🚀 go-pugleaf

Andy,

I wrestled with a similar problem to yours earlier in the year. Let
me sketch my problem and then discuss possible approaches.

In 1967 'every' seven year old in my State was examined for evidence
of the presence of asthma. In 1992, a new study was proposed in
which a sample (i.e. not the whole 'population') of seven year olds
was to be selected with the aim of comparing the incidence of asthma
in seven year olds in 1992 with the incidence in seven year olds in
1967.

I was asked to provide a value for the minimum sample size for the
1992 sample for the comparison of the proportion of children with
asthma in 1967 with the expected proportion of children with asthma
in 1992. Should I regard the observed proportion from the 1967 data
as the expected value in 1967, and therefore having a variance of
zero? Alternatively, should I regard the collection of children
present in 1967 as a particular realization of a potentially
infinite population, and assume the observed proportion in 1967 is a
value of a binomial variate with sample size equal to the observed
population size of children in 1967?

In my case, the decision was not merely an academic exercise. If I
took the latter course, then the minimum sample size I would be
recommending would be about 25% higher than would be the case if I
assumed no random variation in the 1967 readings. This translates
into some thousands of dollars additional cost in data collection.


In your case, Andy, it would seem that you have two options. One is
to presume that the statistics measured on your data are population
values, and therefore no inferential statistics is required. The
second is to assume that the birds on each island are chance
realizations from an infinity of possibilities (dictated by chance
elements of genetics and environmental factors), in which case,
standard inferential methods assuming infinite populations are
applicable.


My view is that the decision is one for the investigator to make,
rather than for the statistician to make. In my case, I took great
care to explain to the chief investigator the two options and what
underlay these options. Armed with this understanding, I left the
decision to the group of investigators.


I look forward to your comments and the comments of others on my
solution.

Regards,  Glen
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|  Glen McPherson            |                                   |  _--_|\  |
|  Department of Mathematics |-----------------------------------| /      \ |
|  University of Tasmania    |               E-Mail:             | \_.--._/ |
|  Australia.                | mcphers@hilbert.maths.utas.edu.au |       *  |
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