In statistics, pooled variance refers to the average of two or more group variances.

We use the word “pooled” to indicate that we’re “pooling” two or more group variances to come up with a single number for the common variance between the groups.

In practice, pooled variance is used most often in a two sample t-test, which is used to determine whether or not two population means are equal.

The pooled variance between two samples is typically denoted as s_{p}^{2} and is calculated as:

s_{p}^{2} = ( (n_{1}-1)s_{1}^{2} + (n_{2}-1)s_{2}^{2} ) / (n_{1}+n_{2}-2)

Unfortunately there is no built-in function to calculate the pooled variance between two groups in R, but we can calculate it fairly easily.

For example, suppose we want to calculate the pooled variance between the following two groups:

The following code shows how to calculate the pooled variance between these groups in R:

#define groups of data x1 <- c(6, 7, 7, 8, 10, 11, 13, 14, 14, 16, 18, 19, 19, 19, 20) x2 <- c(5, 7, 7, 8, 10, 13, 14, 15, 19, 20, 20, 23, 25, 28, 32) #calculate sample size of each group n1 <- length(x1) n2 <- length(x2) #calculate sample variance of each group var1 <- var(x1) var2 <- var(x2) #calculate pooled variance between the two groups pooled <- ((n1-1)*var1 + (n2-1)*var2) / (n1+n2-2) #display pooled variance pooled [1] 46.97143

The pooled variance between these two groups turns out to be **46.97143**.

**Additional Resources**

What is Pooled Variance? (Definition & Example)

Pooled Variance Calculator

How to Calculate Pooled Variance in Excel