Since a number of the most common statistical tests rely on the normality of a sample or population, it is often useful to test whether the underlying distribution is normal, or at least symmetric. This can be done via the following approaches:
- Review the distribution graphically (via histograms, boxplots, QQ plots)
- Analyze the skewness and kurtosis
- Employ statistical tests (esp. Chi-square, Kolmogorov-Smironov, Shapiro-Wilk, Jarque-Barre, D’Agostino-Pearson)
If data is not symmetric, sometimes it is useful to make a transformation whereby the transformed data is symmetric and so can be analyzed more easily.
- Graphical Tests
- Analysis of Skewness and Kurtosis
- Statistical Tests