According to the central limit theorem, the means of a random sample of size, n, from a population with mean, µ, and variance, σ2, distribute normally with mean, µ, and variance, . 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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机译：根据中心极限定理，从均值为µ和方差为σ 2 的总体中随机抽取大小为n的样本的平均值为均值µ和方差为<数学xmlns：mml =“ http://www.w3.org/1998/Math/MathML” id =“ m1”溢出=“ scroll”> σ 2 n 。使用中心极限定理，在关于确定总体概率分布的参数的假设下，开发了各种参数检验。与不需要对总体概率分布进行任何假设的非参数检验相比，参数检验可产生更准确，更精确的估计，并具有更高的统计功效。但是，许多医学研究人员在不了解中心极限定理对此类测试开发的贡献的情况下，使用参数测试来呈现其数据。因此，本综述介绍了中心极限定理的基本概念及其在二项式分布和学生t检验中的作用，并提供了小样本抽样分布的示例。中心极限定理的证明还以其几乎完全理解所需的数学概念进行了描述。
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