# Inverse-variance weighting

In statistics, inverse-variance weighting is a method of aggregating two or more random variables to minimize the variance of the sum. Each random variable in the sum is weighted in inverse proportion to its variance.

Given a sequence of observations yi with independent variances σi2, the inverse-variance weighted sum is given by[1]

$\frac{\sum_i y_i / \sigma_i^2}{\sum_i 1/\sigma_i^2} .$

Inverse-variance weighting is typically used in statistical meta-analysis to combine the results from independent studies.