Content
Group combination

Multiple groups combination

From two or more groups into a single mean and SD

A) Needed values

To combine multiple groups (for ex: mean and standard deviation of two or more groups) into a single group mean and standard deviation, you need the following values (at least):

  1. Sample size (N) of each group

  2. Mean (μ) of each group

  3. Standard deviation (SD) of each group

B) Steps

  1. In the Input table: put each of the previous values into the corresponding cells
  2. Click submit
  3. In the Output table: you will get the combined mean and standard deviation

C) Equations

The output was calculated upon the following equations:

1) Sample size combination: N1 + N2

2) Mean Combination:

N1μ1+N2μ2N1+N2\frac{N_{1} \mu_{1}+N_{2} \mu_{2}}{N_{1}+N_{2}}

3) Standard deviation combination:

(N1−1)SD12+(N2−1)SD22+N1N2N1+N2(μ12+μ22−2μ1μ2)N1+N2−1\sqrt{\frac{\left(N_{1}-1\right) S D_{1}^{2}+\left(N_{2}-1\right) S D_{2}^{2}+\frac{N_{1} N_{2}}{N_{1}+N_{2}}\left(\mu_{1}^{2}+\mu_{2}^{2}-2 \mu_{1} \mu_{2}\right)}{N_{1}+N_{2}-1}}

D) Citation and equations source

Higgins JPT, Thomas J, Chandler J, Cumpston M, Li T, Page MJ, Welch VA (editors). Cochrane Handbook for Systematic Reviews of Interventions version 6.4 (updated August 2023). Cochrane, 2023. Available from www.training.cochrane.org/handbook (opens in a new tab). (Chapter: 6.5.2.10 Combining groups, URL: Chapter 6: Choosing effect measures and computing estimates of effect | Cochrane Training (opens in a new tab))

E) Additional notes

In the meta-analysis, usually, we need to do this conversion when a study or more reports the mean and SD for two or more groups (for example: a study with two groups given a certain drug, the first group dose is 5mg and the second is 7mg, but other studies reported the data about one intervention group with different doses across the different studies [4, 5, 6, 7 mg]). Hence, if you want to conduct a meta-analysis pooling all studies together, then you need to use this calculation to get the combined mean and SD for the intervention group.

Effect size estimationSummary for indvidual patient data