Statistics
Normality
The degree to which a dataset conforms to the shape and mathematical properties of a normal distribution.
What is Normality?
Normality is an assumption required by many parametric statistical tests, specifically assuming that the residuals or sampling distribution follow a bell-shaped, Gaussian curve.
Why Normality Matters
If the assumption of normality is severely violated in small samples, the p-values and confidence intervals produced by parametric tests may be inaccurate.
Example
Before running an ANOVA, a researcher checks the normality of their residuals using a Q-Q plot and a Shapiro-Wilk test to ensure the statistical model is appropriate.
Common Mistakes
- Testing the normality of the raw independent variables, rather than the normality of the residuals or errors in a regression model.
- Relying strictly on significance tests for normality in large datasets, which will almost always flag minor deviations from perfect normality.