Estimates the error variance of standard deviation (\(u\)) ratios.
var_error_u(u, ni, na = NA, dependent_sds = FALSE)A vector of sampling-error variances.
Vector of \(u\) ratios.
Vector of incumbent-group sample sizes.
Vector of applicant-group sample sizes.
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).
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.
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. tools:::Rd_expr_doi("10.1177/1094428119859398")
var_error_u(u = .8, ni = 100, na = 200)
var_error_u(u = .8, ni = 100, na = NA)
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