Re: How to determine if a number is statistically meaningful
From: Bob Wheeler (bwheeler_at_echip.com)
Date: 03/24/05
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Date: Thu, 24 Mar 2005 08:14:49 -0500
Richard Ulrich wrote:
> On Wed, 23 Mar 2005 17:56:32 -0500, Bob Wheeler <bwheeler@echip.com>
> wrote:
>
>
>>>>is, in a county that has 4 children in care, and one has such an
>>>>occurrence, shows a 25% occurrence rate, yet is it meaningful? The
>>>>lowest possible rate for that county, if they have any occurrences, is
>>>>25%. It probably doesn't mean much.
>>>
>>>
>>>Right. 1 out of 4 is not particularly "unusual" to observe,
>>>for a binomial proportion of 4%. But how are you going to
>>>present that?
>>>
>>
>>
>>Huh? The probability of zero occurrences in four is about 0.85 given
>>p=0.04; thus the probability of one or more occurrences is about 0.15,
>>which is rather large to say that it "doesn't mean much."
>
>
> "Huh?" back at you.... Is there a typing error here, Bob?
> Did you mean to say, it "is rather *small*" to say that it
> doesn't mean much? [Or am I parsing something wrong?]
>
> We are looking at a nominal probability that is "about 0.15",
> right?, before any correction for multiple tests?
> This is out of a list of results for multiple counties, and
> for multiple parameters (not named so far).
>
> If the probability was 0.05 or 0.01, it would be more unusual.
>
> The LARGER it is, the more apt you are to conclude that
> it doesn't mean much. Is 0.15 small enough to be concerned
> about? Well, potentially, yes, if you want to scrape that far.
> -Yes, if there were few results to point at, for anything else.
> -No, if this would distract from results that were much more
> serious.
>
Right, I meant "small." I would not use the magic numbers (5% or 1%) in
this case since the probability must be weighted to determine an action
-- we are not making a significance test here. In the particular case of
a population of 4, I would not ignore a probability of 0.15, and in
general determine the "intervention probability level" by the available
resources: in this case the number of counties that can be examined
within budget. If the "bad things" are serious, such a child abuse, I
would examine any county with a probability considerably larger than a
magic number. It is also important to note that the appropriate p is not
0.04, but some smaller value based on social considerations.
-- Bob Wheeler --- http://www.bobwheeler.com/ ECHIP, Inc. --- Randomness comes in bunches.
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