# Spearman's Rho and Hotelling-Pabst T distribution

Menu location: **Analysis_Distributions_Spearman's rho**.

Given a value for the Hotelling-Pabst test statistic (T) or Spearman's rho (ρ) this function calculates the probability of obtaining a value greater than or equal to T.

For two rankings (x1,x2...xn and y1,y2...yn) of n objects without ties:

T is related to the Spearman rank correlation coefficient (ρ) by:

__Technical Validation__

Probabilities are calculated by summation across all permutations when n = 10 and by and Edgeworth series approximation when n > 10 (Best and Roberts, 1975). The exact calculation employs a corrected version of the Best and Roberts (1975) algorithm. The Edgeworth series results for n > 10 are accurate to at least four decimal places.

The inverse is calculated by finding the largest value of T that gives a calculated probability (using the method above) closest to but not less than the P value entered.