What does the Chi-square test analyze?

The Chi-square test specifically analyzes the independence of two categorical variables. This statistical test helps determine whether there is a significant association between the two variables by comparing the observed frequencies in a contingency table to the expected frequencies under the assumption that the variables are independent.

When conducting a Chi-square test, each cell in the contingency table reflects the frequency count of occurrences for each combination of the categories of the variables being examined. By calculating the Chi-square statistic, researchers can assess whether the observed distribution of data significantly deviates from what would be expected if there were no relationship between the variables. A significant result indicates that the variables might indeed be related, while a non-significant result suggests that they are independent of one another.

In contrast, the other options do not accurately represent what the Chi-square test is designed to evaluate, as they involve either numerical relationships, correlations that pertain to different types of variables, or trends over time, which are analyzed using different statistical techniques.