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 (firstname.lastname@example.org)