I have several linear and geometric cranial variables of specimens sampled from about 20 different localities. The sample sizes per locality range between 9 – 100. What would be the best multivariate statistical tests for this dataset to compensate for the unequal sample sizes?
Hi Kenneth-
It sounds to me like you are interested in classification; or using multiple variables to sort experimental units into groupings. For this, I would suggest a hierarchical clustering approach and bootstrap resampling to generate probability values. The R add-on package 'pvclust' works nicely for this and allow you to use multiple clustering methods if so desired. A simpler approach would be to use principal components analysis (PCA) or multidimensional scaling (MDS/NMDS), but these approaches should all give comparable results. In any of these approaches, variable sample sizes from each 'population' should not matter, and allow you to broadly visualize difference among 'groups'.
In any classification the generation of a model should be carried out on well balanced groups sizes and then validated on more 'natural' abundances (I am making the assumption that some are less abundant because when using the method in anger out in the real world this will be the case, i.e. your abundances reflect an unbiased random sampling of the whole population). Random subsampling can be used to reduce the size of larger groups to create a more balanced set for calibration of the model.
The reason is that underrepresented groups will not be well estimated and the resulting classifier will tend to work best for the most prevalent group and not well for less abundant groups. In such cases the apparent performance is explained mainly by relative abundance and not by your model being robust.
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