
Accession Number : AD0725564
Title : Comparisons in a Class of Approximate FTests.
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 chisquare 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 Ftest. A method by Cochran is generalized to obtain true type I error and power of the approximate Ftests 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 Ftest. 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