ON CERTAIN APPROXIMATIONS OF POWER OF A TEST PROCEDURE USING TWO PRELIMINARY TESTS IN A MIXED MODEL

Abstract

The present paper is concerned with the derivation of approxi mate formulae for power components of a sometimes pool test pro cedure applied to a mixed model experiment. A comparison of the values of power components evaluated by these formulae with those calculated using series formulae has been made. I. Introduction. In making inferences from the experimental design models, at times there may arise some doubt regarding the inclusion or not of some of the parameters in the model. For example, in a factorial experiment or an experiment with crossed classi fication the experimenter may be uncertain as to whether interaction parameter(s) should appear in the model. This uncertainty in the model specification may be due to the lack of knowledge, either theoretical or from past experience, in regard to the interaction effect(s) at issue. Such situations of uncertainty lead to conditional speci fication of the model and are to be resolved first before making final inferences. The present study has been made for a mixed model split-plot in time experiment involving conditional specification. We are here mainly interested in making inferences regarding the split-plot treatments (split by time). The uncertainty concerning the inclusion or not of the interactions in this model has been resolved by preliminary tests of significance. 1.1. Related Papers and Objective of the Study. Bozivich, Bancroft and Hartley (1956) have derived approximate formulae and exact formulae for power components of a test procedure in a component of variance model. Derivation of approximate formulae for power in a mixed model has been given by