Package 'Spower'

Title: Power Analyses using Monte Carlo Simulations
Description: Provides a general purpose simulation-based power analysis API for routine and customized simulation experimental designs. The package focuses exclusively on Monte Carlo simulation variants of (expected) prospective power analyses, criterion power analyses, compromise power analyses, sensitivity analyses, and prospective/post-hoc power analyses. The default simulation experiment functions found within the package provide stochastic variants of the power analyses subroutines found in the G*Power 3 software (Faul, Erdfelder, Buchner, and Lang, 2009) <doi:10.3758/brm.41.4.1149>, along with various other power analysis examples (e.g., mediation analyses). Supporting functions are also included, such as for building empirical power curve estimates, which utilize a similar API structure.
Authors: Phil Chalmers [aut, cre]
Maintainer: Phil Chalmers <rphilip.chalmers@gmail.com>
License: GPL (>= 3)
Version: 0.2.2
Built: 2025-03-25 17:22:59 UTC
Source: CRAN

Help Index

Get previously evaluated Spower execution

Description

If the result of Spower was not stored into an object this function will retrieve the last evaluation.

Usage

getLastSpower()

Value

the last object returned from Spower

Author(s)

Phil Chalmers rphilip.chalmers@gmail.com

See Also

Spower

p-value from comparing two or more correlations simulation

Description

Function utilizes cocor to perform correlation comparison for independent, overlapping, and non-overlapping designs.

Usage

p_2r(
  n,
  r.ab1,
  r.ab2,
  r.ac1,
  r.ac2,
  r.bc1,
  r.bc2,
  r.ad1,
  r.ad2,
  r.bd1,
  r.bd2,
  r.cd1,
  r.cd2,
  n2_n1 = 1,
  two.tailed = TRUE,
  type = c("independent", "overlap", "nonoverlap"),
  test = "fisher1925",
  gen_fun = gen_2r,
  ...
)

gen_2r(n, R, ...)

Arguments

n

sample size
r.ab1

correlation between variable A and B in sample 1
r.ab2

correlation between variable A and B in sample 2
r.ac1

same pattern as r.ab1
r.ac2

same pattern as r.ab2
r.bc1

...
r.bc2

...
r.ad1

...
r.ad2

...
r.bd1

...
r.bd2

...
r.cd1

...
r.cd2

...
n2_n1

sample size ratio
two.tailed

logical; use two-tailed test?
type

type of correlation design
test

hypothesis method to use. Defaults to 'fisher1925'
gen_fun

function used to generate the required discrete data. Object returned must be a matrix with n rows. Default uses gen_2r. User defined version of this function must include the argument ...
...

additional arguments to be passed to gen_fun. Not used unless a customized gen_fun is defined
R

a correlation matrix constructed from the inputs to p_2r

Value

a single p-value

Author(s)

Phil Chalmers rphilip.chalmers@gmail.com

Examples

# independent (same x-y pairing across groups)
p_2r(100, r.ab1=.5, r.ab2=.6)



   # estimate empirical power
   p_2r(n=100, r.ab1=.5, r.ab2=.6) |> Spower()

   # estimate n required to reach 80% power
   p_2r(n=NA, r.ab1=.5, r.ab2=.6) |>
        Spower(power=.80, interval=c(100, 5000))



# overlap (same y, different xs)
p_2r(100, r.ab1=.5, r.ab2=.7,
          r.ac1=.3, r.ac2=.3,
          r.bc1=.2, r.bc2=.2, type = 'overlap')

# nonoverlap (different ys, different xs)
p_2r(100, r.ab1=.5, r.ab2=.6,
          r.ac1=.3, r.ac2=.3,
          r.bc1=.2, r.bc2=.2,
          r.ad1=.2, r.ad2=.2,
          r.bd1=.4, r.bd2=.4,
          r.cd1=.2, r.cd2=.2,
          type = 'nonoverlap')

p-value from one-way ANOVA simulation

Description

Generates continuous multi-sample data to be analyzed by a one-way ANOVA, and return a p-value. Uses the function oneway.test to perform the analyses. The data and associated test assume that the conditional observations are normally distributed and have have equal variance by default, however these may be modified.

Usage

p_anova.test(
  n,
  k,
  f,
  n.ratios = rep(1, k),
  two.tailed = TRUE,
  var.equal = TRUE,
  means = NULL,
  sds = NULL,
  gen_fun = gen_anova.test,
  ...
)

gen_anova.test(n, k, f, n.ratios = rep(1, k), means = NULL, sds = NULL, ...)

Arguments

n

sample size per group
k

number of groups
f

Cohen's f effect size
n.ratios

allocation ratios reflecting the sample size ratios. Default of 1 sets the groups to be the same size (n * n.ratio)
two.tailed

logical; should a two-tailed or one-tailed test be used?
var.equal

logical; use the pooled SE estimate instead of the Welch correction for unequal variances?
means

(optional) vector of means. When specified the input f is ignored
sds

(optional) vector of SDs. When specified the input f is ignored
gen_fun

function used to generate the required data. Object returned must be a matrix with k rows and k columns of numeric data. Default uses gen_anova.test. User defined version of this function must include the argument ...
...

additional arguments to be passed to gen_fun. Not used unless a customized gen_fun is defined

Value

a single p-value

Author(s)

Phil Chalmers rphilip.chalmers@gmail.com

See Also

gen_anova.test

Examples

# n=50 in 3 groups, "medium" effect size
p_anova.test(50, k=3, f=.25)

# explicit means/sds
p_anova.test(50, 3, means=c(0,0,1), sds=c(1,2,1))


  # compare simulated results to pwr package
  pwr::pwr.anova.test(f=0.28, k=4, n=20)
  p_anova.test(n=20, k=4, f=.28) |> Spower()

p-value from chi-squared test simulation

Description

Generates multinomial data suitable for analysis with chisq.test.

Usage

p_chisq.test(
  n,
  w,
  df,
  correct = TRUE,
  P0 = NULL,
  P = NULL,
  gen_fun = gen_chisq.test,
  ...
)

gen_chisq.test(n, P, ...)

Arguments

n

sample size per group
w

Cohen's w effect size
df

degrees of freedom
correct

logical; apply continuity correction?
P0

specific null pattern, specified as a numeric vector or matrix
P

specific power configuration, specified as a numeric vector or matrix
gen_fun

function used to generate the required discrete data. Object returned must be a matrix with k rows and k columns of counts. Default uses gen_chisq.test. User defined version of this function must include the argument ...
...

additional arguments to be passed to gen_fun. Not used unless a customized gen_fun is defined

Value

a single p-value

Author(s)

Phil Chalmers rphilip.chalmers@gmail.com

See Also

gen_chisq.test

Examples

# effect size w + df
p_chisq.test(100, w=.2, df=3)

# vector of explicit probabilities (goodness of fit test)
p_chisq.test(100, P0 = c(.25, .25, .25, .25),
                   P = c(.6, .2, .1, .1))

# matrix of explicit probabilities (two-dimensional test of independence)
p_chisq.test(100, P0 = matrix(c(.25, .25, .25, .25), 2, 2),
                   P = matrix(c(.6, .2, .1, .1),2,2))


    # compare simulated results to pwr package

    P0 <- c(1/3, 1/3, 1/3)
    P <- c(.5, .25, .25)
    w <- pwr::ES.w1(P0, P)
    df <- 3-1
    pwr::pwr.chisq.test(w=w, df=df, N=100, sig.level=0.05)

    # slightly less power when evaluated empirically
    p_chisq.test(n=100, w=w, df=df) |> Spower(replications=100000)
    p_chisq.test(n=100, P0=P0, P=P) |> Spower(replications=100000)

    # slightly differ (latter more conservative due to finite sampling behaviour)
    pwr::pwr.chisq.test(w=w, df=df, power=.8, sig.level=0.05)
    p_chisq.test(n=NA, w=w, df=df) |>
           Spower(power=.80, interval=c(50, 200))
    p_chisq.test(n=NA, w=w, df=df, correct=FALSE) |>
           Spower(power=.80, interval=c(50, 200))

    # Spower slightly more conservative even with larger N
    pwr::pwr.chisq.test(w=.1, df=df, power=.95, sig.level=0.05)
    p_chisq.test(n=NA, w=.1, df=df) |>
           Spower(power=.95, interval=c(1000, 2000))
    p_chisq.test(n=NA, w=.1, df=df, correct=FALSE) |>
           Spower(power=.95, interval=c(1000, 2000))

p-value from (generalized) linear regression model simulations with fixed predictors

Description

p-values associated with (generalized) linear regression model. Requires a prespecified design matrix (X).

Usage

p_glm(
  formula,
  X,
  betas,
  test,
  sigma = NULL,
  family = gaussian(),
  gen_fun = gen_glm,
  ...
)

gen_glm(formula, X, betas, sigma = NULL, family = gaussian(), ...)

Arguments

formula

formula passed to either lm or glm
X

a data.frame containing the covariates
betas

vector of slope coefficients that match the model.matrix version of X
test

character vector specifying the test to pass to lht. Can also be a list of character vectors to evaluate multiple tests
sigma

residual standard deviation for linear model. Only used when family = 'gaussian'
family

family of distributions to use (see family)
gen_fun

function used to generate the required discrete data. Object returned must be a data.frame. Default uses gen_glm. User defined version of this function must include the argument ...
...

additional arguments to be passed to gen_fun. Not used unless a customized gen_fun is defined

Value

a single p-value

Author(s)

Phil Chalmers rphilip.chalmers@gmail.com

See Also

p_lm.R2

Examples

X <- data.frame(G = factor(rep(c('control', 'treatment'), each=50)),
                C = sample(50:100, 100, replace=TRUE))
head(X)

# ANCOVA setup
p_glm(y ~ G + C, test="Gtreatment = 0",
  X=X, betas=c(10, .3, 1), sigma=1)

# ANCOVA setup with logistic regression
p_glm(y ~ G + C, test="Gtreatment = 0",
  X=X, betas=c(-2, .5, .01), family=binomial())

# ANCOVA setup with poisson regression
p_glm(y ~ G + C, test="Gtreatment = 0",
  X=X, betas=c(-2, .5, .01), family=poisson())

p-value from Kruskal-Wallis Rank Sum Test simulation

Description

Simulates data given two or more parent distributions and returns a p-value using kruskal.test. Default generates data from Gaussian distributions, however this can be modified.

Usage

p_kruskal.test(
  n,
  k,
  means,
  n.ratios = rep(1, k),
  gen_fun = gen_kruskal.test,
  ...
)

gen_kruskal.test(n, k, n.ratios, means, ...)

Arguments

n

sample size per group
k

number of groups
means

vector of means to control location parameters
n.ratios

allocation ratios reflecting the sample size ratios. Default of 1 sets the groups to be the same size (n * n.ratio)
gen_fun

function used to generate the required data. Object returned must be a list of length k, where each element contains the sample data in each group. Default uses gen_kruskal.test. User defined version of this function must include the argument ...
...

additional arguments to pass to gen_fun

Value

a single p-value

Author(s)

Phil Chalmers rphilip.chalmers@gmail.com

Examples

# three group test where data generate from Gaussian distributions
p_kruskal.test(n=30, k=3, means=c(0, .5, .6))

# generate data from chi-squared distributions with different variances
gen_chisq <- function(n, k, n.ratios, means, dfs, ...){
  dat <- vector('list', k)
  ns <- n * n.ratios
  for(g in 1:k)
 	dat[[g]] <- rchisq(ns[g], df=dfs[g]) - dfs[g] + means[g]
  dat
}

p_kruskal.test(n=30, k=3, means=c(0, 1, 2),
   gen_fun=gen_chisq, dfs=c(10, 15, 20))


  # empirical power estimate
  p_kruskal.test(n=30, k=3, means=c(0, .5, .6)) |> Spower()
  p_kruskal.test(n=30, k=3, means=c(0, 1, 2), gen_fun=gen_chisq,
         dfs = c(10, 15, 20)) |> Spower()

p-value from Kolmogorov-Smirnov one- or two-sample simulation

Description

Generates one or two sets of continuous data group-level data and returns a p-value under the null that the groups were drawn from the same distribution (two sample) or from a theoretically known distribution (one sample).

Usage

p_ks.test(n, p1, p2, n2_n1 = 1, two.tailed = TRUE, parent = NULL, ...)

Arguments

n

sample size per group, assumed equal across groups
p1

a function indicating how the data were generated for group 1
p2

(optional) a function indicating how the data were generated for group 2. If omitted a one-sample test will be evaluated provided that parent is also specified
n2_n1

sample size ratio. Default uses equal sample sizes
two.tailed

logical; should a two-tailed or one-tailed test be used?
parent

the cumulative distribution function to use (e.g., pnorm). Specifying this input will construct a one-sample test setup
...

additional arguments to be passed to the parent distribution function from ks.test, as well as any other relevant parameter to ks.test (e.g., exact = TRUE)

Value

a single p-value

Author(s)

Phil Chalmers rphilip.chalmers@gmail.com

See Also

gen_t.test

Examples

# two-sample test from two Gaussian distributions with different locations
p1 <- function(n) rnorm(n)
p2 <- function(n) rnorm(n, mean=-.5)
p_ks.test(n=100, p1, p2)

# one-sample data from chi-squared distribution tested
#   against a standard normal distribution
pc <- function(n, df=15) (rchisq(n, df=df) - df) / sqrt(2*df)
p_ks.test(n=100, p1=pc, parent=pnorm, mean=0, sd=1)


  # empirical power estimates
  p_ks.test(n=100, p1, p2) |> Spower()
  p_ks.test(n=100, p1=pc, parent=pnorm, mean=0, sd=1) |> Spower()

p-value from global linear regression model simulation

Description

p-values associated with linear regression model using fixed/random independent variables. Focus is on the omnibus behavior of the R^2 statistic.

Usage

p_lm.R2(n, R2, k, R2_0 = 0, k.R2_0 = 0, R2.resid = 1 - R2, fixed = TRUE, ...)

Arguments

n

sample size
R2

R-squared effect size
k

number of IVs
R2_0

null hypothesis for R-squared
k.R2_0

number of IVs associated with the null hypothesis model
R2.resid

residual R-squared value, typically used when comparing nested models when fit sequentially (e.g., comparing model A vs B when model involves the structure A -> B -> C)
fixed

logical; if FALSE then the data are random generated according to a joint multivariate normal distribution
...

additional arguments to be passed to gen_fun. Not used unless a customized gen_fun is defined

Value

a single p-value

Author(s)

Phil Chalmers rphilip.chalmers@gmail.com

See Also

p_glm

Examples

# 5 fixed IVs, R^2 = .1, sample size of 95
p_lm.R2(n=95, R2=.1, k=5)

# random model
p_lm.R2(n=95, R2=.1, k=5, fixed=FALSE)

p-value from Mauchly's Test of Sphericity simulation

Description

Perform simulation experiment for Mauchly's Test of Sphericity using the function mauchlys.test, returning a p-value. Assumes the data are from a multivariate normal distribution, however this can be modified.

Usage

p_mauchly.test(n, sigma, gen_fun = gen_mauchly.test, ...)

gen_mauchly.test(n, sigma, ...)

mauchlys.test(X)

Arguments

n

sample size
sigma

symmetric covariance/correlation matrix passed to gen_fun
gen_fun

function used to generate the required data. Object returned must be a matrix with K columns and n rows. Default uses gen_mauchly.test to generate multivariate normal samples. User defined version of this function must include the argument ...
...

additional arguments to be passed to gen_fun. Not used unless a customized gen_fun is defined
X

a matrix with k columns and n rows

Value

a single p-value

Author(s)

Phil Chalmers rphilip.chalmers@gmail.com

Examples

sigma <- diag(c(1,2,1))
sigma

p_mauchly.test(100, sigma=sigma)

# Null is true
sigma.H0 <- diag(3)
p_mauchly.test(100, sigma=sigma.H0)



    # empirical power estimate
    p_mauchly.test(100, sigma=sigma) |> Spower()

    # empirical Type I error estimate
    p_mauchly.test(100, sigma=sigma.H0) |> Spower()

p-value from McNemar test simulation

Description

Generates two-dimensional sample data for McNemar test and return a p-value. Uses mcnemar.test.

Usage

p_mcnemar.test(
  n,
  prop,
  two.tailed = TRUE,
  correct = TRUE,
  gen_fun = gen_mcnemar.test,
  ...
)

gen_mcnemar.test(n, prop, ...)

Arguments

n

total sample size
prop

two-dimensional matrix of proportions/probabilities
two.tailed

logical; should a two-tailed or one-tailed test be used?
correct

logical; use continuity correction? Only applicable for 2x2 tables
gen_fun

function used to generate the required discrete data. Object returned must be a matrix with k rows and k columns of counts. Default uses gen_mcnemar.test. User defined version of this function must include the argument ...
...

additional arguments to be passed to gen_fun. Not used unless a customized gen_fun is defined

Value

a single p-value

Author(s)

Phil Chalmers rphilip.chalmers@gmail.com

See Also

gen_mcnemar.test

Examples

# from ?mcnemar.test
Performance <- matrix(c(794, 86, 150, 570),
		   nrow = 2,
		   dimnames = list("1st Survey" = c("Approve", "Disapprove"),
		               "2nd Survey" = c("Approve", "Disapprove")))
(prop <- prop.table(Performance))

# one sample + test and resulting p-value
p_mcnemar.test(n=sum(Performance), prop=prop)



# post-hoc power (not recommended)
Spower(p_mcnemar.test(n=sum(Performance), prop=prop))

p-value from three-variable mediation analysis simulation

Description

Simple 3-variable mediation analysis simulation to test the hypothesis that X -> Y is mediated by the relationship X -> M -> Y. Currently, M and Y are assumed to be continuous variables with Gaussian errors, while X may be continuous or dichotomous.

Usage

p_mediation(
  n,
  a,
  b,
  cprime,
  dichotomous.X = FALSE,
  two.tailed = TRUE,
  method = "wald",
  sd.X = 1,
  sd.Y = 1,
  sd.M = 1,
  gen_fun = gen_mediation,
  ...
)

gen_mediation(
  n,
  a,
  b,
  cprime,
  dichotomous.X = FALSE,
  sd.X = 1,
  sd.Y = 1,
  sd.M = 1,
  ...
)

Arguments

n

total sample size unless dichotomous.X = TRUE, in which the value represents the size per group
a

regression coefficient for the path X -> M
b

regression coefficient for the path M -> Y
cprime

partial regression coefficient for the path X -> Y
dichotomous.X

logical; should the X variable be generated as though it were dichotomous? If TRUE then n represents the sample size per group
two.tailed

logical; should a two-tailed or one-tailed test be used?
method

type of inferential method to use. Default uses the Wald (a.k.a., Sobel) test
sd.X

standard deviation for X
sd.Y

standard deviation for Y
sd.M

standard deviation for M
gen_fun

function used to generate the required two-sample data. Object returned must be a data.frame with the columns "DV" and "group". Default uses gen_mediation to generate conditionally Gaussian distributed samples. User defined version of this function must include the argument ...
...

additional arguments to be passed to gen_fun. Not used unless a customized gen_fun is defined

Value

a single p-value

Author(s)

Phil Chalmers rphilip.chalmers@gmail.com

See Also

gen_mediation

Examples

# joint test H0: a*b = 0
p_mediation(50, a=sqrt(.35), b=sqrt(.35), cprime=.39)
p_mediation(50, a=sqrt(.35), b=sqrt(.35), cprime=.39, dichotomous.X=TRUE)



  # power to detect mediation
  p_mediation(n=50, a=sqrt(.35), b=sqrt(.35), cprime=.39) |>
    Spower(parallel=TRUE, replications=1000)

  # sample size estimate for .95 power
  p_mediation(n=NA, a=sqrt(.35), b=sqrt(.35), cprime=.39) |>
    Spower(power=.95, interval=c(50, 200), parallel=TRUE)

p-value from proportion test simulation

Description

Generates single and multi-sample data for proportion tests and return a p-value. Uses binom.test for one-sample applications and prop.test otherwise.

Usage

p_prop.test(
  n,
  h,
  prop = NULL,
  pi = 0.5,
  n.ratios = rep(1, length(prop)),
  two.tailed = TRUE,
  correct = TRUE,
  exact = FALSE,
  gen_fun = gen_prop.test,
  ...
)

gen_prop.test(
  n,
  h,
  prop = NULL,
  pi = 0.5,
  n.ratios = rep(1, length(prop)),
  ...
)

Arguments

n

sample size per group
h

Cohen's h effect size; only supported for one-sample analysis.

Note that it's important to specify the null value pi when supplying this effect size as the power changes depending on these specific values (see example below).
prop

sample probability/proportions of success. If a vector with two-values or more elements are supplied then a multi-samples test will be used. Matrices are also supported
pi

probability of success to test against (default is .5). Ignored for two-sample tests
n.ratios

allocation ratios reflecting the sample size ratios. Default of 1 sets the groups to be the same size (n * n.ratio)
two.tailed

logical; should a two-tailed or one-tailed test be used?
correct

logical; use Yates' continuity correction?
exact

logical; use fisher's exact test via fisher.test? Use of this flag requires that prop was specified as a matrix
gen_fun

function used to generate the required discrete data. Object returned must be a matrix with two rows and 1 or more columns. Default uses gen_prop.test. User defined version of this function must include the argument ...
...

additional arguments to be passed to gen_fun. Not used unless a customized gen_fun is defined

Value

a single p-value

Author(s)

Phil Chalmers rphilip.chalmers@gmail.com

See Also

gen_prop.test

Examples

# one sample, 50 observations, tested against pi = .5 by default
p_prop.test(50, prop=.65)

# specified using h and pi
h <- pwr::ES.h(.65, .4)
p_prop.test(50, h=h, pi=.4)
p_prop.test(50, h=-h, pi=.65)

# two-sample test
p_prop.test(50, prop=c(.5, .65))

# two-sample test, unequal ns
p_prop.test(50, prop=c(.5, .65), n.ratios = c(1,2))

# three-sample test, group2 twice as large as others
p_prop.test(50, prop=c(.5, .65, .7), n.ratios=c(1,2,1))

# Fisher exact test
p_prop.test(50, prop=matrix(c(.5, .65, .7, .5), 2, 2))


    # compare simulated results to pwr package

    # one-sample tests
    (h <- pwr::ES.h(0.5, 0.4))
    pwr::pwr.p.test(h=h, n=60)

    # uses binom.test (need to specify null location as this matters!)
    Spower(p_prop.test(n=60, h=h, pi=.4))
    Spower(p_prop.test(n=60, prop=.5, pi=.4))

    # compare with switched null
    Spower(p_prop.test(n=60, h=h, pi=.5))
    Spower(p_prop.test(n=60, prop=.4, pi=.5))

    # two-sample test, one-tailed
    (h <- pwr::ES.h(0.67, 0.5))
    pwr::pwr.2p.test(h=h, n=80, alternative="greater")
    p_prop.test(n=80, prop=c(.67, .5), two.tailed=FALSE,
      correct=FALSE) |> Spower()

    # same as above, but with continuity correction (default)
    p_prop.test(n=80, prop=c(.67, .5), two.tailed=FALSE) |>
      Spower()

    # three-sample joint test, equal n's
    p_prop.test(n=50, prop=c(.6,.4,.7)) |> Spower()

p-value from correlation simulation

Description

Generates correlated X-Y data and returns a p-value to assess the null of no correlation in the population. The X-Y data are generated assuming a bivariate normal distribution.

Usage

p_r(n, r, rho = 0, method = "pearson", two.tailed = TRUE, gen_fun = gen_r, ...)

gen_r(n, r, ...)

Arguments

n

sample size
r

correlation
rho

population coefficient to test against. Uses the Fisher's z-transformation approximation when non-zero
method

method to use to compute the correlation (see cor.test). Only used when rho = 0
two.tailed

logical; should a two-tailed or one-tailed test be used?
gen_fun

function used to generate the required dependent bivariate data. Object returned must be a matrix with two columns and n rows. Default uses gen_r to generate conditionally dependent data from a bivariate normal distribution. User defined version of this function must include the argument ...
...

additional arguments to be passed to gen_fun. Not used unless a customized gen_fun is defined

Value

a single p-value

Author(s)

Phil Chalmers rphilip.chalmers@gmail.com

See Also

gen_r

Examples

# 50 observations, .5 correlation
p_r(50, r=.5)
p_r(50, r=.5, method = 'spearman')

# test against constant other than rho = .6
p_r(50, .5, rho=.60)



    # compare simulated results to pwr package

    pwr::pwr.r.test(r=0.3, n=50)
    p_r(n=50, r=0.3) |> Spower()

    pwr::pwr.r.test(r=0.3, power=0.80)
    p_r(n=NA, r=0.3) |> Spower(power=.80, interval=c(10, 200))

    pwr::pwr.r.test(r=0.1, power=0.80)
    p_r(n=NA, r=0.1) |> Spower(power=.80, interval=c(200, 1000))

p-value from tetrachoric/polychoric or polyserial

Description

Generates correlated X-Y data and returns a p-value to assess the null of no correlation in the population. The X-Y data are generated assuming a multivariate normal distribution and subsequently discretized for one or both of the variables.

Usage

p_r.cat(
  n,
  r,
  tauX,
  rho = 0,
  tauY = NULL,
  ML = TRUE,
  two.tailed = TRUE,
  score = FALSE,
  gen_fun = gen_r,
  ...
)

Arguments

n

sample size
r

correlation prior to the discretization (recovered via the polyserial/polychoric estimates)
tauX

intercept parameters used for discretizing the X variable
rho

population coefficient to test against
tauY

intercept parameters used for discretizing the Y variable. If missing a polyserial correlation will be estimated, otherwise a tetrachoric/polychoric correlation will be estimated
ML

logical; use maximum-likelihood estimation?
two.tailed

logical; should a two-tailed or one-tailed test be used?
score

logical; should the SE be based at the null hypothesis (score test) or the ML estimate (Wald test)? The former is the canonical form for a priori power analyses though requires twice as many computations as the Wald test approach
gen_fun

function used to generate the required continuous bivariate data (prior to truncation). Object returned must be a matrix with two columns. Default uses gen_r to generate conditionally dependent data from a bivariate normal distribution. User defined version of this function must include the argument ...
...

additional arguments to be passed to gen_fun. Not used unless a customized gen_fun is defined

Value

a single p-value

Author(s)

Phil Chalmers rphilip.chalmers@gmail.com

See Also

gen_r

Examples

# 100 observations, .5 correlation, tetrachoric estimate
p_r.cat(100, r=.5, tauX=0, tauY=1)

# Wald test
p_r.cat(100, r=.5, tauX=0, tauY=1, score=FALSE)

# polyserial estimate (Y continuous)
p_r.cat(50, r=.5, tauX=0)

p-value from Scale Test simulation

Description

Simulates data given one or two parent distributions and returns a p-value testing that the scale of the type distributions are the same. Default implementation uses Gaussian distributions, however the distribution function may be modified to reflect other populations of interest. Uses ansari.test or mood.test for the analysis.

Usage

p_scale(
  n,
  scale,
  n2_n1 = 1,
  two.tailed = TRUE,
  exact = NULL,
  test = "Ansari",
  parent = function(n, ...) rnorm(n),
  ...
)

Arguments

n

sample size per group
scale

the scale to multiply the second group by (1 reflects equal scaling)
n2_n1

sample size ratio
two.tailed

logical; use two-tailed test?
exact

a logical indicating whether an exact p-value should be computed
test

type of method to use. Can be either 'Ansari' or 'Mood'
parent

data generation function (default assumes Gaussian shape). Must be population mean centered
...

additional arguments to pass to simulation functions (if used)

Value

a single p-value

Author(s)

Phil Chalmers rphilip.chalmers@gmail.com

Examples

# n=30 per group,
#  Distributions Gaussian with sd=1 for first group and sd=2 for second
p_scale(30, scale=2)
p_scale(30, scale=2, test='Mood')

# compare chi-squared distributions
parent <- function(n, df, ...) rchisq(n, df=df) - df
p_scale(30, scale=2, parent=parent, df=3)


  # empirical power of the experiments
  p_scale(30, scale=2) |> Spower()
  p_scale(30, scale=2, test='Mood') |> Spower()

  p_scale(30, scale=2, parent=parent, df=3) |> Spower()
  p_scale(30, scale=2, test='Mood', parent=parent, df=3) |> Spower()

p-value from Shapiro-Wilk Normality Test simulation

Description

Generates univariate distributional data and returns a p-value to assess the null that the population follows a Gaussian distribution shape. Uses shapiro.test.

Usage

p_shapiro.test(dist)

Arguments

dist

expression used to generate the required sample data

Value

a single p-value

Author(s)

Phil Chalmers rphilip.chalmers@gmail.com

Examples

# 50 observations drawn from normal distribution (null is true)
p_shapiro.test(rnorm(50))

# 50 observations from slightly skewed chi-squared distribution (power)
p_shapiro.test(rchisq(50, df=100))


    # empirical Type I error rate estimate
    p_shapiro.test(rnorm(50)) |> Spower()

    # power
    p_shapiro.test(rchisq(50, df=100)) |> Spower()

p-value from independent/paired samples t-test simulation

Description

Generates one or two sets of continuous data group-level data according to Cohen's effect size 'd', and returns a p-value. The data and associated t-test assume that the conditional observations are normally distributed and have have equal variance by default, however these may be modified.

Usage

p_t.test(
  n,
  d,
  mu = 0,
  r = NULL,
  type = c("two.sample", "one.sample", "paired"),
  n2_n1 = 1,
  two.tailed = TRUE,
  var.equal = TRUE,
  means = NULL,
  sds = NULL,
  gen_fun = gen_t.test,
  ...
)

gen_t.test(
  n,
  d,
  n2_n1 = 1,
  r = NULL,
  type = c("two.sample", "one.sample", "paired"),
  means = NULL,
  sds = NULL,
  ...
)

Arguments

n

sample size per group, assumed equal across groups
d

Cohen's standardized effect size d
mu

population mean to test against
r

(optional) instead of specifying d specify a point-biserial correlation. Internally this is transformed into a suitable d value for the power computations
type

type of t-test to use; can be 'two.sample', 'one.sample', or 'paired'
n2_n1

allocation ratio reflecting the same size ratio. Default of 1 sets the groups to be the same size. Only applicable when type = 'two.sample'
two.tailed

logical; should a two-tailed or one-tailed test be used?
var.equal

logical; use the classical or Welch corrected t-test?
means

(optional) vector of means for each group. When specified the input d is ignored
sds

(optional) vector of SDs for each group. When specified the input d is ignored
gen_fun

function used to generate the required two-sample data. Object returned must be a data.frame with the columns "DV" and "group". Default uses gen_t.test to generate conditionally Gaussian distributed samples. User defined version of this function must include the argument ...
...

additional arguments to be passed to gen_fun. Not used unless a customized gen_fun is defined

Value

a single p-value

Author(s)

Phil Chalmers rphilip.chalmers@gmail.com

See Also

gen_t.test

Examples

# sample size of 50 per group, "medium" effect size
p_t.test(n=50, d=0.5)

# point-biserial correlation effect size
p_t.test(n=50, r=.3)

# second group 2x as large as the first group
p_t.test(n=50, d=0.5, n2_n1 = 2)

# specify mean/SDs explicitly
p_t.test(n=50, means = c(0,1), sds = c(2,2))

# paired and one-sample tests
p_t.test(n=50, d=0.5, type = 'paired')
p_t.test(n=50, d=0.5, type = 'one.sample')


  # compare simulated results to pwr package

  pwr::pwr.t.test(d=0.2, n=60, sig.level=0.10,
             type="one.sample", alternative="two.sided")
  p_t.test(n=60, d=0.2, type = 'one.sample', two.tailed=TRUE) |>
         Spower(sig.level=.10)

  pwr::pwr.t.test(d=0.3, power=0.80, type="two.sample",
                  alternative="greater")
  p_t.test(n=NA, d=0.3, type='two.sample', two.tailed=FALSE) |>
         Spower(power=0.80, interval=c(10,200))




###### Custom data generation function

# Generate data such that:
#   - group 1 is from a negatively distribution (reversed X2(10)),
#   - group 2 is from a positively skewed distribution (X2(5))
#   - groups have equal variance, but differ by d = 0.5

args(gen_t.test)   ## can use these arguments as a basis, though must include ...

# arguments df1 and df2 added; unused arguments caught within ...
my.gen_fun <- function(n, d, df1, df2, ...){
 	 group1 <- -1 * rchisq(n, df=df1)
	     group2 <- rchisq(n, df=df2)
	     # scale groups first given moments of the chi-square distribution,
	     #   then add std mean difference
	     group1 <- ((group1 + df1) / sqrt(2*df1))
	     group2 <- ((group2 - df2) / sqrt(2*df2)) + d
	     dat <- data.frame(DV=c(group1, group2),
	        			   group=gl(2, n, labels=c('G1', 'G2')))
	     dat
}

# check the sample data properties
df <- my.gen_fun(n=10000, d=.5, df1=10, df2=5)
with(df, tapply(DV, group, mean))
with(df, tapply(DV, group, sd))

library(ggplot2)
ggplot(df, aes(group, DV, fill=group)) + geom_violin()

p_t.test(n=100, d=0.5, gen_fun=my.gen_fun, df1=10, df2=5)



  # power given Gaussian distributions
  p_t.test(n=100, d=0.5) |> Spower(replications=30000)

  # estimate power given the customized data generating function
  p_t.test(n=100, d=0.5, gen_fun=my.gen_fun, df1=10, df2=5) |>
    Spower(replications=30000)

  # evaluate Type I error rate to see if liberal/conservative given
  # assumption violations (should be close to alpha/sig.level)
  p_t.test(n=100, d=0, gen_fun=my.gen_fun, df1=10, df2=5) |>
    Spower(replications=30000)

p-value from variance test simulation

Description

Generates one or or more sets of continuous data group-level data to perform a variance test, and return a p-value. When two-samples are investigated the var.test function will be used, otherwise functions from the EnvStats package will be used.

Usage

p_var.test(
  n,
  vars,
  n.ratios = rep(1, length(vars)),
  sigma2 = 1,
  two.tailed = TRUE,
  test = "Levene",
  correct = TRUE,
  gen_fun = gen_var.test,
  ...
)

gen_var.test(n, vars, n.ratios = rep(1, length(vars)), ...)

Arguments

n

sample size per group, assumed equal across groups
vars

a vector of variances to use for each group; length of 1 for one-sample tests
n.ratios

allocation ratios reflecting the sample size ratios. Default of 1 sets the groups to be the same size (n * n.ratio)
sigma2

population variance to test against in one-sample test
two.tailed

logical; should a two-tailed or one-tailed test be used?
test

type of test to use in multi-sample applications. Can be either 'Levene' (default), 'Bartlett', or 'Fligner'
correct

logical; use correction when test = 'Bartlett'?
gen_fun

function used to generate the required discrete data. Object returned must be a matrix with k rows and k columns of counts. Default uses gen_var.test. User defined version of this function must include the argument ...
...

additional arguments to be passed to gen_fun. Not used unless a customized gen_fun is defined

Value

a single p-value

Author(s)

Phil Chalmers rphilip.chalmers@gmail.com

See Also

gen_var.test

Examples

# one sample
p_var.test(100, vars=10, sigma2=9)

# three sample
p_var.test(100, vars=c(10, 9, 11))
p_var.test(100, vars=c(10, 9, 11), test = 'Fligner')
p_var.test(100, vars=c(10, 9, 11), test = 'Bartlett')


  # power to detect three-group variance differences
  p_var.test(n=100, vars=c(10,9,11)) |> Spower()

  # sample size per group to achieve 80% power
  p_var.test(n=NA, vars=c(10,9,11)) |>
         Spower(power=.80, interval=c(100, 1000))

p-value from Wilcox test simulation

Description

Simulates data given one or two parent distributions and returns a p-value. Can also be used for power analyses related to sign tests.

Usage

p_wilcox.test(
  n,
  d,
  n2_n1 = 1,
  mu = 0,
  type = c("two.sample", "one.sample", "paired"),
  exact = NULL,
  correct = TRUE,
  two.tailed = TRUE,
  parent1 = function(n, d) rnorm(n, d, 1),
  parent2 = function(n, d) rnorm(n, 0, 1)
)

Arguments

n

sample size per group
d

effect size passed to parent functions
n2_n1

sample size ratio
mu

parameter used to form the null hypothesis
type

type of analysis to use (two-sample, one-sample, or paired)
exact

a logical indicating whether an exact p-value should be computed
correct

a logical indicating whether to apply continuity correction in the normal approximation for the p-value
two.tailed

logical; use two-tailed test?
parent1

data generation function for first group. Ideally should have SDs = 1 so that d reflects a standardized difference
parent2

same as parent1, but for the second group

Value

a single p-value

Author(s)

Phil Chalmers rphilip.chalmers@gmail.com

Examples

# with normal distributions defaults d is standardized
p_wilcox.test(100, .5)
p_wilcox.test(100, .5, type = 'paired')
p_wilcox.test(100, .5, type = 'one.sample')

# using chi-squared distributions (standardizing to 0-1)
p_wilcox.test(100, .5, type = 'one.sample',
   parent1 = function(n, d) rchisq(n, df=10) - 10 + d)
p_wilcox.test(100, .5,
   parent1 = function(n, d) (rchisq(n, df=10) - 10)/sqrt(20) + d,
   parent2 = function(n, d) (rchisq(n, df=10) - 10)/sqrt(20))

Simulation-based Power Analyses

Description

General purpose function that provides power-focused estimates for a priori, prospective/post-hoc, compromise, sensitivity, and criterion power analysis. Function provides a general wrapper to the SimDesign package's runSimulation and SimSolve functions. As such, parallel processing is automatically supported, along with progress bars, confidence/prediction intervals for the results estimates, safety checks, and more.

Usage

Spower(
  ...,
  power = NA,
  sig.level = 0.05,
  interval,
  beta_alpha,
  replications = 10000,
  integer,
  parallel = FALSE,
  cl = NULL,
  packages = NULL,
  ncores = parallelly::availableCores(omit = 1L),
  predCI = 0.95,
  predCI.tol = 0.01,
  verbose = TRUE,
  check.interval = FALSE,
  maxiter = 150,
  wait.time = NULL,
  control = list()
)

## S3 method for class 'Spower'
print(x, ...)

Arguments

...

expression to use in the simulation that returns a numeric vector containing only p-value information, where the first p-value in this vector is treated as the focus for all analyses other than prospective/post-hoc power, or a similarly structure logical vector when utilizing confidence intervals (CIs).

Internally the first expression is passed to either SimSolve or runSimulation depending on which element (including the power and sig.level arguments) is set to NA. For instance, Spower(p_t.test(n=50, d=.5)) will perform a prospective/post-hoc power evaluation since power = NA by default, while Spower(p_t.test(n=NA, d=.5), power = .80) will perform an a priori power analysis to solve the missing n argument.

For expected power computations the arguments to this expression can themselves be specified as a function to reflect the prior uncertainty. For instance, if d_prior <- function() rnorm(1, mean=.5, sd=1/8) then Spower(p_t.test(n=50, d=d_prior()) will compute the expected power over the prior sampling distribution for d
power

power level to use. If set to NA then the empirical power will be estimated given the fixed ... inputs (e.g., for prospective/post-hoc power analysis)
sig.level

alpha level to use. If set to NA then the empirical alpha will be estimated given the fixed conditions input (e.g., for criterion power analysis)
interval

search interval to use when SimSolve is required. Note that for compromise analyses, where the sig.level is set to NA, if not set explicitly then the interval will default to c(0,1)
beta_alpha

(optional) ratio to use in compromise analyses corresponding to the Type II errors (beta) over the Type I error (alpha). Ratios greater than 1 indicate that Type I errors are worse than Type II, while ratios less than one the opposite. A ratio equal to 1 gives an equal trade-off between Type I and Type II errors
replications

number of replications to use when runSimulation is required
integer

a logical value indicating whether the search iterations use integers or doubles.

If missing, automatically set to FALSE if interval contains non-integer numbers or the range is less than 5, as well as when sig.level = NA, though in general this should be set explicitly
parallel

for parallel computing for slower simulation experiments (see runSimulation for details).
cl

see runSimulation
packages

see runSimulation
ncores

see runSimulation
predCI

predicting confidence interval level (see SimSolve)
predCI.tol

predicting confidence interval consistency tolerance for stochastic root solver convergence (see SimSolve). Default converges when the power rate CI is consistently within .01/2 of the target power
verbose

logical; should information be printed to the console?
check.interval

logical; check the interval range validity (see SimSolve). Disabled by default
maxiter

maximum number of stochastic root-solving iterations
wait.time

(optional) argument to indicate the time to wait (specified in minutes if supplied as a numeric vector). See SimSolve for details and See timeFormater for further specifications
control

a list of control parameters to pass to runSimulation or SimSolve
x

object of class 'Spower'

Details

Five types of power analysis flavors can be performed with Spower, which are triggered based on which supplied input is set to missing (NA):

A Priori

Solve for a missing sample size component (e.g., n) to achieve a specific target power rate

Prospective (and Post-hoc)

Estimate the power rate given a set of fixed conditions. If estimates of effect sizes and other empirical characteristics (e.g., observed sample size) are supplied instead this results in post-hoc/observed/retrospective power (not recommended)

Sensitivity

Solve a missing effect size value as a function of the other supplied constant components

Criterion

Solve the error rate (argument sig.level) as a function of the other supplied constant components

Compromise

Solve a Type I/Type II error trade-off ratio as a function of the other supplied constant components and the target ratio q=β/αq = \beta/\alpha (argument beta_alpha)

Prospective and compromise analyses utilize the runSimulation function, while the remaining three approaches utilize the stochastic root solving methods in the function SimSolve. See the example below for a demonstration with an independent samples t-test analysis.

Value

an invisible tibble/data.frame-type object of class 'Spower' containing the power results from the simulation experiment

Author(s)

Phil Chalmers rphilip.chalmers@gmail.com

See Also

update, SpowerCurve, getLastSpower

Examples

############################
# Independent samples t-test
############################

# Internally defined p_t.test function
args(p_t.test)    # missing arguments required for Spower()
# help(p_t.test)  # additional information

# p_* functions generate data and return single p-value
p_t.test(n=50, d=.5)
p_t.test(n=50, d=.5)

# test that it works
Spower(p_t.test(n = 50, d = .5), replications=10)

# also behaves naturally with a pipe
p_t.test(n = 50, d = .5) |> Spower(replications=10)



# Estimate power given fixed inputs (prospective power analysis)
out <- Spower(p_t.test(n = 50, d = .5))
summary(out)   # extra information
as.data.frame(out)  # coerced to data.frame

# increase precision
p_t.test(n = 50, d = .5) |> Spower(replications=30000)

# previous analysis not stored to object, but can be retrieved
out <- getLastSpower()
out   # as though it were stored from Spower()

# Same as above, but executed with multiple cores (not run)
p_t.test(n = 50, d = .5) |>
   Spower(replications=30000, parallel=TRUE, ncores=2)

# Solve N to get .80 power (a priori power analysis)
p_t.test(n = NA, d = .5) |>
  Spower(power=.8, interval=c(2,500)) -> out
summary(out)  # extra information
plot(out)
plot(out, type = 'history')

# total sample size required
ceiling(out$n) * 2

# same as above, but in parallel with 2 cores
out.par <- p_t.test(n = NA, d = .5) |>
  Spower(power=.8, interval=c(2,500), parallel=TRUE, ncores=2)
summary(out.par)

# similar information from pwr package
(pwr <- pwr::pwr.t.test(d=.5, power=.80))
ceiling(pwr$n) * 2

# If greater precision is required and the user has a specific amount of time
# they are willing to wait (e.g., 5 minutes) then wait.time can be used. Below
# estimates root after searching for 1 minute, and run in parallel
#  with 2 cores (not run)
p_t.test(n = NA, d = .5) |>
  Spower(power=.8, interval=c(2,500), wait.time='1', parallel=TRUE, ncores=2)

# Solve d to get .80 power (sensitivity power analysis)
p_t.test(n = 50, d = NA) |> Spower(power=.8, interval=c(.1, 2))
pwr::pwr.t.test(n=50, power=.80) # compare

# Solve alpha that would give power of .80 (criterion power analysis)
#    interval not required (set to interval = c(0, 1))
p_t.test(n = 50, d = .5) |> Spower(power=.80, sig.level=NA)

# Solve beta/alpha ratio to specific error trade-off constant
#   (compromise power analysis)
out <- p_t.test(n = 50, d = .5) |> Spower(beta_alpha = 2)
with(out, (1-power)/sig.level)   # solved ratio

# update beta_alpha criteria without re-simulating
(out2 <- update(out, beta_alpha=4))
with(out2, (1-power)/sig.level)   # solved ratio

##############
# Power Curves
##############

# SpowerCurve() has similar input, though requires varying argument
p_t.test(d=.5) |> SpowerCurve(n=c(30, 60, 90))

# solve n given power and plot
p_t.test(n=NA, d=.5) |> SpowerCurve(power=c(.2, .5, .8), interval=c(2,500))

# multiple varying components
p_t.test() |> SpowerCurve(n=c(30,60,90), d=c(.2, .5, .8))

################
# Expected Power
################

# Expected power computed by including effect size uncertainty.
# For instance, belief is that the true d is somewhere around d ~ N(.5, 1/8)
dprior <- function(x, mean=.5, sd=1/8) dnorm(x, mean=mean, sd=sd)
curve(dprior, -1, 2, main=expression(d %~% N(0.5, 1/8)),
      xlab='d', ylab='density')

# For Spower, define prior sampler for specific parameter(s)
d_prior <- function() rnorm(1, mean=.5, sd=1/8)
d_prior(); d_prior(); d_prior()

# Replace d constant with d_prior to compute expected power
p_t.test(n = 50, d = d_prior()) |> Spower()

# A priori power analysis using expected power
p_t.test(n = NA, d = d_prior()) |>
  Spower(power=.8, interval=c(2,500))
pwr::pwr.t.test(d=.5, power=.80) # expected power result higher than fixed d


###############
# Customization
###############

#   Make edits to the function for customization
if(interactive()){
    p_my_t.test <- edit(p_t.test)
    args(p_my_t.test)
    body(p_my_t.test)
}

# Alternatively, define a custom function (potentially based on the template)
p_my_t.test <- function(n, d, var.equal=FALSE, n2_n1=1, df=10){

    # Welch power analysis with asymmetric distributions
    # group2 as large as group1 by default

    # degree of skewness controlled via chi-squared distribution's df
    group1 <- rchisq(n, df=df)
    group1 <-  (group1 - df) / sqrt(2*df)   # Adjusted mean to 0, sd = 1
    group2 <- rnorm(n*n2_n1, mean=d)
    dat <- data.frame(group = factor(rep(c('G1', 'G2'),
                                     times = c(n, n*n2_n1))),
    				  DV = c(group1, group2))
    obj <- t.test(DV ~ group, dat, var.equal=var.equal)
    p <- obj$p.value
    p
}

# Solve N to get .80 power (a priori power analysis), using defaults
p_my_t.test(n = NA, d = .5, n2_n1=2) |>
  Spower(power=.8, interval=c(2,500)) -> out

# total sample size required
with(out, ceiling(n) + ceiling(n * 2))

# Solve N to get .80 power (a priori power analysis), assuming
#   equal variances, group2 2x as large as group1, large skewness
p_my_t.test(n = NA, d=.5, var.equal=TRUE, n2_n1=2, df=3) |>
  Spower(power=.8, interval=c(30,100)) -> out2

# total sample size required
with(out2, ceiling(n) + ceiling(n * 2))

# prospective power, can be used to extract the adjacent information
p_my_t.test(n = 100, d = .5) |> Spower() -> post

Draw power curve from simulation functions

Description

Draws power curves that either a) estimate the power given a set of varying conditions or b) solves a set of root conditions given fixed values of power. Confidence/prediction intervals are included in the output to reflect the estimate uncertainties, though note that fewer replications/iterations are used compared to Spower as the goal is visualization of competing variable inputs rather than precision of a given input.

Usage

SpowerCurve(
  ...,
  interval = NULL,
  power = NA,
  sig.level = 0.05,
  replications = 2500,
  integer,
  plotCI = TRUE,
  plotly = TRUE,
  parallel = FALSE,
  cl = NULL,
  ncores = parallelly::availableCores(omit = 1L),
  predCI = 0.95,
  predCI.tol = 0.01,
  verbose = TRUE,
  check.interval = FALSE,
  maxiter = 50,
  wait.time = NULL,
  control = list()
)

Arguments

...

first expression input must be identical to ... in Spower, while the remaining named inputs must match the arguments to this expression to indicate which variables should be modified in the resulting power curves. Providing NA values is also supported to solve the missing component

Note that only the first three named arguments will be plotted using the x-y, colour, and facet wrap aesthetics, respectively. However, if necessary the data can be extracted for further visualizations via ggplot_build to provide more customized control
interval

search interval to use when SimSolve is required. Can be a vector of length two to apply the same interval across the varying information or a matrix with two columns to apply intervals on a per-row basis
power

power level to use. If set to NA then the empirical power will be estimated given the fixed ... input; otherwise, can be specified as a vector to solve the missing elements in ...
sig.level

see Spower
replications

see Spower, though set to 2500 instead of 10000
integer

see Spower
plotCI

logical; include confidence/prediction intervals in plots?
plotly

logical; draw the graphic into the interactive plotly interface? If FALSE the ggplot2 object will be returned instead
parallel

see Spower
cl

see Spower
ncores

see Spower
predCI

see Spower
predCI.tol

see Spower
verbose

see Spower
check.interval

see Spower, though is set to FALSE by default instead
maxiter

see Spower, though set to 50 instead of 150
wait.time

see Spower
control

see Spower

Value

a ggplot2 object automatically rendered with plotly for interactivity

Author(s)

Phil Chalmers rphilip.chalmers@gmail.com

See Also

Spower

Examples

# estimate power given varying sample sizes
gg <- p_t.test(d=0.2) |> SpowerCurve(n=c(30, 90, 270, 550))

# Output is a ggplot2 (rendered with plotly by default); hence, can be modified
library(ggplot2)
gg + geom_text(aes(label=power), size=5, colour='red', nudge_y=.05) +
  ylab(expression(1-beta)) + theme_grey()

# Increase precision by using 10000 replications. Parallel computations
#   generally recommended in this case to save time
p_t.test(d=0.2) |> SpowerCurve(n=c(30, 90, 270, 550), replications=10000)

# estimate sample sizes given varying power
p_t.test(n=NA, d=0.2) |>
  SpowerCurve(power=c(.2, .4, .6, .8), interval=c(10, 1000))

# get information from last printed graphic instead of saving
gg <- last_plot()
gg + coord_flip() # flip coordinates to put power on y-axis

# estimate power varying d
p_t.test(n=50) |> SpowerCurve(d=seq(.1, 1, by=.2))

# estimate d varying power
p_t.test(n=50, d=NA) |>
  SpowerCurve(power=c(.2, .4, .6, .8), interval=c(.01, 1))


#####

# vary two inputs instead of one (second input uses colour aesthetic)
p_t.test() |> SpowerCurve(n=c(30, 90, 270, 550),
                         d=c(.2, .5, .8))

# extract data for alternative presentations
build <- ggplot_build(last_plot())
build

df <- build$plot$data
head(df)
ggplot(df, aes(n, power, linetype=d)) + geom_line()

# vary three arguments (third uses facet_wrap ... any more than that and
#   you're on your own!)
p_t.test() |> SpowerCurve(n=c(30, 90, 270, 550),
                         d=c(.2, .5, .8),
                         var.equal=c(FALSE, TRUE))

Update compromise or prospective/post-hoc power analysis without re-simulating

Description

When a power or compromise analysis was performed in Spower this function can be used to update the compromise or power criteria without the need for re-simulating the experiment. For compromise analyses a beta_alpha criteria must be supplied, while for prospective/post-hoc power analyses the sig.level must be supplied.

Usage

## S3 method for class 'Spower'
update(object, sig.level = 0.05, beta_alpha = NULL, predCI = 0.95, ...)

Arguments

object

object returned from Spower where power was estimated or the bete_alpha criteria were supplied
sig.level

Type I error rate (alpha)
beta_alpha

Type II/Type I error ratio
predCI

confidence interval precision (see Spower for similar input)
...

arguments to be passed

Value

object of class Spower with updated information

Author(s)

Phil Chalmers rphilip.chalmers@gmail.com

Examples

########
## Prospective power analysis update

# Estimate power using sig.level = .05 (default)
out <- p_t.test(n = 50, d = .5) |> Spower()

# update power estimate given sig.level=.01 and .20
update(out, sig.level=.01)
update(out, sig.level=.20)


########
## Compromise analysis update

# Solve beta/alpha ratio to specific error trade-off constant
out <- p_t.test(n = 50, d = .5) |> Spower(beta_alpha = 2)

# update beta_alpha criteria without re-simulating
update(out, beta_alpha=4)

# also works if compromise not initially run but prospective/post-hoc power was
out <- p_t.test(n = 50, d = .5) |> Spower()
update(out, beta_alpha=4)