean_sd_nexp2n_nexpmean_nexp2+mean_sd_nexp42n_nexp2mean_nexp4+n_nexp(n_nexp1)2vt\_nexp = \frac{mean\_sd\_nexp^2}{n\_nexp * mean\_nexp^2} + \frac{mean\_sd\_nexp^4}{2 * n\_nexp^2 * mean\_nexp^4} + \frac{n\_nexp}{(n\_nexp - 1)^2}

logcvr_se=vt_exp+vt_nexplogcvr\_se = \sqrt{vt\_exp + vt\_nexp}

logcvr_ci_lo=logcvrqnorm(.975)logcvr_selogcvr\_ci\_lo = logcvr - qnorm(.975) * logcvr\_se

logcvr_ci_up=logcvr+qnorm(.975)logcvr_selogcvr\_ci\_up = logcvr + qnorm(.975) * logcvr\_se

Value

This function estimates VR and CVR

natural effect size measure VR + CVR
converted effect size measure No conversion performed
required input data See 'Section 23. User's input (crude)'
https://metaconvert.org/html/input.html

References

Senior, A. M., Viechtbauer, W., & Nakagawa, S. (2020). Revisiting and expanding the meta-analysis of variation: The log coefficient of variation ratio. Research Synthesis Methods, 11(4), 553-567. https://doi.org/10.1002/jrsm.1423

Examples

es_variab_from_means_sd(
  n_exp = 55, n_nexp = 55,
  mean_exp = 2.3, mean_sd_exp = 1.2,
  mean_nexp = 1.9, mean_sd_nexp = 0.9
)

Convert means and/or standard errors of two independent groups into two effect measures (VR/CVR)

Description

Convert means and/or standard errors of two independent groups into two effect measures (VR/CVR)

Usage

es_variab_from_means_se(
  mean_exp,
  mean_nexp,
  mean_se_exp,
  mean_se_nexp,
  n_exp,
  n_nexp,
  reverse_means_variability
)

Arguments

mean_exp

mean of participants in the experimental/exposed group.

mean_nexp

mean of participants in the non-experimental/non-exposed group.

mean_se_exp

standard error of participants in the experimental/exposed group.

mean_se_nexp

standard error of participants in the non-experimental/non-exposed group.

n_exp

number of participants in the experimental/exposed group.

n_nexp

number of participants in the non-experimental/non-exposed group.

reverse_means_variability

a logical value indicating whether the direction of the generated effect sizes should be flipped.

Details

This function converts the standard errors into standard deviations.

mean_sd_exp=mean_se_expn_exp1mean\_sd\_exp = mean\_se\_exp * \sqrt{n\_exp - 1}

mean_sd_nexp=mean_se_nexpn_nexp1mean\_sd\_nexp = mean\_se\_nexp * \sqrt{n\_nexp - 1}

Then, calculations of the es_variab_from_means_sd are applied.

Value

This function estimates VR and CVR

natural effect size measure VR + CVR
converted effect size measure No conversion performed
required input data See 'Section 23. User's input (crude)'
https://metaconvert.org/html/input.html

References

Senior, A. M., Viechtbauer, W., & Nakagawa, S. (2020). Revisiting and expanding the meta-analysis of variation: The log coefficient of variation ratio. Research Synthesis Methods, 11(4), 553-567. https://doi.org/10.1002/jrsm.1423

Examples

es_variab_from_means_se(
  mean_exp = 42, mean_se_exp = 11,
  mean_nexp = 42, mean_se_nexp = 15,
  n_exp = 43, n_nexp = 34
)

Print a summary of an object of class “metaConvert”

Description

Print a summary of an object of class “metaConvert”

Usage

## S3 method for class 'metaConvert'
print(x, ...)

Arguments

x

an object of class “metaConvert”

...

other arguments that can be passed to the function

Details

Summary method for objects of class “metaConvert”.

Value

Implicitly calls the summary.metaConvert function.

See Also

summary.metaConvert

Examples

### print the results of an object of class metaConvert
convert_df(df.haza, measure = "g")

Overview of effect size measures generated from each type of input data

Description

Overview of effect size measures generated from each type of input data

Usage

see_input_data(
  measure = c("all", "d", "g", "md", "or", "rr", "nnt", "r", "z", "logvr", "logcvr",
    "irr"),
  type_of_measure = c("natural+converted", "natural"),
  name = "mcv_input_data",
  extension = c("data.frame", ".txt", ".csv", ".xlsx"),
  verbose = TRUE
)

Arguments

measure

Target effect size measure (one of the 11 available in metaConvert). Default is "all".

type_of_measure

One of "natural+converted" or "natural" (see details).

name

Name of the file created

extension

Extension of the file created. Most common are ".xlsx", ".csv" or ".txt". It is also possible to generate an R dataframe object by using the "data.frame" extension.

verbose

logical variable indicating whether some information should be printed (e.g., the location where the sheet is created when using ".xlsx", ".csv" or ".txt" extensions)

Details

This function generates, on your computer on in the console, a dataset showing each effect size measure computed from each type of input data. The exact combination and names of input data required are available in the links.

The measure argument allows to filter the dataset created. Only the input data allowing to estimate the selected effect size measure will be shown. Default is "all". The type_of_measure argument allows to filter the dataset created.

  • If "natural+converted" is selected, the dataset will contain all input data allowing to naturally estimate and to convert the selected effect size measure

  • If "natural" is selected, the dataset will contain all input data allowing to naturally estimate the selected effect size measure

Extension

You can export a file in various formats outside R (by indicating, for example, ".txt", ".xlsx", or ".csv") in the extension argument. You can also visualise this dataset directly in R by setting extension = "R".

This table is designed to be used in combination with tables showing the combination of input data leading to estimate each of the effect size measures (https://metaconvert.org/html/input.html)

Value

This function returns a table dataset presenting the input data enabling to compute each effect size measure.

Examples

see_input_data(measure = "md", extension = "data.frame")

Synthesize information of an object of class “metaConvert” into a dataframe

Description

Synthesize information of an object of class “metaConvert” into a dataframe

Usage

## S3 method for class 'metaConvert'
summary(object, digits = 3, ...)

Arguments

object

an object of class “metaConvert”

digits

an integer value specifying the number of decimal places for the rounding of numeric values. Default is 3.

...

other arguments that can be passed to the function

Details

Summary method for objects of class “metaConvert” produced by the convert_df function. This function automatically:

  1. computes all effect sizes from all available input data

  2. selects, if requested, a main effect size for each association/comparison using the information passed by the user in the es_selected argument of the convert_df function

  3. identifies the smallest and largest effect size for each association/comparison

  4. estimates the absolute difference between the smallest and largest effect size for each association/comparison

  5. estimates the percentage of overlap between the 95% confidence intervals of the smallest and largest effect size for each association/comparison

Value

This function returns a dataframe with many columns. We present below the information stored in each column of the returned dataframe

1. Raw user information. The first columns placed at the left of the returned dataset are simply information provided by the users to facilitate the identification of each row. If the following columns are missing in the original dataset, these columns will not appear in the returned dataset.

row_id Row number in the original dataset.
study_id Identifier of the study.
author Name of the author of the study.
year Year of publication of the study.
predictor Name of the predictor (intervention, risk factor, etc.).
outcome Name of the outcome.
info_expected Types of input data users expect to be used to estimate their effect size measure.

2. Information on generated effect sizes. Then, the function returns information on calculations. For example, users can retrieve the effect size measure estimated, the number and type(s) of input data allowing to estimate the chosen effect size measure, and the method used to obtain a unique effect size if overlapping input data were available. These columns could have several suffix.

  • If users requested to separate crude and adjusted estimates, then the following columns will be presented with both a "_crude" suffix and a "_adjusted" suffix.

  • If users did not request to separate the presentation of crude and adjusted estimates, the following columns will have no suffix.

For example, let's take column "all_info". It can be "all_info_crude" (all input data used to estimate any crude effect size), "all_info_adjusted" (all input data leading to estimate any adjusted effect size), or "all_info" (all input data leading to estimate any crude or adjusted effect sizes).

To facilitate the presentation, we thus refer to these columns as name_of_the_column*, the * meaning that it could end by _crude, _adjusted or "".

all_info* list of input data available in the dataset that was used to estimate any effect size measure.
measure* effect size measure requested by the user.
info_measure* input data available to estimate the requested effect size measure.
n_estimations* number of input data available to estimate the requested effect size measure.
es_selected* method chosen by users to estimate the main effect size when overlapping data are present.
info_used* type of input data used to estimate the main effect size.

3. Main effect size. The following columns contain the key information, namely, the main effect size + standard error + 95% CI.

Again, the suffix of these columns can vary depending on the separation of effect sizes estimated from crude and adjusted input data.

es* main effect size value.
se* standard error of the effect size.
es_ci_lo* lower bound of the 95% CI around the effect size.
es_ci_up* upper bound of the 95% CI around the effect size.

4. Overlapping effect sizes These columns are useful ONLY if a given comparison (i.e., row) has multiple input data enabling to compute the requested effect size measure.

These columns identify the smallest/largest effect size per comparison, and some indicators of consistency.

Again, the suffix of these columns can vary depending on the separation of effect sizes estimated from crude and adjusted input data.

min_info* type of input data leading to the smallest effect size for the comparison.
min_es_value* smallest effect size value for the comparison.
min_es_se* standard error of the smallest effect size for the comparison.
min_es_ci_lo* lower bound of the 95% CI of the smallest effect size for the comparison.
min_es_ci_up* upper bound of the 95% CI of the smallest effect size for the comparison.
max_info* type of input data leading to the largest effect size for the comparison.
max_es_value* largest effect size value for the comparison.
max_es_se* standard error of the largest effect size for the comparison.
max_es_ci_lo* lower bound of the 95% CI of the largest effect size for the comparison.
max_es_ci_up* upper bound of the 95% CI of the largest effect size for the comparison.
diff_min_max* difference between the smallest and largest effect size for the comparison.
overlap_min_max* % of overlap between the 95% CIs of the largest/smallest effect sizes for the comparison.
dispersion_es* standard deviation of all effect sizes for the comparison.

See Also

metaConvert-package for the formatting of well-formatted datasets
convert_df for estimating effect sizes from a dataset

Examples

### generate a summary of the results of an umbrella object
summary(
  convert_df(df.haza, measure = "g"),
  digits = 5)