AI Article Synopsis
- The central limit theorem states that the means of random samples from a population with a certain mean and variance will distribute normally as the sample size increases.
- Parametric tests, which rely on this theorem, offer more accurate estimates and higher statistical power compared to non-parametric tests but often lack proper understanding among medical researchers.
- The review highlights key concepts of the central limit theorem, its importance in binomial distributions and t-tests, and includes a proof and examples related to sampling distributions of small populations.
Article Abstract
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.
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| http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5370305 | PMC |
| http://dx.doi.org/10.4097/kjae.2017.70.2.144 | DOI Listing |
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