Hi Ting-Wen,
as Ted pointed out, if and how one has to correct for multiple tests is a huge topic. Perhaps looking at the literature and making your own opinion on this matter would be the best choice (for example, Perneger 1998 - British Medical Journal and Garcia 2004 - Oikos, present two different points of view in a very accessible way).


A few extra points:
- There are other methods that are generally less conservative than the Holm procedure ("Sequential Bonferroni"); these include the Benjamini-Hochberg procedure (Benjamini & Hochberg 1995 - Journal of the Royal Statistical Society; see also Benjamini & Yekutieli 2001 - The Annals of Statistics) and other more recent procedures (such as Carvajal-Rodriguez & de Una-Alvarez 2011 - Plos One); most of these are worth checking out, making your opinion on them and, possibly, using them (most of them have R implementations)

- If your dataset is multidimensional/multivariate in nature, you might want to consider using multivariate approaches for estimating and testing for phylogenetic signal (e.g., Adams 2014 - Systematic Biology), rather than many univariate tests

- If your dataset/hypothesis is multivariate in nature, testing individual PCs separately might be a poor choice (especially for PCs of order higher than 1), if it is not multivariate in nature, there might be no reason to use PCA

I hope this is of some help.
Best,
Carmelo



--
Carmelo Fruciano
Postdoctoral Fellow - Queensland University of Technology - Brisbane, Australia
Honorary Fellow - University of Catania - Catania, Italy
e-mail c.fruci...@unict.it
http://www.fruciano.it/research/



"Chen, Ting-Wen" <ting-wen.c...@biologie.uni-goettingen.de> ha scritto:

Dear Ted, dear Fabio,

thank you so much for your suggestions. I found that people applied bonferroni corrections in p-values in Pagel’s lambda, as shown in this paper: http://www.pnas.org/content/106/43/18097.abstract

In my case, I decide to use p.adjust (x,method=“holm”,n=length(x)) to correct the p-values, hope this would be better. I also did some PCA to reduce the trait dimensions and to avoid trait correlation with each other, and then tested phylogenetic signal for the first several PCs.

All the best
Ting-Wen

--
Ting-Wen Chen
J.F. Blumenbach Institute of Zoology and Anthropology
Georg August University Goettingen
Berliner Str. 28
D-37073 Goettingen, Germany
Tel: +49-55139-10943

r-sig-phylo-requ...@r-project.org<mailto:r-sig-phylo-requ...@r-project.org> 於 2016年12月13日 19:00 寫道:

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Today's Topics:

  1. Re: bonferroni corrections in Blomberg's K and Pagel's lambda
     (F?bio Machado)


----------------------------------------------------------------------

Message: 1
Date: Tue, 13 Dec 2016 08:49:59 -0200
From: F?bio Machado <macfa...@gmail.com>
To: "r-sig-phylo@r-project.org" <r-sig-phylo@r-project.org>
Subject: Re: [R-sig-phylo] bonferroni corrections in Blomberg's K and
Pagel's lambda
Message-ID: <bc3b8326-2692-44b9-94ae-56fc2d28b...@gmail.com>
Content-Type: text/plain; charset="UTF-8"

Recently I came across a similar issue, but I had a far greater number of repeated tests, 595 actually. If i used 10.000 permutations to access significance, I noticed that I could never reject the null hypothesis. That is because for 10.000 permutations, the minimum p value is 1e-04 and the bonferroni adjusted value is 0.0595. So, instead of using any multiple test corrections, I simply rejected the null-hypothesis when the observed statistic fell completely outside the distribution constructed by simulation. This produced nearly identical results to a parametric approach with bonferroni correction (I was analyzing correlations in that case).

I don?t know if that adds to the question initially raised, since for 18 tests, the minimum adjusted pvalues are still lower than 0.05, but this experience led me to believe that applying bonferroni correction to non-parametric p-value estimates is not that straightforward. I don?t know if another multiple-test correction method is more adequate for these cases. Any thoughts would be appreciated.

best regards,

Fabio Andrade Machado
Laborat?rio de Evolu??o de Mam?feros
Departamento de Gen?tica e Biologia Evolutiva- USP
f.mach...@usp.br <mailto:f.mach...@usp.br> ; macfa...@gmail.com <mailto:macfa...@gmail.com>
+55 11 982631029
skype: fabio_a_machado

Lattes: http://lattes.cnpq.br/3673327633303737 <http://lattes.cnpq.br/3673327633303737> Google Scholar: http://scholar.google.com/citations?hl=en&user=2l6-VrQAAAAJ <http://scholar.google.com/citations?hl=en&user=2l6-VrQAAAAJ> ResearchGate: https://www.researchgate.net/profile/Fabio_Machado2 <https://www.researchgate.net/profile/Fabio_Machado2>
On Dec 11, 2016, at 21:55, Theodore Garland <theodore.garl...@ucr.edu> wrote:

Dear Ting-Wen,

This is a question about statistical philosophy in general, not specific to
tests for phylogenetic signal.  How best to correct for making multiple
tests with related data is a huge and complicated topic.  Another issue is
whether your traits are correlated with each other, which would affect
views on what would be best to do.  In any case, beware that
simple Bonferroni correction is probably overly conservative, so perhaps at
least try something like sequential Bonferroni correction, if you do
attempt correction.

(Aside from the points above, I am assuming that the 18 compounds do not
add up to 100% of the sample.  If they do, then you would only want to
analyze 17 of them.)

Sincerely,
Ted Garland

On Sun, Dec 11, 2016 at 2:06 PM, Chen, Ting-Wen <
ting-wen.c...@biologie.uni-goettingen.de> wrote:

Dear all,

I?m analysing some chemical compositions of species and considering them
as ?traits?, let?s say, 18 different compounds concentration in 37 species.
I test phylogenetic signals in the percentage concentration of these
compounds using Blomberg?s K and Pagel?s lambda using the function
?phylosig". In Blomberg?s K I apply randomisation for the traits values on
the tree to have a p-value for the corresponding trait and in Pagel?s
lambda using likelihood test to get the p-value, resulting in several
traits with phylogenetic signals as indicated by both K and lambda. Because
phylogenetic signal is tested one by one, i.e. repeating 18 times for 18
compounds. Would you suggest that I have to adjust the p-values using e.g.
bonferroni corrections? I have some compounds with p-values for both K and
lambda about 0.02 (e.g. compound ?I", K=0.656, lambda=0.633), while some
other about 0.002 (compound ?R", K=0.849, lambda=0.817). Is it safe to
conclude that compound ?I? also has a phylogenetic signal?

Any idea will be very appreciated. Thank you!

All the best
Ting-Wen

--
Ting-Wen Chen
J.F. Blumenbach Institute of Zoology and Anthropology
Georg August University Goettingen
Berliner Str. 28
D-37073 Goettingen, Germany
Tel: +49-55139-10943

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