Compute the effect size for t-test. T-test conventional effect sizes, proposed by Cohen, are: 0.2 (small effect), 0.5 (moderate effect) and 0.8 (large effect).
Cohen's d is calculated as the difference between means or mean minus
mu divided by the estimated standardized deviation.
For independent samples t-test, there are two possibilities implemented. If the t-test did not make a homogeneity of variance assumption, (the Welch test), the variance term will mirror the Welch test, otherwise a pooled estimate is used.
If a paired samples t-test was requested, then effect size desired is based on the standard deviation of the differences.
It can also return confidence intervals for the effect size, either by
bootstrap (the default) or by an analytic, deterministic method (see
ci.method).
See the Datanovia tutorial Cohen’s d Effect Size in R for a worked walkthrough.
cohens_d(
data,
formula,
comparisons = NULL,
ref.group = NULL,
paired = FALSE,
mu = 0,
var.equal = FALSE,
hedges.correction = FALSE,
ci = FALSE,
conf.level = 0.95,
ci.type = "perc",
nboot = 1000,
boot.parallel = getOption("boot.parallel", "no"),
boot.ncpus = getOption("boot.ncpus", 1L),
id = NULL,
ci.method = c("boot", "analytic")
)return a data frame with some of the following columns:
.y.: the y variable used in the test.
group1,group2: the compared groups in the pairwise tests.
n,n1,n2: Sample counts.
effsize: estimate of the effect
size (d value).
magnitude: magnitude of effect size.
conf.low,conf.high: lower and upper bound of the effect size
confidence interval.
a data.frame containing the variables in the formula.
a formula of the form x ~ group where x is a
numeric variable giving the data values and group is a factor with
one or multiple levels giving the corresponding groups. For example,
formula = TP53 ~ cancer_group.
A list of length-2 vectors specifying the groups of
interest to be compared. For example to compare groups "A" vs "B" and "B" vs
"C", the argument is as follow: comparisons = list(c("A", "B"), c("B",
"C"))
a character string specifying the reference group. If specified, for a given grouping variable, each of the group levels will be compared to the reference group (i.e. control group).
If ref.group = "all", pairwise two sample tests are performed for
comparing each grouping variable levels against all (i.e. basemean).
a logical indicating whether you want a paired test.
the theoretical mean (one-sample test) or the hypothesized difference
in means (two-sample test). It is subtracted from the mean difference before
standardizing, so a non-zero mu shifts the effect size accordingly.
Default is 0.
a logical variable indicating whether to treat the two variances as being equal. If TRUE then the pooled variance is used to estimate the variance otherwise the Welch (or Satterthwaite) approximation to the degrees of freedom is used. Used only for unpaired or independent samples test.
logical indicating whether apply the Hedges
correction by multiplying the usual value of Cohen's d by
(N-3)/(N-2.25) (for unpaired t-test) and by (n1-2)/(n1-1.25) for paired t-test;
where N is the total size of the two groups being compared (N = n1 +
n2).
If TRUE, returns confidence intervals by bootstrap. May be slow.
The level for the confidence interval.
The type of confidence interval to use. Can be any of "norm",
"basic", "perc", or "bca". Passed to boot::boot.ci.
The number of replications to use for bootstrap.
The type of parallel operation to be used when computing
the bootstrap confidence interval. Allowed values are "no" (default),
"multicore" and "snow". Passed to boot().
Defaults to getOption("boot.parallel", "no"), so it can also be set
globally with options(boot.parallel = "multicore"). Only used when
ci = TRUE.
Integer. The number of processes to be used in the parallel
bootstrap. Defaults to getOption("boot.ncpus", 1L). Note that
boot.parallel has no effect unless boot.ncpus > 1. Only used
when ci = TRUE.
(optional) character string with the name of the column holding the
sample/subject identifier, used only for a paired test
(paired = TRUE). When supplied, the two groups are matched by
id (instead of by row order) before the paired d is computed, as in
t_test(). Only complete pairs (subjects measured in both
groups) are used.
the method used to compute the confidence interval when
ci = TRUE. Either "boot" (default) for a percentile bootstrap,
or "analytic" for a deterministic interval obtained by inverting the
noncentral t distribution (Steiger, 2004; Cumming & Finch, 2001) --
the same machinery anova_test(ci = ) uses for partial
eta-squared. The analytic interval covers the one-sample, paired and
two-sample (equal-variance and Welch) cases, is reproducible across runs
(no seed), and matches effectsize::cohens_d(ci = ). With
hedges.correction = TRUE the estimate and both bounds are scaled by
the documented \((N - 3)/(N - 2.25)\) approximation, so they are not
identical to effectsize::hedges_g(ci = ), which applies the exact
gamma-function correction at the design's degrees of freedom. The gap is
proportional to the effect size and grows as the samples shrink.
When the interval is not defined for a given input (for
example a degenerate group), the bootstrap is used as a fallback. The
default "boot" leaves the returned interval unchanged from previous
versions.
Quantification of the effect size magnitude is performed using the
thresholds defined in Cohen (1992). The magnitude is assessed using the
thresholds provided in (Cohen 1992), i.e. |d| < 0.2 "negligible",
|d| < 0.5 "small", |d| < 0.8 "medium", otherwise "large".
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). New York:Academic Press.
Cohen, J. (1992). A power primer. Psychological Bulletin, 112, 155-159.
Hedges, Larry & Olkin, Ingram. (1985). Statistical Methods in Meta-Analysis. 10.2307/1164953.
Navarro, Daniel. 2015. Learning Statistics with R: A Tutorial for Psychology Students and Other Beginners (Version 0.5).
Steiger, J. H. (2004). Beyond the F test: Effect size confidence intervals and tests of close fit in the analysis of variance and contrast analysis. Psychological Methods, 9(2), 164-182.
Cumming, G., & Finch, S. (2001). A primer on the understanding, use, and calculation of confidence intervals that are based on central and noncentral distributions. Educational and Psychological Measurement, 61(4), 532-574.
The Datanovia tutorial: Cohen’s d Effect Size in R.
# One-sample t test effect size
ToothGrowth %>% cohens_d(len ~ 1, mu = 0)
# Two indepedent samples t-test effect size
ToothGrowth %>% cohens_d(len ~ supp, var.equal = TRUE)
# Paired samples effect size
df <- data.frame(
id = 1:5,
pre = c(110, 122, 101, 120, 140),
post = c(150, 160, 110, 140, 155)
)
df <- df %>% gather(key = "treatment", value = "value", -id)
head(df)
df %>% cohens_d(value ~ treatment, paired = TRUE)
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