Understanding Chi-Square Tests
The chi-square test measures how much observed data deviates from what you'd expect under the null hypothesis. A larger χ² statistic means a bigger difference between observed and expected values — and a smaller p-value.
Common P-Value Thresholds
| P-Value | Interpretation | Action |
|---|---|---|
| < 0.001 | Extremely significant | Reject H₀ (very strong) |
| 0.001 – 0.01 | Highly significant | Reject H₀ (strong) |
| 0.01 – 0.05 | Significant | Reject H₀ (standard) |
| 0.05 – 0.10 | Marginal | Context-dependent |
| > 0.10 | Not significant | Fail to reject H₀ |
Frequently Asked Questions
A p-value is the probability of observing your chi-square statistic (or a more extreme value) if the null hypothesis is true. A p-value below 0.05 typically indicates statistical significance, meaning your results are unlikely due to chance alone.
Degrees of freedom (df) represent the number of independent values in your calculation. For a goodness-of-fit test, df = number of categories − 1. For an independence test, df = (rows − 1) × (columns − 1).
A chi-square statistic of zero means the observed frequencies perfectly match the expected frequencies — there is no difference at all between observed and expected values, giving a p-value of 1.0.
Compare your p-value to your significance level (α). If p < α (commonly 0.05), you reject the null hypothesis. If p ≥ α, you fail to reject the null hypothesis. Always decide your α before running the test.
Chi-square tests are designed for categorical (count) data, not continuous measurements. For continuous data, consider t-tests, ANOVA, or correlation analysis instead.
The chi-square distribution is a family of probability distributions defined by degrees of freedom. It arises when you sum the squares of independent standard normal variables. It is always non-negative and right-skewed.