| Title: | Synthesise and Correlate Likert Scale and Related Rating-Scale Data |
|---|---|
| Description: | Synthesise Likert scale and related rating-scale data with predefined first and second moments (mean and standard deviation), and, optionally, correlate multiple vectors using a predefined correlation matrix. Additionally, generate synthetic rating-scale items with a predefined Cronbach's Alpha, or create rating-scale items based on a predefined summated scale. |
| Authors: | Hume Winzar [cre, aut]
|
| Maintainer: | Hume Winzar <[email protected]> |
| License: | MIT + file LICENSE |
| Version: | 0.4.0 |
| Built: | 2024-11-20 07:53:07 UTC |
| Source: | CRAN |
alpha() calculate Cronbach's Alpha from a given
correlation matrix or a given dataframe.
alpha(cormatrix = NULL, data = NULL)alpha(cormatrix = NULL, data = NULL)
cormatrix |
(real) a square symmetrical matrix with values ranging from -1 to +1 and '1' in the diagonal |
data |
(real) a dataframe or matrix |
a single value
## Sample data frame df <- data.frame( V1 = c(4, 2, 4, 3, 2, 2, 2, 1), V2 = c(4, 1, 3, 4, 4, 3, 2, 3), V3 = c(4, 1, 3, 5, 4, 1, 4, 2), V4 = c(4, 3, 4, 5, 3, 3, 3, 3) ) ## example correlation matrix corMat <- matrix( c( 1.00, 0.35, 0.45, 0.70, 0.35, 1.00, 0.60, 0.55, 0.45, 0.60, 1.00, 0.65, 0.70, 0.55, 0.65, 1.00 ), nrow = 4, ncol = 4 ) ## apply function examples alpha(cormatrix = corMat) alpha(, df) alpha(corMat, df)## Sample data frame df <- data.frame( V1 = c(4, 2, 4, 3, 2, 2, 2, 1), V2 = c(4, 1, 3, 4, 4, 3, 2, 3), V3 = c(4, 1, 3, 5, 4, 1, 4, 2), V4 = c(4, 3, 4, 5, 3, 3, 3, 3) ) ## example correlation matrix corMat <- matrix( c( 1.00, 0.35, 0.45, 0.70, 0.35, 1.00, 0.60, 0.55, 0.45, 0.60, 1.00, 0.65, 0.70, 0.55, 0.65, 1.00 ), nrow = 4, ncol = 4 ) ## apply function examples alpha(cormatrix = corMat) alpha(, df) alpha(corMat, df)
correlateScales() creates a dataframe of
scale items representing correlated constructs,
as one might find in a completed questionnaire.
correlateScales(dataframes, scalecors)correlateScales(dataframes, scalecors)
dataframes |
a list of 'k' dataframes to be rearranged and combined |
scalecors |
target correlation matrix - should be a symmetric k*k positive-semi-definite matrix, where 'k' is the number of dataframes |
Correlated rating-scale items generally are summed or averaged to create a measure of an "unobservable", or "latent", construct.
correlateScales() takes several such dataframes of rating-scale
items and rearranges their rows so that the scales are correlated according
to a predefined correlation matrix. Univariate statistics for each dataframe
of rating-scale items do not change,
but their correlations with rating-scale items in other dataframes do.
Returns a dataframe whose columns are taken from the starter dataframes and whose summated values are correlated according to a user-specified correlation matrix
## three attitudes and a behavioural intention n <- 32 lower <- 1 upper <- 5 ### attitude #1 cor_1 <- makeCorrAlpha(items = 4, alpha = 0.90) means_1 <- c(2.5, 2.5, 3.0, 3.5) sds_1 <- c(0.9, 1.0, 0.9, 1.0) Att_1 <- makeItems( n = n, means = means_1, sds = sds_1, lowerbound = rep(lower, 4), upperbound = rep(upper, 4), cormatrix = cor_1 ) ### attitude #2 cor_2 <- makeCorrAlpha(items = 5, alpha = 0.85) means_2 <- c(2.5, 2.5, 3.0, 3.0, 3.5) sds_2 <- c(1.0, 1.0, 0.9, 1.0, 1.5) Att_2 <- makeItems( n = n, means = means_2, sds = sds_2, lowerbound = rep(lower, 5), upperbound = rep(upper, 5), cormatrix = cor_2 ) ### attitude #3 cor_3 <- makeCorrAlpha(items = 6, alpha = 0.75) means_3 <- c(2.5, 2.5, 3.0, 3.0, 3.5, 3.5) sds_3 <- c(1.0, 1.5, 1.0, 1.5, 1.0, 1.5) Att_3 <- makeItems( n = n, means = means_3, sds = sds_3, lowerbound = rep(lower, 6), upperbound = rep(upper, 6), cormatrix = cor_3 ) ### behavioural intention intent <- lfast(n, mean = 3.0, sd = 3, lowerbound = 0, upperbound = 10) |> data.frame() names(intent) <- "int" ### target scale correlation matrix scale_cors <- matrix( c( 1.0, 0.6, 0.5, 0.3, 0.6, 1.0, 0.4, 0.2, 0.5, 0.4, 1.0, 0.1, 0.3, 0.2, 0.1, 1.0 ), nrow = 4 ) data_frames <- list("A1" = Att_1, "A2" = Att_2, "A3" = Att_3, "Int" = intent) ### apply the function my_correlated_scales <- correlateScales( dataframes = data_frames, scalecors = scale_cors ) head(my_correlated_scales)## three attitudes and a behavioural intention n <- 32 lower <- 1 upper <- 5 ### attitude #1 cor_1 <- makeCorrAlpha(items = 4, alpha = 0.90) means_1 <- c(2.5, 2.5, 3.0, 3.5) sds_1 <- c(0.9, 1.0, 0.9, 1.0) Att_1 <- makeItems( n = n, means = means_1, sds = sds_1, lowerbound = rep(lower, 4), upperbound = rep(upper, 4), cormatrix = cor_1 ) ### attitude #2 cor_2 <- makeCorrAlpha(items = 5, alpha = 0.85) means_2 <- c(2.5, 2.5, 3.0, 3.0, 3.5) sds_2 <- c(1.0, 1.0, 0.9, 1.0, 1.5) Att_2 <- makeItems( n = n, means = means_2, sds = sds_2, lowerbound = rep(lower, 5), upperbound = rep(upper, 5), cormatrix = cor_2 ) ### attitude #3 cor_3 <- makeCorrAlpha(items = 6, alpha = 0.75) means_3 <- c(2.5, 2.5, 3.0, 3.0, 3.5, 3.5) sds_3 <- c(1.0, 1.5, 1.0, 1.5, 1.0, 1.5) Att_3 <- makeItems( n = n, means = means_3, sds = sds_3, lowerbound = rep(lower, 6), upperbound = rep(upper, 6), cormatrix = cor_3 ) ### behavioural intention intent <- lfast(n, mean = 3.0, sd = 3, lowerbound = 0, upperbound = 10) |> data.frame() names(intent) <- "int" ### target scale correlation matrix scale_cors <- matrix( c( 1.0, 0.6, 0.5, 0.3, 0.6, 1.0, 0.4, 0.2, 0.5, 0.4, 1.0, 0.1, 0.3, 0.2, 0.1, 1.0 ), nrow = 4 ) data_frames <- list("A1" = Att_1, "A2" = Att_2, "A3" = Att_3, "Int" = intent) ### apply the function my_correlated_scales <- correlateScales( dataframes = data_frames, scalecors = scale_cors ) head(my_correlated_scales)
eigenvalues() calculate eigenvalues of a correlation
matrix and optionally produces a scree plot.
eigenvalues(cormatrix, scree = FALSE)eigenvalues(cormatrix, scree = FALSE)
cormatrix |
(real, matrix) a correlation matrix |
scree |
(logical) default = |
a vector of eigenvalues
report on positive-definite status of cormatrix
## define parameters correlationMatrix <- matrix( c( 1.00, 0.25, 0.35, 0.40, 0.25, 1.00, 0.70, 0.75, 0.35, 0.70, 1.00, 0.80, 0.40, 0.75, 0.80, 1.00 ), nrow = 4, ncol = 4 ) ## apply function evals <- eigenvalues(cormatrix = correlationMatrix) evals <- eigenvalues(correlationMatrix, 1)## define parameters correlationMatrix <- matrix( c( 1.00, 0.25, 0.35, 0.40, 0.25, 1.00, 0.70, 0.75, 0.35, 0.70, 1.00, 0.80, 0.40, 0.75, 0.80, 1.00 ), nrow = 4, ncol = 4 ) ## apply function evals <- eigenvalues(cormatrix = correlationMatrix) evals <- eigenvalues(correlationMatrix, 1)
lcor_C() rearranges values in each column of a
data-frame so that columns are correlated to match a predefined
correlation matrix.
lcor(data, target)lcor(data, target)
data |
data-frame that is to be rearranged |
target |
target correlation matrix - should be a symmetric k*k positive-semi-definite matrix |
Values in a column do not change, so univariate statistics remain the same.
Returns a dataframe whose column-wise correlations approximate a user-specified correlation matrix
## parameters n <- 32 lowerbound <- 1 upperbound <- 5 items <- 5 mydat3 <- data.frame( x1 = lfast(n, 2.5, 0.75, lowerbound, upperbound, items), x2 = lfast(n, 3.0, 1.50, lowerbound, upperbound, items), x3 = lfast(n, 3.5, 1.00, lowerbound, upperbound, items) ) cor(mydat3) |> round(3) tgt3 <- matrix( c( 1.00, 0.50, 0.75, 0.50, 1.00, 0.25, 0.75, 0.25, 1.00 ), nrow = 3, ncol = 3 ) ## apply function new3 <- lcor(mydat3, tgt3) ## test output cor(new3) |> round(3)## parameters n <- 32 lowerbound <- 1 upperbound <- 5 items <- 5 mydat3 <- data.frame( x1 = lfast(n, 2.5, 0.75, lowerbound, upperbound, items), x2 = lfast(n, 3.0, 1.50, lowerbound, upperbound, items), x3 = lfast(n, 3.5, 1.00, lowerbound, upperbound, items) ) cor(mydat3) |> round(3) tgt3 <- matrix( c( 1.00, 0.50, 0.75, 0.50, 1.00, 0.25, 0.75, 0.25, 1.00 ), nrow = 3, ncol = 3 ) ## apply function new3 <- lcor(mydat3, tgt3) ## test output cor(new3) |> round(3)
lexact is DEPRECATED. Replaced by new version of
lfast.
lexact remains as a legacy for earlier package users.
It is now just a wrapper for lfast
Previously, lexact used a Differential Evolution (DE) algorithm to
find an optimum solution with desired mean and standard deviation,
but we found that the updated lfast function is much faster and just
as accurate.
Also the package is much less bulky.
lexact(n, mean, sd, lowerbound, upperbound, items = 1)lexact(n, mean, sd, lowerbound, upperbound, items = 1)
n |
(positive, int) number of observations to generate |
mean |
(real) target mean |
sd |
(real) target standard deviation |
lowerbound |
(positive, int) lower bound (e.g. '1' for a 1-5 rating scale) |
upperbound |
(positive, int) upper bound (e.g. '5' for a 1-5 rating scale) |
items |
(positive, int) number of items in the rating scale. Default = 1 |
a vector of simulated data approximating user-specified conditions.
x <- lexact( n = 256, mean = 4.0, sd = 1.0, lowerbound = 1, upperbound = 7, items = 6 ) x <- lexact(256, 2, 1.8, 0, 10)x <- lexact( n = 256, mean = 4.0, sd = 1.0, lowerbound = 1, upperbound = 7, items = 6 ) x <- lexact(256, 2, 1.8, 0, 10)
lfast() applies a simple Evolutionary Algorithm to
find a vector that best fits the desired moments.
lfast() generates random discrete values from a
scaled Beta distribution so the data replicate a rating scale -
for example, a 1-5 Likert scale made from 5 items (questions) or 0-10
likelihood-of-purchase scale.
lfast(n, mean, sd, lowerbound, upperbound, items = 1, precision = 0)lfast(n, mean, sd, lowerbound, upperbound, items = 1, precision = 0)
n |
(positive, int) number of observations to generate |
mean |
(real) target mean, between upper and lower bounds |
sd |
(positive, real) target standard deviation |
lowerbound |
(positive, int) lower bound (e.g. '1' for a 1-5 rating scale) |
upperbound |
(positive, int) upper bound (e.g. '5' for a 1-5 rating scale) |
items |
(positive, int) number of items in the rating scale. Default = 1 |
precision |
(positive, real) can relax the level of accuracy required. (e.g. '1' generally generates a vector with moments correct within '0.025', '2' generally within '0.05') Default = 0 |
a vector approximating user-specified conditions.
## six-item 1-7 rating scale x <- lfast( n = 256, mean = 4.0, sd = 1.25, lowerbound = 1, upperbound = 7, items = 6 ) ## four-item 1-5 rating scale with medium variation x <- lfast( n = 128, mean = 3.0, sd = 1.00, lowerbound = 1, upperbound = 5, items = 4, precision = 5 ) ## eleven-point 'likelihood of purchase' scale x <- lfast(256, 3, 3.0, 0, 10)## six-item 1-7 rating scale x <- lfast( n = 256, mean = 4.0, sd = 1.25, lowerbound = 1, upperbound = 7, items = 6 ) ## four-item 1-5 rating scale with medium variation x <- lfast( n = 128, mean = 3.0, sd = 1.00, lowerbound = 1, upperbound = 5, items = 4, precision = 5 ) ## eleven-point 'likelihood of purchase' scale x <- lfast(256, 3, 3.0, 0, 10)
makeCorrAlpha() generates a random correlation
matrix of given dimensions and predefined Cronbach's Alpha
makeCorrAlpha(items, alpha, variance = 0.5, precision = 0)makeCorrAlpha(items, alpha, variance = 0.5, precision = 0)
items |
(positive, int) matrix dimensions: number of rows & columns to generate |
alpha |
(real) target Cronbach's Alpha (usually positive, must be between -1 and +1) |
variance |
(positive, real) Default = 0.5. User-provided standard deviation of values sampled from a normally-distributed log transformation. |
precision |
(positive, real) Default = 0. User-defined value ranging from '0' to '3' to add some random variation around the target Cronbach's Alpha. '0' gives an exact alpha (to two decimal places) |
a correlation matrix
Random values generated by makeCorrAlpha() are highly volatile.
makeCorrAlpha() may not generate a feasible (positive-definite)
correlation matrix, especially when
variance is high relative to
desired Alpha, and
desired correlation dimensions
makeCorrAlpha() will inform the user if the resulting correlation
matrix is positive definite, or not.
If the returned correlation matrix is not positive-definite, a feasible solution may still be possible. The user is encouraged to try again, possibly several times, to find one.
# define parameters items <- 4 alpha <- 0.85 variance <- 0.5 # apply function set.seed(42) cor_matrix <- makeCorrAlpha(items = items, alpha = alpha, variance = variance) # test function output print(cor_matrix) alpha(cor_matrix) eigenvalues(cor_matrix, 1) # higher alpha, more items cor_matrix2 <- makeCorrAlpha(items = 8, alpha = 0.95) # test output cor_matrix2 |> round(2) alpha(cor_matrix2) |> round(3) eigenvalues(cor_matrix2, 1) |> round(3) # large random variation around alpha set.seed(42) cor_matrix3 <- makeCorrAlpha(items = 6, alpha = 0.85, precision = 2) # test output cor_matrix3 |> round(2) alpha(cor_matrix3) |> round(3) eigenvalues(cor_matrix3, 1) |> round(3)# define parameters items <- 4 alpha <- 0.85 variance <- 0.5 # apply function set.seed(42) cor_matrix <- makeCorrAlpha(items = items, alpha = alpha, variance = variance) # test function output print(cor_matrix) alpha(cor_matrix) eigenvalues(cor_matrix, 1) # higher alpha, more items cor_matrix2 <- makeCorrAlpha(items = 8, alpha = 0.95) # test output cor_matrix2 |> round(2) alpha(cor_matrix2) |> round(3) eigenvalues(cor_matrix2, 1) |> round(3) # large random variation around alpha set.seed(42) cor_matrix3 <- makeCorrAlpha(items = 6, alpha = 0.85, precision = 2) # test output cor_matrix3 |> round(2) alpha(cor_matrix3) |> round(3) eigenvalues(cor_matrix3, 1) |> round(3)
makeItems() generates a dataframe of random discrete
values so the data replicate a rating scale,
and are correlated close to a predefined correlation matrix.
makeItems() is wrapper function for:
lfast(), generates a dataframe that best fits the desired
moments, and
lcor(), which rearranges values in each column of the dataframe
so they closely match the desired correlation matrix.
makeItems(n, means, sds, lowerbound, upperbound, cormatrix)makeItems(n, means, sds, lowerbound, upperbound, cormatrix)
n |
(positive, int) sample-size - number of observations |
means |
(real) target means: a vector of length k of mean values for each scale item |
sds |
(positive, real) target standard deviations: a vector of length k of standard deviation values for each scale item |
lowerbound |
(positive, int) a vector of length k (same as rows & columns of correlation matrix) of values for lower bound of each scale item (e.g. '1' for a 1-5 rating scale) |
upperbound |
(positive, int) a vector of length k (same as rows & columns of correlation matrix) of values for upper bound of each scale item (e.g. '5' for a 1-5 rating scale) |
cormatrix |
(real, matrix) the target correlation matrix: a square symmetric positive-semi-definite matrix of values ranging between -1 and +1, and '1' in the diagonal. |
a dataframe of rating-scale values
## define parameters n <- 16 dfMeans <- c(2.5, 3.0, 3.0, 3.5) dfSds <- c(1.0, 1.0, 1.5, 0.75) lowerbound <- rep(1, 4) upperbound <- rep(5, 4) corMat <- matrix( c( 1.00, 0.30, 0.40, 0.60, 0.30, 1.00, 0.50, 0.70, 0.40, 0.50, 1.00, 0.80, 0.60, 0.70, 0.80, 1.00 ), nrow = 4, ncol = 4 ) ## apply function df <- makeItems( n = n, means = dfMeans, sds = dfSds, lowerbound = lowerbound, upperbound = upperbound, cormatrix = corMat ) ## test function str(df) # means apply(df, 2, mean) |> round(3) # standard deviations apply(df, 2, sd) |> round(3) # correlations cor(df) |> round(3)## define parameters n <- 16 dfMeans <- c(2.5, 3.0, 3.0, 3.5) dfSds <- c(1.0, 1.0, 1.5, 0.75) lowerbound <- rep(1, 4) upperbound <- rep(5, 4) corMat <- matrix( c( 1.00, 0.30, 0.40, 0.60, 0.30, 1.00, 0.50, 0.70, 0.40, 0.50, 1.00, 0.80, 0.60, 0.70, 0.80, 1.00 ), nrow = 4, ncol = 4 ) ## apply function df <- makeItems( n = n, means = dfMeans, sds = dfSds, lowerbound = lowerbound, upperbound = upperbound, cormatrix = corMat ) ## test function str(df) # means apply(df, 2, mean) |> round(3) # standard deviations apply(df, 2, sd) |> round(3) # correlations cor(df) |> round(3)
makeItemsScale() generates a random dataframe
of scale items based on a predefined summated scale
(such as created by the lfast() function),
and a desired Cronbach's Alpha.
scale, lowerbound, upperbound, items, alpha, variance
makeItemsScale( scale, lowerbound, upperbound, items, alpha = 0.8, variance = 0.5 )makeItemsScale( scale, lowerbound, upperbound, items, alpha = 0.8, variance = 0.5 )
scale |
(int) a vector or dataframe of the summated rating scale. Should range from ('lowerbound' * 'items') to ('upperbound' * 'items') |
lowerbound |
(int) lower bound of the scale item (example: '1' in a '1' to '5' rating) |
upperbound |
(int) upper bound of the scale item (example: '5' in a '1' to '5' rating) |
items |
(positive, int) k, or number of columns to generate |
alpha |
(posiitve, real) desired Cronbach's Alpha for the new dataframe of items. Default = '0.8'. See |
variance |
(positive, real) the quantile from which to select items that give given summated scores. Must lie between '0' and '1'. Default = '0.5'. See |
makeItemsScale() rearranges the item values within each row,
attempting to give a dataframe of Likert-scale items that produce a
predefined Cronbach's Alpha.
Default value for target alpha is '0.8'.
More extreme values for the 'variance' parameter may reduce the chances of achieving the desired Alpha. So you may need to experiment a little.
There may be many ways to find a combination of integers that sum to a specific value, and these combinations have different levels of variance:
low-variance: '3 + 4 = 7'
high-variance: '1 + 6 = 7'
The 'variance' parameter defines guidelines for the amount of variance among item values that your new dataframe should have.
For example, consider a summated value of '9' on which we apply
the makeItemsScale() function to generate three items.
With zero variance (variance parameter = '0'), then we see all items with
the same value, the mean of '3'.
With variance = '1', then we see all items with values
that give the maximum variance among those items.
| variance | v1 | v2 | v3 | sum |
| 0.0 | 3 | 3 | 3 | 9 |
| 0.2 | 3 | 3 | 3 | 9 |
| 0.4 | 2 | 3 | 4 | 9 |
| 0.6 | 1 | 4 | 4 | 9 |
| 0.8 | 2 | 2 | 5 | 9 |
| 1.0 | 1 | 3 | 5 | 9 |
Similarly, the same mean value applied to six items with
makeItemsScale() gives the following combinations at
different values of the 'variance' parameter.
| variance | v1 | v2 | v3 | v4 | v5 | v6 | sum |
| 0.0 | 3 | 3 | 3 | 3 | 3 | 3 | 18 |
| 0.2 | 1 | 3 | 3 | 3 | 4 | 4 | 18 |
| 0.4 | 1 | 2 | 3 | 4 | 4 | 4 | 18 |
| 0.6 | 1 | 1 | 4 | 4 | 4 | 4 | 18 |
| 0.8 | 1 | 1 | 3 | 4 | 4 | 5 | 18 |
| 1.0 | 1 | 1 | 1 | 5 | 5 | 5 | 18 |
And a mean value of '3.5' gives the following combinations.
| variance | v1 | v2 | v3 | v4 | v5 | v6 | sum |
| 0.0 | 3 | 3 | 3 | 4 | 4 | 4 | 21 |
| 0.2 | 3 | 3 | 3 | 3 | 4 | 5 | 21 |
| 0.4 | 2 | 2 | 4 | 4 | 4 | 5 | 21 |
| 0.6 | 1 | 3 | 4 | 4 | 4 | 5 | 21 |
| 0.8 | 1 | 2 | 4 | 4 | 5 | 5 | 21 |
| 1.0 | 1 | 1 | 4 | 5 | 5 | 5 | 21 |
The default value for 'variance' is '0.5' which gives a reasonable range of item values. But if you want 'responses' that are more consistent then choose a lower variance value.
a dataframe with 'items' columns and 'length(scale)' rows
## define parameters k <- 4 lower <- 1 upper <- 5 ## scale properties n <- 64 mean <- 3.0 sd <- 0.85 ## create scale set.seed(42) meanScale <- lfast( n = n, mean = mean, sd = sd, lowerbound = lower, upperbound = upper, items = k ) summatedScale <- meanScale * k ## create new items newItems <- makeItemsScale( scale = summatedScale, lowerbound = lower, upperbound = upper, items = k ) ### test new items str(newItems) alpha(data = newItems) |> round(2) ## create items with higher Alpha but same summated scale newItems <- makeItemsScale( scale = summatedScale, lowerbound = lower, upperbound = upper, items = k, alpha = 0.9, variance = 0.5 ) ### test new items str(newItems) alpha(data = newItems) |> round(2) ## very low variance usually gives higher Cronbach's Alpha mydat_20 <- makeItemsScale( scale = summatedScale, lowerbound = lower, upperbound = upper, items = k, alpha = 0.8, variance = 0.20 ) ### test new data frame str(mydat_20) moments <- data.frame( means = apply(mydat_20, MARGIN = 2, FUN = mean) |> round(3), sds = apply(mydat_20, MARGIN = 2, FUN = sd) |> round(3) ) |> t() moments cor(mydat_20) |> round(2) alpha(data = mydat_20) |> round(2) ## default alpha (0.8) and higher variance (0.8) mydat_80 <- makeItemsScale( scale = summatedScale, lowerbound = lower, upperbound = upper, items = k, variance = 0.80 ) ### test new dataframe str(mydat_80) moments <- data.frame( means = apply(mydat_80, MARGIN = 2, FUN = mean) |> round(3), sds = apply(mydat_80, MARGIN = 2, FUN = sd) |> round(3) ) |> t() moments cor(mydat_80) |> round(2) alpha(data = mydat_80) |> round(2)## define parameters k <- 4 lower <- 1 upper <- 5 ## scale properties n <- 64 mean <- 3.0 sd <- 0.85 ## create scale set.seed(42) meanScale <- lfast( n = n, mean = mean, sd = sd, lowerbound = lower, upperbound = upper, items = k ) summatedScale <- meanScale * k ## create new items newItems <- makeItemsScale( scale = summatedScale, lowerbound = lower, upperbound = upper, items = k ) ### test new items str(newItems) alpha(data = newItems) |> round(2) ## create items with higher Alpha but same summated scale newItems <- makeItemsScale( scale = summatedScale, lowerbound = lower, upperbound = upper, items = k, alpha = 0.9, variance = 0.5 ) ### test new items str(newItems) alpha(data = newItems) |> round(2) ## very low variance usually gives higher Cronbach's Alpha mydat_20 <- makeItemsScale( scale = summatedScale, lowerbound = lower, upperbound = upper, items = k, alpha = 0.8, variance = 0.20 ) ### test new data frame str(mydat_20) moments <- data.frame( means = apply(mydat_20, MARGIN = 2, FUN = mean) |> round(3), sds = apply(mydat_20, MARGIN = 2, FUN = sd) |> round(3) ) |> t() moments cor(mydat_20) |> round(2) alpha(data = mydat_20) |> round(2) ## default alpha (0.8) and higher variance (0.8) mydat_80 <- makeItemsScale( scale = summatedScale, lowerbound = lower, upperbound = upper, items = k, variance = 0.80 ) ### test new dataframe str(mydat_80) moments <- data.frame( means = apply(mydat_80, MARGIN = 2, FUN = mean) |> round(3), sds = apply(mydat_80, MARGIN = 2, FUN = sd) |> round(3) ) |> t() moments cor(mydat_80) |> round(2) alpha(data = mydat_80) |> round(2)