I am using FactomineR to explore a set of continuous variables in a large set of sites (ecological data). I did a PCA and found the relevant principal components and their scores and such. Afterwards I do a hierarchical clustering on the resulting PCA using HCPC with K-means clustering of the sites. The result comes up with 3 clusters, which confirms what I expected when seeing the PCA plot. The data I am using (just for learning this stuff) can be found on http://datadryad.org/resource/doi:10.5061/dryad.rg832/1
The code I am using is the following:
pca <- PCA(pca_data_jouffray, graph=FALSE, scale.unit = TRUE) hcpc <- HCPC(pca, min = 3, max=10, iter.max=10, graph=FALSE)
My question is the following: I can see the significance of each variable for each cluster with (in this case for cluster 1)
hcpc$desc.var$quanti$`1` v.test Mean in category Overall mean sd in category Overall sd p.value Macroalgae 11.646270 38.144928 15.142384 23.438186 18.6474238 2.397240e-31 Sand 9.303437 21.561594 11.087748 13.893514 10.6290048 1.359779e-20 CCA -4.386715 3.094203 6.719785 3.940017 7.8031164 1.150752e-05 Hard.coral -5.755929 6.797101 18.303808 7.952790 18.8740653 8.616669e-09 Complexity -5.934810 1.702899 2.283113 0.737548 0.9230203 2.941863e-09 Turf.algae -7.446795 30.673913 48.649007 14.649733 22.7893314 9.563492e-14
But what I would like to know is if I can find out if the complete cluster is significantly different from the overall mean. So a p-value for each cluster as a whole, not split up by variable. I would think that there could be a test to see if the mean euclidean distances between the individuals of a cluster is significantly different of the overall mean euclidean distance between all individuals?
Is this possible?