, Volume 45, Issue 4, pp 411–424 | Cite as

Statistics as psychometrics

  • Melvin R. Novick


In this paper, modern statistics is considered as a branch of psychometrics and the question of how the central problems of statistics can be resolved using psychometric methods is investigated. Theories and methods developed in the fields of test theory, scaling, and factor analysis are related to the principle problems of modern statistical theory and method. Topics surveyed include assessment of probabilities, assessment of utilities, assessment of exchangeability, preposterior analysis, adversary analysis, multiple comparisons, the selection of predictor variables, and full-rank ANOVA. Reference is made to some literature from the field of cognitive psychology to indicate some of the difficulties encountered in probability and utility assessment. Some methods for resolving these difficulties using the Computer-Assisted Data Analysis (CADA) Monitor are described, as is some recent experimental work on utility assessment.

Key words

Bayesian decision theory utility theory computer assisted data analysis 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Reference notes

  1. Card, W. I., Rusinkiewicz, M., & Phillips, C. I.Estimation of the utilities of states of health with different visual acuities using a wagering technique. Dijon, France: IF/P TC4 Working Conference on Decision Making and Medical Care, 1975.Google Scholar
  2. Fischhoff, B., Slovic, P., & Lichtenstein, S.Fault trees: Sensitivity of estimated failure probabilities to problem representation (Tech. Rep. PTR-1042-77-8), 1977.Google Scholar
  3. Novick, M. R., Turner, N. J., & Novick, L. R.Experimental studies of CADA-based utility assessment procedures (ONR Tech. Rep. No. 2). August, 1980.Google Scholar
  4. Slovic, P. From Shakespeare to Simon: Speculations—and some evidence—about man's ability to process information.Oregon Research Institute Research Bulletin, 1972,12 (2).Google Scholar
  5. Tversky, A. & Kahneman, D.The framing of decisions and the rationality of choice (ONR Tech. Rep. No. 2). March 1980.Google Scholar


  1. Becker, G. M., DeGroot, M. H. & Marschak, J. Measuring utility by a single-response sequential method.Behavioral Science, 1964,9, 226–232.Google Scholar
  2. Bolker, E. D. A simultaneous axiomatization of utility and subjective probability.Philosophy of Science, 1967,34, 333–340.Google Scholar
  3. Coombs, C. H. Portfolio theory and the measurement of risk. In M. F. Kaplan & S. Schwartz (Eds.),Human judgment and decision processes. New York: Academic Press, Inc., 1975, 63–85.Google Scholar
  4. Dawes, R. M. A case study of graduate admissions: Application of three principles of human decision making.American Psychologist, 1971,26, 180–188.Google Scholar
  5. Dawes, R. M. Predictive models as a guide to preference.IEEE Transactions on Systems, Man, and Cybernetics, 1977,SMC-7, 355–358.Google Scholar
  6. DeFinetti, B.Theory of Probability. London: Wiley, 1974.Google Scholar
  7. Fischhoff, B., Slovic, P. & Lichtenstein, S. Knowing what you want: Measuring labile values. In T. Wallsten (Ed.),Cognitive Processes in Choice and Decision Behavior. Hillsdale, New Jersey: Erlbaum, in press.Google Scholar
  8. Fishburn, P. C. A mixture-set axiomatization of conditional subjective expected utility.Econometrica, 1973,41, 1–25.Google Scholar
  9. Fishburn, P. C.,Decisions and value theory. New York: John Wiley & Sons, 1964.Google Scholar
  10. Fishburn, P. C. Independence in utility theory with whole product sets.Operations Research, 1965,13.Google Scholar
  11. Fishburn, P. C.Utility theory for decision making. New York: John Wiley & Sons, 1970.Google Scholar
  12. Friedman, M. & Savage, L. J. The utility analysis of choice involving risk.Journal of Political Economy, 1948,56, 279–304.Google Scholar
  13. Herstein, I. N. & Milnor, J. An axiomatic approach to measurable utility.Econometrica, 1953,21, 291–297.Google Scholar
  14. Hogarth, R. M. Cognitive processes and the assessment of subjective probability distributions.Journal of the American Statistical Association. 1975,70, 271–289.Google Scholar
  15. Hull, J., Moore, P. G. & Thomas, H. Utility and its measurement.Journal of the Royal Statistical Society, Series A, 1973,136, 226–247.Google Scholar
  16. Jackson, P. H., Novick, M. R. & DeKeyrel, D. F. Adversary preposterior analysis for simple parametric models. In A. Zellner (Ed.),Bayesian analysis in econometrics and statistics—Essays in honor of Harold Jeffreys. Studies in Bayesian econometric (Vol. 1). Amsterdam: North-Holland Publishing Company, 1980.Google Scholar
  17. Jeffrey, R. C. New foundations for Bayesian decision theory. In Y. Bar-Hillel (Ed.),Logic, Methodology and Philosophy of Science. Amsterdam: North-Holland Publishing Co., 1965, 289–300.Google Scholar
  18. Kahneman, D. & Tversky, A. Subjective probability: A judgment of representativeness.Cognitive Psychology, 1972,3, 430–454.Google Scholar
  19. Kahneman, D. & Tversky, A. Prospect theory: An analysis of decision under risk.Econometrica, 1979,47, 263–291.Google Scholar
  20. Keeney, D. & Raiffa, H.Decisions with multiple objectives: Preferences and value tradeoffs. New York: John Wiley & Sons, 1976.Google Scholar
  21. Keeney, R. L., Utility functions for multiattributed consequences.Management Science, 1972,18, 276–287.Google Scholar
  22. Keeney, R. L. Utility independence and preference for multiattributed consequences.Operations Research, 1971,19, 875–893.Google Scholar
  23. Krantz, D. H., Luce, R. D., Suppes, P. & Tversky, A.Foundations of measurement. Volume 1: Additive and polynomial representations. New York: Academic Press, 1971.Google Scholar
  24. Lindley, D. V. A class of utility functions.Annals of Statistics, 1976,4, 1–10.Google Scholar
  25. Lindley, D. V. & Smith, A. F. M. Bayes estimates for the linear model.Journal of the Royal Statistical Society, Series B, 1972,34, 1–41.Google Scholar
  26. Lindley, D. V., Tversky, A. & Brown. On the reconciliation of probability assessments.Journal of the Royal Statistical Society, Series B, 1979,Google Scholar
  27. Luce, R. D.Individual choice behavior: A theoretical analysis. New York: John Wiley & Sons, 1959.Google Scholar
  28. Luce, R. D. & Krantz, D. H. Conditional expected utility.Econometrica, 1971,39, 253–271.Google Scholar
  29. Mosteller, F. & Nogee, P. An experimental measurement of utility.Journal of Political Economy, 1951,59, 371–404.Google Scholar
  30. von Neumann, J. & Morgenstern, O.Theory of games and economic behavior. Princeton, N.J.: Princeton University Press, 1944.Google Scholar
  31. Novick, M. R. A Bayesian approach to the selection of predictor variables. In C. E. Lunneborg (Ed.),Current problems and techniques in multivariate psychology. Seattle, Washington: The University of Washington, 1970.Google Scholar
  32. Novick, M. R. The axioms and principal results of classical test theory.Journal of Mathematical Psychology, 1966,3, 1–18.Google Scholar
  33. Novick, M. R., Chuang, D. & DeKeyrel, D. Local and regional coherence utility assessment procedures.Trabajos de Estadistica, in press.Google Scholar
  34. Novick, Melvin R., Hamer, Robert M., Libby, David D., Chen, James J. & Woodworth, George G.Manual for the Computer-Assisted Data Analyais (CADA) Monitor (1980). Iowa City, Iowa: The University of Iowa, 1980.Google Scholar
  35. Novick, M. R., Jackson, P. H. & Thayer, D. T. Bayesian inference and the classical test theory model: Reliability and true scores.Psychometrika, 1971,36, 261–288.Google Scholar
  36. Novick, M. R. & Lindley, D. V. Fixed-state assessment of utility functions.Journal of the American Statistical Association, 1979,24, 306–311.Google Scholar
  37. Novick, M. R. & Lindley, D. V. The use of more realistic utility functions in educational applications.Journal of Educational Measurement, 1978,15, 181–192.Google Scholar
  38. Pratt, J. W. Risk aversion in the small and in the large.Econometrika, 1964,32, 122–136.Google Scholar
  39. Pratt, J. W., Raiffa, H., & Schlaifer, R.Introduction to statistical decision theory (Prelim. Ed). New York: McGraw-Hill, 1965.Google Scholar
  40. Schlaifer, R.Analysis of decisions under uncertainty. New York: McGraw-Hill, 1969.Google Scholar
  41. Schlaifer, R.Computer programs for elementary decision analysis. Boston: Harvard University, 1971.Google Scholar
  42. Slovic, P., Fischoff, B. & Lichtenstein, S. Behavioral decision theory.Annual Review of Psychology, 1977,28, 1–39.Google Scholar
  43. Slovic, P., Lichtenstein, S. C. & Edwards, W. Boredom induced changes in preferences among bets.American Journal of Psychology, 1965,79, 427–434.Google Scholar
  44. Spetzler, C. S. & Staël von Holstein, von Holstein, C-A. S. Probability encoding in decision analysis.Management Science, 1975,22, 340–358.Google Scholar
  45. Swalm, R. O. Utility theory—insights into risk taking.Harvard Business Review, 1966,44, 123–136.Google Scholar
  46. Torgerson, W. S.Theory and methods of scaling. New York: John Wiley & Sons, Inc., 1958.Google Scholar
  47. Tversky, A. Additivity, utility, and subjective probability.Journal of Mathematical Psychology, 1967,4, 175–201.Google Scholar
  48. Tversky, A. Choice by elimination.Journal of Mathematical Psychology, 1972,9, 341–367.Google Scholar
  49. Tversky, A. Elimination by aspects: A theory of choice.Psychological Review, 1972,29, 281–299.Google Scholar
  50. Tversky, A. On the elicitation of preferences: Descriptive and prescriptive considerations. In D. E. Bell, R. L. Keeney & H. Raiffa (Eds.),Conflicting objectives in decisions. Chichester: John Wiley & Sons, 1977, 209–222.Google Scholar
  51. Tversky, A. & Kahneman, D. Judgment under uncertainty: Heuristics and biases.Science, 1974,185, 1124–1131.Google Scholar
  52. Woodworth, George G. Numerical evaluation of preposterior expectations in the two-parameter normal model, with an application to preposterior consenses analysis. In A. Zellner (Ed.),Bayesian analysis in econometrics and statistics. Amsterdam: North-Holland Publishing Company, 1980.Google Scholar
  53. Woodworth, George G.t for two, or preposterior analysis for two decision makers: Interval estimates for the mean.American Statistican, November, 1976.Google Scholar

Copyright information

© The Psychometric Society 1980

Authors and Affiliations

  • Melvin R. Novick
    • 1
  1. 1.Lindquist Center for MeasurementUniversity of IowaIowa City

Personalised recommendations