centralFrommedian

centralFrommedian is a statistical approach used to approximate a population central tendency, typically the mean, and sometimes dispersion from median-based summary statistics. It is commonly employed in meta-analysis, systematic reviews, and clinical research where individual data are unavailable but studies report medians along with other quantiles such as minimum, maximum, or first and third quartiles.

Inputs and outputs

The method takes as input the available summary statistics, which may include the sample size n, median m, minimum a, maximum b, and/or the first and third quartiles q1 and q3. Based on these inputs, centralFrommedian provides an estimated mean and, in many implementations, an estimated standard deviation (SD). The exact estimation depends on which statistics are reported and on assumed distributional properties.

Methods and assumptions

Several empirical estimators exist in the statistical literature, often grouped into families that differ by the data they use and the distribution assumptions they make. Common ideas include treating the median as a robust center and using the range or the interquartile range to infer spread. Some methods assume an approximately normal (or symmetric) distribution, while others are designed to work with skewed data. The choice of estimator depends on the reported statistics and the desired balance between bias and variance. All variants provide a practical means to obtain mean and SD estimates when direct data are unavailable, but they are not exact.

Applications

centralFrommedian is widely used to harmonize data across studies for quantitative synthesis when studies report medians rather than means. It supports pooling of effect sizes and the inclusion of a broader set of studies in meta-analytic workflows.

Limitations

Estimations rely on distributional assumptions and reported statistics; accuracy can be limited for highly skewed data or small samples. Different estimators can yield different results, and the method should be interpreted with caution.

See also

Mean estimation from medians; meta-analysis; imputation of summary statistics.