*Pooled variance* (also called *combined*, *composite*, or *overall variance*) is a way to estimate common variance when you believe that different populations have the same variances.

The pooled sample variance formula is:

Where:

- n = the sample size for the first sample,
- m = the sample size for the second sample,
- S
^{2}_{x}= sample variance for sample 1, - S
^{2}_{y}= sample variance for sample 2.

It’s unlikely you’ll actually need to use the formula though. Most statistical software has an option for pooled variance, like R or SPSS. You can also try this online calculator for Pooling the Means, and Variances.

The square root of pooled variance is the pooled standard deviation.

## When Can I Use Pooled Variance?

If you believe the population variances are the same, **one way to check that you might be able to use pooled variance **is to calculate a ratio of sample standard deviations:

If this ratio is close to 1, then you can probably use pooled variance. This is a judgment call, but in general a ratio of 0.5 to 3 is a reasonable indication the variances are close enough (Penn State).

## References

Penn State Eberly College of Science Department of Statistics. 7.3.1.1 – Pooled Variances. Retrieved February 25, 2020 from: https://online.stat.psu.edu/stat500/lesson/7/7.3/7.3.1/7.3.1.1

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