In practical applications it is frequently assumed that the values obtained by a sampling process are independently drawn from the same normal population. Then confidence intervals and significance tests which were derived under the assumption of independence are applied using these values. Often the assumption of independence between the values may be at best only approximately valid. For some cases, however, it may be permissible to assume that the correlation between each two values is the same (intraclass correlation). The purpose of this paper is to investigate the effect of this intraclass correlation on the confidence coefficients and significance levels of several well known confidence intervals and significance tests which were derived under the assumption of independence, and to extend these considerations to the case of two sets of values. In the first part of the paper the relations given in Table I are used to compute tables which show the effect of intraclass correlation on the confidence coefficients and significance levels of the confidence intervals and significance tests listed in Table II. The second part of the paper consists of the proofs of the relations given in Table I.
"Concerning the Effect of Intraclass Correlation on Certain Significance Tests." Ann. Math. Statist. 18 (1) 88 - 96, March, 1947. https://doi.org/10.1214/aoms/1177730495