When using the X² tests for independence, you should be aware that expected frequencies that are too small will lead to a large Type I error.

Question

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When the expected frequencies are too small, the X² test statistic will be larger than expected and the p-value will be smaller, leading to a higher probability of rejecting the null hypothesis (Type I error). Therefore, it is important to ensure that expected frequencies are not too small before conducting a X² test for independence.

When Using the X² Tests for Independence, You Should Be