Chi-square distribution table

A chi-square table gives the critical value of χ² for a given number of degrees of freedom and upper-tail area — the cutoff a goodness-of-fit or independence test is compared against.

How do I read this table?

Each column is an upper-tail area α, so the 0.05 column holds the value a test statistic must exceed to be significant at the 5% level. For a 2 × 2 table of independence df = 1, and the familiar cutoff is 3.841.

Chi-square is skewed and strictly positive, so unlike t there is no symmetry to exploit: a lower-tail question needs the lower-tail value, which the calculator will give for any α.

Every value here is computed from the same functions the app's tests use, so the table cannot disagree with the calculator, which will also handle any value this table does not list.

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