Permutation tests for Generalized Procrustes Analysis

Generalized Procrustes Analysis (GPA) is a useful tool for sensory professionals to analyze sensory data, especially those from free choice profiling. Over a decade ago, Wakeling introduced a permutation test for determining if the GPA consensus is significant. However, Wakeling’s permutation test lacks specification of an explicit null hypothesis, resulting in different interpretations of what a “significant consensus” signifies. In this paper, a new GPA permutation test analogous to the well established ANOVA permutation procedure is proposed. The proposed approach emphasizes that the null hypothesis dictates how data are permuted to test specific null hypotheses within GPA (e.g., product effect, assessor effect and interaction effect). The only assumption behind permutation testing is exchangeability, which is discussed. Applications of the proposed GPA permutation test are provided using three datasets (two actual datasets and one random dataset).