See comments, interspersed.
> Date: Thu, 28 Nov 2013 21:09:38 -0800
> From:
[hidden email]> Subject: MANOVA
> To:
[hidden email]>
> 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.
"Three types of pets" -- This is the definition of the universe being studied?
With samples of 10 each, it seems that you might have descriptive study
of "my own pets" or some such. I do know that dog breeds conventionally
have different temperaments attributed to them.
"Anxiety" and "depression" in animals is terminology that is evocative;
the labels will be meet more approval from animal lovers than philosophers.
I skip that issue, but raise the problem that psychologists once called
"operationaizing." Surely this is from observing behavior. (Any other chance?)
My own impression is that cats and dogs do differ in standard activities,
but they are not usually locked in cages like the hamsters.
It seems to me that the best you could hope to conclude from a study is
that "These measurements do (or do not) give similar results when applied
to pets in conditions of stress (or no stress)." In that case, showing the
comparability is far more interesting that a weak (Ns of 10?) test.
>
> 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.
You intend to conclude that var-cov matrices are equal "because Sig.> 0.01"?
No. That is not a proper statement of what you can infer. You can, at best,
say that "The matrices do not differ so much as to reject at the 1% level".
With Ns of 10, that is a very weak claim.
Anyway, if there are such differences, I fully expect them to owe to the
weirdness of scaling or extreme scores in one group or another. For this
pilot study of scaling across species, I would take seriously every piece
of evidence of palpable difference. Thus, you might consider it a
potential warning against the scaling if there is *any* evidence of
heterogeneity, even at the 10% level.
- On a further note: One should be very cautious about using tests of
homogeneity as a preliminary for further testing. Essentially NO
statisticians say that you should (for instance) decide which t-test to
use, based on a test of variances. On the other hand, when doing
Repeated Measures, the test of sphericity is so weak that you should
be wary of a strong risk invalid comparisons whenever p< 0.50, not p< 0.05.
>
> 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?
The hypotheses tested in MANOVA are the set of "all possible combinations"
of differences. I once included Anxiety and Depression and Psychoticism
in a MANOVA because I wanted to test whether there was a different *pattern*
showing in two groups of relapsers. (There was.) Usually, the interest in
symptoms is one-sided: Are these people doing better than those people? -
and the proper test is a composite score. Or, if you insisted on arbitrary
weights, you might look at Roy's Largest Root instead of a predefined composite.
However, given your circumstances of trying to show the equivalence (or
not), your hypotheses deserve the more powerful and meaningful univariate
examinations. No one should complain about "Too many tests" - you are not
testing in that sort of circumstance.
> 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?
Because the scales can't be applied across species, and still use the
same norms?
> and that "The violation of homogeneity of variances poses no threat to the
> validity of our results" I don't undestand why?
You don't say where you are reading that.
Equal Ns make ANOVA very robust. Or maybe they also did the testing in
another fashion to illustrate that?
...
--
Rich Ulrich
Locked
