psychmeta (version 2.7.0)

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:

$$\frac{\left[\left(\frac{1}{n_{1}}\right)+\left(\frac{1}{n_{2}}\right)+\left(\frac{1}{n_{1}n_{2}}\right)\right]}{12}$$

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

$$\frac{\left[\left(\frac{1}{n}\right)+\left(\frac{1}{n^{2}}\right)\right]}{3}$$

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)