Chi-squared test interpretation
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Chi-squared Test: Interpretation and p-values
The chi-squared test compares observed frequencies with the frequencies expected if two categorical variables were independent.
Test statistic
\[\chi^2=\sum \frac{(O-E)^2}{E}\]
Large differences between observed and expected frequencies make \(\chi^2\) larger.
Decision rule
| Using critical value | Using p-value |
|---|---|
| If \(\chi^2_{calc}>\chi^2_{crit}\), reject \(H_0\). | If \(p<\alpha\), reject \(H_0\). |
| If \(\chi^2_{calc}\leq\chi^2_{crit}\), do not reject \(H_0\). | If \(p\geq\alpha\), do not reject \(H_0\). |
Writing the conclusion
Always write the conclusion in context. Avoid saying “accept the null hypothesis” too strongly; use “there is insufficient evidence to suggest…” when you do not reject \(H_0\).
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