Ready to ROC? A tutorial on simulation-based power analyses for null hypothesis significance, minimum-effect, and equivalence testing for ROC curve analyses

Abstract

The receiver operating characteristic (ROC) curve and its corresponding (partial) area under the curve (AUC) are frequently used statistical tools in psychological research to assess the discriminability of a test, method, intervention, or procedure. In this paper, we provide a tutorial on conducting simulation-based power analyses for ROC curve and (p)AUC analyses in R. We also created a Shiny app and the R package "ROCpower" to perform such power analyses. In our tutorial, we highlight the importance of setting the smallest effect size of interest (SESOI) for which researchers want to conduct their power analysis. The SESOI is the smallest effect that is practically or theoretically relevant for a specific field of research or study. We provide how such a SESOI can be established and how it changes hypotheses from simply establishing whether there is a statistically significant effect (i.e., null-hypothesis significance testing) to whether the effects are practically or theoretically important (i.e., minimum-effect testing) or whether the effect is too small to care about (i.e., equivalence testing). We show how power analyses for these different hypothesis tests can be conducted via a confidence interval-focused approach. This confidence interval-focused, simulation-based power analysis can be adapted to different research designs and questions and improves the reproducibility of power analyses.

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