R help - Aug 2010 - Brown-Forsythe test of equality of MEANS

Dear friends,
two years ago (as I found on the web) Paul sent the following message but I was
not able to find if he got an answer. Today I have the same question and it
would be great if I could find out that this test has been implemented (somehow)
in R. Please do not confuse it with the Brown-Forsythe test of equality of
variances. Thank you:

I've been searching around for a function for computing the Brown-Forsythe
F* statistic which is a substitute for the normal ANOVA F statistic for when
there are unequal variances, and when there is evidence of non-normality. A
couple of other people have asked this question, the responses I found have
been:

    ?oneway.test

However, that function appears to use the Welch W statistic which, while good at
handling unequal variances, is not as good as F* at handling non-normal
distributions (or so my textbook tells me). So, two questions:

   1. Is there a function ready to use for calculating the Brown-Forsythe F*?
   2. If not, what do people use for checking the results of a (one-way) ANOVA
when there is non-normality as well as non-constant variances?

Thanks,

      
Dr. Iasonas Lamprianou


Assistant Professor (Educational Research and Evaluation)
Department of Education Sciences
European University-Cyprus
P.O. Box 22006
1516 Nicosia
Cyprus 
Tel.: +357-22-713178
Fax: +357-22-590539


Honorary Research Fellow
Department of Education
The University of Manchester
Oxford Road, Manchester M13 9PL, UK
Tel. 0044  161 275 3485
iasonas.lamprianou at manchester.ac.uk

Inline below.

-- Bert

On Mon, Aug 30, 2010 at 1:05 PM, Iasonas Lamprianou
<lamprianou@yahoo.com>wrote:
>
> Dear friends,
> two years ago (as I found on the web) Paul sent the following message but I
> was not able to find if he got an answer. Today I have the same question
and
> it would be great if I could find out that this test has been implemented
> (somehow) in R. Please do not confuse it with the Brown-Forsythe test of
> equality of variances. Thank you:
>
> I've been searching around for a function for computing the
Brown-Forsythe
> F* statistic which is a substitute for the normal ANOVA F statistic for
when
> there are unequal variances, and when there is evidence of non-normality.

False, I think, as I'm not entirely clear on your meaning. Brown-Fosythe is
a test for the equality of spreads among groups. From Wikipedia:


The transformed response variable is constructed to measure the
spread<http://en.wikipedia.org/wiki/Statistical_dispersion>in each
group. Let
 [image: z_{ij}=\left\vert y_{ij} - \tilde{y}_j \right\vert]

where [image: \tilde{y}_j] is the
median<http://en.wikipedia.org/wiki/Median>of group
*j*. The Brown–Forsythe test statistic is the model *F* statistic from a one
way ANOVA on *zij*:

In particular, it is NOT " a substitute for the normal ANOVA F statistic
for
when there are unequal variances, and when there is evidence of
non-normality."

--

Bert Gunter

Genentech Noclinical Statistics

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The following reference that contains a short Fortran program for the 
Brown-Forsythe ANOVA

Reed, James F., I. & Stark, D. B.
Robust alternatives to traditional analyses of variance: Welch $W^*$, 
James $J_I^*$, James $J_II^*$, and Brown-Forsythe $BF^*$
Computer Methods and Programs in Biomedicine, 1988, 26, 233-238 




Iasonas Lamprianou <lamprianou@yahoo.com> 
Sent by: r-help-bounces@r-project.org
08/30/2010 04:05 PM

To
r-help@r-project.org
cc

Subject
[R] Brown-Forsythe test of equality of MEANS







Dear friends,
two years ago (as I found on the web) Paul sent the following message but 
I was not able to find if he got an answer. Today I have the same question 
and it would be great if I could find out that this test has been 
implemented (somehow) in R. Please do not confuse it with the 
Brown-Forsythe test of equality of variances. Thank you:

I've been searching around for a function for computing the Brown-Forsythe 
F* statistic which is a substitute for the normal ANOVA F statistic for 
when there are unequal variances, and when there is evidence of 
non-normality. A couple of other people have asked this question, the 
responses I found have been:

    ?oneway.test

However, that function appears to use the Welch W statistic which, while 
good at handling unequal variances, is not as good as F* at handling 
non-normal distributions (or so my textbook tells me). So, two questions:

   1. Is there a function ready to use for calculating the Brown-Forsythe 
F*?
   2. If not, what do people use for checking the results of a (one-way) 
ANOVA when there is non-normality as well as non-constant variances? 

Thanks,

 
Dr. Iasonas Lamprianou


Assistant Professor (Educational Research and Evaluation)
Department of Education Sciences
European University-Cyprus
P.O. Box 22006
1516 Nicosia
Cyprus 
Tel.: +357-22-713178
Fax: +357-22-590539


Honorary Research Fellow
Department of Education
The University of Manchester
Oxford Road, Manchester M13 9PL, UK
Tel. 0044  161 275 3485
iasonas.lamprianou@manchester.ac.uk




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