psychmeta (version 2.6.4)

var_error_A: Estimate the error variance of the probability-based effect size (A, AUC, the common language effect size [CLES])

Description

Estimates the error variance of the probability-based common language effect size (A, AUC, CLES)

Usage

var_error_A(A, n1, n2 = NA)
var_error_auc(A, n1, n2 = NA)
var_error_cles(A, n1, n2 = NA)

Value

A vector of sampling-error variances.

Arguments

A

Vector of probability-based effect sizes (common language effect sizes)

n1

Vector of sample sizes from group 1 (or the total sample size with the assumption that groups are of equal size, if no group 2 sample size is supplied).

n2

Vector of sample sizes from group 2.

Details

The sampling variance of a A (also called AUC [area under curve] or CLES [common-language effect size]) value is:

[(1n_1)+(1n_2)+(1n_1n_2)]12var_e = [ (1/n1) + (1/n2) + (1 / (n1 * n2)) ] / 12

When groups 1 and 2 are of equal size, this reduces to

[(1n)+(1n^2)]3var_e = [ (1/n) + (1/n^2) ] / 3

References

Ruscio, J. (2008). A probability-based measure of effect size: Robustness to base rates and other factors. *Psychological Methods, 13*(1), 19–30. tools:::Rd_expr_doi("10.1037/1082-989X.13.1.19")

Examples

var_error_A(A = 1, n1 = 30, n2 = 30)
var_error_auc(A = 1, n1 = 60, n2 = NA)
var_error_cles(A = 1, n1 = 30, n2 = 30)