I don't have further comments, except to underline
the importance of respecting the dependence of
the data.
Fortuitously, I am reviewing a paper in a quite
different field in which the authors fuss about normality
of univariate distributions (or otherwise) but neglect to
discuss the consequences of stark dependence in their own
data for the P-values they display with great reverence.
The late William Kruskal (whose name you mentioned in your
reference to Kruskal-Wallis) had some pointed remarks on casually
assuming independence in his presidential
address to the American Statistical Association that seem
every bit as applicable now as when published.
William Kruskal. 1988.
Miracles and Statistics: The Casual Assumption of Independence.
Journal of the American Statistical Association
83: 929-940.
It is difficult to find (e.g.) introductory texts that tell
a straight story on this. How many examples have you seen
in which (e.g.) the states of the US are tacitly treated as
generating mutually independent data?
With Kruskal-Wallis itself, my point was that the method
never sees differences in variances in the original
variable _as such_, given the transformation to ranks. But
that doesn't necessarily make it a self-sufficient answer to
problems of heteroscedasticity. The ranking will subdue the
effects of outliers, but it won't wash out all that you
might want washed out.
Nick
[email protected]
Thomas Erdmann
> Given your comments a short description of the underlying substantive
> problem:
>
> I am sorting monthly observations of a cross section of
> companies into 10
> portfolios (deciles) according to one attribute (e.g.
> "Earnings per Share")
> from high to low. This is done each month. Afterwards the
> average return
> over all months is calculated for all portfolios with the
> same number (from
> 1 to 10). The question is wether returns in those portfolios differ
> significantly, i.e. if high EPS porfolios (10) have higher
> return than low
> EPS portfolios (1).
>
> Originally I wanted to follow a practice using GMM, robust to
> heterskedasticity and autocorrelatoin as follows, but
> couldn't find a way to
> implement it with Stata:
>
> Assess the equality of portfolios using the moment conditions
>
> e1= R1 - MR
> e2= R2 - MR
> ...
> e10 = R10 - MR
>
> where R1 to R10 are the return of ten decile portfolios and
> MR is the mean
> return parameter to be estimated (over-identified equation
> with 10 moment
> conditions and one parameter to be estimated).
> ( http://www.stata.com/statalist/archive/2006-11/msg00353.html )
>
> I would appreciate any further comments.
>
>
> Regarding your other comments:
>
> Regarding Bartlett: in the meantime I encountered postings that using
> -robvar- is better then the Bartlett displayed after -oneway- , which
> together with your comment makes me wonder why it is still displayed.
>
> This source led me to believe that the Kruskal-Wallis also
> assumes equal
> variances, but maybe I just missintepreted what is written.
> http://www.basic.northwestern.edu/statguidefiles/oneway_anova_
> alts.html
Nick Cox
> There is a bundle of different questions here
> on quite different levels.
>
> I'll restrict myself to a few comments:
>
> The Kruskal-Wallis test knows nothing whatsover about
> variances; that is, in a strong sense, most of the point
> to the test.
>
> Bartlett's test is embedded in the literature and
> in programs but I don't think many practical data
> analysts pay much attention to it. Like many such
> tests, it is likely to be oversensitive to small
> differences, especially at large sample sizes.
>
> If you are seriously worried about heteroscedasticity
> then either you should be working on transformed scales
> or else -oneway- is not really the answer to your
> substantive question. I don't think that seeking
> an answer that is -oneway- plus some small trick
> is the best way to proceed.
>
> In any case, although you say nothing about
> your substantive problem, the mention of returns leads me
> to suspect a time series context. If that is
> true, any P-values coming out of -oneway- are
> likely to be pure garbage. Otherwise put, violation
> of independence assumptions is a whole heap more
> problematic than unequal variances. Nor will Kruskal-
> Wallis help in this situation.
>
> Rupert G. Miller's book "Beyond ANOVA" is
> a wonderful source in this terrain. It was originally
> published by Wiley in 1986 and reissued by Chapman
> and Hall in 1997.
>
> Nick
> [email protected]
>
> Thomas Erdmann
>
> > comparing ten portfolios of returns using -oneway- ,
> > Bartlett's test for
> > equal variances always highly rejects the null hypothesis.
> >
> > 1.) What routines can be used in Stata if the assumptions
> of ANOVA are
> > violated?
> >
> > 2.) Generally speaking, does the violation of ANOVA
> > assumption shift the
> > F-test to more conservative results (i.e. tends not to reject H0 of
> > equality)?
> >
> > I am aware that nonparametric tests like the Kruskal-Wallis
> > test ( -kwallis-
> > , -kwallis2- ) can help with settings where the normality
> > assumption of the
> > ANOVA is violated, but it still assumes equal variance.
> >
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