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Chi-square tests are primarily utilized to assess the relationship between two nominal or ordinal variables. This statistical method allows researchers to determine whether there is a significant association between categories in a contingency table, which summarizes the frequencies of different combinations of two categorical variables. For example, a chi-square test can evaluate whether gender and preference for a particular product are related by analyzing the distribution of responses across categories.

The chi-square test does this by comparing the observed frequencies in each category with the expected frequencies that would occur if there were no association between the variables. A significant result suggests that changes in one variable are related to changes in another, indicating a potential relationship worth exploring further.

In contrast, the other options focus on different types of analysis. Regression analysis is used for predicting the value of a dependent variable based on one or more independent variables, while time-series analysis examines trends over time within a single variable. The central tendency of a single sample pertains to measures such as the mean or median but does not investigate relationships between multiple variables. Therefore, the primary function of chi-square tests is specifically tied to evaluating associations between categorical variables, making the initial answer appropriate.