Normality Calculator
Test if your data follows a normal distribution using various statistical tests.
Test for Normality
Table of Contents
What is Normality?
A normal distribution (also known as Gaussian distribution) is a continuous probability distribution characterized by a symmetric bell-shaped curve. It is defined by its mean and standard deviation.
- Bell-shaped curve
- Symmetric around the mean
- 68% of data within 1 standard deviation
- 95% of data within 2 standard deviations
- 99.7% of data within 3 standard deviations
Normality Tests
Shapiro-Wilk Test
Best for small samples (n < 50)
Anderson-Darling Test
Good for larger samples
Kolmogorov-Smirnov Test
Works for any sample size
Interpreting Results
P-Value Interpretation
- p-value > α: Fail to reject normality
- p-value ≤ α: Reject normality
- Common α values: 0.01, 0.05, 0.1
Common Examples
Example 1 Normally Distributed Data
Data: [1, 2, 2, 3, 3, 3, 4, 4, 5]
Result: Likely normal (p-value > 0.05)
Example 2 Skewed Data
Data: [1, 1, 1, 2, 2, 3, 4, 5, 10]
Result: Not normal (p-value < 0.05)
Example 3 Bimodal Data
Data: [1, 1, 1, 2, 2, 8, 9, 9, 10]
Result: Not normal (p-value < 0.05)