Skip to main content
SpringerLink
Log in

Statistics as psychometrics

  • Published:
Psychometrika Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Reference notes

  • 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 

  • Fischhoff, B., Slovic, P., & Lichtenstein, S.Fault trees: Sensitivity of estimated failure probabilities to problem representation (Tech. Rep. PTR-1042-77-8), 1977.

  • Novick, M. R., Turner, N. J., & Novick, L. R.Experimental studies of CADA-based utility assessment procedures (ONR Tech. Rep. No. 2). August, 1980.

  • 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).

  • Tversky, A. & Kahneman, D.The framing of decisions and the rationality of choice (ONR Tech. Rep. No. 2). March 1980.

References

  • Becker, G. M., DeGroot, M. H. & Marschak, J. Measuring utility by a single-response sequential method.Behavioral Science, 1964,9, 226–232.

    Google Scholar 

  • Bolker, E. D. A simultaneous axiomatization of utility and subjective probability.Philosophy of Science, 1967,34, 333–340.

    Google Scholar 

  • 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 

  • 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 

  • Dawes, R. M. Predictive models as a guide to preference.IEEE Transactions on Systems, Man, and Cybernetics, 1977,SMC-7, 355–358.

    Google Scholar 

  • DeFinetti, B.Theory of Probability. London: Wiley, 1974.

    Google Scholar 

  • 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.

  • Fishburn, P. C. A mixture-set axiomatization of conditional subjective expected utility.Econometrica, 1973,41, 1–25.

    Google Scholar 

  • Fishburn, P. C.,Decisions and value theory. New York: John Wiley & Sons, 1964.

    Google Scholar 

  • Fishburn, P. C. Independence in utility theory with whole product sets.Operations Research, 1965,13.

  • Fishburn, P. C.Utility theory for decision making. New York: John Wiley & Sons, 1970.

    Google Scholar 

  • Friedman, M. & Savage, L. J. The utility analysis of choice involving risk.Journal of Political Economy, 1948,56, 279–304.

    Google Scholar 

  • Herstein, I. N. & Milnor, J. An axiomatic approach to measurable utility.Econometrica, 1953,21, 291–297.

    Google Scholar 

  • Hogarth, R. M. Cognitive processes and the assessment of subjective probability distributions.Journal of the American Statistical Association. 1975,70, 271–289.

    Google Scholar 

  • 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 

  • 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 

  • 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 

  • Kahneman, D. & Tversky, A. Subjective probability: A judgment of representativeness.Cognitive Psychology, 1972,3, 430–454.

    Google Scholar 

  • Kahneman, D. & Tversky, A. Prospect theory: An analysis of decision under risk.Econometrica, 1979,47, 263–291.

    Google Scholar 

  • Keeney, D. & Raiffa, H.Decisions with multiple objectives: Preferences and value tradeoffs. New York: John Wiley & Sons, 1976.

    Google Scholar 

  • Keeney, R. L., Utility functions for multiattributed consequences.Management Science, 1972,18, 276–287.

    Google Scholar 

  • Keeney, R. L. Utility independence and preference for multiattributed consequences.Operations Research, 1971,19, 875–893.

    Google Scholar 

  • 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 

  • Lindley, D. V. A class of utility functions.Annals of Statistics, 1976,4, 1–10.

    Google Scholar 

  • 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 

  • Lindley, D. V., Tversky, A. & Brown. On the reconciliation of probability assessments.Journal of the Royal Statistical Society, Series B, 1979,

  • Luce, R. D.Individual choice behavior: A theoretical analysis. New York: John Wiley & Sons, 1959.

    Google Scholar 

  • Luce, R. D. & Krantz, D. H. Conditional expected utility.Econometrica, 1971,39, 253–271.

    Google Scholar 

  • Mosteller, F. & Nogee, P. An experimental measurement of utility.Journal of Political Economy, 1951,59, 371–404.

    Google Scholar 

  • von Neumann, J. & Morgenstern, O.Theory of games and economic behavior. Princeton, N.J.: Princeton University Press, 1944.

    Google Scholar 

  • 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 

  • Novick, M. R. The axioms and principal results of classical test theory.Journal of Mathematical Psychology, 1966,3, 1–18.

    Google Scholar 

  • Novick, M. R., Chuang, D. & DeKeyrel, D. Local and regional coherence utility assessment procedures.Trabajos de Estadistica, in press.

  • 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 

  • 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 

  • Novick, M. R. & Lindley, D. V. Fixed-state assessment of utility functions.Journal of the American Statistical Association, 1979,24, 306–311.

    Google Scholar 

  • 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 

  • Pratt, J. W. Risk aversion in the small and in the large.Econometrika, 1964,32, 122–136.

    Google Scholar 

  • Pratt, J. W., Raiffa, H., & Schlaifer, R.Introduction to statistical decision theory (Prelim. Ed). New York: McGraw-Hill, 1965.

    Google Scholar 

  • Schlaifer, R.Analysis of decisions under uncertainty. New York: McGraw-Hill, 1969.

    Google Scholar 

  • Schlaifer, R.Computer programs for elementary decision analysis. Boston: Harvard University, 1971.

    Google Scholar 

  • Slovic, P., Fischoff, B. & Lichtenstein, S. Behavioral decision theory.Annual Review of Psychology, 1977,28, 1–39.

    Google Scholar 

  • Slovic, P., Lichtenstein, S. C. & Edwards, W. Boredom induced changes in preferences among bets.American Journal of Psychology, 1965,79, 427–434.

    Google Scholar 

  • Spetzler, C. S. & Staël von Holstein, von Holstein, C-A. S. Probability encoding in decision analysis.Management Science, 1975,22, 340–358.

    Google Scholar 

  • Swalm, R. O. Utility theory—insights into risk taking.Harvard Business Review, 1966,44, 123–136.

    Google Scholar 

  • Torgerson, W. S.Theory and methods of scaling. New York: John Wiley & Sons, Inc., 1958.

    Google Scholar 

  • Tversky, A. Additivity, utility, and subjective probability.Journal of Mathematical Psychology, 1967,4, 175–201.

    Google Scholar 

  • Tversky, A. Choice by elimination.Journal of Mathematical Psychology, 1972,9, 341–367.

    Google Scholar 

  • Tversky, A. Elimination by aspects: A theory of choice.Psychological Review, 1972,29, 281–299.

    Google Scholar 

  • 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 

  • Tversky, A. & Kahneman, D. Judgment under uncertainty: Heuristics and biases.Science, 1974,185, 1124–1131.

    Google Scholar 

  • 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 

  • Woodworth, George G.t for two, or preposterior analysis for two decision makers: Interval estimates for the mean.American Statistican, November, 1976.

Download references

Author information

Authors and Affiliations

  1. Lindquist Center for Measurement, University of Iowa, 52242, Iowa City, Iowa

    Melvin R. Novick

Authors
  1. Melvin R. Novick
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

1980 Psychometric Society presidential address.

I am indebted to Paul Slovic and David Libby for valuable consultation on the issues discussed in this paper and to Nancy Turner and Laura Novick for assistance in preparation.

Research reported herein was supported under contract number N00014-77-C-0428 from the Office of Naval Research to The University of Iowa, Melvin R. Novick, principal investigator. Opinions expressed herein reflect those of the author and not those of sponsoring agencies.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Novick, M.R. Statistics as psychometrics. Psychometrika 45, 411–424 (1980). https://doi.org/10.1007/BF02293605

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02293605

Key words

Search

Navigation