From firstname.lastname@example.org 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'?
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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!-)
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