Definition
A normality test checks whether data come from a normal distribution — an assumption of the t-test, ANOVA, regression and capability indices. The Shapiro–Wilk test is the most powerful for small and medium samples; Kolmogorov–Smirnov (with Lilliefors correction) is used for larger ones. The null hypothesis is "the data are normal", so a small p rejects normality.
Statistical tests
Always pair the test with a graph: a histogram with a normal curve and a normal probability (Q-Q) plot, where normal data fall on a straight line. With large samples the test rejects even negligible deviations; with small ones it lacks power to detect even marked ones — the graph shows what kind of deviation it is and whether it matters.
If normality fails: try a transformation (logarithm for right-skewed data), use a nonparametric test, or rely on the robustness of the method with a large enough sample (central limit theorem). For regression and ANOVA test the residuals, not the raw variables.
In Statistica
Normality tests are in Descriptive statistics on the Normality tab (Shapiro–Wilk W, Kolmogorov–Smirnov d with Lilliefors correction) together with a histogram and fitted normal curve; Q-Q and normal probability plots come from Graphs → 2D Graphs. The Distribution Fitting module also compares other distributions (lognormal, Weibull, exponential).
Related terms
- Normal distributionThe normal (Gaussian) distribution is a symmetric bell-shaped distribution described by its mean and standard deviation.
- Nonparametric testsNonparametric tests do not assume a normal distribution — they work with the ranks of values rather than the values themselves.
- HistogramA histogram shows the distribution of a continuous variable: values are divided into intervals (bins) and the height of…
- t-testThe t-test compares means: the one-sample version compares a mean with a fixed value, the two-sample version the means…
Knowledgebase guides
FAQ
- Shapiro–Wilk or Kolmogorov–Smirnov?
- Shapiro–Wilk is generally more powerful, especially up to a few hundred observations. Use K–S with the Lilliefors correction, otherwise it is too lenient.
- The test rejected normality — now what?
- Look at the graph. Mild skewness in a large sample is usually harmless; otherwise transform the data or use a nonparametric method.
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Statistical tests
Updated: September 2026.