In performing a chi-square test of independence, as the difference between the respective observed and expected frequencies calculated by assuming independence decreases, the probability of concluding that the row variable is independent of the column variable decreases.

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When a chi-square test for independence is large (observed frequencies differ substantially from the expected frequencies), then doubt will be cast on the null hypothesis of independence. Therefore, a small chi-square would result in a larger probability.

In Performing a Chi-Square Test of Independence, as the Difference