Onormalitet

Onormalitet, in Swedish usage, refers to non-normality—that is, a departure of a dataset or a statistical model from the normal distribution or from a normality assumption. In statistics, many parametric methods rely on normality of data, residuals, or sampling distributions to justify inference.

Non-normality can arise from several features of the data, including skewness (asymmetry), excess kurtosis (heavy or light tails), multimodality, or the presence of outliers. It may affect observed data or the residuals of a fitted model. Causes include measurement limits, population structure, data transformation issues, or inherently non-normal processes.

Implications and remedies depend on context. Parametric tests and confidence intervals can be affected by non-normality, especially with small samples. Remedies range from data transformations (for example, log or Box-Cox transformations) and non-parametric methods (such as Mann-Whitney or Kruskal-Wallis tests) to bootstrap techniques and robust statistical methods. In regression analysis, non-normality of residuals invites alternative modeling choices, such as generalized linear models, different error distributions, or robust standard errors.

Detection and assessment typically combine visual and formal approaches. Visual tools include histograms and Q-Q plots to gauge deviations from normality. Formal tests include Shapiro-Wilk, Kolmogorov-Smirnov, and Anderson-Darling tests, though their reliability varies with sample size and parameter estimation. Because tests can be sensitive to sample size and distributional assumptions, practitioners often report multiple diagnostics and consider practical implications for inference when non-normality is present.