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Likelihood Methods for Testing Group Problem Solving Models with Censored Data

Published online by Cambridge University Press:  01 January 2025

Ronald R. Regal  and
Kinley Larntz
Ronald R. Regal
Affiliation:
University of Minnesota
Kinley Larntz*
Affiliation:
University of Minnesota
*
Requests for reprints should be sent to Kinley Larntz, Department of Applied Statistics, University of Minnesota, 352 Classroom Office Building, 1994 Buford Avenue, St. Paul, MN 55108.
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Abstract

Problem solving models relating individual and group solution times under time limit censoring are presented. Maximum likelihood estimates of parameters of the resulting censored distributions are derived and goodness of fit tests for the individual-group models are constructed. The methods are illustrated on data previously analyzed by Restle and Davis.

Keywords

maximum likelihoodgoodness of fit tests
Type
Article
Information
Psychometrika , Volume 43 , Issue 3 , September 1978 , pp. 353 - 366
Copyright
Copyright © 1978 The Psychometric Society

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Footnotes

Ronald R. Regal is now at the Department of Mathematics, State University of New York at Albany, Albany, New York. This research was supported by grants from the Graduate School, University of Minnesota. Also, work of the second author was aided by a Single Quarter Leave granted by the Regents of the University of Minnesota.

References

Reference Notes

Gehan, E. A. Analyzing survival data by distribution-free methods. Paper presented at the Thirty-Second Annual Princeton Conference on Applied Statistics, December 1976.Google Scholar
Kaplan, E. B. & Elston, R. C. A subroutine package for maximum likelihood estimation (MAXLIK). (Mimeo Series No. 823). University of North Carolina, Institute of Statistics, 1972.Google Scholar

References

Cohen, A. C. The reflected Weibull distribution. Technometrics, 1973, 15, 861–873.CrossRefGoogle Scholar
Cramér, H. Mathematical Methods of Statistics, 1946, Princeton: Princeton University Press.Google Scholar
Davis, J. H. & Restle, F. The analysis of problems and prediction of group problem solving. Journal of Abnormal and Social Psychology, 1963, 66, 103–116.CrossRefGoogle ScholarPubMed
Durbin, J. Weak convergence of the sample distribution function when parameters are estimated. Annals of Statistics, 1973, 1, 279–290.CrossRefGoogle Scholar
Fienberg, S. E. & Larntz, K. Some models for individual-group comparisons and group behavior. Psychometrika, 1971, 36, 349–367.CrossRefGoogle Scholar
Fisher, R. A. On the mathematical foundations of theoretical statistics. Philisophical Transactions of the Royal Society, Series A, 1922, 222, 309–368.Google Scholar
Gross, A. J. & Clark, V. A. Survival distributions: Reliability applications in the biomedical sciences, 1975, New York: Wiley.Google Scholar
Hager, H. W., Bain, L. J. & Antle, C. E. Reliability estimation for the generalized gamma distribution and robustness of the Weibull model. Technometrics, 1971, 13, 547–557.CrossRefGoogle Scholar
Halperin, M. Maximum likelihood estimation in truncated samples. Annals of Mathematical Statistics, 1952, 23, 226–238.CrossRefGoogle Scholar
Lorge, I. & Solomon, H. Two models of group behavior in the solution of eureka-type problems. Psychometrika, 1955, 20, 139–148.CrossRefGoogle Scholar
Mann, N. R., Schafer, R. E., & Singpurwalla, N. D. Methods for statistical analysis of reliability and life data, 1974, New York: Wiley.Google Scholar
Regal, R. R. Some parametric and nonparametric methods for individual and group performance. Unpublished doctoral dissertation, University of Minnesota, 1975.Google Scholar
Restle, F. & Davis, J. H. Success and speed of problem solving by individuals and groups. Psychological Review, 1962, 69, 520–536.CrossRefGoogle ScholarPubMed
Shaw, M. E. Comparison of individuals and small groups in the rational solution of complex problems. American Journal of Psychology, 1932, 44, 491–504.CrossRefGoogle Scholar