Definition
The normal (Gaussian) distribution is a symmetric bell-shaped distribution described by its mean and standard deviation. Many natural and manufacturing quantities approximate it, and many classical methods — t-test, ANOVA, regression, control charts — assume that data or residuals are roughly normal.
Foundations & hypothesis testing
The 68–95–99.7 rule of thumb: 68 % of values fall within one standard deviation of the mean, 95 % within two and 99.7 % within three. That is exactly where the ±3σ control limits in SPC and the usual 95 % confidence interval come from.
Normality is not dogma. Thanks to the central limit theorem, means of larger samples are approximately normal even when the raw data are not. For small samples and strongly skewed data (durations, incomes, concentrations) consider a transformation (logarithm) or nonparametric tests that do not require normality.
In Statistica
Check normality in Descriptive statistics (Normality tab: Shapiro–Wilk and Kolmogorov–Smirnov tests) and visually with a histogram with a fitted normal curve or a normal probability plot (Graphs → 2D Graphs → Probability Plots). Distributions can also be fitted and compared in the Distribution Fitting module.
Related terms
- Normality testA normality test checks whether data come from a normal distribution — an assumption of the t-test, ANOVA, regression and capability indices.
- Standard deviation and varianceVariance is the average squared deviation of values from the mean; the standard deviation (SD) is its square root and has the same units as the data.
- HistogramA histogram shows the distribution of a continuous variable: values are divided into intervals (bins) and the height of…
- Nonparametric testsNonparametric tests do not assume a normal distribution — they work with the ranks of values rather than the values themselves.
Knowledgebase guides
FAQ
- How do I know my data are not normal?
- Combine a histogram, a normal probability plot and a normality test. With large samples the test "rejects" even tiny deviations — what matters is whether the deviation hurts the method you use.
- Must the data be normal, or the residuals?
- For regression and ANOVA it is the residuals (model errors), not the dependent variable itself. For a t-test, the differences or the values within each group.
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Foundations & hypothesis testing
Updated: September 2026.