In using the chi-square test for independence,one should be aware that the expected frequencies that are too small will lead to too big value of the probability of Type I error.

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This is true. When the expected frequencies are too small, the chi-square distribution does not approximate the true distribution well, which can lead to an inflated probability of Type I error (rejecting the null hypothesis when it is true).

In Using the Chi-Square Test for Independence,one Should Be Aware