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Large values indicate a stronger association between methods than would be expected by chance, and the introduction of effects that capture this association (X^) could improve the fit of the model.

Hence, the adjusted cell residuals of the independence model (as the test) can be used to detect agreement as well as general associations. As Table 17.5 shows, the expected cell frequencies of the independence model differ greatly from the observed cell frequencies, whereas the marginal distributions are perfectly reproduced. A first glance at the table reveals that cells on the main diagonal are chosen much more frequently than would be expected if both ratings were independent.

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