On Tue, 20 Jun 2000 [EMAIL PROTECTED] wrote:
> Hello, I "inherited" the reporting system for our escapes and have some
> questions about how data has been reported in the past.
>
> First, I have a question about the formula used to calculate escape
> rates which is (escapes)/(average daily population - escapes). Then
> this is reported as a rate per 100 inmates. Isn't this actually a ratio
> of escapees to non-escapees.
Right. AKA an odds ratio (before multiplying by 100).
One might take the reciprocal (e.g., 1/0.0008 = 1,250, from your .08 per
100 below) as representing the odds AGAINST escaping (1250:1), rather
than the odds IN FAVOR OF escaping (0.08 chance in 100, or 1:1250).
> Maybe I'm just picking at semantics, let me know. I thought that the
> formula for rates was (a/(a+b)) * k where the numerator is included in
> the denominator.
Right again.
> Then I also have a rule of thumb question. At what point is a rate
> considered unreliable or a useless piece of information? My example
> again and remember that it uses the "formula" I first presented above.
> The previous reports show rates of .44 per 100 or .08 per 100, etc.
> Of course I find this comical because I imagine that .44 means an
> escapee with only a torso, legs and head and .08 as an escapee with
> only the torso!
Mmm. Only the left shin, I would have thought...
But this is no more comical than expressions like 0.44% (do you remember
the old Ivory Soap ads, claiming that Ivory was 99.44% pure? Only they
wrote it as a fraction, 44/100.)
"Unreliable" or "useless"? Well, the basic graininess in a rate
is one escapee more (or less) than was reported. A rate of .08 per 100
is about 1 out of 1250. If the data on which the rate was based were 1
escapee out of 1250 inmates, one cannot _reliably_ tell the rate from
zero. If the data were 13 escapees out of 16,200 inmates, one would have
more faith in the rate, at least insofar as representing a small value
different from (not equal to!) zero. Unfortunately, the rate itself
does not tell one how grainy the data were.
> But, many folks around here take those numbers to indicate that the
> escape "rate" has decreased substantially!
Well, in fairness, .08 is only 20% -- that is, 1/5 -- of 0.44. Dividing
one's number of escapees by 5 might well reflect substantial success, in
some terms. But part of the point, as Dennis has mentioned, is whether
the comparison is between the same institution at two different times
(then one could suppose the "average daily population" to be, if not
essentially constant, at least comparable), or between two different
institutions with very different sizes of population.
> I have seen CDC tables with a caveat regarding
> small rates and will pull those as evidence for my argument.
>
> So here's a real life problem for my colleagues out there. I am going
> through all the statistics books in my office and have started to
> search for references to present my case. I'm not kidding because I
> was told that this is the way it has always been calculated so don't
> mess with tradition.
Sounds depressingly realistic.
> If anyone has any references, suggestions, openings for positions,
> cites [ Sites? -- dfb ] to search, etc. I would really appreciate it.
> Many thanks in advance, Fran
------------------------------------------------------------------------
Donald F. Burrill [EMAIL PROTECTED]
348 Hyde Hall, Plymouth State College, [EMAIL PROTECTED]
MSC #29, Plymouth, NH 03264 603-535-2597
184 Nashua Road, Bedford, NH 03110 603-471-7128
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