This correction is mathematically equivalent to correcting the correlation for direct range restriction in the split variable.
correct_r_split(r, pi, pa = 0.5, n = NULL)Vector of correlations corrected for unrepresentative splits (if n is supplied, corrected error variance and adjusted sample size is also reported).
Vector of correlations affected by an uneven or unrepresentative split of a dichotomous variable.
Vector of proportions of incumbent/sample cases in one of the categories of the dichotomous variable.
Vector of proportions of applicant/population cases in one of the categories of the dichotomous variable.
Optional vector of sample sizes.
r_c=r_obsu(1u^2-1)r_obs^2+1r_c = r / (sqrt((pi*(1-pi))/(pa*(1-pa))) * sqrt(((pa*(1-pa))/(pi*(1-pi)) - 1) * r^2 + 1)) where u=p_i(1-p_i)p_a(1-p_a)sqrt((pi*(1-pi))/(pa*(1-pa))), the ratio of the dichotomous variance in the sample (p_ipi is the incumbent/sample proportion in one of the two groups) to the dichotomous variance in the population (p_apa 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.
Schmidt, F. L., & Hunter, J. E. (2015). Methods of meta-analysis: Correcting error and bias in research findings (3rd ed.). Sage. tools:::Rd_expr_doi("10.4135/9781483398105"). pp. 287-288.
correct_r_split(r = 0.3, pi = .9, pa = .5, n = 100)
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