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 .
"Normal Regression Theory in the Presence of Intra-Class Correlation." Ann. Math. Statist. 22 (4) 573 - 580, December, 1951. https://doi.org/10.1214/aoms/1177729547