The pooled standard deviation is the positive square root of the pooled variance. For independent samples
with sample sizes 
and unbiased sample variances 
,
it is
It estimates a common population standard deviation under the assumption that the group variances
are equal. For two groups, 
is the scale estimate used by the equal-variance two-sample
t-test.
See also
Pooled Variance,
Population Standard Deviation,
Sample Standard Deviation,
Standard Deviation,
Two-Sample
t-Test
Explore with Wolfram|Alpha
References
Casella, G. and Berger, R. L. Statistical
Inference, 2nd ed. Pacific Grove, CA: Duxbury, 2002.
Cite this as:
Weisstein, Eric W. "Pooled Standard Deviation."
From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PooledStandardDeviation.html
Subject classifications
