Advertisement

Some Distribution Theory Related to the Analysis of Subjective Performance in Inferential Tasks

  • J. Aitchison
Part of the NATO Advanced study Institutes Series book series (ASIC, volume 79)

Summary

When inferences made by a subject differ from normative statistical inferences it is possible to define measures of this divergence which throw considerable light on the nature of the deficiencies in the subjective performance. These measures involve quantifying differences between distributions. For the analysis of a single subject performing a single task the paper generalizes previous work by replacing absolute measures by more meaningful relative measures and by extending the scope of the inferential tasks involved. For a single subject performing many tasks and for groups of different subjects statistical analysis requires a rich parametric class of distributions to describe patterns of variability of probabilistic data, and the use of logistic-normal distributions is advocated for this purpose. Simple illustrations are provided of the main analytical techniques.

Key Words

Degree of uncertainty feature selection discrepancy inference discrepancy inferential tasks information gain index logistic normal distributions normative models performance analysis probabilistic data subjective inference 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aitchison, J. (1974). Hippocratic inference. Bulletin of the Institute of Mathematics and its Applications, 10, 48–53.Google Scholar
  2. Aitchison, J. (1975). Goodness of prediction fit. Biometrika, 62, 547–554.MathSciNetzbMATHCrossRefGoogle Scholar
  3. Aitchison, J. (1981). Distributions on the simplex for the analysis of neutrality. In Statistical Distributions in Scientific Work, C. Taillie, G.P. Patil, B. Baldessari, eds. D. Reidel Publishing Company, Dordrecht, Holland. Vol. 4, pp. 147–156.Google Scholar
  4. Aitchison, J., Dunsmore, I. R. (1976). Statistical Prediction Analysis. Cambridge University Press. Aitchison, J., Habbema, J.D.F., Kay, J.W. (1977). A critical comparison of two methods of statistical discrimination. Applied Statistics, 26, 15–25.Google Scholar
  5. Aitchison, J., Kay, J.W. (1973). A diagnostic competition. Bulletin of the Institute of Mathematics and its Applications, 9, 382.Google Scholar
  6. Aitchison, J., Kay, J.W. (1975). Principles, practice and performance in decision making in clinical medicine. In The Role and Effectiveness of Theories of Decision in Practice, D.J. White, K.C. Bowen, eds. Hodder, Stoughton, London.Google Scholar
  7. Aitchison, J., Moore, M.F., West, S.A., Taylor, T.R. (1973). Consistency of treatment allocation in thyrotoxicosis. Quarterly Journal of Medicine, 42, 573–583.Google Scholar
  8. Aitchison, J., Shen, S.M. (1980). Logistic-normal distributions: some properties and uses. Biometrika, 67, 261–272.MathSciNetzbMATHCrossRefGoogle Scholar
  9. Davidson, D., Suppes, P., Siegel, S. (1957). Decision-making: An Experimental Approach. Stanford University Press.zbMATHGoogle Scholar
  10. Edwards, W., Phillips, L.D. (1964). Emerging technologies for making decisions. In Human Judgments and Optimality, pp. 360–401. Wiley, New York.Google Scholar
  11. Goldberg, L.R. (1970). Man versus model of man: a rationale, plus some evidence for a method of improving on clinical inferences. Psychological Bulletin, 73, 422–432.CrossRefGoogle Scholar
  12. Good, I. J. (1952). Rational decisions. Journal of the Royal Statistical Society, Series B, 14, 107–114.MathSciNetGoogle Scholar
  13. Kay, J. W. (1976). Diagnosis and performance. Ph.D. dissertation, University of Glasgow.Google Scholar
  14. Khinchin, A.I. (1957). Mathematical Foundations of Information Theory. Dover, New York.zbMATHGoogle Scholar
  15. Kullback, S., Leibler, R.A. (1951). On information and sufficiency. Annals of Mathematical Statistics, 22, 525–540.MathSciNetCrossRefGoogle Scholar
  16. Lindley, D.V. (1956). On a measure of the information provided by an experiment. Annals of Mathematical Statistics, 27, 986–1005.MathSciNetzbMATHCrossRefGoogle Scholar
  17. Phillips, L.D., Edwards, W. (1966). Conservatism in a simple probability inference task. Journal of Experimental Psychology, 72, 346–354.CrossRefGoogle Scholar
  18. Raiffa, H. (1968). Decision Analysis. Addison-Wesley, Reading, Massachusetts.zbMATHGoogle Scholar
  19. Shannon, C.E. (1948). A mathematical theory of communication. Bell System Technical Journal, 27, 379–423 amd 623–656.MathSciNetzbMATHGoogle Scholar
  20. Taylor, T. R., Aitchison, J., McGirr, E.M. (1971). Doctors as decision makers: a computer-assisted study of diagnosis as a cognitive skill. British Medical Journal, 3, 35–40.CrossRefGoogle Scholar

Copyright information

© D. Reidel Publishing Company 1981

Authors and Affiliations

  • J. Aitchison
    • 1
  1. 1.Department of StatisticsUniversity of Hong KongHong Kong

Personalised recommendations