Re: basic stats question

[Lise DeShea]

Re probability/independence, I've found that the most effective way to communicate this concept to my students (College of Education, not heavily math-oriented) is the following:

Consider the student population of your university.  Perhaps there is a fairly equal split of males and females in the student body.  Now, put a condition upon the student body -- only those majoring in, say, psychology.  Do you find the same proportion of students who are male within only psych majors, compared with the proportion of students in the entire student body who are male?  If gender and psych major are independent, then the probability of a randomly chosen person at the university being male should equal the probability of a randomly chosen psych major being male.  That is,

p(male) = p(male|psych major)    <==(p. of male, given you're looking at psych majors)

Then you can move to an example of racial profiling.  Out of all the people in your city who  drive, what proportion are African-American?  [p(African-American).] Now, GIVEN that you look only at drivers who are pulled over, what proportion of these people are African American?  [p(African-American|pulled over).]  If being black and being pulled over are independent events, then the probabilities should be equal. 

You can illustrate this graphically by drawing a  large box to represent all the drivers, then mark the proportion representing African-American drivers.  Then draw a smaller box representing the people being pulled over, with a proportion of the box marked to represent the African-American drivers who are pulled over.  If the proportions of each box are equal, then the events are independent.

So now,  I would welcome comments from the more mathematically/statistically rigorous list members among us!

~~~
Lise DeShea, Ph.D.
Assistant Professor
Educational and Counseling Psychology Department
University of Kentucky
245 Dickey Hall
Lexington KY 40506
Email:  [EMAIL PROTECTED]
Phone:  (859) 257-9884