A New Bivariate Sign Test

A sign test for the hypothesis that the medians of two or more variables (not necessarily independent) have a particular value is described in detail for the bivariate case. The slopes of the vectors from the bivariate median to the n sample points are ordered and we let ai = ±1 according as the vector corresponding to the jth slope is above or below a horizontal line through the median. The bivariate test is based on the statistic v 2 = 2 (v 1 2+v 2 2)/n, where v 1 [Sgrave]ai cos (πj/n), v 2 = [Sgrave]ai sin (πj/n), and the sum is over the integers j = 1, 2, …, n. The statistic has the chi-square distribution for large samples. The power of this test relative to other possible sign tests and Hotelling's T 2 is discussed.