What does a chi-square test primarily assess in categorical data?

A chi-square test primarily assesses independence between variables in categorical data. When applying this test, researchers aim to determine whether there is a significant association between two categorical variables. The chi-square test evaluates how the observed frequencies of occurrence of events compare to the expected frequencies if the two variables were truly independent.

For instance, if you are studying the relationship between gender and preference for a particular product, the chi-square test can help identify whether the preferences differ significantly between the genders or if the observed distribution of preferences fits the expected distribution that there is no relationship (independence) between gender and product preference.

Understanding independence in this context is crucial for researchers, as it provides insights into potential correlations or influences that could warrant further investigation. The other options focus on different statistical concepts, such as comparing means, assessing correlation, or examining variance, which are not the primary focus of the chi-square test.