Accession Number : AD0725564

Title :   Comparisons in a Class of Approximate F-Tests.

Descriptive Note : Technical rept.,

Corporate Author : SOUTHERN METHODIST UNIV DALLAS TEX DEPT OF STATISTICS

Personal Author(s) : Davenport,James M.

Report Date : 13 APR 1971

Pagination or Media Count : 63

Abstract : In statistical methods, it is often desirable to test the relation Summation, m=1 to k of (Cm Sm) = Summation, j = (k+1) 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 nivi/Si 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 Satterthwaite's 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)

Descriptors :   (*ANALYSIS OF VARIANCE, *STATISTICAL TESTS), COMBINATORIAL ANALYSIS, EXPERIMENTAL DESIGN, MONTE CARLO METHOD, STATISTICAL DISTRIBUTIONS, MATHEMATICAL MODELS

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE