Median/IQR to Mean/SD Estimator

A median to mean converter solves one of the most common data extraction challenges in quantitative evidence synthesis. Many primary studies, particularly those measuring skewed outcomes such as hospital length of stay, biomarker concentrations, or cost data, report medians and interquartile ranges rather than means and standard deviations. Because standard meta-analytic pooling methods require means and SDs, the Cochrane Handbook (Higgins et al., 2023, Chapter 6) recommends using validated estimation techniques to convert summary statistics when direct computation is not possible. Hozo et al. (2005) provided the earliest widely adopted formulas for estimating the mean from the median and range, establishing the foundation upon which subsequent methods have built. These conversions enable reviewers to include studies that would otherwise be excluded from quantitative synthesis, strengthening the comprehensiveness demanded by PRISMA 2020 (Page et al., 2021). Clinical data frequently follow a log-normal distribution, common for biomarker concentrations, hospital costs, and length of stay, in which case a Box–Cox transformation can stabilize variance before estimation, and Cochrane RevMan requires the resulting mean and SD in its standard input format for inverse-variance pooling. With batch mode, reviewers can process dozens of study arms simultaneously using an editable table, eliminating the repetitive entry that slows down large reviews. CSV and Excel import lets you upload extraction spreadsheets containing median, IQR, min, max, and sample size columns, converting an entire dataset in a single step rather than re-keying each value. When the extraction spreadsheet itself needs cleaning, restructuring, or a full statistical analysis, our research data analysis services take on the whole dataset.

The IQR to standard deviation calculator in this tool implements three validated approaches that differ in their data requirements and statistical precision. The Wan method calculator (Wan et al., 2014) improved upon Hozo's formulas by incorporating sample size into the SD estimation through normal quantile functions, producing more accurate results especially for samples below 50. The Luo method estimator (Luo et al., 2018) further refined the mean estimation by applying an optimal weighted combination of range-based and IQR-based estimates, giving greater weight to the IQR component as sample sizes increase. Shi et al. (2020) derived the matching optimally weighted standard deviation when all five values are reported, and McGrath et al. (2020) proposed Box-Cox and quantile estimation methods for outcomes that are clearly skewed. After estimating the SD, you may need to interconvert between standard deviation and standard error for your pooling software. Our SE/SD converter handles that step using the sample size. The pipeline workflow bar at the top of the tool shows this converter's position within the Data Extraction phase, making it easy to see what comes before and after in your review workflow.

All three estimation methods assume the underlying data follow an approximately symmetric distribution. When this assumption is violated, as indicated by a median that sits much closer to Q1 than Q3, or by a range that is disproportionately wide relative to the IQR, the estimated mean may diverge meaningfully from the true population mean. The Cochrane Handbook advises reviewers to conduct sensitivity analyses excluding converted studies to assess the robustness of pooled results. Conducting a sensitivity analysis that compares estimates from different methods (Wan vs. Luo vs. Hozo) helps reviewers gauge how sensitive pooled results are to the choice of estimation approach. If your outcomes are heavily skewed and peer reviewers are likely to question the method, a PhD biostatistician from our biostatistics consulting for clinical research service can select and justify the approach before you pool. With your estimated means, SDs, and sample sizes in hand, you can compute standardized mean differences using our effect size calculator, which derives Cohen's d, Hedges' g, and their confidence intervals from group-level summary statistics. The Send to Pipeline button makes this transition seamless: click it to push your estimated means and SDs directly into the Effect Size Calculator, pre-populating the input fields so you can compute standardized effect sizes without re-entering any data. This connected workflow embodies the tool pipeline philosophy, where each converter hands its output to the next stage. For studies that report p-values but omit confidence intervals, our p-value to confidence interval converter provides a complementary back-calculation pathway.

Transparent reporting of statistical conversions is essential for reproducibility. PRISMA 2020 requires reviewers to document how effect estimates and their precision measures were obtained, including any derivations from non-standard summary statistics. Reviewers should cite the specific estimation method used (Wan et al., 2014; Luo et al., 2018; McGrath et al., 2020; or Hozo et al., 2005) and identify which studies required conversion in both the Methods section and a supplementary table. To organize all extracted and converted data systematically, our extraction template builder generates structured forms with dedicated fields for original summary statistics, estimated means and SDs, and the conversion method applied. Once your synthesis is complete, present the results visually with our forest plot generator, which creates publication-ready diagrams showing each study's weight, confidence interval, and the pooled diamond summary estimate. If you would rather hand off the conversions and the pooling entirely, you can hire a statistician for your meta-analysis data.