skevheter

Skevheter is the property of a distribution or dataset to deviate from symmetry, meaning that its values are not distributed evenly around a central value such as the mean. In practice, skewness describes which tail of the distribution is longer or fatter and whether the mean, median, and mode align.

One standard measure is the Fisher-Pearson skewness g1, defined as the ratio of the third central moment to the cube of the standard deviation: g1 = E[(X−μ)^3]/σ^3. A sample version used in data analysis is g1 = [n^2/(n−1)(n−2)] · ∑(xi−x̄)^3 / [∑(xi−x̄)^2]^(3/2). Positive values indicate right (positive) skew, negative values indicate left (negative) skew, and values near zero indicate approximate symmetry. Pearson's and Bowley's skewness are alternative summaries: Pearson's uses (mean − median)/standard deviation, while Bowley's uses quartile-based measures.

Skevheter can arise from the data-generating process, outliers, or truncation, and it has implications for statistical methods that assume normality. Many analyses, including regression and hypothesis tests, can be affected by skewness, especially with small samples.

Transformations such as logarithmic, square-root, or Box-Cox can reduce skewness and stabilize variance. Reported skewness, its standard error, and, when relevant, the context and data source are important for interpretation.