# Residuals - normality

Normality is the assumption that the underlying residuals are normally distributed, or approximately so.

While a residual plot, or normal plot of the residuals can identify non-normality, you can formally test the hypothesis using the Shapiro-Wilk or similar test.

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

Violation of the normality assumption only becomes an issue with small sample sizes. For large sample sizes, the assumption is less important due to the central limit theorem, and the fact that the F- and t-tests used for hypothesis tests and forming confidence intervals are quite robust to modest departures from normality.

**Available in Analyse-it Editions**

Standard edition

Method Validation edition

Quality Control & Improvement edition

Ultimate edition

- What is Analyse-it?
- Administrator's Guide
- User's Guide
- Statistical Reference Guide
- Distribution
- Compare groups
- Compare pairs
- Contingency tables
- Correlation and association
- Principal component analysis (PCA)
- Factor analysis (FA)
- Item reliability
- Fit model
- Linear fit
- Simple regression models
- Fitting a simple linear regression
- Advanced models
- Fitting a multiple linear regression
- Performing ANOVA
- Performing 2-way or higher factorial ANOVA
- Performing ANCOVA
- Fitting an advanced linear model
- Scatter plot
- Summary of fit
- Parameter estimates
- Effect of model hypothesis test
- ANOVA table
- Predicted against actual Y plot
- Lack of Fit
- Effect of terms hypothesis test
- Effect leverage plot
- Effect means
- Plotting main effects and interactions
- Multiple comparisons
- Multiple comparison procedures
- Comparing effect means
- Residual plot
- Residuals - normality
- Residuals - independence
- Plotting residuals
- Outlier and influence plot
- Identifying outliers and other influential points
- Prediction
- Making predictions
- Saving variables
- Logistic fit
- Study design
- Method comparison
- Measurement systems analysis (MSA)
- Reference interval
- Diagnostic performance
- Control charts
- Process capability
- Pareto analysis
- Study Designs
- Bibliography

Version 5.30

Published 15-Apr-2019