Combine Independent Group Means and SDs Correctly

Check whether the groups can be combined

Start with a reason for combining the groups: perhaps a report separates two eligible subgroups that your extraction requires together. Confirm that their participants do not overlap and that the outcome, units, measurement window, and analysis population align. Two time points from the same people are not two independent groups to concatenate.

Record each subgroup's analyzed number, mean, and sample SD. Check that the uncertainty column really contains SDs rather than standard errors or confidence limits. Keep a source location for every input so the calculation can be reviewed without reopening an entire study report.

Include differences between subgroup means

The combined mean is the sample-size-weighted average of the group means. The combined variance must include both variation within each subgroup and separation between their means. Simply averaging SDs or calculating a pooled within-group SD omits the latter component.

Cochrane's guidance on combining group summaries explicitly distinguishes these two SDs. Its combined summary describes the observations as though the eligible subgroups had been one group all along; the within-group pooled SD has a different purpose.

Reconstruct a fictional example

Suppose group one contains three observations with mean 2 and sample SD 1, while group two contains three observations with mean 5 and sample SD 1. Their combined number is six and mean is 3.5.

The within-group sum of squares is 2 × 1² + 2 × 1² = 4. The between-group contribution is 3 × (2 − 3.5)² + 3 × (5 − 3.5)² = 13.5. Dividing the total 17.5 by six minus one gives sample variance 3.5, so the combined SD is about 1.87083. The fictional raw lists 1, 2, 3 and 4, 5, 6 provide an independent check.

Preserve the calculation and its limits

Use the combined-summary tool and audit worksheet to retain the inputs and output. Record the group labels and reason for merging them. If a review includes multiple intervention variants, determine their eligibility and grouping before inspecting which combination produces a preferred result.

Do not interpret the combined descriptive mean as an intervention effect. This arithmetic does not adjust for baseline differences, missing outcomes, survey design, or clustering. Combining published summaries also cannot resolve incompatible instruments or uncertain participant overlap.

Finish by reconciling the combined number with the report's participant flow and checking that the resulting unit and time label remain correct. Keep both subgroup summaries alongside the derived result. If an input is corrected later, another analyst should be able to reproduce the revision without guessing which groups were merged.

Source checked on 2 November 2026; fictional summaries independently recalculated.