Hostname: page-component-745bb68f8f-hvd4g Total loading time: 0 Render date: 2025-01-07T19:22:14.375Z Has data issue: false hasContentIssue false
  • English
  • Français

ANOVA and ANCOVA of Pre- and Post-Test, Ordinal Data

Published online by Cambridge University Press:  01 January 2025

Mark L. Davison  and
Anu R. Sharma
Mark L. Davison*
Affiliation:
University of Minnesota
Anu R. Sharma
Affiliation:
Search Institute, Minneapolis, MN
*
Requests for reprints should be addressed to Mark L. Davison, Department of Educational Psychology, University of Minnesota, Minneapolis, MN 55455.
Get access Rights & Permissions [Opens in a new window]

Abstract

With random assignment to treatments and standard assumptions, either a one-way ANOVA of post-test scores or a two-way, repeated measures ANOVA of pre- and post-test scores provides a legitimate test of the equal treatment effect null hypothesis for latent variable Θ. In an ANCOVA for pre- and post-test variables X and Y which are ordinal measures of η and Θ, respectively, random assignment and standard assumptions ensure the legitimacy of inferences about the equality of treatment effects on latent variable Θ. Sample estimates of adjusted Y treatment means are ordinal estimators of adjusted post-test means on latent variable Θ.

Keywords

analysis of varianceanalysis of covariancegain scoresordinal dataparametric statistics
Type
Original Paper
Information
Psychometrika , Volume 59 , Issue 4 , December 1994 , pp. 593 - 600
Copyright
Copyright © 1994 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.)

References

Brunk, H. D. (1965). An introduction to mathematical statistics, Blaisdell, MA: Blaisdell.Google Scholar
Davison, M. L., Sharma, A. R. (1988). Parametric statistics and levels of measurement. Psychological Bulletin, 104, 137–144.CrossRefGoogle Scholar
Davison, M. L., Sharma, A. R. (1990). Parametric statistics and levels of measurement: Factorial designs and multiple regression. Psychological Bulletin, 107, 394–400.CrossRefGoogle Scholar
Huck, S. W., McClean, R. A. (1975). Using a repeated measures ANOVA to analyze the data from a pretest-posttest design: A potentially confusing task. Psychological Bulletin, 82, 511–518.CrossRefGoogle Scholar
Lord, F. M. (1967). A paradox in the interpretation of group comparisons. Psychological Bulletin, 68, 304–305.CrossRefGoogle ScholarPubMed
Luce, R. D., Krantz, D. H., Suppes, P., Tversky, A. (1990). Foundations of measurement (Vol. 3), New York: Academic Press.Google Scholar
Maxwell, S. E., Delaney, H. D. (1985). Measurement scales and statistics: An examination of variable validity. Psychological Bulletin, 97, 85–93.CrossRefGoogle Scholar
Mitchell, J. (1986). Measurement scales and statistics: A clash of paradigms. Psychological Bulletin, 100, 398–407.CrossRefGoogle Scholar
Mosteller, F., Tukey, J. W. (1977). Data analysis and regression: A second course in statistics, Reading, MA: Addison-Wesley.Google Scholar
Porter, A. C., Raudenbush, S. W. (1987). Analysis of covariance: Its model and use in psychological research. Journal of Counseling Psychology, 34, 383–392.CrossRefGoogle Scholar
Suppes, P. (1959). Measurement, empirical meaningfulness, and three-valued logic. In Churchman, C. W., Ratoosh, P. (Eds.), Measurement: Definitions and theories (pp. 129–143). New York: Wiley.Google Scholar
Townsend, J. T. (1990). Truth and consequences of ordinal differences in statistical distributions: Toward a theory of hierarchical inference. Psychological Bulletin, 108, 551–567.CrossRefGoogle Scholar
Townsend, J. T., Ashby, F. G. (1984). Measurement scales and statistics: The misconception misconceived. Psychological Bulletin, 96, 394–401.CrossRefGoogle Scholar