What Don's post lacks in speed in certainly makes up in thoroughness.
This posts concerns Jan De Leeuw's definition, in which two variables
were not independent if the expected variance changed. Maybe a good
example is IQ scores, in which the expected mean does not vary with
gender, but the standard deviation does. Does IQ depend on gender?
Don, if I understand him correctly, is saying that we can define
independence any way we want. While technically correct, I think it odd
(after reading Jan's post) to define independence completely on the
average. Why not variance, or why not median, or even mode? In light
of Jan's comment, I think my intuitive understanding of the phrase
"Variable A is independent of Variable B" is that the probability
distribution of A does not change with the value of B.
If one wanted to talk about the expected average of A being independent
of B, one could say that directly. So, I conclude that the average IQ
is independent of gender, but IQ is not.
Bob
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