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Estimating the Relationship within the Population

To simplify matters from here on, a notation system will be used in which the mean rxx and ryy will be denoted as a and b respectively and the variance of the two reliabilities will be denoted as s2a and s2b. Similarly the mean range departure is denoted as c and its variance as s2c.

Given these statistics, the sample weighted mean r, corrected error variance, a, b, c, and the variances for the mean reliabilities and the range departures, the relationship within the population (rho) can be estimated. First, correct the sample weighted mean r for measurement error and range departure using the following formula:

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