From: nichols@spss.com (David Nichols)
Subject: Re: multivariate contrast test
Organization: SPSS Inc.
Date: Wed, 11 Nov 1992 19:44:38 GMT

In article <SPSSX-L%92111105501424@UGA.CC.UGA.EDU> Gerbert Haselager <U212230@HNYKUN11.BITNET> writes:
>Hello experts,
>
>I have some question about an application of manova. This is the
>(core of) my situation:
>MANOVA D1 TO D6 BY IV (4)
>    /WSFACTORS = SCALE (6)
>    /WSDESIGN
>    /DESIGN
>The six dependent variables "D1 TO D6" are six different scales,
>measured at the same time.
>My aim is to decide wether IV-level 3 differs from IV-level 4 or not.
>I found and overall multivariate effect on IV, and a significant inter-
>action between IV and SCALE. The IV-effect was also found in some, but
>not all, univariate tests on the scales. I explored univariate contrasts
>using Scheffe's tests in procedure ONEWAY. The resulting picture was
>fuzzy, some of the relevant contrasts were significant, others were not.
>What I need - I think - is a multivariate-contrast-test for my between
>subject factor (IV), something like a multivariate variant on the
>Scheffe-test. It must be a test for the contrast on a pair of levels of
>a factor, given two more other levels, on six dependent variables
>simultaneously. How can I do this with MANOVA or any other procedure,
>preferably in SPSSX (v 4.0 on CMS v 8.0)?
>Some additional information:
>-- I tried using CONTRASTS (IV) = SIMPLE (4) but discovered that effects
>of contrasts were not reported separately. My local support specialists
>stated that this strategy cannot be used for between subject factors,
>but I still do not understand the reason. What are your comments on
>this?
>-- I considered using SELECT IF IV = 3 OR IV = 4, before running the
>MANOVA. In this way I can test the difference between this two levels,
>but this test is then performed in a not aselect sample, and
>therefore not acceptable. Am I right?

I'm not at all certain that you have this set up the way you really want
it. In particular, the WSFACTORS is treating the 6 scales as repeated
measures (or the equivalent, a within subjects factor). The tests on IV
are done only on what MANOVA by default calls T1, which is a transformed
variable representing the average of the 6 scales (technically, it is
the sum of the six divided by the square root of six, but the hypotheses
tested are the same as if it were divided by six rather than the
normalizing value). Thus there is no multivariate analysis being done
on the between subjects factor IV. You can create a variable as the
sum or average of your scales and run a oneway ANOVA on it and see that
you get the same results for your F-test (to have the sums of squares
match exactly, you'd have to use the same scale as MANOVA did when it
created transformed variables and divide the sum by sqrt(6)). 

So you have not found an overall multivariate effect on IV, comparing
level 3 to level 4, or anything. If you want this, you should drop the
WSFACTORS and WSDESIGN subcommands and simply run it as a multivariate
analysis. You would then get an overall multivariate test for IV and
univariate tests for IV for each of the six scales. If you want a
test for IV 3 vs. IV 4, use one of the contrast types that would include
such a comparison (SPECIAL, giving it your own, or perhaps SIMPLE,
REPEATED or HELMERT--check the documentation to see how each of these
can include the comparison you want), then ask for PRINT=PAR to see the
univariate comparisons for each scale. To see a multivariate test for
each comparison, use DESIGN=IV(1), IV(2), IV(3), which will separate
out each degree of freedom in your factor. (Note that PRINT=SIG(SINGLEDF)
gives different results if there are different numbers of observations
in each cell; it does an orthogonal partition of the sums of squares
within each effect, which you generally would not want.) 

There isn't a Scheffe test or set of confidence intervals for the
multivariate case, but the version of MANOVA you're using does offer
four different multivariate confidence intervals (Morrison's multivariate
book documents some of them). You have choices of individual or joint
intervals (meaning dealing separately with each df in a factor or taking
them all together--watch out with Bonferroni intervals here--send me a
note if you want to use them, because they're tricky), and univariate
or multivariate, taking each dependent variable separately or taking
into account the fact that multiple variables are being looked at. It
sounds to me like what you want here are probably individual multivariate
confidence intervals. Check the documentation of the CINTERVAL subcommand.

--
 David Nichols        Senior Statistical Support Specialist         SPSS, Inc.
 Phone: (312) 329-3684     Internet:  nichols@spss.com     Fax: (312) 329-3657
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 Any correlation between my views and those of SPSS is strictly due to chance.