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Re: Testing the significance of difference in set means at different times
Posted:
Nov 2, 2012 4:30 AM
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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.)
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