115 lines
3.4 KiB
Markdown
115 lines
3.4 KiB
Markdown
---
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name: hypothesis-test
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description: "Guide selection and interpretation of statistical hypothesis tests. Use when: (1) Choosing appropriate test for research data, (2) Checking assumptions before analysis, (3) Interpreting test results correctly, (4) Reporting statistical findings, (5) Troubleshooting assumption violations."
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allowed-tools: Read, Write
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version: 1.0.0
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---
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# Hypothesis Testing Skill
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## Purpose
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Guide appropriate selection and interpretation of statistical hypothesis tests for research data analysis.
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## Test Selection Decision Tree
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### Step 1: How many variables?
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**One variable:**
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- Categorical → Chi-square goodness of fit
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- Continuous → One-sample t-test
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**Two variables:**
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- Both categorical → Chi-square test of independence
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- One categorical, one continuous → T-test or ANOVA
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- Both continuous → Correlation or regression
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**Three+ variables:**
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- Multiple predictors → Multiple regression or ANOVA
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- Complex designs → Mixed models or advanced methods
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### Step 2: Check assumptions
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**For t-tests:**
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1. Independence of observations
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2. Normality (especially for small N)
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3. Homogeneity of variance
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**Violations?**
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- Non-normal → Mann-Whitney U (non-parametric)
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- Unequal variance → Welch's t-test
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- Dependent observations → Paired t-test or mixed models
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**For ANOVA:**
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1. Independence
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2. Normality
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3. Homogeneity of variance
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4. No outliers
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**Violations?**
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- Non-normal → Kruskal-Wallis test
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- Unequal variance → Welch's ANOVA
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- Outliers → Robust methods or transformation
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### Step 3: Interpret results
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Always report:
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1. **Test statistic** (t, F, χ²)
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2. **Degrees of freedom**
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3. **p-value**
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4. **Effect size with CI**
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5. **Descriptive statistics**
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**Example:**
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```
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Independent samples t-test showed a significant difference between
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groups, t(98) = 3.45, p < .001, d = 0.69, 95% CI [0.29, 1.09].
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The experimental group (M = 45.2, SD = 8.3) scored higher than
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control (M = 37.8, SD = 9.1).
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```
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## Common Tests Reference
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| Research Question | Test | Assumptions |
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|------------------|------|-------------|
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| 2 groups, continuous outcome | Independent t-test | Normality, equal variance |
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| 2 measurements, same people | Paired t-test | Normality of differences |
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| 3+ groups, one factor | One-way ANOVA | Normality, homogeneity |
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| 3+ groups, multiple factors | Factorial ANOVA | Normality, homogeneity |
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| Relationship between variables | Pearson correlation | Linearity, normality |
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| Predict continuous outcome | Linear regression | Linearity, normality of residuals |
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| 2 categorical variables | Chi-square test | Expected frequencies ≥5 |
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| Ordinal data, 2 groups | Mann-Whitney U | None (non-parametric) |
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| Ordinal data, paired | Wilcoxon signed-rank | None (non-parametric) |
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## Assumption Checking
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### Normality
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```
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Visual: Q-Q plot, histogram
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Statistical: Shapiro-Wilk test (N < 50), Kolmogorov-Smirnov (N ≥ 50)
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Guideline: Robust to moderate violations if N ≥ 30
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```
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### Homogeneity of Variance
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```
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Visual: Box plots, residual plots
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Statistical: Levene's test, Bartlett's test
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Guideline: Ratio of largest/smallest variance < 4
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```
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### Independence
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```
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Check: Research design, data collection
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Red flags: Time series, clustered data, repeated measures
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Solution: Use appropriate model (mixed effects, GEE)
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```
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## Integration
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Use with data-analyst agent for complete statistical analysis workflow and experiment-designer agent for planning appropriate analyses.
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---
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**Version:** 1.0.0
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