testing whether clusters in a PCA plot are significantly different from one another

In that case you should be able to use manova where pc1 and pc2 are the independent (response) variables and group (Baseline, HFD+P, HFD) is the dependent (explanatory) variable. Something like lm(cbind(pc1, pc2)~group). That will give you slopes for HFD+P and HFD (difference in mean relative to Baseline), t-values, and p-values for each component. You can get further diagnostics using package candisc. But your sample size is very small so there may be better approaches that a statistician specializing in medical research could suggest.

David C

-----Original Message-----
From: Marchesi, Julian [mailto:j.marchesi at imperial.ac.uk] 
Sent: Friday, January 6, 2017 9:02 AM
To: David L Carlson
Subject: Re: [R] testing whether clusters in a PCA plot are significantly different from one another

Dear David

The clusters are defined by the metadata which tells R where to draw the lines - no more no less

How would I put a P value to those clusters?

cheers

Julian

Julian R. Marchesi

Deputy Director and Professor of Clinical Microbiome Research at the  Centre for Digestive and Gut Health, Imperial College London, London W2 1NY Tel: +44 (0)20 331 26197

and

Professor of Human Microbiome Research at the School of Biosciences, Museum Avenue, Cardiff University, Cardiff, CF10 3AT, Tel: +44 (0)29 208 74188, Fax: +44 (0)29 20874305, Mobile 07885 569144