# 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
n

_{1} ≠ n

_{2}. 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 (n

_{1} - 1 +
n

_{2} - 1) and SSE is:

SSE = SSE

_{1} +
SSE

_{2}
SSE

_{1} = Σ(X - M

_{1})²
where the X's are from the first group (sample) and M

_{1 }is the
mean of the first group. Similarly, SSE

_{2}= Σ(X- M

_{2})² where
the X's are from the second group and M

_{2} is the mean of the second group.