Interval Estimation for Linear Combinations of Means
Abstract The simultaneous interval estimation for a given set of linear combinations of means whose estimates are jointly normally distributed is treated. In order to give the exact confidence intervals, t 2 M , the maximum of several quasi-independent t 2-statistics, is introduced. Using the inclusion-exclusion formula, a procedure and tables are given for obtaining a good approximation to the exact upper percentage point of t 2 M . As illustrative examples, the procedure is applied to the interval estimations for parameters in the model of a randomized block design and for coefficients in a normal regression equation.