Central limit theorem: the cornerstone of modern statistics

• Published in: Korean journal of anesthesiology Vol. 70; no. 2; pp. 144 - 156
• Main Authors: Kwak, Sang Gyu, Kim, Jong Hae
• Format: Journal Article
• Language: English
• Published: Korea (South) The Korean Society of Anesthesiologists 01.04.2017; Korean Society of Anesthesiologists; 대한마취통증의학회
• Subjects: normal distribution; probability; statistical distributions; Statistical Round; statistics; 마취과학; Probability; Normal distribution; Statistics; Statistical distributions
• ISSN: 2005-6419; 2005-7563
• DOI: 10.4097/kjae.2017.70.2.144

According to the central limit theorem, the means of a random sample of size, , from a population with mean, µ, and variance, σ , distribute normally with mean, µ, and variance, [Formula: see text]. Using the central limit theorem, a variety of parametric tests have been developed under assumptions about the parameters that determine the population probability distribution. Compared to non-parametric tests, which do not require any assumptions about the population probability distribution, parametric tests produce more accurate and precise estimates with higher statistical powers. However, many medical researchers use parametric tests to present their data without knowledge of the contribution of the central limit theorem to the development of such tests. Thus, this review presents the basic concepts of the central limit theorem and its role in binomial distributions and the Student's t-test, and provides an example of the sampling distributions of small populations. A proof of the central limit theorem is also described with the mathematical concepts required for its near-complete understanding.