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Confidence Intervals for the Means of Dependent, Normally Distributed Variables

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Methods report constructing confidence intervals for means of dependent variables, suggesting further investigation into correlation effects.

This research explores methods for creating confidence intervals for the means of dependent, normally distributed variables without known correlations.
Evaluated various methods for confidence interval construction, focusing on the Student t distribution, Hotelling's T, and Scheffé's intervals.
Analyzed the performance of these methods based on degrees of freedom and correlation knowledge.
The t distribution provides confidence intervals that are almost optimally short when degrees of freedom are adequate.
Intervals produced using Hotelling's T and Scheffé's methods are significantly longer than those using the t distribution.
Suggests future research on how knowing correlation structures can shorten these intervals.

Olive Jean Dunn (1959) studied this question.

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Methods report constructing confidence intervals for means of dependent variables, suggesting further investigation into correlation effects.