Normality Test Suite

Comprehensive normality assessment with multiple statistical tests and visualizations

Input Data

Enter your numeric data (one value per line or comma-separated)

Significance Level

Typical values: 0.01, 0.05, 0.10

Help

How to Use
  1. Enter your numeric data (comma or newline separated)
  2. Or generate sample data with different distributions
  3. Set your desired significance level (typically 0.05)
  4. Click "Run Normality Tests"
  5. Review the overall assessment and individual test results
  6. Examine Q-Q plot and histogram for visual confirmation
Understanding the Tests
  • Shapiro-Wilk: Most powerful test for n < 2000; null hypothesis: data is normal
  • Anderson-Darling: Gives more weight to tails; good for detecting tail deviations
  • Kolmogorov-Smirnov: Tests maximum difference between empirical and theoretical CDF
  • D'Agostino-Pearson: Based on skewness and kurtosis; omnibus test
Interpreting Results
  • Green (Normal): Most tests accept normality (p > α)
  • Yellow (Questionable): Mixed results; some tests reject, others accept
  • Red (Non-Normal): Most tests reject normality (p < α)
  • P-value: Probability of observing the data if it were normal; lower values indicate non-normality
Skewness and Kurtosis
  • Skewness = 0: Symmetric distribution (like normal)
  • Skewness > 0: Right-skewed (tail extends right)
  • Skewness < 0: Left-skewed (tail extends left)
  • Excess Kurtosis = 0: Normal tail behavior
  • Excess Kurtosis > 0: Heavy tails (more outliers than normal)
  • Excess Kurtosis < 0: Light tails (fewer outliers than normal)