Population Power Curves in ASCA With Permutation Testing

In this paper, we revisit the power curves in ANOVA simultaneous component analysis (ASCA) based on permutation testing and introduce the population curves derived from population parameters describing the relative effect among factors and interactions. The relative effect has important practical implications: The statistical power of a given factor depends on the design of other factors in the experiment and not only of the sample size. Thus, understanding the relative power in a specific experimental design can be extremely useful to maximize our capability of success when planning the experiment. In the paper, we derive relative and absolute population curves, where the former represent statistical power in terms of the normalized effect size between structure and noise, and the latter in terms of the sample size. Both types of population curves allow us to make decisions regarding the number and nature (fixed/random) of factors, their relationships (crossed/nested), and the number of levels and replicates, among others, in an multivariate experimental design (e.g., an omics study) during the planning phase of the experiment. We illustrate both types of curves through simulation.