> -----Original Message-----
> From: Analysis of animal remains from archaeological sites
> [mailto:[log in to unmask]] On Behalf Of D.C. Orton
> Sent: 11 January 2008 12:24
>
> Chi-squared and Fisher's both have sample size built into the
> calculations. Sample size with fragment counts is a product of
> fragmentation as much as of the original number of independent
> data points. Thus the test statistics are to a great extent a
> measure of how smashed up your bones are rather than anything
> else. Simple thought experiment: you have two element types in
> two units. Element A appears more common in unit 1, and
> element B in unit 2. You use chi-squared to compare
> frequencies but get no significant results (say, p = 0.2). So
> you smash each specimen into n pieces, run the test again and,
> hey presto, p = 0.01. Same pattern, bigger sample.
David, you are right of course. My thinking was muddled.
> Incidentally, Andrew, I'm well aware that you know far more
> about statistics than I do, but I just can't see any way round
> this problem.
Most of my statistical work is model-based, which is probably why I
wasn't thinking clearly about the classical inference problem here.
Phi-square or Cramer's V have been sugggested, but although they offer a
measure of association independent of sample size, the fragmentation and
sample size issue also muddies things here. Two assemblages with
identical counts, but one consisting of fragments and the other whole
bones will show strong association with these procedures, even though
they clearly differ. These and almost all other standard statistical
tests assume indpendence of observations, which is only going to occur
under very specific circumstances for zooarchaeological assemblages, and
they are therefore generally not useful for hypothesis testing, though
*some* of the test statistics may be useful for comparison of *some*
assemblages.
I think a model-based approach is what is required, which explicitly
says what is happening with the taphonomy, and thus allows for the
likely non-independence of the observations. Alan Rogers' Analysis of
bone counts by maximum likelihood
(http://www.anthro.utah.edu/~rogers/abcml/) does this, but only for a
specific range of situations and it has rather strong requirements for
knowledge about potential taphonomic processes. As far as I am aware no
one else has developed similar methods.
Andrew
--
Dr. Andrew Millard [log in to unmask]
Durham University
Senior Lecturer in Archaeology Tel: +44 191 334 1147
Deputy Director of Combined Honours Tel: +44 191 334 3006
Archaeology: http://www.dur.ac.uk/archaeology/
Combined Honours: http://www.dur.ac.uk/combined.honours/
Personal webpage: http://www.dur.ac.uk/a.r.millard/
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