Interval Estimates for Linear Combinations of Means

A. J. Scott and T. M. F. Smith

Journal of the Royal Statistical Society Series C, 1971, vol. 20, issue 3, 276-285

Abstract: If xij (i = 1, …, k; j = 1, …, ni) are independent normal random variables with mean μi and variance σ2i, then interval estimates for linear combinations of the μi's based on a simple normal approximation to Student's t‐distribution, are shown to be adequate approximations to the available alternative intervals for values of α near 0·05. The approximate intervals can be regarded either as conservative confidence intervals or as posterior probability intervals and do not require the use of special tables such as those for the Behrens–Fisher or Welch solutions of the two means problems. The approximation holds good for k > 2 for which no tables of the alternative solutions exist.

Date: 1971
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