P.S. if your data are investment returns (after/before portfolio value ratios), then you might like to log the data, and then use -regress- with the -eform- and -robust- options to get geometric mean ratios instead of arithmetic mean differences. See Newson (2003).
This Stata Tip, and 32 more, are published together as Newton and Cox (2006), which you might like to order from
http://www.stata-press.com/
I hope this helps.
Roger
References
Newson R. Stata tip 1: The eform() option of regress. The Stata Journal 2003; 3(4): 445. Download post-publication update from
http://www.imperial.ac.uk/nhli/r.newson/papers.htm
Newton HJ, Cox NJ (eds). Thirty-three Stata Tips. College Station, TX: Stata Press; 2006.
Roger Newson
Lecturer in Medical Statistics
Respiratory Epidemiology and Public Health Group
National Heart and Lung Institute
Imperial College London
Royal Brompton campus
Room 33, Emmanuel Kaye Building
1B Manresa Road
London SW3 6LR
UNITED KINGDOM
Tel: +44 (0)20 7352 8121 ext 3381
Fax: +44 (0)20 7351 8322
Email: [email protected]
www.imperial.ac.uk/nhli/r.newson/
Opinions expressed are those of the author, not of the institution.
-----Original Message-----
From: [email protected] [mailto:[email protected]] On Behalf Of Newson, Roger B
Sent: 09 January 2007 16:22
To: [email protected]
Subject: st: RE: AW: RE: RE: RE: -oneway- and unequal variances
I do not know the details of your project. However, if you have approximately 1000 observations for each portfolio, then tiny group sample numbers are probably not a problem, and I would probably use -regress-, with Huber variances (given by the -robust- option) and dummy identifier variables for groups.. This will be robust to unequal variability, and probably to most forms of non-normality, if all the group numbers are as large as this.
I hope this helps.
Best wishes
Roger
Roger Newson
Lecturer in Medical Statistics
Respiratory Epidemiology and Public Health Group
National Heart and Lung Institute
Imperial College London
Royal Brompton campus
Room 33, Emmanuel Kaye Building
1B Manresa Road
London SW3 6LR
UNITED KINGDOM
Tel: +44 (0)20 7352 8121 ext 3381
Fax: +44 (0)20 7351 8322
Email: [email protected]
www.imperial.ac.uk/nhli/r.newson/
Opinions expressed are those of the author, not of the institution.
-----Original Message-----
From: [email protected] [mailto:[email protected]] On Behalf Of Thomas Erdmann
Sent: 09 January 2007 12:11
To: [email protected]
Subject: st: AW: RE: RE: RE: -oneway- and unequal variances
Thanks again to all for the ongoing suggestions.
Suggestions on -simanova-, -fstar-, -wtest- :
I have followed the advice given by the link posted by Michael Mitchell
( http://www.ats.ucla.edu/stat/stata/library/homvar.htm )In general, the
-robvar- command implies that variance is indeed not homogenous for the ten
portfolios, but testing with -simanova- and -fstar- and -wtest- afterwards
indicates that -oneway- results seem pretty robust. My assumption is that
this is due to the high number of observations and almost equal-sized groups
(10 portfolios containing each approx. 1000 observations).
Roger:
thanks for your feedback - I can loosely follow your argumentation, but
cannot really translate it into a concrete suggestion on what to do in your
opinion, maybe you could rephrase or add suggestions, thanks in advance.
General comment on the context of my analysis:
I might add to the discussion that the portfolio analysis comparing the
means of the 10 portfolios is the first step of my analysis. In later steps
I use panel regressions using robust estimation techniques with cluster
option respectively a new ado file (-xtscc-) implementing Driscoll and Kraay
(Rev. Ec. Stat. 1998) estimators correcting for spatial dependence. (
http://ideas.repec.org/c/boc/bocode/s456787.html ). Basically the portfolios
are a simple method which result in a simple measure (return spread between
portfolio 1 and 10) that is straightforward to interpret.
- Tom
-----Urspr�ngliche Nachricht-----
Von: [email protected]
[mailto:[email protected]] Im Auftrag von Newson, Roger B
Gesendet: Dienstag, 9. Januar 2007 12:48
An: [email protected]
Betreff: st: RE: RE: RE: -oneway- and unequal variances
In a one-way ANOVA with 10 groups, we are usually interested in
calculating confidence intervals for differencers between pairs of group
means. The principles involved are a generalization of the principles of
the 2-sample t-test. The main change is that, when calculating
confidence intervals for the difference between 2 group means (out of
10), the classical regression formula (used by Stata in the absence of
the -robust- option) uses residuals from all 10 groups, instead of
residuals from only the 2 groups being compared. In general, this means
that the Huber confidence interval is more robust to heteroskedasticity,
but the classical confidence interval is more robust to tiny group
numbers, because, if heteroskedasticity is not too severe, then you may
be able to estimate the population variance of a small sample better
using the sample variance of a larger sample (or the sample variances of
9 similarly-sized samples) than using the sample variance of the small
sample.
Roger
Roger Newson
Lecturer in Medical Statistics
Respiratory Epidemiology and Public Health Group
National Heart and Lung Institute
Imperial College London
Royal Brompton campus
Room 33, Emmanuel Kaye Building
1B Manresa Road
London SW3 6LR
UNITED KINGDOM
Tel: +44 (0)20 7352 8121 ext 3381
Fax: +44 (0)20 7351 8322
Email: [email protected]
www.imperial.ac.uk/nhli/r.newson/
Opinions expressed are those of the author, not of the institution.
-----Original Message-----
From: [email protected]
[mailto:[email protected]] On Behalf Of Nick Cox
Sent: 08 January 2007 09:22
To: [email protected]
Subject: st: RE: RE: -oneway- and unequal variances
How does this apply to one-way analysis of variance
with 10 groups?
Nick
[email protected]
Newson, Roger B
> A good pair of definitive references on the issues affecting
> unequal-variance and equal-variance t-tests is Moser et al. (1989) and
> Moser and Stevens (1992). These papers recomment the unequal-variance
> t-test as the "standard default", and recommend the equal-variance
> t-test as a "special case" for the "special occasion" where we "know"
> that the population variance of the smaller sample can be estimated
> using the sample variance of the l;arger sample. They do not recommend
> the use of heteroskedasticity tests, essentially because
> heteroskedasticity starts to affect the validity of confidence limits
> before it starts to register in heteroskedasticity tests.
[...]
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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