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. We distinguish Relative from 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. Relative Population Curves are useful to find the optimal ASCA model (e.g., fixed/random factors, crossed/nested relationships, interactions, the test statistic, transformations, etc.) for the analysis of an experimental design at hand. Absolute Population Curves are useful to determine the sample size and the optimal number of levels for each factor during the planning phase on an experiment. We illustrate both types of curves through simulation. We expect Population Curves to become the go-to approach to plan the optimal analysis pipeline and the required sample size in an omics study analyzed with ASCA.

翻译：本文基于置换检验重新审视了方差分析同步分量分析（ASCA）中的统计功效曲线，并引入了由描述因子及交互作用相对效应的总体参数推导出的总体曲线。我们将相对总体曲线与绝对总体曲线加以区分：前者以结构与噪声之间的归一化效应量表征统计功效，后者则以样本量表征统计功效。相对总体曲线有助于为当前实验设计找到最优ASCA模型（例如固定/随机因子、交叉/嵌套关系、交互作用、检验统计量、变换等）。绝对总体曲线则有助于在实验规划阶段确定各因子的样本量和最优水平数。我们通过模拟示例说明了两类曲线的应用。我们预期总体曲线将成为使用ASCA分析组学研究中规划最优分析流程和所需样本量的首选方法。