Abstract
For ordinal measurement the concept of an individual propensity distribution is developed. For any given individual the mean of this distribution is his true score, for which estimation procedures are discussed. Two measures of individual dispersion are considered and their distributions derived in the null case. These measures are shown to be counterparts at the individual level of Kendall's tau and Spearman's rho. Estimation of the two dispersion measures from sample data is investigated, and the relation of these estimates to the variance of the individual propensity distribution is derived.
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References
Cochran, W. G.Sampling techniques. New York: John Wiley & Sons, Inc., 1963.
Daniels, H. E. Note on Durbin and Stuart's formula forE(R s ).Journal of the Royal Statistical Society, Series B, 1951,13, 310.
Durbin, J. & Stuart, A. Inversions and rank correlation coefficients.Journal of the Royal Statistical Society, Series B, 1951,13, 303–309.
Kendall, M. G.Rank correlation methods. London: Charles Griffin & Company, 1970.
Lord, F. M. & Novick, M. R.Statistical theories of mental test scores. Reading, Mass.: Addison-Wesley, 1968.
Schulman, R. S. Correlation and prediction in ordinal test theory.Psychometrika, 1976,41, 329–340.
Schulman, R. S. & Haden, R. L. A test theory model for ordinal measurements.Psychometrika, 1975,40, 455–472.
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Schulman, R.S. Individual distributions under ordinal measurement. Psychometrika 43, 19–29 (1978). https://doi.org/10.1007/BF02294086
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DOI: https://doi.org/10.1007/BF02294086