What Is Chi-Square Table?
A chi-square table lists the χ² values that cut off a given right-tail area for each number of degrees of freedom. If your test statistic is larger than the tabled value, the result is significant at that level.
Enter the degrees of freedom and α for an exact critical value, with no interpolation. Add your own χ² statistic to get its p-value and a reject or do-not-reject decision.
The table covers df 1 to 30, then 40 to 100 in steps of 10, for the five levels most often used.
How to Use the Chi-Square Table Calculator
- Enter the degrees of freedom.
- Choose α.
- Optionally enter your χ² statistic.
- Read the critical value, or find it in the table.
Chi-Square Table Formula
Right-tail critical value
Chi-Square Table Variables Explained
| Symbol | Meaning | Notes |
|---|---|---|
| df | Degrees of freedom | |
| α | Right-tail area | |
| χ² | Chi-square statistic | |
| p | Right-tail p-value |
Chi-Square Table Worked Example
A test of independence on a 3 × 4 table has (3 − 1)(4 − 1) = 6 degrees of freedom. At α = 0.05 the critical value is 12.592. If your χ² statistic is 14.3, it is larger, so you reject independence. If it is 9.1, you do not.
With the example values loaded in the calculator above, the steps are:
- Right-tail critical value: the χ² value with area 0.05 above it, df = 4. That is χ²₍α₎ = 9.48773.
- Left-tail critical value: the value with area 0.05 below it, 0.710723.
- Your χ² = 11.2 is larger than 9.48773, so the right-tail p-value is 0.024406.
Result: Right-tail critical value = 9.48773.
How to Read a Chi-Square Critical Value
The critical value is the χ² cut-off for your degrees of freedom and α. A test of independence on a 3 × 4 table has (3 − 1)(4 − 1) = 6 degrees of freedom, and at α = 0.05 the critical value is 12.592. A statistic of 14.3 is larger, so you reject independence. A statistic of 9.1 is not.
Chi-square tests of fit and independence use the right tail only. The left-tail value matters mainly for tests about a variance. The full table below the calculator lets you scan the critical values for several α levels at once.
Where Chi-Square Table Is Used
Tests of independence
Look up the cut-off for a contingency table.
Goodness of fit
Compare observed and expected counts.
Checking a table lookup
Confirm a value from a textbook table.
Variance tests
Use both tails for a test about a single variance.
Common Chi-Square Table Mistakes to Avoid
- Degrees of freedom for goodness of fit are categories − 1.
- For a contingency table use (rows − 1)(columns − 1).
- Printed tables skip some df values. This calculator gives exact values for any df.
- Reject H₀ when the statistic is larger than the right-tail critical value.
Chi-Square Table Terms and Definitions
- Critical value
- The χ² value that cuts off an area of α in the right tail.
Chi-Square Table FAQs
How do you read a chi-square table?
Find your degrees of freedom in the left column, move across to the column for your α, and read the critical value. Reject H₀ if your statistic is larger.
What is the chi-square critical value for df = 1 at 0.05?
3.841.
Is the chi-square test one-tailed or two-tailed?
Tests of independence and goodness of fit are right-tailed, because only large values of χ² indicate a poor fit.