Power-based sample size justification for tests of congruence hypotheses with response surface analysis

• Applicant: Dr. Sarah Humberg
• Subject Area: Personality Psychology, Clinical and Medical Psychology, Methodology
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 563840845

A congruence hypothesis posits that the degree of congruence between two variables is associated with a third variable. Congruence hypotheses are prevalent across psychological disciplines, referring to, for example, the psychological outcomes of accurate self-perceptions, dyadic similarity, or person-environment fit. Their empirical test is frequently achieved by using Response Surface Analysis (RSA), which is a valid tool for this purpose. However, a key limitation in RSA applications is the lack of proper sample size justifications. RSA is based on estimating a second-order polynomial regression model and interpreting multiple significance tests. The hereby required constellation of tests renders standard approaches to a-priori power analysis inapplicable. To date, no viable alternative has been proposed, leaving RSA studies to either omit considerations of power entirely or rely on invalid methods. This project aims to develop a suitable approach for power-based sample size justification in tests of congruence hypotheses and to facilitate its practical adoption. Specifically, we will design a method to replace the standard power analysis approach, enabling researchers to make data-analytic decisions that maximize statistical power while accommodating the restrictions of their research context. The method will be implemented in an accessible R package and ShinyApp, supported by tutorial-style guidelines. To ensure broad applicability, our contributions will cover three common data structures in RSA applications: simple, dyadic, and hierarchically nested data. Additionally, we will establish reporting standards for congruence effect sizes, which will improve the basis for determining expected effect sizes in future power analyses. Ultimately, the project aims to provide a comprehensive foundation and practical toolkit to achieve well-powered studies and enhance the robustness of inferences in research on congruence theories.

• DFG Programme: Research Grants