Approximations of the critical region for spearman’s rho with and without ties present

Exact tables for Spearman’s rho are available only for n ≤ 16 and no ties in the data. Some accurate methods of approximating the distribution with no ties present have been used to obtain approximate tables for larger values of n. Often ties are present in the data so these tables are no longer exact. Also sometimes the tables are not conveniently available to the user. In such situations an approximation that is both simple and accurate would be useful. Such an approximation is presented in this paper. Comparisons are made with other standard approximations for all cases where exact tables (no ties) are available, and for one case where exact tables were generated for a situation with ties. The results show the approximation presented here to be the most accurate of the approximations examined. Also it is simple enough to be readily understood by the average user of Spearman’s rho.