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Date:   Wed, 6 Nov 1996 14:35:47 -0500
Reply-To:   "William B. Ware" <wbware@EMAIL.UNC.EDU>
Sender:   "SPSSX(r) Discussion" <SPSSX-L@UGA.CC.UGA.EDU>
From:   "William B. Ware" <wbware@EMAIL.UNC.EDU>
Subject:   Re: "methods" in ANOVA
Comments:   To: Bob Keefer <keefer@MSMARY.EDU>
In-Reply-To:   <96Nov6.140642-0500_est.14407-89134+1124@email.unc.edu>

On Wed, 6 Nov 1996, Bob Keefer wrote:

> I had a disconcerting moment in class today. I had run a 2X4 ANOVA > problem through SPSSX (unix), with 'method' set to 'experimental', as that > is supposed to decompose the variance in the 'traditional' way. However, > it quickly became apparent that the division of variance between the two > main effects as well as the interaction that the students were calculating > by hand -were not- what was on my print out! I rechecked the numbers > after class (I thought I had put the values on the board incorrectly) and > found no errors. I then re-ran the problem with each of the three methods > available, and got three different answers (not that surprising, I > suppose) > > So, exactly how is the "experimental" methods decomposing the 'explained' > variance? Why isn't it the same as you'd get by hand (it was -way- off, > not just rounding errors, and the N was only 42)?

As you point out, there are three different ways available in SPSS to partition the SS to the main effects and interaction. If your eight groups are of the same number of cases, all three methods should give the same result.

If the cell sizes are not equal, then the three methods diverge. The "experimental" approach estimates the SS for each main effect, partialling out the other main effect, but not the interaction effect. The interaction effect is estimated, partialling out both main effects.

In the "regression" approach, the SS for each main effect is estimated, partialling out both the other main effect and the interaction effect. This gives the "unique" SS. The interaction is estimated as above.

The hierarchical approach estimates the SS as directed. The first main effect is estimated, in total. The second main effect is estimated after partialling out the first main effect. The interaction effect is... as above.

There is a considerable literature on this matter. My reading of the current state of the matter is that when the samples sizes are unequal "accidentally", one should use the "unique" approach. The "experimental" approach tests somewhat bizarre hypotheses that are a function of the marginal n's. If the unequal cell sizes result from "real relationships" between the IVs (as can occur in non-experimental situations), one should use the "hierarchical" approach.

______________________________________________________________________________

William B. Ware, Professor and Chair Educational Psychology CB# 3500 EMAIL: wbware@unc.edu University of North Carolina PHONE: (919)-966-5266 Chapel Hill, NC 27599-3500 FAX: (919)-962-1533

URL:http://www.unc.edu/~wbware/ ______________________________________________________________________________


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