Accelerating the Calculation of Friedman Test Tables on Many-Core Processors

Abstract

The Friedman Test has been proposed in 1937 to analyze tables of ranks, like those arising from a wine contest. If we have N judges and k wines, the standard problem is to analyze a table of N rows and k columns holding the opinion of the judges. The Friedman’s Test is used to accept/reject the null hypothesis that all the wines are equivalent. Friedman offered an asymptotically valid approximation as well as exact tables for low k and N. The accuracy of the asymptotic approximation for moderate k and N was low, and extended tables were required. The published ones were mostly computed using Monte Carlo techniques. The effort required to compute the extended tables for the case without ties was significant (over 100 years of CPU time) and an alternative using many-core processors is described here for the general case with ties. The solution can be used also for other similar tests which yet lack for large enough tables.