Chi-square and classical exact tests often wildly misreport significance; the remedy lies in computers

Abstract

If a discrete probability distribution in a model being tested for goodness-of-fit is not close to uniform, then forming the Pearson chi-square statistic can involve division by nearly zero. This often leads to serious trouble in practice -- even in the absence of round-off errors -- as the present article illustrates via numerous examples. Fortunately, with the now widespread availability of computers, avoiding all the trouble is simple and easy: without the problematic division by nearly zero, the actual values taken by goodness-of-fit statistics are not humanly interpretable, but black-box computer programs can rapidly calculate their precise significance.

63 pages, 51 figures, 7 tables

Cited by in corpus (4)

• Computing the confidence levels for a root-mean-square test of goodness-of-fit, II
• A comparison of the discrete Kolmogorov-Smirnov statistic and the Euclidean distance
• Testing the significance of assuming homogeneity in contingency-tables/cross-tabulations
• Computing the asymptotic power of a Euclidean-distance test for goodness-of-fit