A Corner Test for Association

Abstract

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.