ON TESTING SOME LINEAR RELATIONS AMONG VARIANCES.
SOUTHERN METHODIST UNIV DALLAS TEX DEPT OF STATISTICS
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In statistical methods, it is often desirable to test that the following relation holds among the variances theta sub i The sum from m1 to mk of C sub m theta sub m the sum from jk1 to jp of C sub jtheta sub j. An assumption made in this paper is that there exists independent mean square estimates v sub i of the variances theta sub i such that n sub iv sub itheta sub i follows the chi-square distribution for each i 1, 2,..., p. An approximate test of the above relation is Satterthwaites approximate F-test. A solution, when testing the relation theta sub 3 theta sub 1 theta sub 2, is developed for finding the true probability of being in the rejection region, when the Satterthwaite approximate F-test is used, and these probabilities are presented for several values of the parameters involved. A comparison of the results obtained is made with the work done by W. G. Cochran in this area. In addition, methods are developed for finding the true probabilities of being in the rejection region, when using Satterthwaites approximate F-test for testing the relations theta sub 1 theta sub 2 theta sub 3 theta sub 4 and theta sub 1 theta sub 2 theta sub 3 - theta sub 4. However, in these cases none of the probabilities are presented. Author
- Statistics and Probability