But what does this (in)dependence really mean?
Can it change on conditioning?
Suppose that we take into account a plausible confounder: defective
equipment. Suppose blacks are more likely to have "defective equipment
(broken light, etc.). Suppose we find that percentage who are black among
those stopped for defective equipment is the same as the percentage who are
black among those having defective equipment. Now we have independence at
one level and non-independence at another.
This seems related to Simpson's paradox.
In any event, it seems that independence can be conditional.
Is this so? If so, where is this discussed in more detail?
"Lise DeShea" <[EMAIL PROTECTED]> wrote in message
[EMAIL PROTECTED]">news:[EMAIL PROTECTED]...
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:
<SNIP>
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
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