[R] quick question about binary data

[(Ted Harding)]

On 15-Feb-11 09:35:08, Jonathan Hughes wrote:
> Dear all,This is both an R and a statistics question. I want to test
> whether males and females of a given species tend to co-occur in a
> given sampling unit more frequently than expected by chance. I'm
> thinking about using a binomial distribution with p as the sex ratio of
> the entire population. So, even though the population sex ratio is
> close to 50:50, each sampling unit would have disproportionately more
> males than females. Given that the test is not about p per se, how
> would you go about testing this hypothesis?
> (by the way, the total number of individuals in each sampling unit
> might not be the same).
> Thanks!Jonathan

I'm not sure of your logic in stating that "each sampling unit would
have disproportionately more males than females", given that you
apparently expect that "males and females of a given species tend
to co-occur in a given sampling unit more frequently than expected
by chance."

The extreme case of co-occurrence between males and females would
be where, with equal numbers of M & F in the whole population,
the individuals form couples so that each M is paired with a
unique F. Then every samnpling unit would contain exactly 50:50
of M and F. This would be an instance of failure of an "independence"
assumption involved in a Null Hypothesis of "expected by chance".
An appropriate test here would be that (for instance) a significantly
*small" value of a chi-squared statistic would be evidence against
random occurrence of individuals (from a 50:50 population) in the
sampling units.

You may alternatively mean that Males tend to co-occur with other
Males where some Males starting chasing Females (prompting other
Males to home in as well). A model for this would have to be more
complicated, since with a 50:50 M:F population, when sampling units
have a majority of M resulting from this "clustering", the other
Females must be somewhere. This aspect of the matter is not covered
in your description. Then we certainly have nonindependence between
Males, but what about the Females? Do they also form clusters out
of solidarity (non-independence again), or do they disperse randomly
for the sake of a quiet life or to avoid competition from other
Females?

It would help a lot if you could expound the potential mechanisms
in more detail!

Hoping this helps,
Ted.

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Date: 15-Feb-11                                       Time: 10:57:38
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