At 08:05 09/11/2007 +1100, Harry Feldman wrote:
>That geographical area with about 400 was just one I noticed in the
>published output. A little later when I got into the dataset and ran a
>table, I found areas with as few as 4,....
OK. The fact that 'units' as small as that exist does not, in itself,
prove much - but, as you will have seen, others have indicated that they DO
have very small 'units of interest', so that tends to put paid to sample
surveys...
... or does it? Is the problem perhaps that we are trying to make the
Census be 'all things for all (wo)men'? Those with an interest in 'very
small units' may well only be interested in very limited bits of
information about those units. Is it necessarily appropriate to ask an
additional 50 million (or whatever) people _all_ of the questions just to
satisfy that need? If a 10% 'all questions' sample survey was undertaken
on the entire population in order to answer 'large unit questions', that
would leave an awful lot of money with which people could address much more
specific local 'small unit' questions. Just a thought!
>It's curious you mention oversampling particular areas of interest, as we
>had a seminar here a few weeks ago on exactly that subject in the context
>of attempts to oversample parts of New Zealand thought to have
>concentrations of Maori. Although I can't claim to understand the
>reasoning very well, as I'm not 'that kind of statistician', what they
>found was that it makes a big difference how you go about it and in some
>approaches larger samples provide even higher standard error than smaller
>ones. I can probably dig up some references, or at least a link to the
>presentation, if you're interested.
I presume that various 'practical considerations' must underlie that
'result'. Even though I'm no theoretician, if all other things were equal,
I just can't see how sampling error could increase with increasing sample size!
>One of the things about refusals is that we don't have data about them or
>about what motivated their refusal. When one woman aged 25-29 in Melbourne
>evades the interviewer, we lose data pertaining to, say, 250 other such
>women who may or may not share whatever it was about the refuser that led
>her to refuse. To get the same effect in the Census, each and every one of
>those persons would have to also refuse. Is that any clearer? To be
>honest, I'm no surer of my ground here than you are, but that's more or
>less my reasoning and it makes sense to me. I hope someone on this list
>who's clueyer about sampling than I am will set one or both of us straight
>on this matter.
I also hope that there is such a person, since I remain (at least
'intuitively') unconvinced by your argument. In essence, I'm not really
convinced that you are saying any more than that, when one undertakes a
sample survey, there will be sampling error.
>Similarly with the sampling error, my understanding is that because of the
>diminishing returns, even if you had a 90% sample, estimates of small
>populations would remain too volatile to trust.
Well, we're almost back there to the (usually perpetual!) discussion about
whether concepts analogous to sampling error, confidence interval etc. can
be applied to 'whole population data'. In a literal sense, those concepts
obviously have no meaning when one has data on a whole (or nearly a whole)
population. However, if one considers that the actual 'state of the
population' at the moment of a Census will have been influenced by chance
factors (i.e. that the data would be different with each hypothetical
're-run of history'), then such concepts come to have more meaning - and
would, amongst other things, provide a mathematic basis for confirming that
we can't be very confident in data based on very small numbers.
Kind Regards,
John
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