>If the question about is simply about
>whether there is a difference in the proportions of recovered material,
>then NISP and chi-squared (or Fisher's exact) test are sufficient:
I'm sorry, but I'm going to have to contest even this.
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. Only
it's not really bigger, because the specimens aren't independent. That's
effectively what we're doing if we use these tests on fragmentary
assemblages.
Phrasing the question in terms of recovered material doesn't help - even if
we're only interested in the number of individual pieces coming from each
element type (or each taxon, if that's what you're looking at) we still run
into the non-independence problem. You may have five frags of element A and
fifteen of element B but your sample size is only twenty if you're happy to
accept that the data are non-independent. In which case you shouldn't be
using the test. I'd have no objection to using phi/Cramer's V to describe
the strength of association, but the moment you move into inferential stats
you're on the path to a bizarre situation in which one can draw conclusions
more easily from highly fragmented assemblages than from pristine ones.
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. And
I'm not trying to advocate minimum number counts either, just pointing out
that they have a different set of statistical problems.
David
they
>test whether the proportions in two assemblages are within the expected
>random variation after two sets of animals have been subject to the same
>butchery, taphonomic and identification processes. MNE and MAU are
>derived measures that attempt to account for differing taphonomic
>processes, including fragmentation, and as has been noted in this
>discussion their statistical properties are not well understood, but I
>am not clear whether they are relevant.
>
>Andrew
>
|