The differences between the numbers of positive and negative residuals in each row and column of a two-way analysis of variance are used to define an approximate chi-squared statistic which can be used to test for the presence of outlying observations. The chi-squared approximation rests on a Central Limit Theorem for the number of positive residuals in the two-way table. Extensions to other classifications are also discussed.
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Bruce M. Brown (1975) studied this question.
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