Testing the Equality of Two Independent αCoefficients Adjusted by the Spearman-Brown Formula

Abstract

An approximate statistical test is developed for the hypothesis of equality between the Spearman-Brown extrapolations of two independent values of Cronbach’s alpha reliability coefficient (α). This test assumes that the units added to or deleted from each instrument are classically parallel to the units included in the original version of each instrument. The projections for Tests 1 and 2 are based on lengthening or shortening factors of K1 and K2, which may or may not be equal. Special cases of this test include applications in which the projected values are intraclass coefficients or only one of the instruments is presumed to be altered in length. Monte carlo simulations demonstrated that the procedure effectively controls Type I error even when the original αs are based on as few as two test parts or two raters.