Definition

Pooled Variance is a method to estimate the common variance of two or more populations (the underlying assumption here is that the variance of these populations is the same) by using the sample variances from these populations.

Formula

Pooled variance is calculated by taking the weighted average of the variances of the samples. The formula is:

s_{p}^{2}\textup{ is the pooled variance,}
s_{1}^{2}, s_{2}^{2}, s_{3}^{2} \cdot \cdot \cdot s_{k}^{2} \textup{ are sample variances,}
\left (n_{1}-1 \right ),\left (n_{2}-1 \right ),\left (n_{3}-1 \right ),\cdot \cdot \cdot \left (n_{k}-1 \right ) \textup{ are the degrees of freedom.}

The weights in the above formula are the degrees of freedom for each sample. The numerator is the sum of the product of each sample variance with its degree of freedom . The denominator is simply the sum of all the degrees of freedom for each sample.

Note
Pooled variance does not calculate the variance of the combined sample. It only estimates the population variance of the constituent samples.
What is Pooled Variance and how is it calculated

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One thought on “What is Pooled Variance and how is it calculated”

  • Anil katiyar
    February 10, 2019 at 3:10 AM
    Permalink

    Very usefull

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