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Standardization

Standardizzazione

Standardization is the technique that transforms a numeric variable so it has a mean of zero and a standard deviation of one, bringing data with different scales and distributions to a common statistical reference. It is a close relative of normalization, but instead of forcing values into a fixed range like 0-1, it expresses them in terms of how many standard deviations they fall above or below the mean.

Definition

How it works

The calculation subtracts the variable's mean from each value and divides the result by its standard deviation, producing what is called a z-score. A standardized value of 2 indicates a data point two standard deviations above its variable's mean, regardless of the original unit of measurement, which makes different quantities like age, income or a risk score immediately comparable. Unlike min-max normalization, standardization does not produce a bounded range and is less affected by extreme outliers.

Applications

It is preferred over min-max normalization in many statistical and machine learning algorithms that implicitly assume data distributed around a mean, such as linear and logistic regression, principal component analysis, and many gradient-based optimization algorithms, where it helps gradient descent converge faster and more stably. It is also the basic tool for spotting anomalous values, since a very high or very low z-score flags an unusual observation.

History & etymology

The term derives from the statistical concept of a standardized variable, formalized in the first half of the twentieth century within inferential statistics, when it became common practice to compare different measurements by bringing them to the same relative scale of their distribution. With the spread of computational machine learning, standardization became one of the most common steps in data preparation before training a model.

Related terms

• Data normalization
• Outlier
• PCA (Principal Component Analysis)
• Linear regression
• Feature engineering

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