Hostname: page-component-745bb68f8f-v2bm5 Total loading time: 0 Render date: 2025-01-07T18:10:49.054Z Has data issue: false hasContentIssue false
  • English
  • Français

Testing the Identity of Trends under the Restriction of Monotonicity in Repeated Measures Designs

Published online by Cambridge University Press:  01 January 2025

Huynh Huynh
Huynh Huynh*
Affiliation:
University of South Carolina
*
Requests for reprints should be sent to Huynh Huynh, College of Education, University of South Carolina, Columbia, South Carolina 29208.
Get access Rights & Permissions [Opens in a new window]

Abstract

Procedures are described for the analysis of profiles of means in repeated measures designs under order restriction for patterns of mean change. The exact likelihood ratio is derived for the case of two groups of subjects, and a computationally simple alternative to the exact likelihood ratio test is provided for designs involving more than two groups. Tables of critical values are provided for the case of simple-order alternatives.

Keywords

order restrictionstrend analysisrepeated measures designsprofile analysisordered interaction
Type
Original Paper
Information
Psychometrika , Volume 46 , Issue 3 , September 1981 , pp. 295 - 305
Copyright
Copyright © 1981 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

The author wishes to thank Joseph C. Saunders for his editorial assistance.

References

Abelson, R. P., & Tukey, J. W. Efficient utilization of non-numerical information in quantitative analysis: General theory and the case of simple order. Annals of Mathematical Statistics, 1963, 34, 1347–1369.CrossRefGoogle Scholar
Abramowitz, M., & Stegun, I. A. Handbook of mathematical functions, 1968, Washington: National Bureau of Standards.Google Scholar
Barlow, R. E., Bartholomew, D. J., Bremner, J. M., & Brunk, H. D. Statistical inference under order restrictions, 1972, New York: John Wiley & Sons.Google Scholar
Bartholomew, D. J. A test of homogeneity of means under restricted alternatives. Journal of the Royal Statistical Society, Series B, 1961, 23, 239–281.CrossRefGoogle Scholar
Hogg, R. V. On models and hypotheses with restricted alternatives. Journal of the American Statistical Association, 1965, 60, 1153–1162.CrossRefGoogle Scholar
Huynh, H. Some approximate tests for repeated measurement designs. Psychometrika, 1978, 43(2), 161–175.CrossRefGoogle Scholar
Huynh, H., & Feldt, L. S. Conditions under which mean square ratios in repeated measurement designs have exact F-distributions. Journal of the American Statistical Association, 1970, 65, 1582–1589.CrossRefGoogle Scholar
Huynh, H., & Mandeville, G. K. Validity conditions in repeated measures designs. Psychological Bulletin, 1979, 86, 964–973.CrossRefGoogle Scholar
IBM Application Program, System/360. Scientific subroutines package (360-CM-03X) Version III, Programmer's manual, 1971, White Plains, New York: IBM Corporation Technical Publication Department.Google Scholar
IMSL Library 1. Houston: International Mathematical and Statistical Library, 1977.Google Scholar
Kudô, A. A multivariate analogue of the one-sided test. Biometrika, 1963, 50, 403–418.CrossRefGoogle Scholar
Nelson, L. S. Tables for testing ordered alternatives in analysis of variance. Biometrika, 1977, 64, 335–338.CrossRefGoogle Scholar
Pearson, K. Tables of the Incomplete Beta Function, 1934, Cambridge: University Press.Google Scholar