Normal Regression Theory in the Presence of Intra-Class Correlation

Abstract

In this paper we prove that certain estimators and tests of significance used in regression analysis when observations are independent are equally valid in the presence of intra-class correlation. An application of this result is presented for the situation in which several replications of the correlated set of observations are available. As a special case of this application, it is shown that the usual test of ``column effects'' in the analysis of variance for a two-way classification remains valid when rows are independent and columns are uniformly correlated. This latter fact is also pointed out in [3].