In recent years, power analysis has become widely used in applied sciences, with the increasing importance of the replicability issue. When distribution-free methods, such as Partial Least Squares (PLS)-based approaches, are considered, formulating power analysis turns out to be challenging. In this study, we introduce the methodological framework of a new procedure for performing power analysis when PLS-based methods are used. Data are simulated by the Monte Carlo method, assuming the null hypothesis of no effect is false and exploiting the latent structure estimated by PLS in the pilot data. In this way, the complex correlation data structure is explicitly considered in power analysis and sample size estimation. The paper offers insights into selecting statistical tests for the power analysis procedure, comparing accuracy-based tests and those based on continuous parameters estimated by PLS. Simulated and real datasets are investigated to show how the method works in practice.

翻译：近年来，随着可重复性问题日益受到重视，功效分析在应用科学领域得到广泛使用。当考虑无分布假设方法（如偏最小二乘法）时，开展功效分析面临严峻挑战。本研究提出了一种适用于PLS方法的新功效分析程序的方法学框架。通过蒙特卡洛方法模拟数据，在设定零效应假设不成立的前提下，利用预实验数据中PLS估计的潜在结构进行数据生成。该方法将复杂的数据相关结构显式纳入功效分析与样本量估算过程。本文深入探讨了功效分析程序中统计检验的选择问题，比较了基于准确度的检验方法以及基于PLS连续参数估计的检验方法。通过模拟数据集与真实数据集验证了该方法在实际应用中的表现。