var_error_u {psychmeta}

Estimate the error variance of u ratios

Description

Estimates the error variance of standard deviation (u) ratios.

Usage

var_error_u(u, ni, na = NA, dependent_sds = FALSE)

Arguments

u

Vector of u ratios.

ni

Vector of incumbent-group sample sizes.

na

Vector of applicant-group sample sizes.

dependent_sds

Logical vector identifying whether each u ratio is based on standard deviations from independent samples (FALSE) or based on standard deviations from an applicant sample and an incumbent sample that is a subset of that applicant sample (TRUE).

Details

The sampling variance of a u ratio is computed differently for independent samples (i.e., settings where the referent unrestricted standard deviation comes from an different sample than the range-restricted standard deviation) than for dependent samples (i.e., unrestricted samples from which a subset of individuals are selected to be in the incumbent sample).

The sampling variance for independent samples (the more common case) is:

var_{e}=\frac{u^{2}}{2}\left(\frac{1}{n_{i}-1}+\frac{1}{n_{a}-1}\right)

and the sampling variance for dependent samples is:

var_{e}=\frac{u^{2}}{2}\left(\frac{1}{n_{i}-1}-\frac{1}{n_{a}-1}\right)

where u is the u ratio, n_{i} is the incumbent sample size, and n_{a} is the applicant sample size.

Value

A vector of sampling-error variances.

References

Dahlke, J. A., & Wiernik, B. M. (2020). Not restricted to selection research: Accounting for indirect range restriction in organizational research. Organizational Research Methods, 23(4), 717–749. doi:10.1177/1094428119859398

Examples

var_error_u(u = .8, ni = 100, na = 200)
var_error_u(u = .8, ni = 100, na = NA)