unormal

Unormal is a term sometimes used in statistics and data analysis to describe data, models, or assumptions that deviate from normality. It is not a standard statistical term and does not appear in major reference works. When data are unormal, the underlying distribution may exhibit skewness, heavy tails, kurtosis, multimodality, or other departures from the bell-shaped Gaussian curve.

Because many parametric methods rely on normality, indicators of unormality prompt alternative approaches. Analysts may employ nonparametric tests, robust statistics, or data transformations to reduce departure from normality or to adapt inference. Common tools for assessing normality include the Shapiro-Wilk test, Anderson-Darling test, and Kolmogorov-Smirnov test. If unormal, practitioners might apply Box-Cox, logarithmic, or power transformations, or opt for nonparametric procedures such as the Mann-Whitney U test, Wilcoxon signed-rank test, or Kruskal-Wallis test. Bootstrapping and Bayesian methods can also accommodate non-normal features.

Criticism: the label unORMAL is informal and can be ambiguous. Because it lacks a precise probabilistic definition, it is often better to specify the exact distributional features (skewness, kurtosis, multimodality) rather than rely on a general term.

See also: Normal distribution, Non-normal data, Nonparametric statistics, Robust statistics, Normality test.