Final answer:
Numerically, an association between variables can be determined using the correlation coefficient and p-value or by using regression analysis and the chi-square test. The null hypothesis for the correlation coefficient suggests no association, and if the p-value is less than the significance level, the null is rejected.
Step-by-step explanation:
The two numerical ways to find an association between variables are: 1) Correlation coefficient and p-value and 2) Regression analysis and chi-square test. When testing the significance of the correlation coefficient, the null hypothesis typically states that there is no linear correlation between the two variables. Conversely, the alternative hypothesis suggests that there is a significant linear correlation between them. For instance, if the p-value is less than the level of significance (0.05), such as a p-value of 0.04, we reject the null hypothesis and conclude that there is a significant association between the variables.
Regression analysis involves fitting a line of best fit to the data points to describe the relationship between an independent and a dependent variable. As for the chi-square test, it is used to assess whether two categorical variables are independent of each other.