Graphical Methods for Investigating the Size and Power of Hypothesis Tests

Abstract

Simple techniques for the graphical display of simulation evidence concerning the size and power of hypothesis tests are developed and illustrated. Three types of figures—called P value plots, P value discrepancy plots and size–power curves—are discussed. Some Monte Carlo experiments on the properties of alternative forms of the information matrix test for linear regression models and probit models are used to illustrate these figures. Tests based on the outer‐product‐of‐the‐gradient (OPG) regression generally perform much worse in terms of both size and power than efficient score tests.