A Statistical Method for Comparing Aggregate Data Across A Priori Groups

Abstract

This article introduces a new method for statistically comparing pairs of aggregate data series. Aggregate data series refers to a set of values, each of which is averaged or otherwise aggregated across respondents. The motivating problem is the comparison of aggregate proximity matrices, such as those obtained from pile sort exercises. The standard approach to this problem uses the nonparametric, permutation-based quadratic assignment program (QAP) technique. However, the null distribution that QAP is based on is inappropriate for comparing subsamples of a data set and may lead to misleading conclusions. The new method can yield different results than QAP, results more in line with researchers' intuition. Furthermore, the method can be applied to a variety of data types beyond those appropriate for QAP.