What is pooled variance?

Pooled variance is a method used to estimate the variance of two or more samples that are drawn from populations with the same variance. It combines the variances of the individual samples into a single overall estimate of the variance for all the samples.

The formula for pooled variance is:

s²P = [(n1 - 1)s1² + (n2 - 1)s2² + ... + (nk - 1)sk²] / [n1 + n2 + ... + nk - k]

Where:

• s²P is the pooled variance
• n1, n2, ..., nk are the sample sizes of the individual samples
• s1, s2, ..., sk are the standard deviations of the individual samples
• k is the total number of samples

Pooled variance is commonly used in analysis of variance (ANOVA) and in certain statistical tests, such as the t-test for independent samples. By pooling the variances together, it can provide a more accurate estimate of the overall variance of the populations from which the samples were drawn.