  As the most important tool to provide high-level evidence-based medicine,
researchers can statistically summarize and combine data from multiple studies
by conducting meta-analysis. In meta-analysis, mean differences are frequently
used effect size measurements to deal with continuous data, such as the Cohen's
d statistic and Hedges' g statistic values. To calculate the mean difference
based effect sizes, the sample mean and standard deviation are two essential
summary measures. However, many of the clinical reports tend not to directly
record the sample mean and standard deviation. Instead, the sample size,
median, minimum and maximum values and/or the first and third quartiles are
reported. As a result, researchers have to transform the reported information
to the sample mean and standard deviation for further compute the effect size.
Since most of the popular transformation methods were developed upon the
normality assumption of the underlying data, it is necessary to perform a
pre-test before transforming the summary statistics. In this article, we had
introduced test statistics for three popular scenarios in meta-analysis. We
suggests medical researchers to perform a normality test of the selected
studies before using them to conduct further analysis. Moreover, we applied
three different case studies to demonstrate the usage of the newly proposed
test statistics. The real data case studies indicate that the new test
statistics are easy to apply in practice and by following the recommended path
to conduct the meta-analysis, researchers can obtain more reliable conclusions.
