Standardization

Standardization transforms a variable by subtracting its mean and dividing by its standard deviation, producing values centered at zero with unit standard deviation.

Z-score: A value expressed as its distance from a distribution’s mean in standard deviation units. Standardization converts each observation into its z-score.
Feature scaling: The rescaling of numerical variables to make their magnitudes suitable for analysis or computation. Standardization is a common method of feature scaling.
Robust scaling: A scaling method that centers at the median and divides by an interquartile-range measure. It resists outlier influence more than mean-and-standard-deviation scaling.
Normal distribution: A symmetric, bell-shaped probability distribution determined by its mean and variance. For normally distributed data, standardized values follow the standard normal distribution.
Mean: A measure of central tendency equal to the sum of values divided by their count. Subtracting the mean centers the transformed variable at zero.
Principal component analysis: A method that replaces correlated variables with orthogonal components capturing decreasing amounts of variance. Standardizing features prevents variables with larger units from dominating its components.
Normalization (statistics): Transformations that make data conform to a chosen scale, range, or distributional form. The broader term is often used imprecisely for standardization and distinct rescaling methods.
Standard normal distribution: A normal distribution with mean zero and standard deviation one. Standardization maps a normally distributed variable to this distribution.
Standard deviation: A measure of dispersion equal to the square root of variance. Dividing by standard deviation sets the transformed variable’s scale.
Linear regression: A statistical method that models an outcome as a linear combination of predictors. Standardized coefficients express predictor effects in standard-deviation units.

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