If two variables are independent, we would anticipate a chi-square test statistic close to zero.

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When two variables are independent, a chi-square test statistic close to zero is expected because there should be no significant association or relationship between them to reject the null hypothesis. On the other hand, a large chi-square value indicates a significant association or dependence between the variables, leading to rejection of the null hypothesis.

If Two Variables Are Independent, We Would Anticipate a Chi-Square