A Formal Graphical Inference Framework for Combining Effect Size with Statistical Significance: Application to Multivariate and Functional Linear Models
This study addresses the limitations of traditional hypothesis testing, which often neglects practical effect sizes and provides only weak error rate control. We propose a graphical inference framework that integrates effect sizes with uncertainty quantification for multivariate and functional linear models. The core methodology employs step-down global envelopes, combining resampling techniques with hypothesis test correction to achieve exact strong family-wise error rate (FWER) control under exchangeability conditions. This framework yields visual interpretations of effects alongside adjusted subset p-values, effectively overcoming the constraints of conventional binary testing. By simultaneously accounting for magnitude and variability, our approach substantially enhances both the interpretability and rigor of statistical inference.