correct_r_split {psychmeta} | R Documentation |
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. doi:10.4135/9781483398105. pp. 287-288.
Examples
correct_r_split(r = 0.3, pi = .9, pa = .5, n = 100)