On Nov 6, 8:45 pm, Stuart.Pal...@deakin.edu.au wrote: > 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. > > Do you have a reference for this approach? > > Regards, Stuart Palmer.
Research Design and Statistical Analysis Jerome L. Myers and Arnold D. Well 1st ed (HarperCollins, 1991): sec 6.8, p 187 2nd ed (Erlbaum, 2003): sec 9.3.2, pp 239-241