Estimating standard deviation via sample mean extended quantile estimation

It is common practice in meta-analysis to estimate the mean and standard deviation (SD) when only the median and other ordered statistics are published in an included study. There are several methods for this purpose. Often, the advantages of including additional studies in the meta-analysis of means by using these methods outweigh the disadvantages of estimation errors. Sometimes, in addition to the median and other ordered statistics, the sample mean is also available, e.g. it can be displayed in box plots as additional information. In this case, only the standard deviation should be estimated. The popular quantile estimation (QE) method was modified by incorporating the known mean into the standard deviation (SD) estimation. We analysed the performance of the original and the mean-extended quantile estimation (MEQE) methods with extensive simulations. A wide range of visual and quantitative tools, including average relative error (ARE) with and without absolute value and root mean squared error, were used to evaluate the performance of the methods across various simulated scenarios. ARE was calculated both against the theoretical and the sample SD. Besides simulations, we also compared the methods on real dataset. In the scenario where only the median, lower and upper quartiles were used, for gamma Weibull and lognormal distributions, the mean-boosted version resulted in an absolute ARE decrease of 43%-65%, 28%-40%, and 8%-23%, respectively, depending on the sample size. For the normal distribution, the improvement was negligible (1%-3%). When both the QE and MEQE methods also used the minimum and maximum, their performance was essentially the same. Interestingly, in most cases, the joint performance was worse than the performance obtained without using the extreme values. We incorporated the mean into the QE method. When only the median, lower and upper quartiles, and the mean are available, the MEQE method may provide more accurate SD estimates. This study may encourage the modification of other algorithms used in meta-analysis to incorporate additional information that may occasionally become available. The results suggest that the usage of the minimum and maximum may decrease the performance of both QE and MEQE.