Using Thorndike's Case II correction,
caseIII corrects the xy
correlation for direct restriction on x
caseII(rxy, sx, sxs)
the restricted correlation between x (the indirectly selected variable) and y (the outcome variable).
the unrestricted standard deviation of x
the restricted standard deviation of x
The Case II correction is defined as follows insert later The result is an unbiased estimate of the unattenuated correlation between X and Y
a scalar that is the unbiased estimate of the correlation between X and Y.
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.
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# correct assuming direct selection on X corrected = caseII(rxy=.5, sx=1.5, sxs=.9) corrected