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

----- Forwarded message from Singleton -----

From Fri Dec 20 19:55:43 1996
Message-Id: <>
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
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