```Date: Dec 20, 1996 10:04 PM
Author: Bob Hayden
Subject: conditional r. f.

----- Forwarded message from Singleton -----From apstat-l-owner@cln.etc.bc.ca Fri Dec 20 19:55:43 1996Message-Id: <32AF9BCC.4BC1@erols.com>Date: Thu, 12 Dec 1996 00:44:44 -0500Dear GroupI'm on a curriculum committee for an AP-Stat course coming on line nextyear.  Looking at the Acorn book under I.E.2. What are 'conditional'relative frequencies and 'associations'?----- End of forwarded message from Singleton -----This just arrived, more than a week after its date!They are the empirical, descriptive alalog of conditionalprobabilities and what we test with chi-squared on a contingencytable.  For example, suppose a college faculaty looks like this:		Faculty Members		Male	FemaleAssistant Prof.	23%	48%Associate Prof.	52%	39%Full Professor	25%	13%	 If we pick a male at random, the probability he is a full professor is0.25.  If we pick a female at random, the probability she is a fullprofessor is 0.13.  This is the probability of being a full professorgiven that the chosen person is male/female.  And there seems to be anassociation between sex and rank.BTW, since Ph.D.s are not randomly assigned to colleges, we have to becareful about interpreting data like this.  The table above could bethe result of policies that make it hard for women to get promoted.It could also be the result of intense efforts to recruit womenfaculty in recent years!I think it is essential to do a lot of work with concrete data likethis if you are going to do conditional probability.  It's much moreconcrete.  There is a reasonable treatment of these topics in Siegeland Morgan.  The Minitab (sub)commands are "rowpercents" and"colpercents" on "table".Since alpha is a conditional probability, you probably want to doconditional probability if you want to do hypothesis testing!-)      _     | |          Robert W. Hayden     | |          Department of Mathematics    /  |          Plymouth State College MSC#29   |   |          Plymouth, New Hampshire 03264  USA   | * |          Rural Route 1, Box 10  /    |          Ashland, NH 03217-9702 |     )          (603) 968-9914 (home) L_____/          hayden@oz.plymouth.edu                  fax (603) 535-2943 (work)
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