
Re: Testing the significance of difference in set means at different times
Posted:
Nov 6, 2012 11:45 PM


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 crosssectional (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 oneway ANOVA to explore the significance of the difference in mean score between A1 and A2, B1 and B2, A1 and B1 (ie, [Ma1Mb1]), and, A2 and B2 (ie, [Ma2Mb2]). > > > > > > My interest/question was about testing the significance of the 'difference of the differences' (Ma1Mb1)(Ma2Mb2). > > > > > > I had considered a twoway 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 ttest with the composite variance extended for more than two groups.
Do you have a reference for this approach?
Regards, Stuart Palmer.

