Chi-Square Calculator
Pearson chi-square hub: goodness-of-fit for one categorical variable or test of independence on a contingency table, with p-value and step-by-step working.
Enter values separated by commas or spaces
Enter values separated by commas or spaces; must match observed length and total
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Chi-Square Test Explained
Goodness-of-fit and independence, both worked in full: expected counts, the (O−E)²/E statistic, decisions against the chi-square table, and the validity rules.
Chi-Square Test in Excel: CHISQ.TEST Step by Step
Run a chi-square test of independence or goodness of fit in Excel: expected counts, CHISQ.TEST, cell contributions, Cramér's V and a checked 2×3 example.
Choose the right chi-square test
Goodness-of-fit compares one row of counts to a model. Independence compares two categorical variables in an r×c table. For expected-count options and G statistic, use goodness-of-fit calculator or Fisher exact for 2×2 tables with small counts.
χ² = Σ (O − E)² / E
Worked example: fair die (goodness of fit)
Observed 5, 8, 9, 8, 10, 20 vs expected 10 each: χ² = 13.4, df = 5, p ≈ 0.0199, significant bias at α = 0.05. See chi-square test guide and chi-square critical value table.
Frequently Asked Questions
What is the difference between goodness-of-fit and independence tests?
Goodness-of-fit compares one set of observed category counts against expected counts from a theoretical model. Independence tests whether two categorical variables in a contingency table are related.
Why must expected frequencies be at least 5?
The chi-square distribution approximates the sampling distribution when expected counts are large enough; otherwise combine categories or use Fisher's exact test for 2×2 tables.
Do observed and expected totals need to match?
Yes for goodness-of-fit: expected counts must sum to the observed total. The dedicated goodness-of-fit page rejects mismatched totals instead of rescaling.
Can I run this test on means?
No. Chi-square applies to categorical counts. For continuous data use t-tests or ANOVA.
My result is significant. What should I report?
Report χ², df, N, and p (for the die example: χ²(5, N=60)=13.4, p≈0.02) and inspect which categories deviate most.
TI-84?
χ²GOF-Test for goodness of fit; χ²-Test for independence on matrix [A].
Already have χ² and df?
Use the chi-square CDF tool to convert the statistic to a p-value.
Where is Cramér's V?
On the independence test page and when you select independence mode here; it measures association strength after a significant test.
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