  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.
