# Normality hypothesis test

A hypothesis test formally tests if the population the sample represents is normally-distributed.

The null hypothesis states that the population is normally distributed, against the alternative hypothesis that it is not normally-distributed. If the test p-value is less than the predefined significance level, you can reject the null hypothesis and conclude the data are not from a population with a normal distribution. If the p-value is greater than the predefined significance level, you cannot reject the null hypothesis.

Note that small deviations from normality can produce a statistically significant p-value when the sample size is large, and conversely it can be impossible to detect non-normality with a small sample. You should always examine the normal plot and use your judgment, rather than rely solely on the hypothesis test. Many statistical tests and estimators are robust against moderate departures in normality due to the central limit theorem.

**Related concepts**

**Available in Analyse-it Editions**

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- What is Analyse-it?
- What's new?
- Administrator's Guide
- User's Guide
- Statistical Reference Guide
- Distribution
- Continuous distributions
- Univariate descriptive statistics
- Calculating univariate descriptive statistics
- Univariate plot
- Creating a univariate plot
- Frequency distribution
- Normality
- Normal distribution
- Normal probability (Q-Q) plot
- Creating a normal probability plot
- Normality hypothesis test
- Tests for normality
- Testing the normality of a distribution
- Central limit theorem and the normality assumption
- Inferences about distribution parameters
- Discrete distributions
- Study design
- Compare groups
- Compare pairs
- Contingency tables
- Correlation and association
- Principal component analysis (PCA)
- Factor analysis (FA)
- Item reliability
- Fit model
- Method comparison
- Measurement systems analysis (MSA)
- Reference interval
- Diagnostic performance
- Control charts
- Process capability
- Pareto analysis
- Study Designs
- Bibliography

Version 5.60

Published 27-Apr-2020