Introduction to Chi-Square Hypothesis Testing
The Chi-Square (χ^2) test is a fundamental inferential statistics method used to analyze categorical data. Developed by Karl Pearson in 1900, it helps researchers determine whether there is a significant difference between expected categorical frequencies and observed frequencies. It is widely used in sociology, biology, marketing research, and medical trials to evaluate survey responses, genetic traits, and demographic variables.
There are two main types of Chi-Square tests: the Goodness-of-Fit test and the Test of Independence. The Goodness-of-Fit test determines if a sample distribution matches a hypothesized population distribution (e.g., checking if a die is fair). The Test of Independence evaluates whether two categorical variables (such as gender and voting preference) are associated, using a contingency table. This calculator implements the Goodness-of-Fit version only — a single list of observed counts against a single list of expected counts.
Enter your observed category counts and the expected counts you are testing against (equal-length comma-separated lists), and the solver computes the test statistic, degrees of freedom (df = k - 1), and the P-value using a Wilson-Hilferty normal approximation to the Chi-Square distribution.