Critical Chi-Square Calculator

Significance Level (α)

A value between 0 and 1, e.g. 0.05 for a 5% significance level.

Degrees of Freedom

Depends on your test — e.g. categories minus 1 for a goodness-of-fit test.

About This Test

What Is a Critical Chi-Square Value?

The critical chi-square value is the cutoff on the chi-square distribution that separates "likely due to chance" from "statistically significant." If your calculated chi-square test statistic goes past this cutoff, you reject the null hypothesis.

When to Use It

Chi-square goodness-of-fit tests, checking if observed data matches an expected distribution
Chi-square tests of independence between two categorical variables
Confidence intervals or hypothesis tests involving a population variance

The Concept

\[ P(\chi^2 > \chi^2_{\alpha,\,df}) = \alpha \]

Worked Example

For a goodness-of-fit test with 10 degrees of freedom at α = 0.05, what's the critical value?

\( \alpha = 0.05, \ df = 10 \)
Right-tailed critical value: \( \chi^2_{0.05,\,10} \approx 18.307 \)
If your calculated test statistic exceeds 18.307, you reject the null hypothesis at the 5% significance level.

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