The chi-square table provides critical values for the chi-square distribution, which is commonly used in tests of independence, goodness of fit tests, and testing hypotheses about population variance.
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How to Use the Chi-Square Table
- Locate your degrees of freedom (df) in the leftmost column
- Choose the desired significance level (α) from the column headers
- The intersection gives you the critical chi-square value
- Hover over any value to see the corresponding area in the distribution chart
Important Notes
- The table shows right-tail critical values
- For goodness of fit tests: df = number of categories - 1
- For independence tests: df = (rows - 1) × (columns - 1)
- The chi-square distribution is always right-skewed, but becomes more symmetric as df increases
- All chi-square values are non-negative since they're based on squared differences
Examples of Finding Critical Values
Example 1: Goodness of Fit Test
Suppose you are conducting a goodness of fit test with 5 categories (df = 4) and a significance level of α = 0.05.
- Find df = 4 in the leftmost column
- Look for the column with α = 0.05
- The critical value is 9.488
- Reject H₀ if your calculated chi-square statistic is greater than 9.488
R
qchisq(1 - 0.05, 4)
# [1] 9.487729Example 2: Test of Independence
For a chi-square test of independence with a 3×4 contingency table (df = (3-1)×(4-1) = 6) and a significance level of α = 0.01:
- Find df = 6 in the leftmost column
- Look for the column with α = 0.01
- The critical value is 16.812
- Reject H₀ if your calculated chi-square statistic is greater than 16.812
R
qchisq(1 - 0.01, 6)
# [1] 16.81189