Lack-of-Fit Tests Based on Near or Exact Replicates

Abstract

This article shows how to modify an approximate lack-of-fit test proposed by Neill and Johnson (1985) to obtain an exact $F$ test. The modified test is shown to be consistent and to yield uniformly most powerful invariant tests for two specific types of lack of fit. Pure types of lack of fit are (1) lack of fit that exists between clusters of near replicates and (2) lack of fit that is contained within clusters of near replicates. Lack of fit that is a mixture of these two types can be difficult or impossible to find depending on the nature of the mixture.