Tm 001 697

U.S. DEPARTMENT OF HEALTH. EDUCATION & WELFARE OFFICE OF EDUCATION THIS DOCUMENT HAS BEEN REPRODUCED EXACTLY AS RECEIVED FROM THE PERSON OR ORGANIZATION ORIGINATING IT, POINTS OF VIEW OR OPINIONS STATED DO NOT NECESSARILY REPRESENT OFFICIAL OFFICE OF EDUCATION POSITION OR POLICY. The multivariate analog of Hays w 2 for estimating the strength of the relationship in the multivariate analysis of variance has been proposed in this paper. The multivariate w 2 (denoted by w2 ) iS obtained through mult 2 the use of WilksIs A test criterion. Application of 41Mul t to a numerical example haa been provided so as to help unders4and the mechanics of the formulas necessary for the computation of w 2 mule ** Paper presented at the 56th Annual Meeting of the American Educational Research Association, Chicago, Ui. April 3 T 7, 1972. FILMED FROM BEST AVAILABLE COPY 2 Multivariate Analog of Hays c.,) Darshan Sachdeva University of California, Berkeley It has periodically been suggested to the behavioral researchors that test statistics such as t-ratios or F-raties serve to indicate the statistical significance of observed results and these statistics do not describe their practical importance. The assessment of the practical significance of the.experimental effects, given that they have been found to be statistically significant,. has received attention fro:a time . to time and Hays (1963) saggested 'the following statdstió for this purpose: k 1 SSB SSW W k 2 W SSB (k 1)MSW ,SST. + MSW: SST + SSW' N k (1) where SSB is the between-group sum of squares; MSd is the.within-group mean square, and SST is the total sum Of squares for k groapsin one-way analysis of variance. Clearly, /V as given by (1) is.applicable to Univariate analysis of.variance. The univariate analysis of variance .Yefers to experiments in which one or more independent variables.maybe employed but.Only one.dependent.variable...0n.the other hand, multivariate analysis Of variance is a simple extension of the Univariate analysis of variance where analysis is being' carried out using two or more dependent variables