Archive for December, 2015

My 2015 blogging report

December 29, 2015


Estimating the mean and standard deviation from the median and the range

December 3, 2015

While preparing the data for a meta-analysis, I run into the problem that a few of my sources did not report the outcome of interest as means and standard deviations, but rather as medians and range of values. After looking around, I found this interesting paper which derived (and validated through simple simulations), simple formulas that can be used to convert the median/range into a mean and a variance in a distribution free fashion.  With

  • a = min of the data
  • b = max of the data
  • m = median
  • n = size of the sample

the formulas are as follows:

Mean  \bar{m} = \frac{a+2 m+b}{4} +\frac{a-2 m+b}{4 n}

Variance  \frac{1}{n-1} \Big(a^2+m^2+b^2+\frac{n-3}{2} \frac{(a+m)^2+(b+m)^2}{4}-n \bar{m} \Big)


The following R function will carry out these calculations



Surfing around arxiv, I found another paper that handles additional scenarios and proposes alternative formulas