# 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 ( M

_{1} -
M

_{2}) is:

M

_{d} ± (t)(

)

where M

_{d} = M

_{1} - M

_{2} 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
(n

_{1} = n

_{2}) 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: