A Bayesian Significance Test for the Difference and Linear Combination of Factor Means between Groups

Abstract

The present article proposes Bayesian inference for multiple group factor analysis, via a Gibbs sampling algorithm. When this method is used, a significance test for the difference of factor means between groups and a test for linear contrast can be done to determine whether a point hypothesis is in the Bayesian canfidemce interval of the posterior distribution. Baysian inference is not used in research in educational psychology because of its arbitrariness in the selection of the prior distribution. However, all the methods described in the present article can be done with a noninformative prior distribution, thus excluding subjectivity. As a result, researchers will be able to use Bayesian inference easily and objectively. In order to compare the proposed method with a x2 asymptotic likelihood test in terms of their respective power, 1400 simulation data sets for N = 160 and N = 80 were generated. The proposed method has some advantages over the x2 test in that control of Type-1 errors is complete with small-sized samples, and also in that the Haywood case problem does not occur. The proposed method was used to analyze the relationship of age and intelligence as measured by the WAIS-R, and a composite hypothesis was evaluated.