Order Tests

  • B. L. van der Waerden
Part of the Die Grundlehren der mathematischen Wissenschaften book series (GL, volume 156)

Abstract

Order tests are tests which use not the exact values of the observations, but only their order relations — i.e., only the relations x < y and x > y between the observed x and y. Since such tests are not based upon definite distribution functions for the quantities x and y, they are also called distribution-free, or nonparametric, tests.

Keywords

Assure 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    J. Hemelrijk, A theorem on the sign test when ties are present. Proc. Kon. Ned. Akad. Section on Sciences A 55 (1952) p. 322.MathSciNetGoogle Scholar
  2. 2.
    H. Fritz-Niggli, Vergleichende Analyse der Strahlenschädigung von Drosophila-Eiern. Fortschr. auf dem Geb. d. Röntgenstrahlen 83 (1955) p. 178.CrossRefGoogle Scholar
  3. 3.
    J. Hemelrijk, A family of parameter-free tests for symmetry. Proc. Kon. Ned. Akad. Section on Sciences 53 (1950) pp.945–955 and 1186-1198.MathSciNetMATHGoogle Scholar
  4. 4.
    N. Smirnov, Estimation of the discrepancy between empirical distributions for two samples. Bull. Math. Univ. Moscow 2 (1939) p. 1.Google Scholar
  5. 5.
    H. B. Mann and D. R. Whitney, On a test whether one of two random variables is stochastically larger than the other. Ann. of Math. Stat. 18 (1947) p. 50.MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    See E. L. Lehmann, Consistency and unbiasedness of nonparametric tests. Ann. of Math. Stat. 22 (1951) p. 167Google Scholar
  7. Theorem 3.2, and the literature cited there, as well as W. Hoeffding, A combinatorial central limit theorem. Ann. of Math. Stat. 22 (1951) p. 558.MathSciNetMATHCrossRefGoogle Scholar
  8. 9.
    B. L. van der Waerden, Proc. Kon. Ned. Akad. Amsterdam, A 55 (1952) p. 456.Google Scholar
  9. 12.
    B. L. van der Waerden and E. Nievergelt, Tafeln zum Vergleich zweier Stichproben mittels X-test und Zeichentest. Berlin, Göttingen, Heidelberg: Springer-Verlag 1956.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1969

Authors and Affiliations

  • B. L. van der Waerden
    • 1
  1. 1.Mathematisches InstitutUniversität ZürichSchweiz

Personalised recommendations