Consistency of Invariants for the Multivariate Analysis of Variance
Technical rept. no. 20
STANFORD UNIV CA DEPT OF STATISTICS
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Two notions of consistency of invariant tests for tbe MANOVA testing problems are examined and compared sample size consistency the classical notion and parameter consistency, which requires chat for fixed sample size, the power of the test approaches one for any sequence of alternatives whose distance from the null hypothesis approaches infinity. The Roy, Lawley-Hotelling, and likelihood ratio Wilks criterion tests are consistent in both senses, whereas the Bartlett-Nanda-Pillai trace test, although sample size consistent, is not parameter consistent unless the significance level a or the error degrees of freedom n is sufficiently large.
- Statistics and Probability