Abstract
To date, virtually all techniques appropriate for ordinal data are based on the uniform probability distribution over the permutations. In this paper we introduce and examine an alternative probability model for the distribution of ordinal data. Preliminary to deriving the expectations of Spearman's rho and Kendall's tau under this model, we show how to compute certain conditional expectations of rho and tau under the uniform distribution. The alternative probability model is then applied to ordinal test theory, and the calculation of true scores and test reliability are discussed.
Similar content being viewed by others
References
Durbin, J. & Stuart, A. Inversions and rank correlation coefficients.Journal of the Royal Statistical Society, Series B, 1951,13, 303–309.
Ehrenberg, A. S. C. On sampling from a population of rankers.Biometrika, 1952,39, 82–87.
Kendall, M. G. A new measure of rank correlation.Biometrika, 1938,30, 81–93.
Kendall, M. G. Partial rank correlation.Biometrika, 1942,32, 277–283.
Kendall, M. G. Discussion on symposium on ranking methods.Journal of the Royal Statistical Society, Series B, 1950,12, 189.
Kendall, M. G.Rank correlation methods. London: Charles Griffin and Company, 1970.
Kendall, M. G. & Babington Smith, B. The problem ofm rankings.Annals of Mathematical Statistics, 1939,10, 275–287.
Linhart, H. Approximate tests form rankings.Biometrika, 1960,47, 476–480.
Lyerly, S. B. The average Spearman rank correlation coefficient.Psychometrika, 1952,17, 421–428.
Page, E. B. Ordered hypotheses for multiple treatments: A significance test for linear ranks.Journal of the American Statistical Association, 1963,58, 216–230.
Plackett, R. L. The analysis of permutations.Applied Statistics, 1975,24, 193–202.
Schucany, W. R. & Frawley, W. H. A rank test for two group concordance.Psychometrika, 1973,38, 249–258.
Schulman, R. S. Correlation and prediction in ordinal test theory.Psychometrika, 1976,41, 329–340.
Schulman, R. S. Individual distributions under ordinal measurement.Psychometrika, 1978,43, 19–29.
Schulman, R. S. & Haden, R. L. A test theory model for ordinal measurements.Psychometrika, 1975,40, 455–472.
Spearman, C. The proof and measurement of association between two things.American Journal of Psychology, 1904,15, 72–101.
Stuart, A. An application of the ranking concordance coefficient.Biometrika, 1951,38, 33–42.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Schulman, R.S. Ordinal data: An alternative distribution. Psychometrika 44, 3–20 (1979). https://doi.org/10.1007/BF02293781
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02293781