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# How Do We Assess Association Between a Categorical and a Continuous Variable?

### How Do We Assess Association Between a Categorical and a Continuous Variable?

Grouping variables are categorical, and we often want to know if the mean of some continuous variable differs by group membership. For example, does education vary by gender? If the categorical variable has two values, then we can use a statistical technique called an independent samples t-test. A t-test assesses the null hypothesis that the mean is equal across both groups. The alternative hypothesis is that they are not equal. The larger the difference between the groups, the more likely it is to be statistically significant.

Table 84.1 presents the results of a t-test on years of education grouped by gender. The difference in mean educational level is very small at .11, ...