Hostname: page-component-745bb68f8f-d8cs5 Total loading time: 0 Render date: 2025-01-08T09:52:44.775Z Has data issue: false hasContentIssue false
  • English
  • Français

Tests of Hypothesis in a Repeated Measures Design from a Permutation Viewpoint

Published online by Cambridge University Press:  01 January 2025

Raymond O. Collier Jr. ,
Frank B. Baker  and
Garrett K. Mandeville
Raymond O. Collier Jr.
Affiliation:
University of Minnesota
Frank B. Baker
Affiliation:
University of Wisconsin
Garrett K. Mandeville
Affiliation:
University of Minnesota
Get access Rights & Permissions [Opens in a new window]

Abstract

Repeated measures designs have been widely employed in psychological experimentation, however, such designs have rarely been analyzed by means of permutation procedures. In the present paper certain aspects of hypothesis tests in a particular repeated measures design (one non-repeated factor (A) and one repeated factor (B) with K subjects per level of A) were investigated by means of permutation rather than sampling processes. The empirical size and power of certain normal theory F-tests obtained under permutation were compared to their nominal normal theory values. Data sets were established in which various combinations of kurtosis of subject means and intra-subject variance heterogeneity existed in order that their effect upon the agreement of these two models could be ascertained. The results indicated that except in cases of high intra-subject variance heterogeneity, the usual F-tests on B and AB exhibited approximately the same size and power characteristics whether based upon a permutation or normal theory sampling basis.

Type
Original Paper
Information
Psychometrika , Volume 32 , Issue 1 , March 1967 , pp. 15 - 24
Copyright
Copyright © 1967 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

*

This research prepared under Contract No. 2593 from the Cooperative Research Branch of the U. S. Office of Education.

References

Baker, F. B. and Collier, R. O. Monte Carlo F-II: A computer program for analysis of varianceF-tests by means of permutation. Educ. Psych. Measmt., 1966, 26, 169–173.CrossRefGoogle Scholar
Baker, F. B. and Collier, R. O. Some empirical results on variance ratios under permutation in the completely randomized design. J. Amer. Statist. Assoc., 1966, 61, 814–820.CrossRefGoogle Scholar
Box, G. E. P. Some theorems on quadratic forms applied in the study of analysis of variance problems, I. Effect of inequality of variance in the one-way classification. Ann. Math. Stat., 1954, 25, 290–302.CrossRefGoogle Scholar
Box, G. E. P. Some theorems on quadratic forms applied in the study of analysis of variance problems, II. Effects of inequality of variance and of correlation between errors in a two-way classification. Ann. Math. Stat., 1954, 25, 484–498.CrossRefGoogle Scholar
Collier, R. O., Baker, F. B., Mandeville, G., and Hayes, T. F. An empirical comparison of three test procedures in a repeated measures design. (Unpublished manuscript).Google Scholar
Friedman, M. The use of ranks to avoid the assumption of normality implicit in the analysis of variance. J. Amer. Statist. Assoc., 1937, 32, 675–701.CrossRefGoogle Scholar
Geisser, S. and Greenhouse, S. W. An extension of Box's results on the use of theF distribution in multivariate analysis. Ann. Math. Stat., 1958, 29, 885–891.CrossRefGoogle Scholar
Greenhouse, S. W. and Geisser, S. On methods in the analysis of profile data. Psychometrika, 1959, 24, 95–112.CrossRefGoogle Scholar
Kempthorne, O., Zyskind, G., Addleman, S., Throckmorton, T., and White, R. Analysis of variance procedures. ARL Report 149, U.S.A.F., 1961.Google Scholar
Lana, R. E. and Lubin, A. The effect of correlation on the repeated measures design. Educ. Psych. Measmt., 1963, 23, 729–739.CrossRefGoogle Scholar
Pearson, E. S. and Hartley, H. O. Charts of the power function for analysis of variance tests, derived from the non-centralF-distribution. Biometrika, 1951, 38, 112–130.CrossRefGoogle Scholar
Pitman, E. J. G. Significance tests which may be applied to samples from any populations. J. Roy. Stat. Soc. Suppl., 1937, 4, 119–130.CrossRefGoogle Scholar
Pitman, E. J. G. Significance tests which may be applied to samples from any populations: III. The analysis of variance test. Biometrika, 1937, 29, 322–335.Google Scholar
Scheffé, H.. The analysis of variance, New York: Wiley and Sons, 1959.Google Scholar
Welch, B. L. On thez-test in randomized blocks and Latin squares. Biometrika, 1937, 29, 21–52.CrossRefGoogle Scholar
Wilk, M. B. and Kempthorne, O. Derived linear models and their use in the analysis of randomized experiments. WADC Technical Report, 1956, II, 55–244.Google Scholar
Winer, B. J. Statistical principles in experimental design, New York: McGraw-Hill, 1962.CrossRefGoogle Scholar