Chi-Square Calculator: Independence Test
This chi-square calculator runs the two most common chi-square tests. For a test of independence, type your contingency table with commas between columns and semicolons between rows, such as 20, 30; 30, 20. For a goodness-of-fit test, type the observed counts and, if you like, the expected counts or percentages; leave expected blank to test against equal counts. You get the chi-square statistic ฯ², the degrees of freedom, the p-value, the critical value at your significance level, a plain-English decision and a table of expected counts with each cell's contribution.
Chi-Square Calculator
Run a chi-square test of independence on a contingency table or a goodness-of-fit test on counts.
How to use the Chi-Square Calculator
- Choose test of independence or goodness of fit.
- Type the table or the observed counts.
- Pick the significance level ฮฑ.
- Read ฯ², df, the p-value and the decision.
Chi-square formula
ฯ² = ฮฃ (O − E)² ÷ E · Expected (table) = row total × column total ÷ N · df = (r − 1)(c − 1) or k − 1
Features
- Test of independence (any r × c table)
- Goodness of fit vs equal or given expected counts
- p-value and critical value
- Expected counts and cell contributions
- Warns when expected counts are below 5
Frequently asked questions
What is a chi-square test?
A chi-square test compares observed counts with the counts you would expect if there were no effect. A large ฯ² means the observed counts are far from expected.
How do I calculate expected counts?
For a contingency table, expected = row total × column total ÷ grand total. For goodness of fit, expected = total × the expected proportion of each category.
How many degrees of freedom does a chi-square test have?
For independence, df = (rows − 1) × (columns − 1). For goodness of fit, df = number of categories − 1.
What does the p-value mean?
It is the chance of a ฯ² this large or larger if the null hypothesis is true. If p is below ฮฑ, such as 0.05, you reject the null hypothesis.
When should I not use a chi-square test?
When many expected counts are below 5 the test is unreliable. Combine categories or use Fisher's exact test for small 2 × 2 tables.