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Brown-Forsythe test of equality of MEANS

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Brown-Forsythe test of equality of MEANS

Iasonas Lamprianou

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
[hidden email]




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Re: Brown-Forsythe test of equality of MEANS

Bert Gunter
Inline below.

-- Bert

On Mon, Aug 30, 2010 at 1:05 PM, Iasonas Lamprianou <[hidden email]>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

        [[alternative HTML version deleted]]


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Re: Brown-Forsythe test of equality of MEANS

JRG-2
On 30 Aug 2010 at 13:25, Bert Gunter wrote:

> Inline below.
>
> -- Bert

Wrong.  There *is* a Brown-Forsythe test of equality of means given heterogeneity of variance.  
[Kirk's experimental design tst, 3rd Ed. p. 155 describes the test.]

---JRG

John R. Gleason

>
> On Mon, Aug 30, 2010 at 1:05 PM, Iasonas Lamprianou <[hidden email]>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
>
> [[alternative HTML version deleted]]
>
>

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Re: Brown-Forsythe test of equality of MEANS

Bert Gunter
Thanks. I stand corrected, then.

-- Bert

On Mon, Aug 30, 2010 at 1:45 PM, JRG <[hidden email]> wrote:

> On 30 Aug 2010 at 13:25, Bert Gunter wrote:
>
> > Inline below.
> >
> > -- Bert
>
> Wrong.  There *is* a Brown-Forsythe test of equality of means given
> heterogeneity of variance.
> [Kirk's experimental design tst, 3rd Ed. p. 155 describes the test.]
>
> ---JRG
>
> John R. Gleason
>
> >
> > On Mon, Aug 30, 2010 at 1:05 PM, Iasonas Lamprianou <
> [hidden email]>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
> >
> >       [[alternative HTML version deleted]]
> >
> >
>
>
>


--
Bert Gunter
Genentech Nonclinical Biostatistics
467-7374
http://devo.gene.com/groups/devo/depts/ncb/home.shtml

        [[alternative HTML version deleted]]

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Re: Brown-Forsythe test of equality of MEANS

Iasonas Lamprianou
In reply to this post by Bert Gunter
Thank you for replying. But there is another test with the same name which tests for equality of means. It is a robust version of ANOVA, like the Welch (ANOVA) test. They are both available at SPSS. the Welch test is available through the oneway.test in R but the Brown-Forsythe test for the equality of means is not. You may have a look at
       
       
De
Beuckelaer, A. (1996). A closer examination on some parametric
alternatives to the ANOVA F test. Statistical Papers, 37, 291-305 if you like to see what I mean.
But thank you for replying so soon. I hope that somebody else solved this issue. Also, by the way, I have a second question, if anyone can help. I am looking for an R package to run a Dunnett's T3 or C test for Post Hoc comparisons when we 'suffer' from heteroscedasticity. (Even Games-Howell would do if the Dunnett's tests are not available )

Thank you again for your help.




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

[hidden email]

--- On Mon, 30/8/10, Bert Gunter <[hidden email]> wrote:

From: Bert Gunter <[hidden email]>
Subject: Re: [R] Brown-Forsythe test of equality of MEANS
To: "Iasonas Lamprianou" <[hidden email]>
Cc: [hidden email]
Date: Monday, 30 August, 2010, 21:25

Inline below.
 
-- Bert


On Mon, Aug 30, 2010 at 1:05 PM, Iasonas Lamprianou <[hidden email]> 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 in each group. Let


 
where  is the 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
 



     
        [[alternative HTML version deleted]]


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https://stat.ethz.ch/mailman/listinfo/r-help
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and provide commented, minimal, self-contained, reproducible code.
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Re: Brown-Forsythe test of equality of MEANS

JLucke
In reply to this post by Iasonas Lamprianou
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 <[hidden email]>
Sent by: [hidden email]
08/30/2010 04:05 PM

To
[hidden email]
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
[hidden email]




______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.


        [[alternative HTML version deleted]]

______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
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Re: Brown-Forsythe test of equality of MEANS

Iasonas Lamprianou
Thank you. It seems that nobody has implemented it in R yet. I'll have a look, thank you very much

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

[hidden email]

--- On Tue, 31/8/10, [hidden email] <[hidden email]> wrote:

From: [hidden email] <[hidden email]>
Subject: Re: [R] Brown-Forsythe test of equality of MEANS
To: "Iasonas Lamprianou" <[hidden email]>
Cc: [hidden email], [hidden email]
Date: Tuesday, 31 August, 2010, 20:26



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 <[hidden email]>


Sent by: [hidden email]
08/30/2010 04:05 PM




To
[hidden email]


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

[hidden email]









______________________________________________

[hidden email] mailing list

https://stat.ethz.ch/mailman/listinfo/r-help

PLEASE do read the posting guide http://www.R-project.org/posting-guide.html

and provide commented, minimal, self-contained, reproducible code.






     
        [[alternative HTML version deleted]]


______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
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Re: Brown-Forsythe test of equality of MEANS

Bert Gunter
In reply to this post by JLucke
Learned Folks:

Well, I've already advertised my ignorance about these matters, so I have
nothing to lose by plunging ahead with further Questionable "advice."

>From the references cited, Brown-Forsythe originated in the statistical
medieval age -- that is, prior to large scale, cheap computing (to be
honest, I have dim memories of it in BMD!). Then cameth Brad Efron and the
enlightenment: If you are concerned about the distribution of this -- or
indeed any reasonably smooth statistic (and some not so smooth: Hinkley -
Davison's Bootstrap book has details) -- then bootstrap it. That is, get a
confidence interval for the difference in means and see whether 0 falls
within (or whatever Null you wish to test). If you are concerned about
robustness (whatever that means in this context), well, gosheth! -- we
have journeyed a long way since the 1970's. Indeed, there are several
packages (e.g. robust, robustbase) with lots of robust alternatives. Most
(maybe all?) of which can be bootstrapped, of course.

So walketh with thy computers, my brethren, and enter the great age of
enlightenment.

(Thus endeth the lesson. Caveat Emptor!)

Cheers to all,
Bert

On Tue, Aug 31, 2010 at 12:26 PM, <[hidden email]> wrote:

> 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 <[hidden email]>
> Sent by: [hidden email]
> 08/30/2010 04:05 PM
>
> To
> [hidden email]
> 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
> [hidden email]
>
>
>
>
> ______________________________________________
> [hidden email] mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html<http://www.r-project.org/posting-guide.html>
> and provide commented, minimal, self-contained, reproducible code.
>
>
>        [[alternative HTML version deleted]]
>
> ______________________________________________
> [hidden email] mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html<http://www.r-project.org/posting-guide.html>
> and provide commented, minimal, self-contained, reproducible code.
>

        [[alternative HTML version deleted]]

______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
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Re: Brown-Forsythe test of equality of MEANS

Iasonas Lamprianou
Combining humor with useful information is nice! Thank you for the advice Bert. I'll try it and see what happens. Are you aware of any free! (on the internet) alternatives to the book you have recommended? Academics are not, usually, known for their deep pockets!
Thank you again for the suggestions

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

[hidden email]

--- On Tue, 31/8/10, Bert Gunter <[hidden email]> wrote:

From: Bert Gunter <[hidden email]>
Subject: Re: [R] Brown-Forsythe test of equality of MEANS
To: [hidden email]
Cc: "Iasonas Lamprianou" <[hidden email]>, [hidden email], [hidden email]
Date: Tuesday, 31 August, 2010, 21:41

Learned Folks:
 
Well, I've already advertised my ignorance about these matters, so I have nothing to lose by plunging ahead with further Questionable "advice."
 
From the references cited, Brown-Forsythe originated in the statistical medieval age -- that is, prior to large scale, cheap computing (to be honest, I have dim memories of it in BMD!). Then cameth Brad Efron and the enlightenment: If you are concerned about the distribution of this -- or indeed any reasonably smooth statistic (and some not so smooth: Hinkley - Davison's Bootstrap book has details) -- then bootstrap it. That is, get a confidence interval for the difference in means and see whether 0 falls within (or whatever Null you wish to test). If you are concerned about robustness (whatever that means in this context), well, gosheth! -- we have journeyed a long way since the 1970's. Indeed, there are several packages (e.g. robust, robustbase) with lots of robust alternatives. Most (maybe all?) of which can be bootstrapped, of course.

 
So walketh with thy computers, my brethren, and enter the great age of enlightenment.
 
(Thus endeth the lesson. Caveat Emptor!)
 
Cheers to all,
Bert


On Tue, Aug 31, 2010 at 12:26 PM, <[hidden email]> wrote:

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 <[hidden email]>

Sent by: [hidden email]
08/30/2010 04:05 PM


To
[hidden email]
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
[hidden email]





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Re: Brown-Forsythe test of equality of MEANS

JLucke
In reply to this post by Bert Gunter
Yes. I too remember BMD, BMDP, punch cards, computer printouts, and
24-hour turn-around.  However, I am also old enough that when someone asks
for an antique method, I will gladly supply it if I can, if only for
historical reasons.




Bert Gunter <[hidden email]>
08/31/2010 04:41 PM

To
[hidden email]
cc
Iasonas Lamprianou <[hidden email]>, [hidden email],
[hidden email]
Subject
Re: [R] Brown-Forsythe test of equality of MEANS






Learned Folks:
 
Well, I've already advertised my ignorance about these matters, so I have
nothing to lose by plunging ahead with further Questionable "advice."
 
>From the references cited, Brown-Forsythe originated in the statistical
medieval age -- that is, prior to large scale, cheap computing (to be
honest, I have dim memories of it in BMD!). Then cameth Brad Efron and the
enlightenment: If you are concerned about the distribution of this -- or
indeed any reasonably smooth statistic (and some not so smooth: Hinkley -
Davison's Bootstrap book has details) -- then bootstrap it. That is, get a
confidence interval for the difference in means and see whether 0 falls
within (or whatever Null you wish to test). If you are concerned about
robustness (whatever that means in this context), well, gosheth! -- we
have journeyed a long way since the 1970's. Indeed, there are several
packages (e.g. robust, robustbase) with lots of robust alternatives. Most
(maybe all?) of which can be bootstrapped, of course.
 
So walketh with thy computers, my brethren, and enter the great age of
enlightenment.
 
(Thus endeth the lesson. Caveat Emptor!)
 
Cheers to all,
Bert

On Tue, Aug 31, 2010 at 12:26 PM, <[hidden email]> wrote:
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 <[hidden email]>
Sent by: [hidden email]
08/30/2010 04:05 PM

To
[hidden email]
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
[hidden email]




______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.


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and provide commented, minimal, self-contained, reproducible code.




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