4.2.5—Difference confidence intervals

For two independent means, an interval for μ₁−μ₂ is the sample difference plus or minus a critical value times its standard error. The order of subtraction fixes the sign.

Check independence, variance assumptions and whether a paired design should instead be analysed through within-pair differences. If zero lies in the interval, a two-sided 5% test would not reject equality.

An interval for μA−μB of (1.2,4.8) supports a positive difference; an interval (−0.6,2.1) does not establish a direction at that confidence level.

An interval crossing zero is not proof of no effect, and separate intervals for μA and μB are not equivalent to an interval for their difference.