psychmeta (version 2.3.0)

unmix_r_2group: Estimate the average within-group correlation from a mixture correlation for two groups

Description

Estimate the average within-group correlation from a mixture correlation for two groups

Usage

unmix_r_2group(rxy, dx, dy, p = 0.5)

Arguments

rxy

Overall mixture correlation.

dx

Standardized mean difference between groups on X.

dy

Standardized mean difference between groups on Y.

p

Proportion of cases in one of the two groups.

Value

A vector of average within-group correlations

Details

The mixture correlation for two groups is estimated as:

$$r_{xy_{Mix}}\frac{\rho_{xy_{WG}}+\sqrt{d_{x}^{2}d_{y}^{2}p^{2}(1-p)^{2}}}{\sqrt{\left(d_{x}^{2}p(1-p)+1\right)\left(d_{y}^{2}p(1-p)+1\right)}}$$

where \(\rho_{xy_{WG}}\) is the average within-group correlation, \(\rho_{xy_{Mix}}\) is the overall mixture correlation, \(d_{x}\) is the standardized mean difference between groups on X, \(d_{y}\) is the standardized mean difference between groups on Y, and p is the proportion of cases in one of the two groups.

References

Oswald, F. L., Converse, P. D., & Putka, D. J. (2014). Generating race, gender and other subgroup data in personnel selection simulations: A pervasive issue with a simple solution. International Journal of Selection and Assessment, 22(3), 310-320.

Examples

# NOT RUN {
unmix_r_2group(rxy = .5, dx = 1, dy = 1, p = .5)
# }