## Chi-Square Test Interpretation ### Critical Value Reference **Key Point:** For χ² with df = 1, the critical value at α = 0.05 is 3.84. Since 8.64 > 3.84, the result is statistically significant (p ≈ 0.003). ### Why This Matters in PSM **High-Yield:** The chi-square test assesses **association**, not causation. It determines whether observed frequencies differ significantly from expected frequencies under the null hypothesis of independence. ### Assumptions for Chi-Square | Assumption | Requirement | Status in Q | |---|---|---| | Expected frequency in each cell | ≥ 5 | Likely met (n=500, 2×2 table) | | Independence of observations | Each subject counted once | Met in cross-sectional design | | Categorical data | Nominal or ordinal | Met (exposed/unexposed, asthma yes/no) | **Clinical Pearl:** Statistical significance (p < 0.05) indicates the association is unlikely due to chance alone, but does NOT establish cause-and-effect. Confounding variables, selection bias, or reverse causality may explain the association. ### Correct Interpretation With χ² = 8.64, df = 1: - **p ≈ 0.003** (highly significant at α = 0.05) - We reject the null hypothesis of independence - Exposure and asthma prevalence are significantly associated - The strength and direction of association require further analysis (odds ratio, relative risk) **Mnemonic: CHISQ** — **C**ategorical data, **H**ypothesis of independence, **I**ndependent observations, **S**ignificance testing, **Q**uantifies association (not causation).
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