Normality & Power
Two of the most common analytical questions researchers ask: "How many samples do I need?" (before the experiment) and "Is my data normal enough to use parametric tests?" (after data collection). Licklider provides defensible, journal-ready answers to both.
Section covers: Shapiro-Wilk · Kolmogorov-Smirnov · D'Agostino-Pearson ·
Q-Q plots · Power analysis (G*Power-equivalent) · Effect size input (Cohen's d, η², f) ·
Alpha and beta specification · Sample size output with assumptions declared
When to Use This Section
Use Normality & Power workflows when:
- You need to justify a sample size before starting an experiment (grant application, ethics committee)
- You want to check whether your data distribution is consistent with parametric test assumptions
- You need to report power and α level in your Methods section as required by journals
- A reviewer or editor asks you to justify why you used (or did not use) a parametric test
Available Scenarios
Pre-Study Power Calculation
Sample size calculation for a two-group experiment — PhD student planning an animal study with 80% power at α=0.05.
Normality Testing Workflow
Data profiling for test selection — postdoc checking if distributions warrant parametric vs. non-parametric analysis (n=15–20 per group).
Key Concepts
- Power (1-β): Probability of detecting a true effect. Typically set to 0.80 (80%) or 0.90 (90%).
- α (Type I error): Probability of a false positive. Typically set to 0.05.
- Effect size: The magnitude of the difference you expect to detect. Must be estimated from pilot data, literature, or clinically meaningful differences — not set arbitrarily.
- Normality testing: With small n (<10 per group), Shapiro-Wilk has low power — failing to reject normality does not prove normality. With large n (>100), trivial deviations from normality will be significant — clinical significance matters more than statistical significance.
- Parametric vs. non-parametric: The decision is based on the distribution of residuals (in ANOVA) or data (in t-tests), not group means. Visual inspection (Q-Q plot, histogram) alongside a formal test provides the most defensible justification.