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Pooled Variance

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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:
pooled sample variance formula

Where:

  • n = the sample size for the first sample,
  • m = the sample size for the second sample,
  • S2x = sample variance for sample 1,
  • S2y = 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: ratio of standard deviations for pooled variance

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

CITE THIS AS:
Stephanie Glen. "Pooled Variance" From StatisticsHowTo.com: Elementary Statistics for the rest of us! https://www.statisticshowto.com/pooled-variance/
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