I am working on the dorsal fin morphology of a single shark species from three different populations (Angola, Western Cape and Eastern Cape). I am trying to find significant differences between the populations and therefor I have run ANOVA and PCA.
PCA Biplot excludes three variables (D1B, D1I and IDS) as R2 < 0.400. My confusion lies in the fact that the ANOVA (LSD) shows highly significant differences for D1I between Angola-Eastern Cape (p = 0.003) and between Easter Cape-Western Cape (p = 0.002). I do not understand why if highly significant differences are present in the ANOVA this variable would be excluded from the biplot. Similarly, there are two variables (D1L and D1A) that appear on the biplot but do not show significant differences in the ANOVA.
I am not sure how to interpret this, whether the PCA or ANOVA takes preference when interpreting results?
Since conclusion arrived at a number of factors is more sound, so you should look PCA. Please also check your questions to be answered.
Both tests, although complementary are different. When performing a PCA you are analyzing the relationship among a set of variables (first), and then these relationships are plotted in the population-differences context (Factor loadings). But when doing an ANOVA you are investigating differences (if there are) between populations (levels of factors). Thus, although two variables present a low correlation value (however P can be < 0.05) can show differences between two populations. Furthermore, if you know that two variables are related I recommend using a MANOVA.
One also should realize that PCA, unlike a canonical discrimination analysis, does NOT differentiate between the within-group and among-group variation. A trait which exhiubits very poor differences among the study samples, while showing a high level of the within-group variabilty, can strongly contribute to shaping PC1 if the total variation of the other characters is modest (even though they differentiate populations better than character 1).
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