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

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The calculations are only slightly more complicated when the sample sizes are different (n₁ does not equal n₂). 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 = 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. The formula:



cannot be used without modification since there is not one value of n but two: (n₁ and n₂).