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Re: Testing the significance of difference in set means at different times
Posted:
Nov 7, 2012 7:53 PM
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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:
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> >>>
>
> >>> [...]
>
> >>>
>
> >>> 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]).
>
> >>>
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> >>> My interest/question was about testing the significance of the 'difference of the differences' (Ma1-Mb1)-(Ma2-Mb2).
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> >>>
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> >>> 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.
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> >>>
>
> >>> Thanks again.
>
> >>
>
> >> If you have the following:
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> >>
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> >> Sample Sizes: Na1 Nb1 Na2 Nb2
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> >>
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> >> Means: Ma1 Mb1 Ma2 Mb2
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> >>
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> >> Variances: Va1 Vb1 Va2 Vb2
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> >>
>
> >> then calculate
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> >>
>
> >> (Ma1 - Mb1) - (Ma2 - Mb2)
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> >>
>
> >> z = -------------------------------------------,
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> >>
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> >> sqrt(Va1/Na1 + Vb1/Nb1 + Va2/Na2 + Vb2/Nb2)
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> >>
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> >> and refer it to the standard normal distribution in the usual way.
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> >>
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> >> (Actually, what you have is not strictly a z, but an approximate t
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> >> whose degrees of freedom are at least in the hundreds, and possibly
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> >> in the thousands, so there is little lost by treating it as a z.)
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> >
>
> > Hi Ray,
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> > Sorry to Pester.
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> >
>
> > If I understand correctly, this is essentially Welch's t-test
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> > with the composite variance extended for more than two groups.
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> >
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> > Do you have a reference for this approach?
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> >
>
> > 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
Cheers Ray!
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