[BioC] Re: Manova nuances

Baker, Stephen Stephen.Baker at umassmed.edu
Fri Nov 21 21:04:59 MET 2003

Andy et al.

(Thanks for correcting my typo on the spelling of "principal").

Yes I know that ANOVA of n principal components will result in n
p-values, however the SMALLEST p-value will be equivalent to a
multivariate test of his hypotheses on his data. 

MANOVA and univariate ANOVA on the principal components are essentially
equivalent in theory and quite similar in that both approaches involve
the characteristic roots and functions of the same design and covariance

The equivalence is based on the fact that multivariate hypotheses will
be rejected only if the equivalent univariate hypotheses do not hold for
all variates (Morrison,1976).  Principle components simply transforms
the original variates into new variates which conserve all the original
information. Michael Benjamin's problem is that he CANNOT run MANOVA as
he has fewer cases than variates however my suggested approach WOULD

With regards to Michael's request/need for a SINGLE SUMMARY STATISTIC,
he would use the minimum of the p-values for the appropriate effect from
the univariate ANOVA's on the principal components as his single
p-value.  These are orthogonal tests and the minimum would be equivalent
to testing the same hypotheses with MANOVA on his dataset.

The only caveat is that with K genes and n<K and he will be able to test
his hypotheses on the first n principal components which account for the
largest portions of the variation.  However, in my 20 years experience,
in most datasets the number of "significant" components (with
eigenvalues >1) is usually much smaller than the number of variates.  It
would be unusual for any real biological effect to not be represented
among one or more of the first n components given n is not too small. In
his case that's 35 and I think that's probably enough.

Best wishes

-.- -.. .---- .--. ..-.
Stephen P. Baker, MScPH, PhD (ABD)            (508) 856-2625
Sr. Biostatistician- Information Services
Lecturer in Biostatistics                     (775) 254-4885 fax
Graduate School of Biomedical Sciences
University of Massachusetts Medical School, Worcester
55 Lake Avenue North                          stephen.baker at umassmed.edu
Worcester, MA 01655  USA

-----Original Message-----
From: Liaw, Andy [mailto:andy_liaw at merck.com] 
Sent: Friday, November 21, 2003 8:13 AM
To: Baker, Stephen; bioconductor at stat.math.ethz.ch
Cc: 'msb1129 at bellsouth.net'
Subject: RE: [BioC] Re: Manova nuances

> From: Stephen P. Baker [mailto:stephen.baker at umassmed.edu]
> Principle component analyses should reduce your data array to

> as many independent components as you have samples, and  for
> each sample get a score for each dimension.  These will have 
> the same total information as the original data.  These can 
> then be analysed separately with univariate anova but since 
> these are "orthogonal" analyses, multiple comparisons 
> adjustments would not be needed.

The analysis you described is quite different than MANOVA, so 
the conclusion/interpretation would be quite different, too. MANOVA
treats the data as coming from multivariate normal distribution, and
tests whether all groups have the same mean vector.  What you described
is n (number of samples) ANOVA analyses that gives n p-values.

Andy Liaw, PhD
Biometrics Research      PO Box 2000, RY33-300     
Merck Research Labs           Rahway, NJ 07065
mailto:andy_liaw at merck.com        732-594-0820

> -.- -.. .---- .--. ..-.
> Stephen P. Baker, MScPH , PhD(ABD)                      (508) 856-2625
> Senior Biostatistician
> (775) 254-4885 fax
> Academic Computing Services
> Lecturer in Biostatistics , Graduate School of Biomedical
> Sciences University of Massachusetts Medical School
> 55 Lake Avenue North                          
> stephen.baker at umassmed.edu
> Worcester, MA 01655  USA
> --------------------------------------------------------------
> --------------
> ----
> Date: Fri, 21 Nov 2003 00:18:54 -0500
> From: "Michael Benjamin" <msb1129 at bellsouth.net>
> Subject: [BioC] Manova nuances
> To: <bioconductor at stat.math.ethz.ch>
> Message-ID: <003401c3afee$f7eff000$7a05fea9 at amd>
> Content-Type: text/plain; charset="US-ASCII"
> Anybody here using manova?  It's powerful and pretty fast,
> but I'm finding that you can't have more variables than 
> samples (limits its applicability to microarray research).  
> Is there any way around this? Assume
> dim(eset)
> 1200 35
> transeset<-t(eset)
> fit<-manova(transeset ~ categories)
> summary(fit)
> There is probably a complicated mathematical truth that
> underlies this limitation--if anybody can shed some light, 
> that would be great.
> Also, if anyone knows of a quick, free multivariate tool that
> summarizes all the tests into a single test statistic, that 
> would be much appreciated.
> Regards,
> Michael Benjamin, MD
> Emory University
> Winship Cancer Institute
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> Bioconductor mailing list
> Bioconductor at stat.math.ethz.ch
> https://www.stat.math.ethz.ch/mailman/listinfo> /bioconductor

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