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Extended and updated tables for the Friedman rank test

ABSTRACT The Friedman's test is used for assessing the independence of repeated experiments resulting in ranks, summarized as a table of integer entries ranging from 1 to k, with k columns and N rows. For its practical use, the hypothesis testing can be derived either from published tables with exact values for small k and N, or using an asymptotic analytical approximation valid for large N or large k. The quality of the approximation, measured as the relative difference of the true critical values with respect those arising from the asymptotic approximation is simply not known. The literature review shows cases where the wrong conclusion could have been drawn using it, although it may not be the only cause of opposite decisions. By Monte Carlo simulation we conclude that published tables do not cover a large enough set of (k, N) values to assure adequate accuracy. Our proposal is to systematically extend existing tables for k and N values, so that using the analytical approximation for values outside it will have less than a prescribed relative error. For illustration purposes some of the tables have been included in the paper, but the complete set is presented as a source code valid for Octave/Matlab/Scilab etc., and amenable to be ported to other programming languages.