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Date:         Thu, 22 Feb 1996 21:12:36 GMT
Reply-To:     David Nichols <nichols@SPSS.COM>
Sender:       "SPSSX(r) Discussion" <SPSSX-L@UGA.CC.UGA.EDU>
From:         David Nichols <nichols@SPSS.COM>
Organization: SPSS, Inc.
Subject:      Re: Simultaneous confidence intervals in MANOVA

In article <4giche$38h@info.uci.kun.nl>, Rinus Voeten <m.voeten@ped.kun.nl> wrote: >The MANOVA procedure in SPSS (version 6.1 for Windows) can provide >simultaneous confidence intervals for parameter estimates using the >Bonferroni-procedure or the Scheffi-procedure. In some cases, however, >at first sight SPSS seems to give the wrong output. >An example is given below, using the Bonferroni-procedure. For the >first design the intervals were correctly adjusted. But for the second >design individual 95%-confidence intervals were outputted, though the >output claims these are joint univariate Bonferroni intervals. >One might get trapped here, because the output does not make clear to >what set of contrasts the simultaneous confidence intervals apply. >Using partitioned contrasts on the design statement, apparently, >changes the definition of the "family" for which the family-wise >error-rate is controlled. It took me some time to realize that. >So, if I understand it well, the simultaneous confidence intervals are >determined for the sets of contrasts specified in the design >statement. These might be main effects or interactions, >but also subsets of contrasts belonging to a particular factor. In the >second design there is just one contrast for each partition, and thus >there can be no Bonferroni correction. Am I correct? > >-> MANOVA >-> score BY conditie(1 4) >-> /CONTRAST (conditie) = SPECIAL (1 1 1 1 >-> -3 1 1 1 >-> 0 -2 1 1 >-> 0 0 1 -1 ) >-> /PRINT PARAM(ESTIM) >-> /METHOD=UNIQUE >-> /ERROR WITHIN+RESIDUAL >-> /CINTERVAL= JOINT(.95) UNIVARIATE(BONFER) >-> /DESIGN >-> /DESIGN conditie(1) conditie(2) conditie(3) . > >* * * * * * A n a l y s i s o f V a r i a n c e -- design 1 * * > > Estimates for SCORE > --- Joint univariate .9500 BONFERRONI confidence intervals > > CONDITIE > > Parameter Coeff. Std. Err. t-Value Sig. t Lower -95% >CL- Upper > > 2 10.8333333 1.74786 6.19806 .00000 6.54296 >15.12371 > 3 2.66666667 1.23592 2.15763 .03449 -.36709 >5.70042 > 4 .666666667 .71356 .93428 .35346 -1.08487 >2.41820 > > - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - > > >* * * * * * A n a l y s i s o f V a r i a n c e -- design 2 > > Estimates for SCORE > --- Joint univariate .9500 BONFERRONI confidence intervals > > CONDITIE(1) > Parameter Coeff. Std. Err. t-Value Sig. t Lower -95% >CL- Upper > 2 10.8333333 1.74786 6.19806 .00000 7.34554 >14.32113 > > CONDITIE(2) > Parameter Coeff. Std. Err. t-Value Sig. t Lower -95% >CL- Upper > 3 2.66666667 1.23592 2.15763 .03449 .20042 >5.13291 > > CONDITIE(3) > Parameter Coeff. Std. Err. t-Value Sig. t Lower -95% >CL- Upper > 4 .666666667 .71356 .93428 .35346 -.75722 >2.09055

Yes, you are right: MANOVA is using the set of contrasts listed together as the family in "joint" contrasts. You would need to run the first approach to obtain the correct Bonferroni intervals, OR simply adjust the alpha level for the second approach set to make it correct for the number you want (and of course with only one in a set this can be done with individual univariate intervals as well as joint ones, since they're the same with one in a set). This is very handy when you want to do pairwise comparisons using a Bonferroni approach. MANOVA thinks you're doing K-1 if there are K levels to the factor, but you're really doing K(K-1)/2 pairwise comparisons, so you would recompute alpha as 2/K times the nominal value and tell MANOVA to give you 1-(2/K)*alpha intervals and you'd get the right values.

-- ----------------------------------------------------------------------------- David Nichols Senior Support Statistician SPSS, Inc. Phone: (312) 329-3684 Internet: nichols@spss.com Fax: (312) 329-3668 -----------------------------------------------------------------------------


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