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Hypothesis Testing 假設檢定
Released已發布 methodology analytics
Conduct statistical hypothesis testing including null/alternative hypothesis formulation, p-values, Type I/II errors, and test statistic selection. Use this skill when the user needs to determine whether a result is statistically significant, choose the right statistical test, interpret p-values correctly, or evaluate research findings — even if they say 'is this result significant', 'which statistical test should I use', or 'what does this p-value mean'.
統計方法論技能：Hypothesis Testing 分析與應用。
Methodology 方法論
IRON LAW: Statistical Significance ≠ Practical Significance
A p-value < 0.05 means the result is unlikely under the null hypothesis.
It does NOT mean the result is important, large, or practically meaningful.
With a large enough sample, a 0.1% conversion rate difference becomes
"statistically significant" but is practically worthless.
ALWAYS report effect size alongside p-value.
IRON LAW: State Hypotheses BEFORE Looking at Data
H₀ (null) and H₁ (alternative) must be defined before data analysis.
Choosing hypotheses after seeing the data = p-hacking = scientific fraud.
"We found an interesting pattern, let's test it on the same data" is invalid.
Core Concepts
| Concept | Definition |
|---|---|
| H₀ (Null) | Default assumption: no effect, no difference |
| H₁ (Alternative) | What you want to show: there IS an effect/difference |
| p-value | Probability of seeing this result (or more extreme) IF H₀ is true |
| α (significance level) | Threshold for rejecting H₀ (typically 0.05) |
| Type I error (α) | Rejecting H₀ when it's actually true (false positive) |
| Type II error (β) | Failing to reject H₀ when H₁ is true (false negative) |
| Power (1-β) | Probability of detecting a real effect (target: ≥ 0.8) |
| Effect size | Magnitude of the difference (Cohen's d, odds ratio, R²) |
Test Selection Guide
| Data Type | Groups | Test |
|---|---|---|
| Continuous, normal, 2 groups | Independent | Independent t-test |
| Continuous, normal, 2 groups | Paired/before-after | Paired t-test |
| Continuous, normal, 3+ groups | Independent | One-way ANOVA |
| Continuous, non-normal | 2 groups | Mann-Whitney U |
| Categorical | 2+ groups | Chi-square test |
| Continuous, relationship | 2 variables | Pearson correlation (normal) / Spearman (non-normal) |
| Binary outcome | Predictors | Logistic regression |
Testing Process
- State hypotheses: H₀ and H₁ with specific parameters
- Choose test: Based on data type, distribution, and groups (use guide above)
- Set α: Usually 0.05 (justify if different)
- Calculate: Run the test, get test statistic and p-value
- Decide: p < α → reject H₀; p ≥ α → fail to reject H₀
- Report: Effect size + confidence interval + p-value (not just "significant")
Output Format輸出格式
# Hypothesis Test: {Research Question}
Gotchas注意事項
- "Fail to reject H₀" ≠ "H₀ is true": Absence of evidence is not evidence of absence. You may lack power to detect a real effect.
- Multiple comparisons inflate Type I error: Testing 20 hypotheses at α=0.05 → expect 1 false positive by chance. Apply Bonferroni or FDR correction.
- Check assumptions before testing: t-test assumes normality and equal variance. Violating assumptions invalidates results. Use non-parametric alternatives when assumptions fail.
- Sample size determines power: Small samples miss real effects (Type II error). Calculate required sample size BEFORE collecting data.
- p-value is NOT the probability that H₀ is true: It's the probability of the data given H₀. These are fundamentally different things (base rate fallacy).
References參考資料
- For sample size calculation, see
references/sample-size.md - For non-parametric test alternatives, see
references/nonparametric-tests.md
Tags標籤
statisticshypothesis-testingp-valueinference