What is Chi-Square Calculator?

Chi-Square Calculator performs chi-square goodness-of-fit and independence tests with full statistical output. Enter observed and expected frequencies, and get the chi-square statistic, degrees of freedom, p-value, and Cramer's V effect size. Includes a visual chi-square distribution curve showing your result.

The tool runs both flavours of the test on the same screen: goodness-of-fit when you have one categorical variable with predicted frequencies, and independence when you have a contingency table of two variables. Output includes the chi-square statistic, degrees of freedom, p-value, critical value at α 0.01, 0.05, or 0.10, and Cramer's V effect size for independence tables. A distribution curve plots your statistic against the critical region so you can see at a glance whether the result lands in the reject zone.

How to use

1. Choose your test type: Goodness of Fit (one variable vs expected distribution) or Test of Independence (two categorical variables in a contingency table).
2. Enter your observed frequencies in the table cells. For goodness of fit, also enter expected frequencies. For independence, the expected values are calculated automatically.
3. Click Calculate to see the chi-square statistic, degrees of freedom, p-value, and whether to reject the null hypothesis at your chosen significance level (0.01, 0.05, or 0.10).

When to use

• Checking whether a dice roll or random sample matches a uniform distribution.
• Testing if two categorical variables (e.g. gender vs product preference) are related.
• A/B testing more than two variants where t-tests aren't appropriate.

Result

A marketer tests whether 4 ad variants perform equally. Observed clicks: A=142, B=186, C=121, D=151. Expected: 150 each. The chi-square test yields X2=14.2, df=3, p=0.0026 — significant difference, Variant B wins.

FAQ

When should I pick goodness-of-fit over independence?

Use goodness-of-fit when you have one categorical variable with observed counts and a known or predicted distribution to compare against. Use independence when you have two categorical variables in rows and columns and want to know if they move together.

What does Cramer's V tell me that the p-value doesn't?

P-value tells you whether the association is statistically significant; Cramer's V tells you how strong it is, scaled 0 to 1. With large samples you can get a tiny p-value on a relationship so weak it's not meaningful. V under 0.1 is negligible, 0.1–0.3 small, 0.3–0.5 medium, above 0.5 large.

Are my results valid if some expected cell counts are below 5?

The chi-square approximation gets shaky when expected frequencies drop under 5. Most textbooks require at least 80% of cells to have expected counts above 5 and none below 1. If you violate that, merge sparse categories or switch to Fisher's exact test.

What significance level should I use?

0.05 is the convention in most social science and marketing work. Choose 0.01 when a false positive is costly (medical, regulatory). 0.10 is sometimes used for exploratory pilots where you'd rather investigate further than miss a real effect.

Why does the test return df = (rows-1) × (cols-1)?

For an independence table, once row totals and column totals are fixed, only (r-1)(c-1) cells are free to vary — the rest are determined by the totals. That count of free parameters is the degrees of freedom that anchors the chi-square distribution.

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