Re: How to compare with one number?

From: Bob Wheeler (bwheeler_at_echip.com)
Date: 03/21/05 

Date: Mon, 21 Mar 2005 13:02:03 -0500

Bruce Weaver wrote:
> davegb wrote:
>
>> I'm definitely not a statistician, so I'm looking for some help. If
>> I've posted to the wrong group, please re-direct me to the correct NG.
>> I am working for the state Child Welfare Dpt., doing some moderately
>> sophisticated Excel spread*** for them. I've been asked to create a
>> comparator to give them one number to rank the 64 counties in certain
>> state and federal mandated areas. I'm sure I'm not the first person to
>> have this need.
>> In each of the 64 counties, we measure how many clients we have total,
>> how many had a certain event occur while they were our clients. We post
>> these numbers in a spread***, along with the percentage of occurences
>> within each county and percentage that occured in county compared to
>> the total clients in state. The problem it this. In the large counties
>> (population wise), we have statistically significant numbers of clients
>> (100's or even 1000's) so the percentage of occurences is relevant. In
>> some of the smaller counties, we may have as few as 3 or 4 clients
>> (actually, some have zero, but they're not the problem). If there is an
>> event occurence with 1 client out of 4, that's 25% of the county client
>> population, and extremely large number in this dataset. It looks bad in
>> the state percentage column until you look at total number of clients
>> in that county.
>> I'm looking for a way to create an additional column on the spread***
>> with one number that takes into account the total number of clients,
>> and reflects the fact that even thought the percentage might be high,
>> the sampling is too small to be revelant.
>> One thing that's occured to me is to create a formula that sets a
>> minimum number of clients, and if it is below that minimum, shows a
>> test message saying something to the effect of "Sampling not relevant".
>> But if there's a statistically better way of doing this, I'd like to
>> use it.
>> Thanks for your help. If my explanation is unclear, please ask for more
>> information so you can suggest ideas.
>>
>
>
> A good graph showing the (binomial) proportions with their 95%
> confidence intervals would get the point across, I think. The
> proportions from small counties will have much wider confidence
> intervals than those from the large counties.
>

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

-- 
Bob Wheeler --- http://www.bobwheeler.com/
         ECHIP, Inc. ---
Randomness comes in bunches.
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