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A chi-square statistic can be large if either there is a large difference between the observed and expected values for one or more categories. However, it can also be large if the expected value in a category is very small.

In the first case, it is likely that the data are not distributed according to the null hypothesis. In the second case, it can often mean that that, because of low expected values, adjacent categories need to be combined before the chi-square statistic is calculated.

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Q: What will produce a large value for the chi-square statistic?
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