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Topic: first day activities, one more time...
Replies: 1   Last Post: Aug 31, 1996 3:50 PM

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Posts: 144
Registered: 12/6/04
first day activities, one more time...
Posted: Aug 28, 1996 5:38 PM
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I broadcasted the following item on the edstat-l list a day or two ago.
Bob Hayden told me that most of that discussion took place on apstat-l;
so, for whatever it's worth, here 'tis:
A week ago, Beth Chance wrote:

> I also like to use some interesting
> activities the first day. One of my favorites is the Capture/
> Recapture activity with Goldfish precisely because I do
> think it shows students some of the "power" of statstics in
> a very simple algebraic idea.

I think she's right, and I intend to try it this year. What's not so
obvious from the usual activity, however, is how good the estimate N-hat
= (first-capture sample size)*(recapture sample size)/(number tagged fish
in recapture sample) is. There's a nice little article in the Spring
1996 issue of _Teaching Statistics_ by Roger Johnson (Carleton College)
entitled "How Many Fish are in the Pond?" Johnson offers a Minitab Exec
macro that simulates the process of generating N-hat.

What will surprise many students is the fact that, as Johnson puts it,
"...there is substantial bias and variability in using N-hat to estimate
N" and this bias and excessive variability is obvious when you run
Johnson's macro. Johnson then mentions a better estimator of N, shows
results from an analogous simulation, and gives a reference where one can
learn more about it.

Many of us have read that capture/recapture methods are planned for use
to improve the undercount in the U.S. Census. Johnson also mentions that
it has been used to estimate the number of prostitutes in Glasgow!

Bruce King
Department of Mathematics and Computer Science
Western Connecticut State University
181 White Street
Danbury, CT 06810

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