# Normality

Normality is the assumption that the underlying random variable is normally distributed, or approximately so.

In some cases, the normality of the data itself may be important in describing a process that generated the data. However, in many cases, it is hypothesis tests and parameter estimators that rely on the assumption of normality, although many are robust against moderate departures in normality due to the central limit theorem.

**Normal distribution**

A normal (or Gaussian) distribution is a continuous probability distribution that has a bell-shaped probability density function. It is the most prominent probability distribution in used statistics.**Normal probability (Q-Q) plot**

A normal probability plot, or more specifically a quantile-quantile (Q-Q) plot, shows the distribution of the data against the expected normal distribution.**Normality hypothesis test**

A hypothesis test formally tests if the population the sample represents is normally-distributed.**Central limit theorem and the normality assumption**

Due to central limit theory, the assumption of normality implied in many statistical tests and estimators is not a problem.

**Available in Analyse-it Editions**

Standard edition

Method Validation edition

Quality Control & Improvement edition

Ultimate edition

- 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 / Agreement
- Measurement systems analysis (MSA)
- Reference interval
- Diagnostic performance
- Survival/Reliability
- Control charts
- Process capability
- Pareto analysis
- Study Designs
- Bibliography

Version 6.15

Published 18-Apr-2023