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What is Chi-square? History and Definition . A chi-square distribution is the distribution of the sum of squares of k independent standard normal random variables with k degree of freedom. A chi-square test is a statistical hypothesis test where the null hypothesis that the distribution of the test statistic is a chi-square distribution, is true. While the chi-square distribution was first introduced by German statistician Friedrich Robert Helmert, the chi-square test was first used by Karl Pearson in 1900.
Using sample data, we will conduct a chi-square test for independence. Analyze sample data. Applying the chi-square test for independence to sample data, we compute the degrees of freedom, the expected frequency counts, and the chi-square test statistic.Based on the chi-square statistic and the degrees of freedom, we determine the P-value. Significance level. 2  Often, researchers choose significance levels equal to 0.01, 0.05, or 0.10; but any value between 0 and 1 can be used. 3  Test method. 4  Use the chi-square test for independence to determine whether there is a significant relationship between two categorical variables.