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A Model for Repeat Trial Product Tests

Published online by Cambridge University Press:  01 January 2025

Bruce Buchanan
Bruce Buchanan*
Affiliation:
Marketing Department, New York University
*
Requests for reprints should be sent to Bruce Buchanan, 532 Tisch Hall, New York University, Washington Square South, New York, NY 10003.
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Abstract

A non-forced choice model is developed that describes subject behavior on repeat trial discrimination tests of the “pick 1 of k” form. The model is developed from the Dirichlet distribution, and it allows for the derivation of individual true scores and of sampling properties for various constructs of interest. These results permit the analysis and comparison of test designs. The model is applied to issues such as forced vs. non-forced choice formats, the best number of alternatives at a choice point, and the selection of expert panels.

Keywords

discrimination testingDirichlet distributionrandom guessing

Information

Type
Original Paper
Information
Psychometrika , Volume 52 , Issue 1 , March 1987, pp. 61 - 78
Copyright
Copyright © 1987 The Psychometric Society

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References

Buchanan, B. S. (1983). Design issues in discrimination and preference testing, New York: Columbia University.Google Scholar
Buchanan, B. S., Morrison, D. G. (1984). Optimal design of parity tests. Journal of Mathematical Psychology, 28, 453–466.CrossRefGoogle Scholar
Coombs, C. H., Dawes, R. M., Tversky, A. (1970). Mathematical psychology: An elementary introduction, Englewood Cliffs, N J.: Prentice Hall.Google Scholar
Day, R. L. (1969). Position bias in paired product tests. Journal of Marketing Research, 6, 98–100.CrossRefGoogle Scholar
Day, R. L. (1974). Measuring preferences. In Ferber, R. (Eds.), Handbook of Marketing Research (pp. 3-101–3-125). New York: McGraw Hill.Google Scholar
Duncan, G. T. (1974). An empirical Bayes approach to scoring multiple choice tests in the misinformation model. Journal of the American Statistical Association, 69, 50–57.CrossRefGoogle Scholar
Efron, B. (1982). Maximum likelihood and decision theory. The Annals of Statistics, 10, 340–356.CrossRefGoogle Scholar
Greenhalgh, C. (1966). Some techniques and interesting results in discrimination testing. Journal of the Market Research Society, 8, 215–235.Google Scholar
Guilford, J. P. (1936). The determination of item difficulty when chance success is a factor. Psychometrika, 1, 159–164.CrossRefGoogle Scholar
Grier, J. B. (1975). The number of alternatives for optimum test reliability. Journal of Educational Measurement, 12, 109–112.CrossRefGoogle Scholar
Hambleton, R. K. (1980). Contributions to criterion-referenced testing technology: An introduction. Applied Psychological Measurement, 4, 421–424.CrossRefGoogle Scholar
Himmelblau, D. M. (1972). Applied non-linear programming, New York: McGraw Hill.Google Scholar
Hopkins, J. W., Gridgeman, N. T. (1955). Comparitive sensitivity of pair and triad flavor difference tests. Biometrics, 11, 63–68.CrossRefGoogle Scholar
Horst, P. (1933). The difficulty of a multiple-choice test item. Journal of Educational Psychology, 24, 229–232.CrossRefGoogle Scholar
Huynh., H. (1976). Statistical considerations of mastery scores. Psychometrika, 41, 65–78.CrossRefGoogle Scholar
Irwin, F. W. (1958). An analysis of the concepts of discrimination and preference. American Journal of Psychology, 71, 152–163.CrossRefGoogle ScholarPubMed
Kendall, M. G., Stuart, A. (1977). The advanced theory of statistics, London: Griffin.Google Scholar
Lord, F. M. (1959). An approach to mental test theory. Psychometrika, 24, 283–302.CrossRefGoogle Scholar
Lord, F. M. (1975). Formula scoring and number right scoring. Journal of Educational Measurement, 12, 7–11.CrossRefGoogle Scholar
Lord, F. M. (1977). Optimal number of choices per item—a comparison of four approaches. Journal of Educational Measurement, 14, 33–38.CrossRefGoogle Scholar
Lord, F. M., Novick, M. R. (1968). Statistical theories of mental test scores, Reading, MA: Addison-Wesley.Google Scholar
Magnusson, D. (1966). Test theory, Reading, MA: Addison-Wesley.Google Scholar
Morrison, D. G. (1981). Triangle taste tests: Are the subjects who respond correctly lucky or good?. Journal of Marketing, 45, 111–119.CrossRefGoogle Scholar
Morrison, D. G., Brockway, G. (1979). A modified beta binomial model with applications to multiple choice and taste tests. Psychometrika, 44, 427–442.CrossRefGoogle Scholar
Penny, J. C., Hunt, I. M., Twyman, W. A. (1972). Product testing methodology in relation to marketing problems: A review. Journal of the Market Research Society, 14, 1–29.Google Scholar
Rao, C. R. (1973). Linear statistical inference and its applications, New York: John Wiley.CrossRefGoogle Scholar
Stevens, S. S. (1975). Psychophysics: An introduction to its perceptual, neural and social prospects, New York: Wiley.Google Scholar
Tversky, A. (1964). On the optimal number of alternatives at a choice point. Journal of Mathematical Psychology, 1, 386–391.CrossRefGoogle Scholar
Wilcox, R. R. (1979). Comparing examinees to a control. Psychometrika, 44, 55–68.CrossRefGoogle Scholar
Wilcox, R. R. (1979). Applying ranking and selection techniques to determine the length of a mastery test. Educational and Psychological Measurement, 39, 13–23.CrossRefGoogle Scholar
Wilcox, R. R. (1981). Analyzing the distractors of multiple-choice test items or partitioning multinomial cell probabilities with respect to a standard. Educational and Psychological Measurement, 41, 1051–1068.CrossRefGoogle Scholar
Wilcox, R. R. (1981). Solving measurement problems with an answer until correct scoring procedure. Applied Psychological Measurement, 5, 399–414.CrossRefGoogle Scholar
Wilcox, R. R. (1981). A review of the beta binomial model and its extensions. Journal of Educational Statistics, 6, 3–32.CrossRefGoogle Scholar
Wilcox, R. R. (1981). Selecting thet best ofk examinees whose true score is better than a standard. Educational and Psychological Measurement, 41, 709–716.CrossRefGoogle Scholar
Wilcox, R. R. (1982). Some empirical and theoretical results on an answer until correct scoring procedure. British Journal of Mathematical and Statistical Psychology, 35, 57–70.CrossRefGoogle Scholar
Wilcox, R. R. (1983). How do examinees behave when taking multiple choice tests?. Applied Psychological Measurement, 7, 239–240.CrossRefGoogle Scholar