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

William Perkins; Mark Tygert; Rachel Ward

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arXiv · 1108.4126

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

William Perkins·Mark Tygert·Rachel Ward

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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.

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William Perkins, Mark Tygert, Rachel Ward. 2011-09-15. Chi-square and classical exact tests often wildly misreport significance; the remedy lies in computers. https://arxiv.org/abs/1108.4126

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