of cells, rc, in the table), the asymptotic distributions of XP and XW are % . In other words, the two statistics are equivalent, when Ho is true. There is however a problem when the number of observations is small, i.e. less than five times the number of cells. Small numbers of observations often lead to several null observed values (Oj) in the contingency table, with correspondingly very low expected frequencies (Ej). According to Cochran (1954) and Siegel (1956), when there is one value of Ej smaller than 1, or when 20% or more of the expected values Ej are smaller than 5, some states (rows or columns) must be grouped to increase the expected frequencies, provided that there is a logical basis to do so. It now appears that this empirical rule concerning expected frequencies is too conservative. Fienberg (1980, p. 172) cites results of simulations that lead to believe that, for a = 0.05, the computed statistic is distributed
like x2 (if H0 is true) as long as all Ej values are larger than 1.
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