Power and Reliability: The Case of Homogeneous True Score Regression Across Treatments

Abstract

As part of their investigation of the relation between reliability of measures and statistical power, Nicewander and Price (1983) examined the situation in which true score regressions are homogeneous across treatments. They derived an equation indicating that the measure, X or Y, yielding the greater power depends on the reliabilities (p _XX'. and p _YY', respectively) and the squared linear correlation between true scores for X and Y (p_T(X)T(Y) ² ). Typically, however, researchers cannot compute a direct estimate of p_T(X)T(Y) ² The authors eliminate this problem by (a) pointing out situations in which the value of p_T(X)T(Y) ² is either irrelevant or 1.0 and (b) demonstrating that their equation otherwise can be expressed in terms of p _XX' and p _XY only.