Permutation Test for the Equality of Several Independent Cronbach's Alpha Coefficients

Abstract

The statistical inference of Cronbach's alpha measure of internal reliability is known to be inaccurate when sample size is small and the assumption of normality is violated. In this paper, we describe the permutation method in which we compute resampling p-values for testing the difference between two or more independent Cronbach's alpha coefficients. When the over-all permutation test is significant, we also make pairwise post-hoc comparisons using permutaion method. The permutation tests for the equality of two independent Cronbach's alpha coefficients and three independent Cronbach's alpha coefficients are illustrated with an example analysis of survey data.

Table 1. Survey data on female college students’ consumption propensity

Table 2. Observed alpha coefficients($\widehat{{\alpha}_A}$, $\widehat{{\alpha}_B}$)

Table 3. p values for testing equality of two alpha coefficients

Table 4. Survey data on primary school students’(2^nd, 3^rd, 4^th grade) sociality

Table 5. Observed alpha coefficients($\widehat{{\alpha}_A}$, $\widehat{{\alpha}_B}$, $\widehat{{\alpha}_C}$)

Table 6. p values for over-all test and post-hoc test

Table 7. Resampling permutation p values for over-all test and post-hoc test