-------- Original Message --------
Subject: Re: PCA & CVA questions
Date: Thu, 4 Jun 2009 06:19:48 -0700 (PDT)
From: Dennis E. Slice <[email protected]>
To: [email protected]
References: <[email protected]>
Kim, You ask a number of fundamental questions the answers to which
deserve reiterating periodically:
1) PCA is about finding orthogonal linear combinations of your original
variables that capture maximum amounts of your sample variation not
already captured by earlier (PC1, PC2, etc.) PCs.
2) There is nothing in this computation about group differences. Group
differences may show up on PC1, but only if they contribute more to the
sample variability than other sources of variation, e.g., sex,
measurement error. The differences could just as well appear on PC3 or
PC11 or on none of the PCs.
3) The significant MANOVA just means the groups differ in directions in
variable space other than PC1 - see comments 1 and 2.
3.a) You can, of course, test for significance on a particular PC, but
it only makes sense if the linear combination represented by that PC has
some profound meaning (the length of a particular thing on the creature
or an interesting modification of shape or overall size) independent of
group considerations, and you may wonder do the groups differ with
respect to that feature.
4) Statistical significance is about how likely a difference in means is
due to sampling error when populations don't differ at all. It is
influenced by, among other things, sample size - enormous sample sizes
can pretty much guarantee statistical significance. Biological
significance requires consideration of biology. Does having, on average,
a 3mm longer thing make a difference in the quality or type of food
consumed by the creature given the availability of said food types in
the environment? The use of statistics to aid biological research does
not obviate the need for biology in the endeavor.
5) For two groups, you will always get only 1 CVA. That is all that is
necessary to express the separation between two groups - a line between
the means in a covariance-adjusted space. In general, for g groups, you
will get, at most, g-1 CVAs.
Hope this helps, ds
morphmet wrote:
-------- Original Message --------
Subject: PCA & CVA questions
Date: Wed, 3 Jun 2009 19:25:10 -0700 (PDT)
From: Kimberly Tice <[email protected]>
To: [email protected]
Hi,
I am new to the morphometrics world, and am having a bit of trouble
figuring out what tests to use to analyze my data and how to interpret
them. I was hoping someone might be able to offer a bit of advice...
I have two types of snails, and I want to determine if they are
different shapes. I've been using the IMP programs, and when I perform
a principal components analysis, I have 1 distinct principal component,
but the two different groups are almost completely overlapping along
that PC. I did a MANOVA of all of the partial warps/uniform warps, but
in this case, I found that the groups were significantly different. How
do I reconcile this with the PCA? Is there any way to determine whether
the differences in the MANOVA are "biologically significant" or exactly
what the shape differences are? Is it appropriate to do an ANOVA on one
principle component?
I also did a CVA, and found 1 significant CV, with an eigenvalue of
0.8. What does the eigenvalue mean? Is there any way to determine how
important this CV is in terms of the amount of variation it explains?
I know these are relatively basic statistics questions, but these tests
are new to me. I'd really appreciate any advice you might have or
information about resources that might be helpful.
Thank you!
Kim
[email protected] <mailto:[email protected]>
--
Dennis E. Slice
Associate Professor
Dept. of Scientific Computing
Florida State University
Dirac Science Library
Tallahassee, FL 32306-4120
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Guest Professor
Department of Anthropology
University of Vienna
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