Eta-Squared Effect Size

Computes eta-squared, partial eta-squared, and omega-squared from a one-way between-subjects comparison.

Usage

etaSquared(x, groups)

Arguments

x

Numeric vector of values.

groups

Factor or character vector of group membership.

Value

A list with components:

eta_sq

Eta-squared (SS_between / SS_total)

partial_eta_sq

Partial eta-squared (SS_between / (SS_between + SS_within))

omega_sq

Omega-squared (bias-corrected effect size)

Details

Eta-squared is the proportion of total variance explained by group membership: $$\eta^2 = \frac{SS_{between}}{SS_{total}}$$

Omega-squared provides a less biased estimate: $$\omega^2 = \frac{SS_{between} - df_{between} \cdot MS_{within}}{SS_{total} + MS_{within}}$$

For one-way designs, partial eta-squared equals eta-squared.

References

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

See also

cohensD() for pairwise effect sizes, plotEffectSizeForest() for forest plot visualization.

Examples

set.seed(42)
x <- c(rnorm(20, 10, 2), rnorm(20, 12, 2), rnorm(20, 14, 2))
groups <- rep(c("A", "B", "C"), each = 20)
result <- etaSquared(x, groups)
result$eta_sq
#> [1] 0.3118034