Skewing

Skewing is a term used to describe distortion or asymmetry in a shape, distribution, or signal. It can occur intentionally as part of a transformation or unintentionally due to data collection, processing, or natural variation. The central idea in most uses is that symmetry around a central point is broken in some systematic way.

In statistics, skewness refers to the asymmetry of a probability distribution. A distribution is positively skewed when it has a long tail on the right side, a negative skew when the tail is on the left. Common measures of skewness include the third standardized moment and various nonparametric or graphical methods. Skewness affects the relationship between the mean and median and can influence the performance of statistical tests that assume normality. Skewed data are often transformed (for example, via a logarithm or Box-Cox transformation) to stabilize variance and approximate normality, or analyzed with methods that do not assume symmetry.

In geometry and computer graphics, skewing denotes a shear transformation that slants objects without changing their area. This is distinct from rotation or uniform scaling. In 2D, a horizontal skew can be represented by a matrix such as [1 s; 0 1], moving points horizontally in proportion to their vertical coordinate. Skewing is used to create isometric projections, perspective effects, or to simulate certain physical distortions.

Skewing can also describe bias or asymmetry in other contexts, such as sampling bias, returns distributions in finance, or perceptual distortions in images. Interpreting skew requires attention to the underlying mechanism and the domain’s specific definitions.