A study on permutation test strategies in ASCA

ANOVA Simultaneous Component Analysis (ASCA) examines the significance of the effects of experimental factors and possible interaction between them in chemical data, commonly based on permutation tests [1]. Permutation tests are often used to assess the significance of an observed effect by randomly permuting the data and comparing the observed result to the distribution of permuted results. Several permutation test approaches have been applied in ASCA [2, 3], of which two widely-used methods, restricted permutation, and reduced model, are studied in detail. These significant testing methods differ in terms of which matrix is permuted and which units are exchangeable. Restricted permutation tests involve restricting the permutations to maintain a specific null hypothesis, such as the exchangeability of treatment groups or the independence of observations, while permuting the remaining variables. On the other hand, reduced model permutation tests, involve comparing the observed data to a reduced model in which certain variations or interactions have been removed. Determining the appropriate significance test to employ is a matter of uncertainty. Making the wrong selection could result in erroneous conclusions regarding the significance of the factors at hand. This study delved into multiple simulated datasets, each characterized by varying conditions concerning the significance of factors and interactions. Additionally, an experimental dataset involving feral cabbage plants (Brassica oleracea) was incorporated, focusing on two experimental factors: time and treatment. The study s findings showcased that the restricted permutation test outperforms in assessing the significance of the main factors. Nevertheless, when examining the interaction between these main factors, the reduced model test proves to be more effective. The investigation delves deep into the reasons behind these observed outcomes.