  Meta-analysis is the aggregation of data from multiple studies to find
patterns across a broad range relating to a particular subject. It is becoming
increasingly useful to apply meta-analysis to summarize these studies being
done across various fields. In meta-analysis, it is common to use the mean and
standard deviation from each study to compare for analysis. While many studies
reported mean and standard deviation for their summary statistics, some report
other values including the minimum, maximum, median, and first and third
quantiles. Often, the quantiles and median are reported when the data is skewed
and does not follow a normal distribution. In order to correctly summarize the
data and draw conclusions from multiple studies, it is necessary to estimate
the mean and standard deviation from each study, considering variation and
skewness within each study. In past literature, methods have been proposed to
estimate the mean and standard deviation, but do not consider negative values.
Data that include negative values are common and would increase the accuracy
and impact of the me-ta-analysis. We propose a method that implements a
generalized Box-Cox transformation to estimate the mean and standard deviation
accounting for such negative values while maintaining similar accuracy.
