Extracting Data from Figures, Medians and Ranges

Two extraction problems appear in almost every review. A trial reports a median with an interquartile range when your meta-analysis needs a mean and standard deviation. Another reports its primary outcome only as a bar chart.

Both have accepted solutions. Both need recording as derived rather than reported, and the distinction matters more than the technique.

Medians to means

Three main methods, developed in sequence, each improving on the last.

Hozo, Djulbegovic and Hozo (2005) derived estimators from the median, range and sample size. They work but perform poorly with skewed data and small samples.

Wan and colleagues (2014) improved the estimators and extended them to the interquartile range, which is more commonly reported than the full range and less sensitive to outliers.

McGrath and colleagues (2020) developed quantile estimation methods that perform better again, particularly under skew, and implemented them in the metamedian package for R.

Use the most recent method your reported quantities allow, and name the method in the extraction notes. Reviewers accept any of the three; what draws comment is a converted value presented without saying it was converted.

When not to convert

Conversion assumes an underlying distribution that is at least approximately symmetric. The median is reported precisely because many outcomes are not, and a trial reporting a median of 4 with an interquartile range of 2 to 15 is telling you the distribution is badly skewed.

Two indicators that conversion is unwise: the median sits far from the midpoint of the interquartile range, and the range is very wide relative to the interquartile range. In those cases, converting produces a mean that no participant resembles and a standard deviation that misstates the spread.

The alternatives are to synthesise medians directly using methods designed for that purpose, to run the meta-analysis both with and without the converted studies as a sensitivity analysis, or to describe the study narratively and exclude it from the pooled estimate with a stated reason.

Extracting from figures

Digitising graphs is legitimate and routine. WebPlotDigitizer is the usual tool. The practices that make it defensible:

Two people digitise independently, and the values are compared. Agreement within a small tolerance is reassuring; a large discrepancy usually means one person misidentified the axis scale or a log transformation.

Record the source precisely: which figure, which panel, which data series, in the extraction form.

Check the axis. Log scales, truncated axes and axes that do not start at zero are the common traps, and each produces errors in a consistent direction.

Where error bars are shown, establish whether they represent standard deviation, standard error or a confidence interval. The figure legend usually says. If it does not, do not guess: record it as unclear and either contact the authors or exclude the value.

Contacting authors

Worth doing, and worth planning for. Prespecify how many attempts you will make and over what period, typically two emails across four to six weeks, and record the outcome for each study.

Response rates are modest and depend heavily on how old the paper is. What matters for the review is that the attempt is documented, because "data were not available" reads very differently from "the corresponding author did not respond to two requests sent in March and April 2026".

Record what was derived

Every extraction form should have a field indicating whether each value was reported directly, derived by conversion, digitised from a figure, or obtained from the authors. It costs one column.

The payoff comes at two points. A sensitivity analysis restricted to directly reported values becomes possible without re-reading every paper. And when a reviewer asks how a particular figure was obtained, the answer is already recorded rather than reconstructed from memory.

References

Hozo, S. P., Djulbegovic, B., & Hozo, I. (2005). Estimating the mean and variance from the median, range, and the size of a sample. BMC Medical Research Methodology, 5, 13. https://doi.org/10.1186/1471-2288-5-13

McGrath, S., Zhao, X., Steele, R., Thombs, B. D., & Benedetti, A. (2020). Estimating the sample mean and standard deviation from commonly reported quantiles in meta-analysis. Statistical Methods in Medical Research, 29(9), 2520–2537. https://doi.org/10.1177/0962280219889080

Wan, X., Wang, W., Liu, J., & Tong, T. (2014). Estimating the sample mean and standard deviation from the sample size, median, range and/or interquartile range. BMC Medical Research Methodology, 14, 135. https://doi.org/10.1186/1471-2288-14-135