Hypothesis test for the difference of the difference of means?

[CaptainP]

Hello all,

Consider 3 different samples. Each sample is independent.

1: 23, 25, 21, 22, 21, 22, 20, 23, 19, 22, 19, 21
2: 28, 27, 27, 29, 26, 29, 27, 30, 28, 27, 26, 29
3: 23, 20, 25, 21, 22, 23, 21, 20, 19, 20, 22, 21

I am being asked to test whether μ2 - μ1 = μ3 - μ2 with 99% confidence. How am I meant to perform this test? I know how to test for the difference of means, that's quite simple, but how does one test for the difference of differences?

 

[WWGD]

I think this is usually done with ANOVA http://en.wikipedia.org/wiki/Analysis_of_variance, see the section ANOVA for a single factor and below.

 

[CaptainP]

ANOVA tests whether the means of all samples are the same, so in this case an ANOVA test would test whether μ1 = μ2 = μ3. I need something rather different, testing whether the differences between specific pairs are equal.

 

[WWGD]

Sorry I misread the post.