Statistical Hypothesis Testing
Perform rigorous statistical tests including t-tests, ANOVA, chi-square, and non-parametric alternatives to assess whether observed differences are statistically significant. The skill handles independent and paired comparisons, multiple group analysis, categorical independence testing, and includes effect size calculations, confidence intervals, and power analysis to support evidence-based decision-making.
Statistical Hypothesis Testing conducts t-tests, ANOVA, chi-square, and other tests to validate data-driven decisions.
AI-generated summary based on this skill's SKILL.md
Decision gist · record as of 2026-03-04
Statistical Hypothesis Testing conducts t-tests, ANOVA, chi-square, and other tests to validate data-driven decisions. Perform rigorous statistical tests including t-tests, ANOVA, chi-square, and non-parametric alternatives to assess whether observed differences are statistically significant. The skill handles independent and paired comparisons, multiple group analysis, categorical independence testing, and includes effect size calculations, confidence intervals, and power analysis to support evidence-based decision-making.
Use it when
- Statistical Hypothesis Testing uses p-value significance testing to quantify the probability that observed results occurred by chance under.
- Statistical Hypothesis Testing calculates p-values and effect sizes to analyze A/B test results.
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Frequently asked questions
AI-generated answers based on this skill's SKILL.md and metadata
How do I do t-test and ANOVA with Statistical Hypothesis Testing?
Statistical Hypothesis Testing enables you to conduct t-tests for comparing two group means and ANOVA for analyzing multiple groups. Use t-tests to determine if differences between independent or paired samples are statistically significant, and ANOVA to test whether means across three or more groups differ significantly. The skill calculates test statistics and p-values to support your conclusions.
What is p-value significance testing and why does it matter?
Statistical Hypothesis Testing uses p-value significance testing to quantify the probability that observed results occurred by chance under the null hypothesis. A low p-value (typically <0.05) suggests your findings are statistically significant. This metric is central to validating data-driven decisions and determining whether group differences are real or random variation.
How does Statistical Hypothesis Testing analyze A/B test results?
Statistical Hypothesis Testing calculates p-values and effect sizes to analyze A/B test results, helping you determine if observed differences between control and treatment groups are statistically significant. The skill supports comparing group means, computing confidence intervals, and assessing practical significance alongside statistical significance for robust test interpretation.
When should I use parametric vs non-parametric tests?
Statistical Hypothesis Testing guides test selection based on your data characteristics. Use parametric tests like t-tests and ANOVA when data is normally distributed; use non-parametric alternatives like Mann-Whitney U or Kruskal-Wallis when normality assumptions are violated. The skill helps you choose the appropriate test based on data type and distribution properties.
How do I calculate effect sizes and confidence intervals?
Statistical Hypothesis Testing computes effect sizes (such as Cohen's d) and confidence intervals to quantify the magnitude and precision of your findings. These metrics complement p-values by showing practical significance and the range of plausible population values, enabling more complete interpretation of hypothesis test results.
What statistical tests does this skill support for categorical data?
Statistical Hypothesis Testing includes chi-square tests for assessing independence between categorical variables. It also supports multiple testing corrections like Bonferroni to control false positives when conducting many tests, and normality checks via Shapiro-Wilk to verify parametric test assumptions before analysis.
SKILL.md
Rendered from the published skill. Quoted content, verbatim.
Statistical Hypothesis Testing
Overview
Hypothesis testing provides a framework for making data-driven decisions by testing whether observed differences are statistically significant or due to chance.
Testing Framework
- Null Hypothesis (H0): No effect or difference exists
- Alternative Hypothesis (H1): Effect or difference exists
- Significance Level (α): Threshold for rejecting H0 (typically 0.05)
- P-value: Probability of observing data if H0 is true
Common Tests
- T-test: Compare means between two groups
- ANOVA: Compare means across multiple groups
- Chi-square: Test independence of categorical variables
- Mann-Whitney U: Non-parametric alternative to t-test
- Kruskal-Wallis: Non-parametric alternative to ANOVA
Implementation with Python
```python import pandas as pd import numpy as np from scipy import stats import matplotlib.pyplot as plt
Sample data
group_a = np.random.normal(100, 15, 50) # Mean=100,
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skills/statistical-hypothesis-testing/SKILL.md
skills/statistical-hypothesis-testing/scripts/scaffold-analysis.sh
skills/statistical-hypothesis-testing/templates/notebook-template.py
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