Which statistical method is best for testing the independence of two variables?

The Chi-square test is indeed the most appropriate statistical method for testing the independence of two categorical variables. This test evaluates whether there is a significant association between the variables by comparing the observed frequency counts in a contingency table with the expected frequency counts that would occur if the variables were independent.

When performing the Chi-square test, you examine the data to see if the distribution of one variable is consistent across the levels of another variable. A high Chi-square statistic indicates that the variables are likely associated, while a low statistic suggests they are independent of each other. This method is particularly effective for categorical data, making it suitable for many practical applications, such as survey analysis or observational studies.

In contrast, regression analysis is typically used for predicting the value of a continuous dependent variable based on one or more independent variables. The t-test is designed for comparing the means of two groups, and ANOVA is used for comparing the means of three or more groups. None of these methods specifically test for independence between two categorical variables as effectively as the Chi-square test.