Pooled Variance

Pooled Variance

Pooled variance is a method for estimating variance given several different samples taken in different circumstances where the mean may vary between samples but the true variance (equivalently, precision) is assumed to remain the same. It is calculated by

or with simpler notation,

where s_p2 is the pooled variance, n_i is the sample size of the i'th sample, s_i2 is the variance of the ith sample, and k is the number of samples being combined. n − 1 is used instead of n for the same reason it may be used in estimating variances from samples (i.e. Bessel's correction).

The square-root of a pooled variance estimator is known as a pooled standard deviation.