Critical values of some nonparametric statistics used for tests of total stochastic independence

The problem of testing for total independence of the variates of a stochastic p(≧3) component vector using rank correlation statistics is considered. Two distribution free statistics are considered, one based on the determinant of the matrix of rank correlation statistics, the second on their sum of squares. Tables of critical values are given for p=3,4 for the cases when (a) ranks, and (b) exponential scores are used to replace the ordered observations within each variate. Some approximations to the critical values are proposed and evaluated.