In a chi-square test of independence, what does a p-value of 0.03 indicate when testing the association between smoking status and lung cancer at α = 0.05?

Explanation

## Chi-Square Test of Independence: Interpretation of p-value **Key Point:** A p-value is the probability of observing data as extreme as (or more extreme than) what was observed, **assuming the null hypothesis is true**. It is NOT the probability that the null hypothesis is true. ### Decision Rule at α = 0.05 | p-value | Decision | Interpretation | |---------|----------|----------------| | p < 0.05 | Reject H₀ | Statistically significant association | | p ≥ 0.05 | Fail to reject H₀ | No statistically significant association | ### Application to This Question - **p-value = 0.03** - **Significance level (α) = 0.05** - **Comparison**: 0.03 < 0.05 ✓ - **Conclusion**: Reject the null hypothesis of independence **High-Yield:** When p < α, we conclude there IS a statistically significant association between the variables. This means smoking status and lung cancer are NOT independent — they are associated. **Warning:** A statistically significant p-value does NOT tell us: - The magnitude of the association (use effect size measures like Cramér's V or odds ratio) - Whether the association is clinically meaningful - The direction of causation **Mnemonic:** **PHAT** — **P**-value is **H**ypothetical (conditional on H₀), **A**ssociation (not causation), **T**hreshold (compare to α). **Clinical Pearl:** Statistical significance (p < 0.05) and clinical significance are different. A large study may find a statistically significant but clinically trivial association.