Two Variable Statistics Introduction To Chi-Square Test for Independence Correlation Finding the relationship between two quantitative variables without being able to infer causal relationships Correlation is a statistical technique used to determine the degree to which two variables are related What is the Chi-square test for? The chi-squared or Χ2 test is used to determine whether two variables from the same sample are independent or not independent. A chi-squared test is designed to analyze categorical data. That means that the data has been counted and divided into categories. Appropriate Categorical Data For example, if you want to test whether attending class influences how students perform on an exam, using test scores (from 0-100) as data would NOT be appropriate for a Chi-square test. However, arranging students into the categories "Pass" and "Fail" would be appropriate. More Important facts about Chi-Squared Test The chi-squared test is only meant to test the probability of independence of a distribution of data. It will NOT tell you any details about the relationship between them. The variables you consider must be mutually exclusive; participation in one category should not entail or allow participation in another. In other words, the data from all of your cells should add up to the total count, and no item should be counted twice. How do you calculate the chisquared test by hand?