Cohen's d Effect Size

Computes Cohen's d effect size for comparing two groups or conditions, with confidence intervals and qualitative interpretation.

Usage

cohensD(x, y, paired = FALSE, pooled = TRUE)

Arguments

x

Numeric vector for group 1 (or condition 1 if paired).

y

Numeric vector for group 2 (or condition 2 if paired).

paired

Logical; if TRUE, computes effect size for paired data using the SD of differences as the denominator.

pooled

Logical; if TRUE (default), uses pooled SD as denominator. If FALSE, uses the SD of y (Glass's delta, treating y as control). Ignored when paired = TRUE.

Value

A list with components:

d

Cohen's d value

ci_lower

Lower bound of 95 percent confidence interval

ci_upper

Upper bound of 95 percent confidence interval

interpretation

Qualitative label: "negligible", "small", "medium", or "large"

Details

For independent groups with pooled = TRUE, the pooled SD is: $$SD_{pooled} = \sqrt{\frac{(n_1 - 1) s_1^2 + (n_2 - 1) s_2^2}{n_1 + n_2 - 2}}$$

For paired data, the denominator is the SD of the within-pair differences.

Interpretation thresholds follow Cohen (1988):

• |d| < 0.2: negligible

• 0.2 <= |d| < 0.5: small

• 0.5 <= |d| < 0.8: medium

• |d| >= 0.8: large

References

Cohen J (1988). Statistical Power Analysis for the Behavioral Sciences. Lawrence Erlbaum Associates.

See also

etaSquared() for ANOVA-based effect sizes, plotEffectSizeForest() for forest plot visualization of effect sizes.

Examples

set.seed(42)
x <- rnorm(30, mean = 10, sd = 2)
y <- rnorm(30, mean = 8, sd = 2)
result <- cohensD(x, y)
result$d
#> [1] 1.02887
result$interpretation
#> [1] "large"