What is the relationship type of the Chi-squared test?

The Chi-squared test is specifically designed to assess the relationship type between categorical variables and is used to determine if there is a significant association or independence between them. When we refer to the relationship as "independent," it means that the categories represented in the data do not influence each other—that is, the occurrence of one category does not affect the occurrence of another.

In the context of the Chi-squared test, researchers often test the hypothesis that the distribution of sample categorical data matches an expected distribution, or that two categorical variables are associated with one another. If the Chi-squared test results in a significant statistic, it can be concluded that there is a relationship between the variables, indicating they are not independent. Conversely, a non-significant result suggests that the variables are independent.

This focus on testing independence among categories is the hallmark of the Chi-squared test, highlighting its purpose in analyzing frequencies rather than numerical relationships or time-based assessments that might be indicated by other types of relationships, such as paired or repeated measurements.