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 Importance of the Gaussian distribution

Statistical tests analyze a particular set of data to make more general conclusions. There are several approaches to doing this, but the most common is based on assuming that data in the population have a certain distribution. The distribution used most commonly by far is the bell-shaped Gaussian distribution, also called the Normal distribution. This assumption underlies many statistical tests such as t tests and ANOVA, as well as linear and nonlinear regression.

When reading in other books about the Gaussian distribution, two statistical terms might be confusing because they sound like ordinary words:

In statistics, the word “normal” is another name for a Gaussian, bell-shaped, distribution. In other contexts, of course, the word “normal” has very different meanings (absence of disease or common).

Statisticians refer to the scatter of points around the line or curve as “error”. This is a different use of the word than is used ordinarily. In statistics, the word “error” simply refers to deviation from the average. The deviation is usually assumed to be due to biological variability or experimental imprecision, rather than a mistake (the usual use of the word “error”).