Estimating the Population Standard Deviation based on the Sample Range for Non-normal Data

Abstract

Recently, an increasing number of researchers have attempted to overcome the constraints of size and scope in individual medical studies by estimating the overall treatment effects based on a combination of studies. A commonly used method is meta-analysis which combines results from multiple studies. The population standard deviation in primary studies is an essential quantitative value which is absent sometimes, especially when the outcome has a skewed distribution. Instead, the sample size and the sample range of the whole dataset is reported. There are several methods to estimate the standard deviation of the data based on the sample range if we assume the data are normally distributed. For example: Tippett Method2, Ramirez and Cox Method3, Hozo et al Method4, Rychtar and Taylor Method5, Mantel Method6, Sokal and Rohlf Method7 as well as Chen and Tyler Method8. Only a few papers provide a solution for estimating the population standard deviation of non-normally distributed data. In this thesis, some other distributions, which are commonly used in clinical studies, will be simulated to estimate the population standard deviation by using the methods mentioned above. The performance and the robustness of those methods for different sample sizes and different distribution parameters will be presented. Also, these methods will be evaluated on real-world datasets. This article will provide guidelines describing which methods perform best with non-normally distributed data.