Confidence Intervals for the Means of Dependent, Normally Distributed Variables

Abstract

Several possible methods are presented for constructing confidence intervals for the means of normally distributed, dependent variables when nothing is known about the correlations. One, which uses the Student t distribution, is found, when the degrees of freedom is not too small compared to the number of variables, to give intervals almost as short as can possibly be attained. Methods based on Hotelling's T and on Scheffé's confidence intervals for all linear contrasts are found to yield intervals appreciably longer than those using the t distribution. The extent to which these intervals may be shortened when some knowledge of the correlation structure is available is suggested as a problem for investigation.