Normality Calculator

Test if your data follows a normal distribution using various statistical tests.

Calculator

Test for Normality

Concept

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.

Key Characteristics:
  • 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
Guide

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

Guide

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
Examples

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)

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