Comparisons in a Class of Approximate F-Tests.
SOUTHERN METHODIST UNIV DALLAS TEX DEPT OF STATISTICS
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In statistical methods, it is often desirable to test the relation Summation, m1 to k of Cm Sm Summation, j k1 to p of Cj Sj holds among the variances Si. An assumption made in this paper is that there exists independent mean square estimates vi of the variances Si such that niviSi follows the chi-square distribution for each i 1, 2, ..., p. Also each side of the above equation is assumed to be strictly greater than zero. An approximate test of the above relation is Satterthwaites approximate F-test. A method by Cochran is generalized to obtain true type I error and power of the approximate F-tests for the following relations S1 S2 S3 - S4 S1 S2 S3 S4 S1 - S2 S3 - S4 S2 S3 - S4 S1. The alternatives are that the left side of the relation is greater than the right side. These results are then applied to testing the main effects in a three factor factorial design with the random effects. The different methods that are available to carry out this test are all special cases of the approximate F-test. The various methods are compared, and the best testing procedure is chosen. In addition, the properties of this best test are investigated. Author
- Statistics and Probability