Normality

Most classic statistical approaches are built around the normality assumption. However, the normal distribution is just a mathematical abstraction that does not exist in the real world in its “pure” form.

From Some Difficulties of Interpretation Encountered in the Application of the Chi-Square Test · 1938 · Joseph Berkson :

For we may assume that it is practically certain that any series of real observations does not actually follow a normal curve with absolute exactitude in all respects.

From Testing for normality · 1947 · R. C. Geary :

Normality is a myth; there never was, and never will be, a normal distribution.

From Testing the Approximate Validity of Statistical Hypotheses · 1954 · J. L. Hodges et al. :

For example, we may formulate the hypothesis that a population is normally distributed, but we realize that no natural population is ever exactly normal. We would want to reject normality only if the departure of the actual distribution from the normal form were great enough to be material for our investigation.

From Introduction to Robust Estimation and Hypothesis Testing · 2021 · Rand R. Wilcox :

To begin, distributions are never normal. For some this seems obvious, hardly worth mentioning, but an aphorism given by Cramér (1946) and attributed to the mathematician Poincaré remains relevant: “Everyone believes in the [normal] law of errors, the experimenters because they think it is a mathematical theorem, the mathematicians because they think it is an experimental fact.”

See also