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Topic: Testing the significance of difference in set means at different times
Replies: 9   Last Post: Nov 7, 2012 7:53 PM

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 Stuart.Palmer@deakin.edu.au Posts: 6 Registered: 11/1/12
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:
>

> > [...]
>
> >
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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.
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> >
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> > 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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> >
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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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> >
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> > Thanks again.
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>
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> If you have the following:
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> Sample Sizes: Na1 Nb1 Na2 Nb2
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> Means: Ma1 Mb1 Ma2 Mb2
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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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> 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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> (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.)

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.