Mediation testing with polynomial regression: A critical review of extant approaches and a researcher’s toolkit for the future.

New statistical methods are excitedly received by researchers' eager to apply them in their own research. Widespread adoption tends to occur after a critical mass of exemplars is published in top-tier journals such as Journal of Applied Psychology as this serves not only as a credibility signal but also as a template for subsequent researchers. However, this process can inadvertently allow unrecognized limitations, constraints, or suboptimal decisions to be propagated through subsequent research. Such is the case with testing mediation with polynomial regression analyses. After presenting a brief primer on polynomial regression, we critically review three approaches for testing mediation in this context-ad hoc, block variable, and disaggregated-and highlight the flexibility, simplicity, and robustness of the third. We confirm our conclusions in two empirical demonstrations. The first uses simulated data sets, and the second reanalyses a previous article, for which we also provide a state-of-the-science analysis and results section that can be used as a template by future scholars. We also introduce a user-friendly R Shiny app (https://quantkit.shinyapps.io/polymed/) to facilitate these analyses. We thus provide researchers a clear way forward, conceptually enabling them to utilize the empirical tools necessary to conduct transparent, reproducible, and replicable research-the type of research for which Journal of Applied Psychology is widely known. (PsycInfo Database Record (c) 2025 APA, all rights reserved).