# caseIIIR: Corrects correlations using Case III-R In selection: Correcting Biased Estimates Under Selection

## Description

Using Fife, Hunter, and Mendoza's (2013) Case III-R correction, `caseIIIR` corrects the tp correlation for direct restriction on x (and by implication, indirect restriction on x)

## Usage

 `1` ```caseIIIR(data.matrix = NULL, rtp, rsp, rts, SR) ```

## Arguments

 `data.matrix` a data matrix with rows representing observations and columns representing variables. Note: no observations should be present when using case III-R. `rtp` the restricted correlation between t (the predictor variable) and p (the outcome variable). `rsp` the restricted correlation between s (the suitability variable) and p (the outcome variable). `rts` the restricted correlation between t (the predictor variable) and s (the suitability variable). `SR` the selection ratio (i.e., the proportion of applicants who were selected)

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## Value

a scalar that is the unbiased estimate of the correlation between T and P.

Dustin Fife

## References

Thorndike, R. L. (1949). Personnel selection: Test and measurement techniques. Oxford, England: Wiley.

Pearson, K. (1903). Mathematical contributions to the theory of evolution. XI. On the influence of natural selection on the variability and correlation of organs. Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character, 200, 1-66.

`caseIV`, `caseIII`, `em`, `rel.correction`
 ```1 2 3 4 5 6 7 8 9``` ``` # load example data data(selection.example.data) # give me only those rows that have full information new.dat = selection.example.data[!is.na(selection.example.data\$Performance),] # correct assuming direct selection on R, indirect on biodata, and a dv of performance corrected = caseIIIR(data.matrix = new.dat, SR=.5) corrected = caseIIIR(rtp=.4, rsp=.3, rts=.5, SR=.5) ```