12/4/2023 0 Comments Cornerstone universityThis review aims to address these topics. Thus, clinical researchers would benefit from knowing what the central limit theorem is and how it has become the basis for parametric tests. Currently, multiple parametric tests are used to assess the statistical validity of clinical studies performed by medical researchers however, most researchers are unaware of the value of the central limit theorem, despite their routine use of parametric tests. With the central limit theorem, parametric tests have higher statistical power than non-parametric tests, which do not require probability distribution assumptions. Without this theorem, parametric tests based on the assumption that sample data come from a population with fixed parameters determining its probability distribution would not exist. ![]() The central limit theorem is the most fundamental theory in modern statistics. A proof of the central limit theorem is also described with the mathematical concepts required for its near-complete understanding. 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. 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. ![]() ![]() 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. Using the central limit theorem, a variety of parametric tests have been developed under assumptions about the parameters that determine the population probability distribution. According to the central limit theorem, the means of a random sample of size, n, from a population with mean, µ, and variance, σ 2, distribute normally with mean, µ, and variance, σ 2 n.
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