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: