**Core Concept**
The question is testing the understanding of statistical methods used to establish an association between two variables. In research and clinical settings, it is crucial to determine whether there is a relationship between two variables to make informed decisions. This involves using statistical techniques to analyze data and draw conclusions.

**Why the Correct Answer is Right**
The correct answer is **C. Chi-square test**. The chi-square test is a non-parametric test used to determine whether there is a significant association between two categorical variables. It works by comparing the observed frequencies in each category with the expected frequencies if there were no association between the variables. The chi-square statistic is calculated by summing the squared differences between observed and expected frequencies, divided by the expected frequency.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because correlation analysis, such as Pearson's correlation coefficient, is used to measure the strength and direction of a linear relationship between two continuous variables, not to test for association between categorical variables.

**Option B:** This option is incorrect because regression analysis is used to model the relationship between a dependent variable and one or more independent variables, but it does not directly test for association between two variables.

**Option D:** This option is incorrect because ANOVA (Analysis of Variance) is used to compare means between three or more groups, but it does not test for association between two variables.

**Clinical Pearl / High-Yield Fact**
When using the chi-square test, it is essential to check the assumptions of the test, including the expected frequencies in each category, to ensure that the results are valid and reliable.

**Correct Answer: C. Chi-square test**