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A Binomial Test for Hierarchical Dependency

Published online by Cambridge University Press:  01 January 2025

Roland B. Guay  and
George P. McCabe
Roland B. Guay
Affiliation:
Department of Statistics, Purdue University
George P. McCabe*
Affiliation:
Department of Statistics, Purdue University
*
Requests for reprints should be sent to George P. McCabe, Statistics Department, Purdue University, West Lafayette, IN 47907.
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Abstract

A binomial test for hierarchical dependency is presented. The null hypothesis is that all members of a population who possess a certain skill are a subset of the members who possess another skill. This hypothesis is basic to the writings of several prominent theorists, such as Gagné and Piaget. The model, assumptions, formula derivations, and procedures for the test are explained. An illustrative example is also provided.

Keywords

hierarchical dependencybinomial test
Type
Original Paper
Information
Psychometrika , Volume 51 , Issue 3 , September 1986 , pp. 467 - 474
Copyright
Copyright © 1986 The Psychometric Society

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References

Bart, W., Krus, D. (1973). An ordering theoretic method to determine hierarchies among items. Educational and Psychological Measurement, 33, 291–300.CrossRefGoogle Scholar
Dayton, C., Macready, G. B. (1976). A probabilistic model for validation of behavioral hierarchies. Psychometrika, 41, 189–204.CrossRefGoogle Scholar
Gagné, R. (1965). The conditions of learning, NY: Holt, Rinehart and Winston.Google Scholar
Gagné, R. M., Paradise, N. E. (1961). Abilities and learning sets in knowledge acquisition. Psychological Monographs, 75, 1–23.CrossRefGoogle Scholar
Goodman, L. (1959). Simple statistical methods for scalogram analysis. Psychometrika, 24, 29–43.CrossRefGoogle Scholar
Guay, R. B. (1976). The developmental relationship between two Piagetian projective space operations. Dissertation Abstracts International, 36, 3605B.Google Scholar
Guttman, L. (1944). A basis for scaling qualitative data. American Sociological Review, 9, 139–150.CrossRefGoogle Scholar
Hildebrand, D., Laing, J., Rosenthal, H. (1977). Prediction analysis of cross classifications, NY: Wiley.Google Scholar
Keats, J. (1957). A test of significance of differences between correlated proportions. Australian Journal of Psychology, 9, 149–153.CrossRefGoogle Scholar
Mokken, R. J., Lewis, C. (1982). A nonparametric approach to the analysis of dichotomous item responses. Applied Psychological Measurement, 6, 417–430.CrossRefGoogle Scholar
Moore, D. S. (1978). Chi-square tests. In Hogg, R. V. (Eds.), Studies in statistics (pp. 66–106). Washington, DC: Mathematical Association of America.Google Scholar
Piaget, J. (1963). Psychology of intelligence, Paterson, NJ: Littlefield, Adams & Co..Google Scholar
Rao, C. R. (1965). Linear statistical inference and its applications, New York: Wiley.Google Scholar
Sagi, P. (1959). A statistical test for the significance of a coefficient of reproducibility. Psychometrika, 24, 19–27.CrossRefGoogle Scholar
White, R. T. (1974). Indexes used in testing the validity of learning hierarchies. Journal of Research in Science Teaching, 11, 61–66.CrossRefGoogle Scholar
White, R. T., Clark, R. M. (1973). A test of inclusion which allows for errors of measurement. Psychometrika, 38, 77–86.CrossRefGoogle Scholar