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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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KINGB@WCSUB.CTSTATEU.EDU

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
(kingb@wcsub.ctstateu.edu)






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