Estimating Standard Deviation via Sample Mean Extended Quantile Estimation

Background It is common practice in meta-analysis of means 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. Methods We modified the popular quantile estimation (QE) method by incorporating the known mean into the estimation of the SD. We analyzed the performance of the original and the mean-extended QE (MEQE) methods with extensive simulations. A wide range of quantitative and visual tools were used to evaluate the performance of the methods. Results In the scenario where only the median, lower and upper quartiles were used, the mean boosted version provided a slightly/moderately better SD estimation than the original QE method for lognormal, gamma and Weibull distribution families. For the normal distribution, the difference was negligible. When both the QE and MEQE methods also used the minimum and maximum, their performance was essentially the same. Interestingly, their joint performance was worse than the performance obtained without using the extreme values. Conclusions 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 motivate the modification of other algorithms commonly used in meta-analysis to incorporate additional information that may occasionally become available. Both the QE and MEQE methods performed worse when the minimum and maximum values were also used in the estimation. Our recommendation, based on these results, is to avoid using extreme values in SD estimation.