Confidence Interval on Linear Combination of Means, Independent Groups (1 of 5)

Following the general formula for a confidence interval, the formula for a confidence interval on a linear combination of means is:

L ± t sL

where L is the linear combination of the sample means, t depends on the level of confidence desired and the degrees of freedom, and SL is an estimate of σL, the standard error of a linear combination of means.

The formula for SL is:

which is the same as the formula for σL except that MSE (an estimate of σ²) is used in place of σ². The formula for MSE here is very similar to the formula for MSE used in the calculation of a confidence interval on the difference between two means. The formula is:

where is the sample variance of the ith group and k is the number of groups. This formula assumes homogeneity of variance and that the k sample sizes are equal.