In recent years, there has been much progress toward the development of methods for converting three- and five-number summary statistics (i.e. minimum, maximum, median, and quartiles) to means and standard deviations (SDs). This is commonly done in the meta-analysis setting, where some studies report means and SDs, while other report quantile summaries. However, we show that three-number summaries, which are the most common, do not contain enough information to reliably estimate SDs. We show that very poor estimates can result, which may invalidate any inference and provide details of a sensitivity analysis that can allow researchers to have greater confidence in their results, or highlight potential sources of bias. We further explore whether nominating additional information can provide enough information regarding the unknown data shape to improve SD estimations, and in doing so introduce a new estimator using the scaled Beta distribution. Simulations and a real data example are used to highlight the advantages and disadvantages of this approach. A Web application is also provided to help researchers perform sensitivity analyses.

翻译：近年来，将三数和五数汇总统计量（即最小值、最大值、中位数及四分位数）转换为均值和标准差的方法研究取得了显著进展。这在元分析场景中尤为常见，此类场景下部分研究报告均值和标准差，而其他研究则报告分位数汇总。然而，我们的研究表明，最常用的三数汇总所含信息不足以可靠估计标准差。这种估计可能产生极差的估算结果，进而使任何统计推断失效。为此，我们详细阐述了敏感性分析方法，允许研究者对其研究结果建立更高置信度，或识别潜在偏倚来源。进一步地，我们探索了通过补充信息（如未知数据分布形态）来改善标准差估计的可能性，并据此提出基于缩放贝塔分布的新型估计量。通过仿真实验和真实数据案例，我们系统论证了该方法的优劣。此外，我们还提供了在线应用程序以辅助研究者开展敏感性分析。