# st: AW: RE: -oneway- and unequal variances

 From "Thomas Erdmann" <[email protected]> To <[email protected]> Subject st: AW: RE: -oneway- and unequal variances Date Sun, 7 Jan 2007 20:40:46 +0100

```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 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

Tom

-----Urspr�ngliche Nachricht-----
Von: [email protected]
[mailto:[email protected]] Im Auftrag von Nick Cox
Gesendet: Sonntag, 7. Januar 2007 20:00
An: [email protected]
Betreff: st: RE: -oneway- and unequal variances

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
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
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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