On Friday, 2 November 2012 19:30:02 UTC+11, Ray Koopman wrote: > On Nov 1, 3:10 pm, Stuart.Pal...@deakin.edu.au wrote: > > > [...] > > > > > > Sets A and B are cross-sectional (representative) samples of two different populations. The members of the sets at time 1 and 2 are different, though still representative. The principal measure of interest is the mean value (of a rating given by) the respective sets. > > > > > > I have used one-way ANOVA to explore the significance of the difference in mean score between A1 and A2, B1 and B2, A1 and B1 (ie, [Ma1-Mb1]), and, A2 and B2 (ie, [Ma2-Mb2]). > > > > > > My interest/question was about testing the significance of the 'difference of the differences' (Ma1-Mb1)-(Ma2-Mb2). > > > > > > I had considered a two-way ANOVA using all of the data and looking at the significance of interaction term, but was unsure. I will look at this. > > > > > > Thanks again. > > > > If you have the following: > > > > Sample Sizes: Na1 Nb1 Na2 Nb2 > > > > Means: Ma1 Mb1 Ma2 Mb2 > > > > Variances: Va1 Vb1 Va2 Vb2 > > > > then calculate > > > > (Ma1 - Mb1) - (Ma2 - Mb2) > > z = -------------------------------------------, > > sqrt(Va1/Na1 + Vb1/Nb1 + Va2/Na2 + Vb2/Nb2) > > > > and refer it to the standard normal distribution in the usual way. > > > > (Actually, what you have is not strictly a z, but an approximate t > > whose degrees of freedom are at least in the hundreds, and possibly > > in the thousands, so there is little lost by treating it as a z.)
Hi Ray, Sorry to Pester.
If I understand correctly, this is essentially Welch's t-test with the composite variance extended for more than two groups.