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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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Ray Koopman

Posts: 3,383
Registered: 12/7/04
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, 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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