A new method for detecting the skewness of data from the five-number summary

For clinical trials with continuous outcomes, researchers may opt to report the whole or part of the five-number summary rather than the sample mean and standard deviation, especially when the outcome data are skewed. To include such studies in meta-analysis, several popular methods have been proposed in the literature that convert the five-number summary back to the sample mean and standard deviation. Nevertheless, most existing methods are based on the normality assumption, which may not hold for the clinical studies with the five-number summary being reported. Recently, Shi et al. (2023, Stat Methods Med Res, 32, 1338-1360) and Balakrishnan et al. (2023, Math Methods Stat, 32, 260-273) proposed methods for detecting the skewness of data that utilize the whole or part of the five-number summary, together with the sample size. In this article, we show that the max-type test of Shi et al. is not only structurally complex but also conservative in controlling the type I error rate, whereas the test of Balakrishnan et al. has difficulty controlling the type I error rate with small sample sizes. Inspired by these findings, we develop a novel test statistic that leverages the ratio of two tails, a measure known for its heightened sensitivity to data skewness. Simulation results demonstrate that our ratio-based test is both less conservative and more powerful compared to the existing methods, especially when the alternative distribution exhibits mild skewness. Additionally, simulated meta-analyses and real-world data examples are presented to demonstrate the utility of our new method in the context of meta-analysis.