Modifying Spearman's Attenuation Equation to Yield Partial Corrections for Measurement Error-With Application to Sample Size Calculations.

Abstract

Spearman's correction for attenuation (measurement error) corrects a correlation coefficient for measurement errors in either-or-both of two variables, and follows from the assumptions of classical test theory. Spearman's equation removes all measurement error from a correlation coefficient which translates into "increasing the reliability of either-or-both of two variables to 1.0." In this inquiry, Spearman's correction is modified to allow partial removal of measurement error from either-or-both of two variables being correlated. The practical utility of this partial correction is demonstrated in its use to explore increasing the power of statistical tests by increasing sample size versus increasing the reliability of the dependent variable for an experiment. Other applied uses are mentioned.