
Re: Testing the significance of difference in set means at different times
Posted:
Nov 7, 2012 7:53 PM


On Wednesday, 7 November 2012 21:06:11 UTC+11, Ray Koopman wrote: > 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 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. > > > > 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 239241
Cheers Ray!

