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Goodness-of-fit tests based on the Euclidean distance often outperformchi-square and other classical tests (including the standard exact tests) by atleast an order of magnitude when the model being tested for goodness-of-fit isa discrete probability distribution that is not close to uniform. The presentarticle discusses numerous examples of this. Goodness-of-fit tests based on theEuclidean metric are now practical and convenient: although the actual valuestaken by the Euclidean distance and similar goodness-of-fit statistics areseldom humanly interpretable, black-box computer programs can rapidly calculatetheir precise significance.

An introduction to how chi-square and classical exact tests often wildly misreport significance and how the remedy lies in computers