Re: MANOVA

Posted by Bruce Weaver on Nov 29, 2013; 1:59pm
URL: http://spssx-discussion.165.s1.nabble.com/MANOVA-tp5723364p5723369.html

I've just searched the FM for "Brown-Forsythe", and the only place it appears is in the documentation for ONEWAY.  So it would appear that the OP is in fact running univariate ANOVAs.  This makes me think that they want the multivariate test as a preliminary omnibus test, presumably to control Type I error.  If that is so, I suggest that the OP take a look at the classic article by Huberty & Morris (1989):

https://bitbucket.org/eyecat/readinglists/src/d8e8010f0b0d2dbb0863af3050411695254cc6b1/ReadingList_NotreDame/HubertyMorris1989MultivariateVsUnivariate.pdf

Here is the first paragraph of the Discussion section:

"Even though it is a fairly popular analysis route to take in the behavioral sciences, conducting a MANOVA as a preliminary step to multiple ANOVAS is not only unnecessary but irrelevant as well. We consider to be a myth the idea that one is controlling Type I error probability by following a significant MANOVA test with multiple ANOVA tests, each conducted using conventional significance levels. Furthermore, the research questions addressed by a MANOVA and by multiple ANOVAS are different; the results of one analysis may have little or no direct substantive bearing on the results of the other. To require MANOVA as a prerequisite of multiple ANOVAS is illogical, and the comfort of statistical protection is an illusion. The view that it is inappropriate to follow a significant MANOVA overall test with univariate tests is shared by others (e.g., Share, 1984)."

Finally, with equal sample sizes, ANOVA is extremely robust to heterogeneity of variance.  So I would not switch to the Welch or Brown-Forsythe F-tests simply because Levene's test is significant.  Doing so will unnecessarily reduce power (by reducing the denominator df).  

HTH.

Ryan Black wrote

Why are you interested in forming a weighted linear composite of the DVs? Why not perform separate univariate analyses?

Ryan

> On Nov 29, 2013, at 12:09 AM, "Matthia's" <[hidden email]> wrote:
>
> I want study the anxiety and depression scores in three types of pets with
> equal size ( 10 dogs, 10 cats and 10 hamsters). So we have here :
> Independent variable : type of pet
> Dependent variables : Anxiety scores - Depression scores.
>
> I checked the following assumptions :
> - The correlation between the dependant variables because r = 0,30
> - We have homogeneity of between-group for depression scores
> (siginficance>0,05), but not for anxiety scores in (siginficance<0,05) so I
> employ Brown-Forsythe and Welch's F test concerning anxiety.
> - We have homogeneity of variance-covariance matrices because Sig.>0,01, so
> the correlation between the dependant variables is equal across the groups.
>
> My questions :
> 1)- I know we can't choose Hotelling's Trace concerning F test but I read
> that Wilk's Lambda is the best choice even if Pillai's Trace is more
> powerful. But I don't know why we shouldn't choose Pillai's Trace or Roy's
> Largest Root F test?
> 2)- Concerning Post hoc test, I read that the best test for "Equal Variances
> Assumed" is Tukey, and for ""Equal Variances not Assumed" is Games-Howell.
> Why?
> 3)- I did the Brown-Forsythe and Welch's F test concerning anxiety :
>
> I read that "there is highly significant difference is anxiety scores across
> pet type " and I don't understand why?
> and that "The violation of homogeneity of variances poses no threat to the
> validity of our results" I don't undestand why?
>
> Thanks in advance :)
>
>
>
> --
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