GRAPHICAL METHODS FOR INVESTIGATING THE SIZE AND POWER OF HYPOTHESIS TESTS

Simple techniques for the graphical display of simulation evidence con cerning the size and power of hypothesis tests are developed and illus trated. Three types of figures-called P value plots, P value discrepan cy plots and size-power curves-are discussed. Some Monte Carlo experim ents on the properties of alternative forms of the information matrix test for linear regression models and probit models are used to illust rate 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.