Open Access
December, 1947 A Corner Test for Association
Paul S. Olmstead, John W. Tukey
Ann. Math. Statist. 18(4): 495-513 (December, 1947). DOI: 10.1214/aoms/1177730341


This paper proposes a new test (the "quadrant sum") for the association of two continuous variables. Its notable properties are: (1) Special weight is given to extreme values of the variables. (2) Computation is very easy. (3) The test is non-parametric. Significance levels (for the quadrant sum) are given to the accuracy needed for practical use. To this accuracy they are independent of sample size (see Fig. 1). The generating function of the quadrant sum is given for the null hypothesis (no association = independence). A limiting distribution is deduced and compared with the cases $2n$ = 4, 6, 8, 10, and 14. Extension to higher dimensions and application to serial correlation are discussed.


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Paul S. Olmstead. John W. Tukey. "A Corner Test for Association." Ann. Math. Statist. 18 (4) 495 - 513, December, 1947.


Published: December, 1947
First available in Project Euclid: 28 April 2007

zbMATH: 0029.40902
MathSciNet: MR23025
Digital Object Identifier: 10.1214/aoms/1177730341

Rights: Copyright © 1947 Institute of Mathematical Statistics

Vol.18 • No. 4 • December, 1947
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