Normality Testing evaluates whether sample data are reasonably consistent with a normal distribution before using methods that assume normality.
Definition
Normality Testing is the evaluation of whether data plausibly follow a normal distribution. It can include histograms, probability plots, Anderson-Darling, Shapiro-Wilk, and other tests, combined with process knowledge.
Normality matters because some statistical methods assume normal data or normally distributed residuals. It is an assumption check, not the final analysis goal.
History
Normal distribution assumptions are central to many classical statistical methods. Quality practitioners adopted normality testing as capability analysis, hypothesis testing, and DOE became common in process improvement.
When to Use
Use normality testing before normal capability analysis, parametric tests, tolerance studies, or statistical models where the assumption affects interpretation. Use it with graphical analysis and process context.
Step-by-Step
- Define the data source and process scope.
- Check measurement quality and data errors.
- Plot a histogram and probability plot.
- Run an appropriate normality test if useful.
- Check for mixed populations, outliers, and time effects.
- Decide whether normal methods are reasonable.
- Use transformation or non-normal methods if needed.
- Document the decision and assumptions.
Examples
- Capability: Diameter data are checked before calculating Cp/Cpk.
- Hypothesis test: Residuals are reviewed before relying on parametric results.
- Cycle time: Skewed data lead to non-normal analysis.
Common Pitfalls
- Using p-value alone without plots.
- Testing tiny samples and overinterpreting results.
- Testing huge samples and rejecting trivial deviations.
- Ignoring process mixture.
- Deleting outliers without cause.
- Assuming non-normal data are automatically bad.