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KMID : 0356920170700020144
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Korean Journal of Anesthesiology
2017 Volume.70 No. 2 p.144 ~ p.156
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Central limit theorem: the cornerstone of modern statistics
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Kwak Sang-Gyu
Kim Jong-Hae
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Abstract
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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.
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KEYWORD
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Normal distribution, Probability, Statistical distributions, Statistics
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