# Confidence Interval on Difference Between Means, Independent Groups, Standard
Deviation Estimated (4 of 7)

The calculations are only slightly more complicated when the
sample sizes are different (n

_{1} does not equal
n

_{2}). The first difference in the calculations is that MSE
is computed differently. If the two values of s² were
simply averaged as they are in the case of 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 and SSE is the sum of squares
error and is defined as:

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.
The formula:

cannot be used without modification since there is not
one value of n but two: (n

_{1} and n

_{2}).