  In systematic reviews and meta-analysis, researchers often pool the results
of the sample mean and standard deviation from a set of similar clinical
trials. A number of the trials, however, reported the study using the median,
the minimum and maximum values, and/or the first and third quartiles. Hence, in
order to combine results, one may have to estimate the sample mean and standard
deviation for such trials. In this paper, we propose to improve the existing
literature in several directions. First, we show that the sample standard
deviation estimation in Hozo et al. (2005) has some serious limitations and is
always less satisfactory in practice. Inspired by this, we propose a new
estimation method by incorporating the sample size. Second, we systematically
study the sample mean and standard deviation estimation problem under more
general settings where the first and third quartiles are also available for the
trials. Through simulation studies, we demonstrate that the proposed methods
greatly improve the existing methods and enrich the literature. We conclude our
work with a summary table that serves as a comprehensive guidance for
performing meta-analysis in different situations.
