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 1996

Message-Id: <32AF9BCC.4BC1@erols.com>

Date: Thu, 12 Dec 1996 00:44:44 -0500

Dear Group

I'm on a curriculum committee for an AP-Stat course coming on line next

year. 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 conditional

probabilities and what we test with chi-squared on a contingency

table. For example, suppose a college faculaty looks like this:

Faculty Members

Male Female

Assistant 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 is

0.25. If we pick a female at random, the probability she is a full

professor is 0.13. This is the probability of being a full professor

given that the chosen person is male/female. And there seems to be an

association between sex and rank.

BTW, since Ph.D.s are not randomly assigned to colleges, we have to be

careful about interpreting data like this. The table above could be

the result of policies that make it hard for women to get promoted.

It could also be the result of intense efforts to recruit women

faculty in recent years!

I think it is essential to do a lot of work with concrete data like

this if you are going to do conditional probability. It's much more

concrete. There is a reasonable treatment of these topics in Siegel

and Morgan. The Minitab (sub)commands are "rowpercents" and

"colpercents" on "table".

Since alpha is a conditional probability, you probably want to do

conditional probability if you want to do hypothesis testing!-)

_

| | Robert W. Hayden

| | Department of Mathematics

/ | Plymouth State College MSC#29

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