nearnormal

Nearnormal, often written as near-normal, is a term used in statistics to describe data, residuals, or processes whose distribution is approximately the normal distribution but not perfectly normal. It signals a close alignment with normality while acknowledging modest deviations.

In practice, near-normal data are common in applied research. Many parametric methods assume normality of the data or the residuals; when data are near-normal, these methods can perform well, especially with larger samples. When deviations are mild, transformations or robust statistical techniques may not be necessary, but tougher departures may warrant alternatives or adjustments.

Assessing near-normality typically involves both visual and quantitative tools. Skewness and kurtosis provide summary measures of asymmetry and peakedness. Q-Q plots help compare empirical data to a theoretical normal distribution. Normality tests such as the Shapiro-Wilk, Kolmogorov-Smirnov, or Anderson-Darling tests can be used, though their power and interpretation depend on sample size and context.

Implications for analysis include choosing between parametric and nonparametric methods. If data are near-normal, t-tests, ANOVA, and ordinary least squares regression may be appropriate; results are often robust to small deviations. For more pronounced departures, data transformations (for example, log or Box-Cox) or nonparametric alternatives may be preferred.

Terminology and scope: nearnormal is not universally standardized and is often used informally to describe approximate normality rather than exact normality. Related concepts include the normal distribution, normality testing, and robust statistical methods.