Re: How to compare with one number?

From: Bruce Weaver (bweaver_at_lakeheadu.ca)
Date: 03/21/05


Date: Mon, 21 Mar 2005 16:22:03 -0500

davegb wrote:

> Thanks again, Bruce.
>
> Bruce wrote:

Actually, Bob Wheeler wrote it, so thank him. (This is what happens
when there are too many BW's in the room.)

> That is a sensible solution, but he asked for one number, which is
> impossible without imposing an additional restriction.
>
> What kind of restriction?

I'll let Bob take a crack at that one.

>
> Also, I've done some internet research on Binomial Distribution. I
> found this:
>
> Note: The sampling distribution of a count variable is only
> well-described by the binomial distribution is cases where the
> population size is significantly larger than the sample size. As a
> general rule, the binomial distribution should not be applied to
> observations from a simple random sample (SRS) unless the population
> size is at least 10 times larger than the sample size.
>
> This sounds to me like it's saying that the Binomial Distrtibution
> doesn't apply in those counties with a client base of 4 and an
> occurence of one. Leaves me with the same problem I had in the first
> place, unless I'm misinterpreting it. Can you explain?
>

The sample size this is referring to would be all 4 clients in that
smaller county, not the one who had the event of interest. The size of
the population is debatable, I think. On the one hand, someone might
want to define it as the number of clients currently in the system in
County X. By that definition, the sample = the population = the 4
clients. On the other hand, you might wish to make inferences about the
future (not just the current population). The size of the current plus
future population of clients in County X is unknown, but could well be
large enough to warrant use of binomial confidence intervals.

Hope this helps.

-- 
Bruce Weaver
bweaver@lakeheadu.ca
www.angelfire.com/wv/bwhomedir


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