Confidence Interval on Difference Between Means, Independent Groups, Standard Deviation Estimated (1 of 7)
Following the general formula for a confidence interval, the formula for a confidence interval on the difference between means ( M1 - M2) is:
Md ± (t)(
)where Md = M1 - M2 is the statistic and
is
an estimate of 
(the standard error of the
difference between means). t depends
on the level of confidence desired and on the
degrees of freedom. The estimated standard error, ,
is computed assuming that the variances in the two
populations are equal. If the two sample sizes are equal
(n1 = n2) then the population variance σ² (it
is the same in both populations) is estimated by using the following
formula:
where MSE (which stands for mean square error) is an estimate of σ². Once MSE is calculated,
can be computed as
follows: