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A Distinction Between Exact and Approximate Nonparametric Methods

Published online by Cambridge University Press:  01 January 2025

William L. Sawrey
William L. Sawrey*
Affiliation:
University of Colorado Medical Center
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Abstract

Nonparametric tests are discussed in relation to parametric tests. A distinction is made between two types of nonparametric tests. One type leads to an exact significance level, the other to an approximate significance level. The failure to distinguish between these two types has led to confusion and error. Examples are cited.

Information

Type
Original Paper
Information
Psychometrika , Volume 23 , Issue 2 , June 1958 , pp. 171 - 177
Copyright
Copyright © 1958 The Psychometric Society

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Footnotes

*

Based on a paper presented at the annual meeting of the Rocky Mountain Psychological Association, Salt Lake City, Utah, 1957

†

The author is indebted to Dr. John J. Conger for his many suggestions that greatly improved the exposition of this manuscript.

References

Auble, D. Extended tables for the Mann-Whitney statistic. Bull. Inst. educ. Res., 1953, 1, 39–39.Google Scholar
Birnbaum, Z. W. Numerical tabulation of the distribution of Kolmogorov's statistic for finite sample size. J. Amer. statist. Ass., 1952, 47, 425–441.10.1080/01621459.1952.10501182CrossRefGoogle Scholar
Blum, J. R. and Fatta, N. A. Nonparametric methods. Rev. educ. Res., 1954, 24, 467–487.Google Scholar
Cochran, W. G. The comparison of percentages in matched samples. Biometrika, 1950, 37, 256–266.10.1093/biomet/37.3-4.256CrossRefGoogle ScholarPubMed
Cramer, H. Mathematical methods of statistics, Princeton: Princeton Univ. Press, 1946.Google Scholar
Edwards, A. L. Statistical methods for the behavioral sciences, New York: Rinehart, 1954.Google Scholar
Festinger, L. The significance of differences between means without reference to the frequency distribution function. Psychometrika, 1946, 11, 97–105.10.1007/BF02288926CrossRefGoogle Scholar
Fix, Evelyn and Hodges, J. L. Jr. Significance probabilities of the Wilcoxon test. Ann. math. Statist., 1955, 26, 301–312.10.1214/aoms/1177728547CrossRefGoogle Scholar
Freeman, G. H. and Halton, J. H. Note on an exact treatment of contingency, goodness of fit, and other problems of significance. Biometrika, 1951, 38, 141–149.10.1093/biomet/38.1-2.141CrossRefGoogle Scholar
Haldane, J. B. S. and Smith, C. A. B. A simple exact test for birth-order effect. Ann. Eugen., 1947, 14, 117–124.10.1111/j.1469-1809.1947.tb02383.xCrossRefGoogle Scholar
Kamat, A. R. A two-sample distribution-free test. Biometrika, 1956, 43, 377–387.10.1093/biomet/43.3-4.377CrossRefGoogle Scholar
Kendall, M. G. The advanced theory of statistics. Vol. 1, London: Griffin, 1948.Google Scholar
Kruskal, W. H. and Wallis, W. A. Use of ranks in one-criterion variance analysis. J. Amer. statist. Ass., 1952, 47, 583–621.10.1080/01621459.1952.10483441CrossRefGoogle Scholar
Lewis, D. and Burke, C. J. The use and misuse of the chi-square test. Psychol. Bull., 1949, 46, 433–489.10.1037/h0059088CrossRefGoogle ScholarPubMed
McNemar, Q. Psychological statistics, New York: Wiley, 1955.Google Scholar
Mann, H. B. and Whitney, D. R. On a test of whether one of two random variables is stochastically larger than the other. Ann. math. Statist., 1947, 18, 50–60.10.1214/aoms/1177730491CrossRefGoogle Scholar
Mood, A. M. Introduction to the theory of statistics, New York: McGraw-Hill, 1950.Google Scholar
Moses, L. E. Non-parametric statistics for psychological research. Psychol. Bull., 1952, 49, 122–143.10.1037/h0056813CrossRefGoogle ScholarPubMed
Mosteller, F. and Bush, R. R. Selected quantitive techniques. In Lindzey, G. (Eds.), Handbook of social psychology. Vol. 1. Theory and method (pp. 289–334). Cambridge, Mass.: Addison-Wesley, 1954.Google Scholar
Roy, S. N. and Mitra, S. K. An introduction to some non-parametric generalizations of analysis of variance and multivariate analysis. Biometrika, 1956, 43, 361–376.10.1093/biomet/43.3-4.361CrossRefGoogle Scholar
Siegel, S. Non-parametric statistics for the behavioral sciences, New York: McGraw-Hill, 1956.Google Scholar
Smith, K. Distribution-free statistical methods and the concept of power efficiency. In Festinger, L., Katz, D. (Eds.), Research methods in the behavioral sciences (pp. 536–577). New York: Dryden, 1953.Google Scholar
Sukhatme, B. V. On certain two-sample nonparametric tests for variances. Ann. math. Statist., 1957, 28, 188–194.10.1214/aoms/1177707046CrossRefGoogle Scholar
Swed, Frieda S., Eisenhart, C. Tables for testing randomness of grouping in a sequence of alternatives. Ann. math. Statist., 1943, 14, 66–87.10.1214/aoms/1177731494CrossRefGoogle Scholar
Wald, A. and Wolfowitz, J. On a test whether two samples are from the same population. Ann. math. Statist., 1940, 11, 147–162.10.1214/aoms/1177731909CrossRefGoogle Scholar
Walker, Helen M. and Lev, J. Statistical inference, New York: Holt, 1953.10.1037/11773-000CrossRefGoogle Scholar
White, C. The use of ranks in a test of significance for comparing two treatments. Biometrics, 1952, 8, 33–41.10.2307/3001523CrossRefGoogle Scholar
Whitney, D. R. A comparison of the power of nonparametric tests and tests based on the normal distribution under non-normal alternatives. Unpublished doctoral dissertation, Ohio State Univ., 1948..Google Scholar
Wilcoxon, F. Individual comparisons by ranking methods. Biometrics Bull., 1945, 1, 80–83.10.2307/3001968CrossRefGoogle Scholar
Wilcoxon, F. Probability tables for individual comparisons by ranking methods. Biometrics, 1947, 3, 119–122.10.2307/3001946CrossRefGoogle Scholar
Wilson, K. V. A distribution-free test of analysis of variance hypotheses. Psychol. Bull., 1956, 53, 96–101.10.1037/h0047975CrossRefGoogle ScholarPubMed