[R] testing whether clusters in a PCA plot are significantly different from one another
friendly at yorku.ca
Sat Jan 7 18:15:37 CET 2017
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
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