A Test of the Equality of Two Related α Coefficients Adjusted by the Spearman-Brown Formula

Abstract

Internal-consistency reliability coefficients that are Spearman-Brown extrapolations of the original observed coefficients must occasionally be compared. This might occur in a comparison of measurement procedures that need to be differentially shortened or lengthened in order to equalize their administration time. The effect on rating scale reliability of a training program for raters might also require such a comparison. A statistical test was developed for the hypothesis of the equality of extrapolated coefficients when the original values (Cronbach’s α) are based on the same sample of persons and, therefore, are statistically dependent. Monte carlo studies showed that the test precisely controlled Type I error, even with very small numbers of parttest units or raters.

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