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.
The subject of unequal-variance confidence intervals for median
differences is discussed in Newson (2006), and is a project in progress,
on which I am currently writing up a simulation study for publication. A
pre-publication draft of Newson (2006) can be downloaded from my website
(see my signature below). The software to implement these methods is the
-somersd- package, downloadable from SSC by typing
ssc install somersd, replace
in Stata 9.
I hope this helps.
Best wishes
Roger
References
B. K. Moser, G. R. Stevens, C. L. Watts. 1989.
The two--sample t-test versus Satterthwaite's approximate F-test.
Communications in Statistics -- Theory and Methods 18(11): 3963-3975.
B. K. Moser, G. R. Stevens. 1992.
Homogeneity of variance in the two-sample means test.
The American Statistician 46(1): 19-21.
Newson R. 2006. Confidence intervals for rank statistics: Percentile
slopes, differences, and ratios.
The Stata Journal 6(4): 497-520.
Download pre-publication draft from www.imperial.ac.uk/nhli/r.newson/
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: 07 January 2007 18:35
To: [email protected]
Subject: st: -oneway- and unequal variances
Hi,
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.
Thanks for your feedback.
Tom
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