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Defining the pattern of association in two-way contingency tables. (English) Zbl 0534.62036

Consider an \(a\times b\) contingency table with the observed frequencies \(n_{ij}\), which correspond to the probabilities \(p_{ij}\). The row, column and grand totals are denoted by \(R_ i\), \(C_ j\) and N, respectively. The null hypothesis of the row-wise interaction between the i-th and t-th rows is \(H_ 0(i;t):p_{ij}/p_{i.}- p_{tj}/p_{t.}=0\), \(j=1,...,b\). Conditional simultaneous tests of \(H_ 0(i;t)\) can be based on the statistics \[ \chi^ 2(i;t)=N(R_ i^{-1}+R_ t^{-1})^{-1}\sum^{b}_{j=1}C_ j^{- 1}(n_{ij}/R_ i-n_{tj}/R_ t)^ 2,\quad i,t=1,...,a. \] The same procedure is symmetrically defined for the column-wise interaction. The author generalizes this method to multiple comparisons for rows and columns when the column categories are ordered. Another generalization concerns the multiple comparisons for the hypotheses of quasisymmetry. Theoretical results are illustrated on two sets of real data.
Reviewer: J.Anděl

MSC:

62H17 Contingency tables
62J15 Paired and multiple comparisons; multiple testing
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