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 returns confidence intervals by bootstap.

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
)

## Arguments

data

a data.frame containing the variables in the formula.

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.

comparisons

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"))

ref.group

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).

paired

a logical indicating whether you want a paired test.

mu

theoretical mean, use for one-sample t-test. Default is 0.

var.equal

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.

hedges.correction

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).

ci

If TRUE, returns confidence intervals by bootstrap. May be slow.

conf.level

The level for the confidence interval.

ci.type

The type of confidence interval to use. Can be any of "norm", "basic", "perc", or "bca". Passed to boot::boot.ci.

nboot

The number of replications to use for bootstrap.

## Value

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.

## Details

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".

## References

• 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).

## Examples

# One-sample t test effect size
ToothGrowth %>% cohens_d(len ~ 1, mu = 0)
#> # A tibble: 1 × 6
#>   .y.   group1 group2     effsize     n magnitude
#> * <chr> <chr>  <chr>        <dbl> <int> <ord>
#> 1 len   1      null model    2.46    60 large

# Two indepedent samples t-test effect size
ToothGrowth %>% cohens_d(len ~ supp, var.equal = TRUE)
#> # A tibble: 1 × 7
#>   .y.   group1 group2 effsize    n1    n2 magnitude
#> * <chr> <chr>  <chr>    <dbl> <int> <int> <ord>
#> 1 len   OJ     VC       0.495    30    30 small

# 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)
#>   id treatment value
#> 1  1       pre   110
#> 2  2       pre   122
#> 3  3       pre   101
#> 4  4       pre   120
#> 5  5       pre   140
#> 6  1      post   150

df %>% cohens_d(value ~ treatment, paired = TRUE)
#> # A tibble: 1 × 7
#>   .y.   group1 group2 effsize    n1    n2 magnitude
#> * <chr> <chr>  <chr>    <dbl> <int> <int> <ord>
#> 1 value post   pre       1.75     5     5 large