Accession Number : AD0688403

Title :   ON TESTING SOME LINEAR RELATIONS AMONG VARIANCES.

Descriptive Note : Technical rept.,

Corporate Author : SOUTHERN METHODIST UNIV DALLAS TEX DEPT OF STATISTICS

Personal Author(s) : Davenport,James M.

Report Date : 12 APR 1969

Pagination or Media Count : 39

Abstract : In statistical methods, it is often desirable to test that the following relation holds among the variances theta sub i: The sum from m=1 to m=k of (C sub m) (theta sub m) = the sum from j=k+1 to j=p of (C sub j)(theta 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 i)(v sub i)/theta sub i follows the chi-square distribution for each i = 1, 2,..., p. An approximate test of the above relation is Satterthwaite's 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 Satterthwaite's 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)

Descriptors :   (*STATISTICAL TESTS, *ANALYSIS OF VARIANCE), STATISTICAL PROCESSES, PROBABILITY, STATISTICAL DISTRIBUTIONS, DISTRIBUTION THEORY, COMPUTER PROGRAMMING, ERRORS

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE