Cliff's Delta Effect Size

Calculates Cliff's delta (Cd) as a non-parametric effect size for comparing two numeric vectors. Cd quantifies the directional difference between a reference (ref) and comparison (comp) distribution based on pairwise comparisons of their values.

Cd ranges from -1 to 1, where:

• -1: values in comp are consistently larger than those in ref

• 0: both distributions are similar, with no systematic difference

• 1: values in ref are consistently larger than those in comp

Usage

cliffs_d(ref, comp)

es_cdelta(ref, comp)

Arguments

ref

Numeric vector representing the reference group.

comp

Numeric vector representing the comparator group.

Value

A single numeric value: Cliff's delta effect size.

Details

The effect size is calculated as the scaled difference in dominance between groups. Missing or infinite values are removed with a message. Synonyms are

References

Cliff, N. (1993). Dominance statistics: Ordinal analyses to answer ordinal questions. Psychological Bulletin, 114(3), 494–509. doi:10.1037/0033-2909.114.3.494

Examples

ref <- rnorm(100, mean = 0)
comp <- rnorm(100, mean = 1)

hist(ref,  col=rgb(0,0,1,0.3), breaks=50, xlim=c(-4,4))
hist(comp, col=rgb(1,0,0,0.3), breaks=50, add=TRUE)
legend("topright", legend=c("ref","comp"), fill=c("blue","red"))


cliffs_d(ref, comp)
#> [1] -0.532
cliffs_d(comp, ref)
#> [1] 0.532

comp1 <- rnorm(100, mean = 10)
cliffs_d(ref, comp1)
#> [1] -1

cliffs_d(ref, ref)
#> [1] 0