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Scientific journal «Current problems of health care and medical statistics»
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MODERN METHODS FOR CALCULATION OF SAMPLE MEAN AND STANDARD DEVIATION FROM KNOWN DESCRIPTIVE STATISTICS (NARRATIVE REVIEW)

P.A. Shapovalov1, R.E. Lakhin1
1. Military Medical Academy, St. Petersburg, Russia
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Summary:
Introduction. The calculation of the sample mean and standard deviation by right descriptive is an urgent problem for scientists involved in the meta-analysis of continuous data. Currently, there are more than 150 such techniques, differing in different levels of complexity and reliability. This situation can be disorienting for the researcher, especially if they are suspected of causing the problem. Purpose of the work. Consider and systematize the most common and modern methods for estimating the sample mean and standard deviation using known descriptive statistics. Materials and methods. Literature search was carried out in the Google Scholar and arXiv.org databases (Statistics section) for the period 2000-2023. Inclusion criteria: (1) a scientific publication describing a new method for calculating the sample mean and standard deviation from known descriptive statistics; (2) availability of a mathematical description or formula for the proposed methodology; (3) conducting simulation studies of the method and its comparison with the developments of other authors; (4) high use of the method. Ultimately, 10 publications were selected based on their novelty and citation. When considering full-text versions of articles, the advantages and disadvantages of the methods, their relationship with the developments of other authors were analyzed. At the final stage of this study, an attempt was made to classify existing methods. Results and discussion. The approaches used to calculate the sample mean and standard deviation by right of descriptive statistics can be divided into 3 groups: (1) algebraic methods; (2) methods based on mathematical modeling; (3) methods based on mathematical transformations. The first group includes two subgroups: «basic» methods (Hozo et al. (2005), Wan et al. (2014), Bland (2015), Walter and Yao (2007) etc.) and «optimized» methods (Luo et al. (2018), Shi et al.(2020)). The second group includes methods of approximate Bayesian calculations Kwon and Reis. The third group includes the methods of McGrath et al. (2020) and Cai et al. (2021). The method of Balakrishnan et al. (2022) is promising. Despite the presence in the solution of the problem under discussion, there are «white spots» in this area, it is supposed to choose a universal method from those available and applicable to the detection of propagation. Conclusion. In this review, modern and promising methods for calculating the sample mean and standard deviation for the disclosure of descriptive statistics were considered, an attempt was made to analyze them; exploration of their research path with discovery.
Keywords sample mean, standard deviation, descriptive statistics, meta-analysis, narrative review.

Bibliographic reference:
P.A. Shapovalov, R.E. Lakhin, MODERN METHODS FOR CALCULATION OF SAMPLE MEAN AND STANDARD DEVIATION FROM KNOWN DESCRIPTIVE STATISTICS (NARRATIVE REVIEW) // Scientific journal «Current problems of health care and medical statistics». - 2023. - №3;
URL: http://healthproblem.ru/magazines?textEn=1078 (date of access: 15.05.2024).

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