RE: random samples

[F. James Rohlf]

Title: random samples

That is an important concern. Assumptions of random independent sampling are quite fundamental. The use of nonparametric methods is not a solution as their use requires the same assumptions. The issue is not just for morphometric studies!

 

 In the "comparative approach" one samples from species across a phylogeny so the samples are not independent but if one assumes a particular phylogeny and evolutionary model then one can try to take that into account. The problem in your question is that 'nonrandom' is so ambiguous. If one knew precisely the way in which the observations were not independent then one can do something correct for it but just "nonrandom" gives one nothing to work with.

 

In the case of museum collections, the samples are probably haphazard at best. One can still use data analysis methods (cluster analysis, ordination methods) to look for interesting patterns. The problem is when you try to make some inference. Is the pattern "real" or is it just an artifact of how specimens are collected?  Impossible to answer unless one is able to make some assumptions about how the data were collected.

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F. James Rohlf, Distinguished Professor,
Dept. Ecology & Evolution, Stony Brook University, Stony Brook, NY 11794-5345

 

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From: Henderson, Andrew [mailto:[EMAIL PROTECTED]
Sent: Monday, April 11, 2005 7:44 AM
To: morphmet@morphometrics.org
Subject: random samples

Dear Morphometricians: here's a thing that has been troubling me, but first some background. I am a plant systematist using traditional morphometrics to produce revisions of genera. I use herbarium specimens as my data source, and I use morphological data. I use statistical inference (t tests, ANOVA, MANOVA, etc) to help make systematic decisions. For example, do two species differ in some variable, or is some environmental variable (e.g., elevation) associated with some morphological variable.

My question is, samples of herbarium specimens can never be random samples. In fact, far from it. Does this mean that my statistical tests are invalid? If I take a sample of herbarium specimens and say that species A differs significantly from species B in some variable, then do I violate the assumptions of the test because my sample is not randomly selected?

My knowledge of statistics is limited, but my impression is that some statisticians insist on random sampling (e.g., Marcus) while others appear to place far less emphasis on this. Some authors such as Pielou make the distinction between interpreting the data at hand using cluster analysis and ordination, and using multivariate statistics based on inference, as if these were two separate fields of study. In the literature, my impression is that the problem of random sampling is largely ignored in morphometric studies of plants.

Can a case be made that a sample of herbarium specimens is random? Or is this kind of sample a 'convenience sample'. If so, can one proceed with inferential statistics?

Should I use non-parametric statistics?
Or should I be using some kind of randomization test on my data? If so, which?

Thanks in advance. Andrew Henderson
[EMAIL PROTECTED]