correct_r_split: Correct correlations for uneven/unrepresentative splits

In psychmeta/psychmeta: Psychometric Meta-Analysis Toolkit

Correct correlations for uneven/unrepresentative splits

Description

This correction is mathematically equivalent to correcting the correlation for direct range restriction in the split variable.

Usage

correct_r_split(r, pi, pa = 0.5, n = NULL)

Arguments

r	Vector of correlations affected by an uneven or unrepresentative split of a dichotomous variable.
pi	Vector of proportions of incumbent/sample cases in one of the categories of the dichotomous variable.
pa	Vector of proportions of applicant/population cases in one of the categories of the dichotomous variable.
n	Optional vector of sample sizes.

Details

r_{c}=\frac{r_{obs}}{u\sqrt{\left(\frac{1}{u^{2}}-1\right)r_{obs}^{2}+1}}

where u=\sqrt{\frac{p_{i}(1-p_{i})}{p_{a}(1-p_{a})}}, the ratio of the dichotomous variance in the sample (p_{i} is the incumbent/sample proportion in one of the two groups) to the dichotomous variance in the population (p_{a} is the applicant/population proportion in one of the two groups). This correction is identical to the correction for univariate direct range restriction, applied to a dichotomous variable.

Value

Vector of correlations corrected for unrepresentative splits (if n is supplied, corrected error variance and adjusted sample size is also reported).

References

Schmidt, F. L., & Hunter, J. E. (2015). Methods of meta-analysis: Correcting error and bias in research findings (3rd ed.). Sage. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.4135/9781483398105")}. pp. 287-288.

Examples

correct_r_split(r = 0.3, pi = .9, pa = .5, n = 100)

psychmeta/psychmeta documentation built on Feb. 12, 2024, 1:21 a.m.