A NOTE ON CONFIDENCE BOUNDS CONNECTED WITH ANOVA AND MANOVA FOR BALANCED AND PARTIALLY BALANCED INCOMPLETE BLOCK DESIGNS

摘要

It is well known how in the case of any general “testable” linear hypothesis for either ANOVA or MANOVA one can put simultaneous confidence bounds on a set of parametric functions which light be regarded as measures of deviation from the total hypothesis and its various components.nIn this note for both ANOVA and MANOVA the hypothesis considered is that of equality of the treatment effects-vector equality in the case of MANOVA. Starting from such a hypothesis explicit algebraic ex¬pressions are obtained for the total and partial parametric functions that go with the simultaneous confidence statements in the case of both ANOVA and MANOVA and for balanced and partially balanced designs.