Powering the Circumplex: A Practical Guide to Sample Size for the Structural Summary Method

The Structural Summary Method (SSM) provides a central framework for evaluating constructs within circumplex models, yet guidance for prospective power analysis has remained unavailable. Here, I extend the SSM from a retrospective tool to one supporting a priori inference. Across two studies, I derive and validate power functions for amplitude and angular displacement. Study 1 establishes analytical power functions for amplitude, demonstrating that meaningful interpersonal differentiation can be detected with modest sample sizes. Study 2 extends this framework to angular displacement, showing that displacement precision depends critically on amplitude, with important implications for displacement-focused hypotheses. Validation using simulation and resampling across multiple datasets confirms that the proposed formulas provide reliable guidance for study design. These results clarify the distinct inferential properties of amplitude and displacement and strengthen the SSM as a tool for prospective research planning within circumplex models. This study's code and materials are available at https://osf.io/63wyf.