Dear All,
this is something I forgot to mention when we discussed how to replicate
MorphoJ's Procrustes ANOVA in a different software. It's mainly for
Marianna but a few others can be interested.
When the analysis is replicated (for instance, to do the permutation
tests instead of the parametric ones), I suggest to check first the
appropriateness of the design in relation to the study questions. In
MorphoJ, if I am correct, the analysis was originally tailored for the
study of directional (DAS) and fluctuating (FAS) asymmetry, as described
in detail in the ref. below and some of the others available in the help:
Klingenberg, C. P., M. Barluenga, and A. Meyer. 2002. Shape analysis of
symmetric structures: quantifying variation among individuals and
asymmetry. Evolution 56:1909–1920.
Of course, even when the analysis is specific to symmetry/asymmetry,
there can be alternative approaches. My point is not to argue for one or
the other. It's just a clarification for those who want to use the same
precise design as in MorphoJ.
With that design, if I remember well, the main factor (group, if
present) is tested against individual variation; individual variation
against FAS; DAS against FAS, and FAS against residual variation (meas.
error estimated from individual replicates). Check carefully as I may be
wrong. To check, one can copy/paste the ANOVA table in xls and manually
compute the MS ratios: the results should be the same F ratios as in the
table.
Whether this is the design one needs for her/his study it may depend on
the specific questions, as I mentioned. Also, if one has more than one
main factor, the order of the factors matters in MorphoJ (easy to verify
by swapping them) and again depends on the study questions. Finally, the
only interaction in the output is individual by side (FAS).
With R I am sure one can modify the design according to specific needs
(different F ratios, interactions with main factors etc.) and run
permutations.
All the best
Andrea
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Andrea Cardini
E-mail address: [email protected], [email protected]
WEBPAGE: https://sites.google.com/view/alcardini/
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