Some Multiple Decision Problems in Analysis of Variance
PURDUE UNIV LAFAYETTE IN DEPT OF STATISTICS
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In most practical situations to which the analysis of variance tests are applied, they do not supply the information that the experimenter aims at. If, for example, in one-way ANOVA the hypothesis is rejected in actual application of the F-test, the resulting conclusion that the true means theta sub 7, ...,theta sub K are not all equal, would by itself usually be insufficient to satisfy the experimenter. In fact his problems would begin at this stage. The experimenter may desire to select the best population or a subset of the good populations he may like to rank the populations in order of goodness or he may like to draw some other inferences about the parameters of interest. The extensive literature on selection and ranking procedures depends heavily on the use of independence between populations block, treatments, etc. in the analysis of variance. In the present paper, a method was derived to construct locally best in some sense selection procedures to select a non empty subset of the k populations containing the best population as ranked in terms of theta sub 1s which control the size of the selected subset and which maximizes the probability of selecting the best. Also considered was the usual selection procedures in one-way ANOVA based on the generalized least squares estimates and apply the method to two-way layout case.
- Statistics and Probability
- Operations Research