Complete the following steps to interpret a chi-square test of association. Key output includes p-values, cell counts, and each cell's contribution to the chi-square statistic.

To determine whether the variables are independent, compare the p-value to the significance level. Usually, a significance level (denoted as α or alpha) of 0.05 works well. A significance level of 0.05 indicates a 5% risk of concluding that an association between the variables exists when there is no actual association.

- P-value ≤ α: The variables have a statistically significant association (Reject H
_{0}) - If the p-value is less than or equal to the significance level, you reject the null hypothesis and conclude that there is a statistically significant association between the variables.
- P-value > α: Cannot conclude that the variables are associated (Fail to reject H
_{0}) - If the p-value is larger than the significance level, you fail to reject the null hypothesis because there is not enough evidence to conclude that the variables are associated.

To determine which variable levels have the most impact, compare the observed and expected counts or examine the contribution to chi-square

By looking at the differences between the observed cell counts and the expected cell counts, you can see which variables have the largest differences, which may indicate dependence. You can also compare the contributions to the chi-square statistic to see which variables have the largest values that may indicate dependence.