Tests of Differences between Means, Independent Groups, Standard Deviation Estimated (5 of 8)
Unequal Sample Sizes
The calculations in Step 4 are slightly more complex when n1 ≠ n2. The first difference is that MSE is computed differently. If the two values of s² were simply averaged as they are for equal sample sizes, then the estimate based on the smaller sample size would count as much as the estimate based on the larger sample size. Instead the formula for MSE is:
MSE = SSE/df
where df is the degrees of freedom (n1 - 1 + n2 - 1) and SSE is:
SSE = SSE1 + SSE2
SSE1 = Σ(X - M1)² where the X's are from the first group (sample) and M1 is the mean of the first group. Similarly, SSE2= Σ(X- M2)² where the X's are from the second group and M2 is the mean of the second group.