Dear Micheal So I would be much better off just reporting the PCA as is and conclude what i can from plot
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 ________________________________________ From: Michael Friendly <frien...@yorku.ca> Sent: 07 January 2017 17:15 To: Marchesi, Julian; 'r-help@r-project.org' Subject: Re: testing whether clusters in a PCA plot are significantly different from one another Significance tests for group differences in a MANOVA of lm(cbind(pc1, pc2) ~ group) will get you what you want, but you are advised DON'T DO THIS, at least without a huge grain of salt and a slew of mea culpas. Otherwise, you are committing p-value abuse and contributing to the notion that significance tests must be used to justify all conclusions. The p-values will not be correct under standard normal theory of the multivariate GLM because the pc1 and pc2 were chosen to optimize the variance accounted for by their linear combinations and there is no theory that can correct for this, AFAIK. The cluster "group" assignment was also chosen to optimize some (other) criterion. -- Michael Friendly Email: friendly AT yorku DOT ca Professor, Psychology Dept. & Chair, Quantitative Methods York University Voice: 416 736-2100 x66249 Fax: 416 736-5814 4700 Keele Street Web: http://www.datavis.ca Toronto, ONT M3J 1P3 CANADA ______________________________________________ R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see 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.
