cohens.d: Cohen's d
In misty: Miscellaneous Functions 'T. Yanagida'
cohens.d R Documentation
Cohen's d
Description
This function computes Cohen's d for one-sample, two-sample (i.e., between-subject design),
and paired-sample designs (i.e., within-subject design) for one or more variables, optionally
by a grouping and/or split variable. In a two-sample design, the function computes the
standardized mean difference by dividing the difference between means of the two groups
of observations by the weighted pooled standard deviation (i.e., Cohen's d_s
according to Lakens, 2013) by default. In a paired-sample design, the function computes the
standardized mean difference by dividing the mean of the difference scores by the standard
deviation of the difference scores (i.e., Cohen's d_z according to Lakens, 2013) by
default. Note that by default Cohen's d is computed without applying the correction factor
for removing the small sample bias (i.e., Hedges' g).
Usage
cohens.d(x, ...)
## Default S3 method:
cohens.d(x, y = NULL, mu = 0, paired = FALSE, weighted = TRUE, cor = TRUE,
ref = NULL, correct = FALSE, alternative = c("two.sided", "less", "greater"),
conf.level = 0.95, group = NULL, split = NULL, sort.var = FALSE,
digits = 2, as.na = NULL, write = NULL, append = TRUE,
check = TRUE, output = TRUE, ...)
## S3 method for class 'formula'
cohens.d(formula, data, weighted = TRUE, cor = TRUE, ref = NULL,
correct = FALSE, alternative = c("two.sided", "less", "greater"),
conf.level = 0.95, group = NULL, split = NULL, sort.var = FALSE,
na.omit = FALSE, digits = 2, as.na = NULL, write = NULL, append = TRUE,
check = TRUE, output = TRUE, ...)
Arguments
x
a numeric vector or data frame.
...
further arguments to be passed to or from methods.
y
a numeric vector.
mu
a numeric value indicating the reference mean.
paired
logical: if TRUE, Cohen's d for a paired-sample design is computed.
weighted
logical: if TRUE (default), the weighted pooled standard deviation is used
to compute the standardized mean difference between two groups of a two-sample
design (i.e., paired = FALSE), while standard deviation of the difference
scores is used to compute the standardized mean difference in a paired-sample
design (i.e., paired = TRUE).
cor
logical: if TRUE (default), paired = TRUE, and weighted = FALSE,
Cohen's d for a paired-sample design while controlling for the correlation between
the two sets of measurement is computed. Note that this argument is only used in
a paired-sample design (i.e., paired = TRUE) when specifying weighted = FALSE.
ref
character string "x" or "y" for specifying the reference reference
group when using the default cohens.d() function or a numeric value or
character string indicating the reference group in a two-sample design when using
the formula cohens.d() function. The standard deviation of the reference variable
or reference group is used to standardized the mean difference.
Note that this argument is only used in a two-sample design (i.e., paired = FALSE).
correct
logical: if TRUE, correction factor to remove positive bias in small samples is
used.
alternative
a character string specifying the alternative hypothesis, must be one of
"two.sided" (default), "greater" or "less".
conf.level
a numeric value between 0 and 1 indicating the confidence level of the interval.
group
a numeric vector, character vector or factor as grouping variable.
split
a numeric vector, character vector or factor as split variable.
sort.var
logical: if TRUE, output table is sorted by variables when specifying group.
digits
an integer value indicating the number of decimal places to be used for
displaying results.
as.na
a numeric vector indicating user-defined missing values,
i.e. these values are converted to NA before conducting the analysis.
Note that as.na() function is only applied to y but not to group
in a two-sample design, while as.na() function is applied to pre
and post in a paired-sample design.
write
a character string naming a text file with file extension
".txt" (e.g., "Output.txt") for writing the
output into a text file.
append
logical: if TRUE (default), output will be appended
to an existing text file with extension .txt specified
in write, if FALSE existing text file will be
overwritten.
check
logical: if TRUE (default), argument specification is checked.
output
logical: if TRUE (default), output is shown on the console.
formula
a formula of the form y ~ group for one outcome variable or
cbind(y1, y2, y3) ~ group for more than one outcome variable where y
is a numeric variable giving the data values and group a numeric variable,
character variable or factor with two values or factor levels giving the
corresponding groups.
data
a matrix or data frame containing the variables in the formula formula.
na.omit
logical: if TRUE, incomplete cases are removed before conducting the analysis
(i.e., listwise deletion) when specifying more than one outcome variable.
Details
Cohen (1988, p.67) proposed to compute the standardized mean difference in a two-sample design
by dividing the mean difference by the unweighted pooled standard deviation (i.e.,
weighted = FALSE).
Glass et al. (1981, p. 29) suggested to use the standard deviation of the control group
(e.g., ref = 0 if the control group is coded with 0) to compute the standardized
mean difference in a two-sample design (i.e., Glass's \Delta) since the standard deviation of the control group
is unaffected by the treatment and will therefore more closely reflect the population
standard deviation.
Hedges (1981, p. 110) recommended to weight each group's standard deviation by its sample
size resulting in a weighted and pooled standard deviation (i.e., weighted = TRUE,
default). According to Hedges and Olkin (1985, p. 81), the standardized mean difference
based on the weighted and pooled standard deviation has a positive small sample bias,
i.e., standardized mean difference is overestimated in small samples (i.e., sample size
less than 20 or less than 10 in each group). However, a correction factor can be applied
to remove the small sample bias (i.e., correct = TRUE). Note that the function uses
a gamma function for computing the correction factor, while a approximation method is
used if computation based on the gamma function fails.
Note that the terminology is inconsistent because the standardized mean difference based
on the weighted and pooled standard deviation is usually called Cohen's d, but sometimes
called Hedges' g. Oftentimes, Cohen's d is called Hedges' d as soon as the small sample
correction factor is applied. Cumming and Calin-Jageman (2017, p.171) recommended to avoid
the term Hedges' g , but to report which standard deviation was used to standardized the
mean difference (e.g., unweighted/weighted pooled standard deviation, or the standard
deviation of the control group) and whether a small sample correction factor was applied.
As for the terminology according to Lakens (2013), in a two-sample design (i.e.,
paired = FALSE) Cohen's d_s is computed when using weighted = TRUE (default)
and Hedges's g_s is computed when using correct = TRUE in addition. In a
paired-sample design (i.e., paired = TRUE), Cohen's d_z is computed when using
weighted = TRUE, default, while Cohen's d_{rm} is computed when using
weighted = FALSE and cor = TRUE, default and Cohen's d_{av} is computed when
using weighted = FALSE and cor = FALSE. Corresponding Hedges' g_z, g_{rm},
and g_{av} are computed when using correct = TRUE in addition.
Value
Returns an object of class misty.object, which is a list with following
entries:
call
function call
type
type of analysis
sample
type of sample, i.e., one-, two-, or, paired-sample
data
list with the input specified in x, group,
and split
args
specification of function arguments
result
result table
Author(s)
Takuya Yanagida takuya.yanagida@univie.ac.at
References
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.).
Academic Press.
Cumming, G., & Calin-Jageman, R. (2017). Introduction to the new statistics: Estimation, open science,
& beyond. Routledge.
Glass. G. V., McGaw, B., & Smith, M. L. (1981). Meta-analysis in social research. Sage Publication.
Goulet-Pelletier, J.-C., & Cousineau, D. (2018) A review of effect sizes and their confidence intervals,
Part I: The Cohen's d family. The Quantitative Methods for Psychology, 14, 242-265.
https://doi.org/10.20982/tqmp.14.4.p242
Hedges, L. V. (1981). Distribution theory for Glass's estimator of effect size and related estimators.
Journal of Educational Statistics, 6(3), 106-128.
Hedges, L. V. & Olkin, I. (1985). Statistical methods for meta-analysis. Academic Press.
Lakens, D. (2013). Calculating and reporting effect sizes to facilitate cumulative science:
A practical primer for t-tests and ANOVAs. Frontiers in Psychology, 4, 1-12.
https://doi.org/10.3389/fpsyg.2013.00863
See Also
test.t, test.z, effsize, cor.matrix,
na.auxiliary
Examples
dat1 <- data.frame(group1 = c(1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2,
1, 2, 2, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 1),
group2 = c(1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 2, 2,
1, 2, 1, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 2),
group3 = c(1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 2, 1, 1, 1,
1, 2, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1),
x1 = c(3, 2, 5, 3, 6, 3, 2, 4, 6, 5, 3, 3, 5, 4,
4, 3, 5, 3, 2, 3, 3, 6, 6, 7, 5, 6, 6, 4),
x2 = c(4, 4, 3, 6, 4, 7, 3, 5, 3, 3, 4, 2, 3, 6,
3, 5, 2, 6, 8, 3, 2, 5, 4, 5, 3, 2, 2, 4),
x3 = c(7, 6, 5, 6, 4, 2, 8, 3, 6, 1, 2, 5, 8, 6,
2, 5, 3, 1, 6, 4, 5, 5, 3, 6, 3, 2, 2, 4))
#-------------------------------------------------------------------------------
# One-sample design
# Example 1: Cohen's d.z with two-sided 95% CI
# population mean = 3
cohens.d(dat1$x1, mu = 3)
# Example 2: Cohen's d.z (aka Hedges' g.z) with two-sided 95% CI
# population mean = 3, with small sample correction factor
cohens.d(dat1$x1, mu = 3, correct = TRUE)
# Example 3: Cohen's d.z for more than one variable with two-sided 95% CI
# population mean = 3
cohens.d(dat1[, c("x1", "x2", "x3")], mu = 3)
# Example 4: Cohen's d.z with two-sided 95% CI
# population mean = 3, by group1 separately
cohens.d(dat1$x1, mu = 3, group = dat1$group1)
# Example 5: Cohen's d.z for more than one variable with two-sided 95% CI
# population mean = 3, by group1 separately
cohens.d(dat1[, c("x1", "x2", "x3")], mu = 3, group = dat1$group1)
# Example 6: Cohen's d.z with two-sided 95% CI
# population mean = 3, split analysis by group1
cohens.d(dat1$x1, mu = 3, split = dat1$group1)
# Example 7: Cohen's d.z for more than one variable with two-sided 95% CI
# population mean = 3, split analysis by group1
cohens.d(dat1[, c("x1", "x2", "x3")], mu = 3, split = dat1$group1)
# Example 8: Cohen's d.z with two-sided 95% CI
# population mean = 3, by group1 separately1, split by group2
cohens.d(dat1$x1, mu = 3, group = dat1$group1, split = dat1$group2)
# Example 9: Cohen's d.z for more than one variable with two-sided 95% CI
# population mean = 3, by group1 separately1, split by group2
cohens.d(dat1[, c("x1", "x2", "x3")], mu = 3, group = dat1$group1,
split = dat1$group2)
#-------------------------------------------------------------------------------
# Two-sample design
# Example 10: Cohen's d.s with two-sided 95% CI
# weighted pooled SD
cohens.d(x1 ~ group1, data = dat1)
# Example 11: Cohen's d.s with two-sided 99% CI
# weighted pooled SD
cohens.d(x1 ~ group1, data = dat1, conf.level = 0.99)
# Example 12: Cohen's d.s with one-sided 99% CI
# weighted pooled SD
cohens.d(x1 ~ group1, data = dat1, alternative = "greater")
# Example 13: Cohen's d.s with two-sided 99% CI
# weighted pooled SD
cohens.d(x1 ~ group1, data = dat1, conf.level = 0.99)
# Example 14: Cohen's d.s with one-sided 95%% CI
# weighted pooled SD
cohens.d(x1 ~ group1, data = dat1, alternative = "greater")
# Example 15: Cohen's d.s for more than one variable with two-sided 95% CI
# weighted pooled SD
cohens.d(cbind(x1, x2, x3) ~ group1, data = dat1)
# Example 16: Cohen's d with two-sided 95% CI
# unweighted SD
cohens.d(x1 ~ group1, data = dat1, weighted = FALSE)
# Example 17: Cohen's d.s (aka Hedges' g.s) with two-sided 95% CI
# weighted pooled SD, with small sample correction factor
cohens.d(x1 ~ group1, data = dat1, correct = TRUE)
# Example 18: Cohen's d (aka Hedges' g) with two-sided 95% CI
# Unweighted SD, with small sample correction factor
cohens.d(x1 ~ group1, data = dat1, weighted = FALSE, correct = TRUE)
# Example 19: Cohen's d (aka Glass's delta) with two-sided 95% CI
# SD of reference group 1
cohens.d(x1 ~ group1, data = dat1, ref = 1)
# Example 20: Cohen's d.s with two-sided 95% CI
# weighted pooled SD, by group2 separately
cohens.d(x1 ~ group1, data = dat1, group = dat1$group2)
# Example 21: Cohen's d.s for more than one variable with two-sided 95% CI
# weighted pooled SD, by group2 separately
cohens.d(cbind(x1, x2, x3) ~ group1, data = dat1, group = dat1$group2)
# Example 22: Cohen's d.s with two-sided 95% CI
# weighted pooled SD, split analysis by group2
cohens.d(x1 ~ group1, data = dat1, split = dat1$group2)
# Example 23: Cohen's d.s for more than one variable with two-sided 95% CI
# weighted pooled SD, split analysis by group2
cohens.d(cbind(x1, x2, x3) ~ group1, data = dat1, split = dat1$group2)
# Example 24: Cohen's d.s with two-sided 95% CI
# weighted pooled SD, by group2 separately, split analysis by group3
cohens.d(x1 ~ group1, data = dat1,
group = dat1$group2, split = dat1$group3)
# Example 25: Cohen's d.s for more than one variable with two-sided 95% CI
# weighted pooled SD, by group2 separately, split analysis by group3
cohens.d(cbind(x1, x2, x3) ~ group1, data = dat1,
group = dat1$group2, split = dat1$group3)
#-------------------------------------------------------------------------------
# Paired-sample design
# Example 26: Cohen's d.z with two-sided 95% CI
# SD of the difference scores
cohens.d(dat1$x1, dat1$x2, paired = TRUE)
# Example 27: Cohen's d.z with two-sided 99% CI
# SD of the difference scores
cohens.d(dat1$x1, dat1$x2, paired = TRUE, conf.level = 0.99)
# Example 28: Cohen's d.z with one-sided 95% CI
# SD of the difference scores
cohens.d(dat1$x1, dat1$x2, paired = TRUE, alternative = "greater")
# Example 29: Cohen's d.rm with two-sided 95% CI
# controlling for the correlation between measures
cohens.d(dat1$x1, dat1$x2, paired = TRUE, weighted = FALSE)
# Example 30: Cohen's d.av with two-sided 95% CI
# without controlling for the correlation between measures
cohens.d(dat1$x1, dat1$x2, paired = TRUE, weighted = FALSE, cor = FALSE)
# Example 31: Cohen's d.z (aka Hedges' g.z) with two-sided 95% CI
# SD of the differnece scores
cohens.d(dat1$x1, dat1$x2, paired = TRUE, correct = TRUE)
# Example 32: Cohen's d.rm (aka Hedges' g.rm) with two-sided 95% CI
# controlling for the correlation between measures
cohens.d(dat1$x1, dat1$x2, paired = TRUE, weighted = FALSE, correct = TRUE)
# Example 33: Cohen's d.av (aka Hedges' g.av) with two-sided 95% CI
# without controlling for the correlation between measures
cohens.d(dat1$x1, dat1$x2, paired = TRUE, weighted = FALSE, cor = FALSE,
correct = TRUE)
# Example 34: Cohen's d.z with two-sided 95% CI
# SD of the difference scores, by group1 separately
cohens.d(dat1$x1, dat1$x2, paired = TRUE, group = dat1$group1)
# Example 35: Cohen's d.z with two-sided 95% CI
# SD of the difference scores, split analysis by group1
cohens.d(dat1$x1, dat1$x2, paired = TRUE, split = dat1$group1)
# Example 36: Cohen's d.z with two-sided 95% CI
# SD of the difference scores, by group1 separately, split analysis by group2
cohens.d(dat1$x1, dat1$x2, paired = TRUE,
group = dat1$group1, split = dat1$group2)
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| cohens.d | R Documentation |
Cohen's d
Description
This function computes Cohen's d for one-sample, two-sample (i.e., between-subject design),
and paired-sample designs (i.e., within-subject design) for one or more variables, optionally
by a grouping and/or split variable. In a two-sample design, the function computes the
standardized mean difference by dividing the difference between means of the two groups
of observations by the weighted pooled standard deviation (i.e., Cohen's d_s
according to Lakens, 2013) by default. In a paired-sample design, the function computes the
standardized mean difference by dividing the mean of the difference scores by the standard
deviation of the difference scores (i.e., Cohen's d_z according to Lakens, 2013) by
default. Note that by default Cohen's d is computed without applying the correction factor
for removing the small sample bias (i.e., Hedges' g).
Usage
cohens.d(x, ...)
## Default S3 method:
cohens.d(x, y = NULL, mu = 0, paired = FALSE, weighted = TRUE, cor = TRUE,
ref = NULL, correct = FALSE, alternative = c("two.sided", "less", "greater"),
conf.level = 0.95, group = NULL, split = NULL, sort.var = FALSE,
digits = 2, as.na = NULL, write = NULL, append = TRUE,
check = TRUE, output = TRUE, ...)
## S3 method for class 'formula'
cohens.d(formula, data, weighted = TRUE, cor = TRUE, ref = NULL,
correct = FALSE, alternative = c("two.sided", "less", "greater"),
conf.level = 0.95, group = NULL, split = NULL, sort.var = FALSE,
na.omit = FALSE, digits = 2, as.na = NULL, write = NULL, append = TRUE,
check = TRUE, output = TRUE, ...)
Arguments
x |
a numeric vector or data frame. |
... |
further arguments to be passed to or from methods. |
y |
a numeric vector. |
mu |
a numeric value indicating the reference mean. |
paired |
logical: if |
weighted |
logical: if |
cor |
logical: if |
ref |
character string |
correct |
logical: if |
alternative |
a character string specifying the alternative hypothesis, must be one of
|
conf.level |
a numeric value between 0 and 1 indicating the confidence level of the interval. |
group |
a numeric vector, character vector or factor as grouping variable. |
split |
a numeric vector, character vector or factor as split variable. |
sort.var |
logical: if |
digits |
an integer value indicating the number of decimal places to be used for displaying results. |
as.na |
a numeric vector indicating user-defined missing values,
i.e. these values are converted to |
write |
a character string naming a text file with file extension
|
append |
logical: if |
check |
logical: if |
output |
logical: if |
formula |
a formula of the form |
data |
a matrix or data frame containing the variables in the formula |
na.omit |
logical: if |
Details
Cohen (1988, p.67) proposed to compute the standardized mean difference in a two-sample design
by dividing the mean difference by the unweighted pooled standard deviation (i.e.,
weighted = FALSE).
Glass et al. (1981, p. 29) suggested to use the standard deviation of the control group
(e.g., ref = 0 if the control group is coded with 0) to compute the standardized
mean difference in a two-sample design (i.e., Glass's \Delta) since the standard deviation of the control group
is unaffected by the treatment and will therefore more closely reflect the population
standard deviation.
Hedges (1981, p. 110) recommended to weight each group's standard deviation by its sample
size resulting in a weighted and pooled standard deviation (i.e., weighted = TRUE,
default). According to Hedges and Olkin (1985, p. 81), the standardized mean difference
based on the weighted and pooled standard deviation has a positive small sample bias,
i.e., standardized mean difference is overestimated in small samples (i.e., sample size
less than 20 or less than 10 in each group). However, a correction factor can be applied
to remove the small sample bias (i.e., correct = TRUE). Note that the function uses
a gamma function for computing the correction factor, while a approximation method is
used if computation based on the gamma function fails.
Note that the terminology is inconsistent because the standardized mean difference based on the weighted and pooled standard deviation is usually called Cohen's d, but sometimes called Hedges' g. Oftentimes, Cohen's d is called Hedges' d as soon as the small sample correction factor is applied. Cumming and Calin-Jageman (2017, p.171) recommended to avoid the term Hedges' g , but to report which standard deviation was used to standardized the mean difference (e.g., unweighted/weighted pooled standard deviation, or the standard deviation of the control group) and whether a small sample correction factor was applied.
As for the terminology according to Lakens (2013), in a two-sample design (i.e.,
paired = FALSE) Cohen's d_s is computed when using weighted = TRUE (default)
and Hedges's g_s is computed when using correct = TRUE in addition. In a
paired-sample design (i.e., paired = TRUE), Cohen's d_z is computed when using
weighted = TRUE, default, while Cohen's d_{rm} is computed when using
weighted = FALSE and cor = TRUE, default and Cohen's d_{av} is computed when
using weighted = FALSE and cor = FALSE. Corresponding Hedges' g_z, g_{rm},
and g_{av} are computed when using correct = TRUE in addition.
Value
Returns an object of class misty.object, which is a list with following
entries:
call |
function call |
type |
type of analysis |
sample |
type of sample, i.e., one-, two-, or, paired-sample |
data |
list with the input specified in |
args |
specification of function arguments |
result |
result table |
Author(s)
Takuya Yanagida takuya.yanagida@univie.ac.at
References
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Academic Press.
Cumming, G., & Calin-Jageman, R. (2017). Introduction to the new statistics: Estimation, open science, & beyond. Routledge.
Glass. G. V., McGaw, B., & Smith, M. L. (1981). Meta-analysis in social research. Sage Publication.
Goulet-Pelletier, J.-C., & Cousineau, D. (2018) A review of effect sizes and their confidence intervals, Part I: The Cohen's d family. The Quantitative Methods for Psychology, 14, 242-265. https://doi.org/10.20982/tqmp.14.4.p242
Hedges, L. V. (1981). Distribution theory for Glass's estimator of effect size and related estimators. Journal of Educational Statistics, 6(3), 106-128.
Hedges, L. V. & Olkin, I. (1985). Statistical methods for meta-analysis. Academic Press.
Lakens, D. (2013). Calculating and reporting effect sizes to facilitate cumulative science: A practical primer for t-tests and ANOVAs. Frontiers in Psychology, 4, 1-12. https://doi.org/10.3389/fpsyg.2013.00863
See Also
test.t, test.z, effsize, cor.matrix,
na.auxiliary
Examples
dat1 <- data.frame(group1 = c(1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2,
1, 2, 2, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 1),
group2 = c(1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 2, 2,
1, 2, 1, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 2),
group3 = c(1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 2, 1, 1, 1,
1, 2, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1),
x1 = c(3, 2, 5, 3, 6, 3, 2, 4, 6, 5, 3, 3, 5, 4,
4, 3, 5, 3, 2, 3, 3, 6, 6, 7, 5, 6, 6, 4),
x2 = c(4, 4, 3, 6, 4, 7, 3, 5, 3, 3, 4, 2, 3, 6,
3, 5, 2, 6, 8, 3, 2, 5, 4, 5, 3, 2, 2, 4),
x3 = c(7, 6, 5, 6, 4, 2, 8, 3, 6, 1, 2, 5, 8, 6,
2, 5, 3, 1, 6, 4, 5, 5, 3, 6, 3, 2, 2, 4))
#-------------------------------------------------------------------------------
# One-sample design
# Example 1: Cohen's d.z with two-sided 95% CI
# population mean = 3
cohens.d(dat1$x1, mu = 3)
# Example 2: Cohen's d.z (aka Hedges' g.z) with two-sided 95% CI
# population mean = 3, with small sample correction factor
cohens.d(dat1$x1, mu = 3, correct = TRUE)
# Example 3: Cohen's d.z for more than one variable with two-sided 95% CI
# population mean = 3
cohens.d(dat1[, c("x1", "x2", "x3")], mu = 3)
# Example 4: Cohen's d.z with two-sided 95% CI
# population mean = 3, by group1 separately
cohens.d(dat1$x1, mu = 3, group = dat1$group1)
# Example 5: Cohen's d.z for more than one variable with two-sided 95% CI
# population mean = 3, by group1 separately
cohens.d(dat1[, c("x1", "x2", "x3")], mu = 3, group = dat1$group1)
# Example 6: Cohen's d.z with two-sided 95% CI
# population mean = 3, split analysis by group1
cohens.d(dat1$x1, mu = 3, split = dat1$group1)
# Example 7: Cohen's d.z for more than one variable with two-sided 95% CI
# population mean = 3, split analysis by group1
cohens.d(dat1[, c("x1", "x2", "x3")], mu = 3, split = dat1$group1)
# Example 8: Cohen's d.z with two-sided 95% CI
# population mean = 3, by group1 separately1, split by group2
cohens.d(dat1$x1, mu = 3, group = dat1$group1, split = dat1$group2)
# Example 9: Cohen's d.z for more than one variable with two-sided 95% CI
# population mean = 3, by group1 separately1, split by group2
cohens.d(dat1[, c("x1", "x2", "x3")], mu = 3, group = dat1$group1,
split = dat1$group2)
#-------------------------------------------------------------------------------
# Two-sample design
# Example 10: Cohen's d.s with two-sided 95% CI
# weighted pooled SD
cohens.d(x1 ~ group1, data = dat1)
# Example 11: Cohen's d.s with two-sided 99% CI
# weighted pooled SD
cohens.d(x1 ~ group1, data = dat1, conf.level = 0.99)
# Example 12: Cohen's d.s with one-sided 99% CI
# weighted pooled SD
cohens.d(x1 ~ group1, data = dat1, alternative = "greater")
# Example 13: Cohen's d.s with two-sided 99% CI
# weighted pooled SD
cohens.d(x1 ~ group1, data = dat1, conf.level = 0.99)
# Example 14: Cohen's d.s with one-sided 95%% CI
# weighted pooled SD
cohens.d(x1 ~ group1, data = dat1, alternative = "greater")
# Example 15: Cohen's d.s for more than one variable with two-sided 95% CI
# weighted pooled SD
cohens.d(cbind(x1, x2, x3) ~ group1, data = dat1)
# Example 16: Cohen's d with two-sided 95% CI
# unweighted SD
cohens.d(x1 ~ group1, data = dat1, weighted = FALSE)
# Example 17: Cohen's d.s (aka Hedges' g.s) with two-sided 95% CI
# weighted pooled SD, with small sample correction factor
cohens.d(x1 ~ group1, data = dat1, correct = TRUE)
# Example 18: Cohen's d (aka Hedges' g) with two-sided 95% CI
# Unweighted SD, with small sample correction factor
cohens.d(x1 ~ group1, data = dat1, weighted = FALSE, correct = TRUE)
# Example 19: Cohen's d (aka Glass's delta) with two-sided 95% CI
# SD of reference group 1
cohens.d(x1 ~ group1, data = dat1, ref = 1)
# Example 20: Cohen's d.s with two-sided 95% CI
# weighted pooled SD, by group2 separately
cohens.d(x1 ~ group1, data = dat1, group = dat1$group2)
# Example 21: Cohen's d.s for more than one variable with two-sided 95% CI
# weighted pooled SD, by group2 separately
cohens.d(cbind(x1, x2, x3) ~ group1, data = dat1, group = dat1$group2)
# Example 22: Cohen's d.s with two-sided 95% CI
# weighted pooled SD, split analysis by group2
cohens.d(x1 ~ group1, data = dat1, split = dat1$group2)
# Example 23: Cohen's d.s for more than one variable with two-sided 95% CI
# weighted pooled SD, split analysis by group2
cohens.d(cbind(x1, x2, x3) ~ group1, data = dat1, split = dat1$group2)
# Example 24: Cohen's d.s with two-sided 95% CI
# weighted pooled SD, by group2 separately, split analysis by group3
cohens.d(x1 ~ group1, data = dat1,
group = dat1$group2, split = dat1$group3)
# Example 25: Cohen's d.s for more than one variable with two-sided 95% CI
# weighted pooled SD, by group2 separately, split analysis by group3
cohens.d(cbind(x1, x2, x3) ~ group1, data = dat1,
group = dat1$group2, split = dat1$group3)
#-------------------------------------------------------------------------------
# Paired-sample design
# Example 26: Cohen's d.z with two-sided 95% CI
# SD of the difference scores
cohens.d(dat1$x1, dat1$x2, paired = TRUE)
# Example 27: Cohen's d.z with two-sided 99% CI
# SD of the difference scores
cohens.d(dat1$x1, dat1$x2, paired = TRUE, conf.level = 0.99)
# Example 28: Cohen's d.z with one-sided 95% CI
# SD of the difference scores
cohens.d(dat1$x1, dat1$x2, paired = TRUE, alternative = "greater")
# Example 29: Cohen's d.rm with two-sided 95% CI
# controlling for the correlation between measures
cohens.d(dat1$x1, dat1$x2, paired = TRUE, weighted = FALSE)
# Example 30: Cohen's d.av with two-sided 95% CI
# without controlling for the correlation between measures
cohens.d(dat1$x1, dat1$x2, paired = TRUE, weighted = FALSE, cor = FALSE)
# Example 31: Cohen's d.z (aka Hedges' g.z) with two-sided 95% CI
# SD of the differnece scores
cohens.d(dat1$x1, dat1$x2, paired = TRUE, correct = TRUE)
# Example 32: Cohen's d.rm (aka Hedges' g.rm) with two-sided 95% CI
# controlling for the correlation between measures
cohens.d(dat1$x1, dat1$x2, paired = TRUE, weighted = FALSE, correct = TRUE)
# Example 33: Cohen's d.av (aka Hedges' g.av) with two-sided 95% CI
# without controlling for the correlation between measures
cohens.d(dat1$x1, dat1$x2, paired = TRUE, weighted = FALSE, cor = FALSE,
correct = TRUE)
# Example 34: Cohen's d.z with two-sided 95% CI
# SD of the difference scores, by group1 separately
cohens.d(dat1$x1, dat1$x2, paired = TRUE, group = dat1$group1)
# Example 35: Cohen's d.z with two-sided 95% CI
# SD of the difference scores, split analysis by group1
cohens.d(dat1$x1, dat1$x2, paired = TRUE, split = dat1$group1)
# Example 36: Cohen's d.z with two-sided 95% CI
# SD of the difference scores, by group1 separately, split analysis by group2
cohens.d(dat1$x1, dat1$x2, paired = TRUE,
group = dat1$group1, split = dat1$group2)
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