Meta-analysis is the aggregation of data from multiple studies to find patterns across a broad range relating to a particular subject. It is becoming increasingly useful to apply meta-analysis to summarize these studies being done across various fields. In meta-analysis, it is common to use the mean and standard deviation from each study to compare for analysis. While many studies reported mean and standard deviation for their summary statistics, some report other values including the minimum, maximum, median, and first and third quantiles. Often, the quantiles and median are reported when the data is skewed and does not follow a normal distribution. In order to correctly summarize the data and draw conclusions from multiple studies, it is necessary to estimate the mean and standard deviation from each study, considering variation and skewness within each study. In past literature, methods have been proposed to estimate the mean and standard deviation, but do not consider negative values. Data that include negative values are common and would increase the accuracy and impact of the me-ta-analysis. We propose a method that implements a generalized Box-Cox transformation to estimate the mean and standard deviation accounting for such negative values while maintaining similar accuracy.

翻译：荟萃分析是对多项研究数据进行整合，旨在发现特定主题广泛范围内的模式。该方法在各领域研究总结中的应用日益重要。荟萃分析中，通常使用每项研究的均值与标准差进行比较分析。尽管许多研究报告了用于汇总统计的均值和标准差，但部分研究则报告最小值、最大值、中位数及第一、三分位数等其他指标。当数据呈偏态分布且不符合正态分布时，常报告分位数和中位数。为正确汇总多项研究数据并得出结论，需考虑各研究的变异性和偏态性，估计其均值与标准差。既往文献中已提出估计均值与标准差的方法，但未考虑负值存在。包含负值的数据较为常见，考虑此类数据可提升荟萃分析的准确性与影响力。本文提出一种基于广义Box-Cox变换的方法，在保持相似精度的前提下，实现对包含负值数据的均值与标准差估计。