A test of spatial independence

Mardia (1980) proposed a bi-directional test of spatial independence based upon the sample variogram which has a X2-distribution under the null hypothesis. We give here a modified test whichleads to improvement to the X2-distribution approximation to the size. We introduce some other tests including a four-directional extension, and analogous tests based on the sample correlation coefficient. Their power is compared with the modified bi-directional test for a doubly geometric alternative, and this limited power study indicates that the modified bi-directional test is more powerful.