What does the chi square statistic test analyze in a contingency table?

The chi-square statistic specifically analyzes the relationships between categorical variables in a contingency table. This statistical test examines whether the observed frequencies of occurrences in different categories differ significantly from the frequencies expected if there were no association between the variables.

In a contingency table, the data is typically organized in rows and columns, representing different categories of two or more variables. The chi-square test allows researchers to assess whether the distribution of one categorical variable is related to or influenced by the distribution of another categorical variable. This is essential in various fields, including psychology, where understanding the relationships between demographics and behaviors or responses is crucial.

Unlike the other options, which pertain to relationships that might exist between continuous variables or involve correlational analysis, the chi-square test is focused solely on categorical data, making it a fundamental tool for categorical variable analysis in research.