Chi-Square Goodness of Fit Calculator
Test whether observed data follows expected distribution using chi-square goodness of fit test
About this calculator
The Chi-Square Goodness of Fit Calculator determines whether your observed data significantly differs from an expected theoretical distribution. This statistical test is essential for researchers, analysts, and students who need to validate hypotheses about population distributions. By comparing observed frequencies with expected values, it helps you make data-driven decisions about whether your sample represents a specific distribution pattern, providing critical insights for quality control, market research, and scientific studies.
How to use
Enter your observed frequencies and corresponding expected frequencies for each category or class interval. The calculator will compute the chi-square test statistic, degrees of freedom, and p-value. Compare the p-value to your significance level (typically 0.05) to determine if the observed data significantly deviates from the expected distribution.
Frequently asked questions
What is the minimum sample size needed for this test?
Generally, each expected frequency should be at least 5, and no more than 20% of categories should have expected frequencies below 5.
How do I interpret the p-value result?
If p-value < 0.05, reject the null hypothesis - your data doesn't follow the expected distribution. If p-value ≥ 0.05, fail to reject the null hypothesis.
What are the assumptions for this test?
Data must be independent observations, categories should be mutually exclusive, and expected frequencies should be sufficiently large (typically ≥5 per category).