Subject: The 'New Statistics' of resampling, bootstrapping...

From: [email-masked] (Ghermay Araya)
Date: 26 Sep 1993 19:06:32 GMT

Resampling, (bootstrapping, etc.), is revolutionizing the practice of  
statistic, and the way it is taught.  For articles, and information on  
software + books, results of classroom trails, and descriptions of pending  
projects in which teachers can become involved, contact the University of  
Maryland's Resampling Project. We are especially interested in class  
testers.  Contact:
	 Resampling Project,
	 attn. P.G. Bruce
	 College of Business
	 University of Maryland,
	 College Park, MD  20742. 
          Phone: 703-522-2713
	 FAX: 703-522-5846
	 email: [email-masked] 
	 
	 (mark attn. P. G. Bruce). 
         please provide  both  postal and email address.
	 
HERE ARE A COUPLE OF PUZZLES TO GET YOU STARTED.
SOLUTIONS WILL BE POSTED IN TWO(2) DAYS:

Two Puzzles:  Does your reasoning lead you astray on the following  
puzzles?  Most people's does.  In a couple of days, we will post  
resampling (simulation) solutions that illustrate how such an approach,  
though less sophisticated than a formulaic one, yields correct answers and  
offers fewer opportunities to go wrong. 

1)  Three identical boxes each contain two coins. In one box both are  
pennies, in the second both are nickels, and in the third there is one  
penny and one nickel. 
        
A man chooses a box at random and takes out a coin.  If the coin is a  
penny, what is the probability that the other coin in the box is also a  
penny?"   [from Goldberg, 1960, p. 99]

2)  A bag contains one counter, known to be either white or black. A white  
counter is put in, the bag shaken, and a counter drawn out, which proves  
to be white.  What is now the chance of drawing a white counter?  From  
Lewis Carroll's PILLOW PROBLEMS (1895/1958) (p. 2, via Martin Gardner)

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From: [email-masked] (Sean Eddy)
Date: Mon, 27 Sep 1993 10:52:30 GMT

In article <[email-masked]> [email-masked] (Ghermay Araya) writes:
  >statistic, and the way it is taught...

If you're trying to demonstrate the need for a "New Statistics", maybe
your examples are poorly chosen? Both of them are classic toy problems
in conditional probability and are trivially solved with Bayes' rule.

  >penny?"  >[from Goldberg, 1960, p. 99]

2/3.

  >Lewis Carroll's PILLOW PROBLEMS (1895/1958) (p. 2, via Martin Gardner)

Insufficient information, but if the probabilities of the bag
containing white vs. black initially are equal (0.5), then again the
answer is 2/3.

--
- Sean Eddy
- Laboratory of Molecular Biology, MRC, Cambridge UK
- [email-masked]