# correct_r_split: Correct correlations for uneven/unrepresentative splits In psychmeta: Psychometric Meta-Analysis Toolkit

## Description

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

## Usage

 1 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

\mjdeqn

r_c=\fracr_obsu\sqrt\left(\frac1u^2-1\right)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 \mjeqnu=\sqrt\fracp_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 (\mjeqnp_ipi is the incumbent/sample proportion in one of the two groups) to the dichotomous variance in the population (\mjeqnp_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.

## 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. doi: 10.4135/9781483398105. pp. 287-288.

## Examples

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

### Example output

-----------------------------------------------------  psychmeta version 2.3.3  --

Please report any bugs to github.com/psychmeta/psychmeta/issues
or issues@psychmeta.com

We work hard to produce these open-source tools for the R community,
Dahlke, J. A., & Wiernik, B. M. (2018). psychmeta: An R package for
psychometric meta-analysis. Applied Psychological Measurement.

Attaching package: 'psychmeta'

The following object is masked from 'package:stats':

filter