Two Estimates of Variance (4 of 5)

Recall that the formula for s² is:

.

In this application, each "X" will be a sample mean and M will be the mean of the sample means. Since there are "a" means, N = a. Letting M designate the mean of the sample means,

M = (4 + 3 + 2)/3 = 3.

is the estimate of

. For the example,

This means that the estimate of

is 1. But what is really needed is not an estimate of

but an estimate of σ². Fortunately, there is a simple relationship between σ² and

. Since the sampling distribution of the mean has a standard deviation of:

, (click here for details) the sampling distribution of the mean has a variance of:

where N is the number of scores each mean is based upon.