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Pearson's statistic is investigated for nominal-ordinal two-way contingency tables in which we wish to test for identical rows. The statistic is expressed as a sum, the first summand of which is a statistic given by Yates (1948), and examines location effects for the nominal category. The second and subsequent summands reflect the corresponding moments: for example, dispersion, skewness, kurtosis etc. The summands are shown to be weakly optimal in that they are score statistics.
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Rayner et al. (2000) studied this question.
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