Or maybe I didn't understand Don's response to Jan. Pressing ever
onward, though....
I had suggested using
> DEFINITION: There is a *relationship* between the vari-
> ables x and y if for at least one pair of values x'
> and x" of x
>
> E(y|x') ~= E(y|x").
as opposed to Don's
>> DEFINITION: There is a *relationship* between the vari-
>> ables x and y if for at least one value x' of x
>>
>> E(y|x') ~= E(y)
We agree that the two are mathematically equivalent. But I think
mines better, psychologically. I think in terms of my definition and I
actually had to translate Don's definition to mine in order to
understand why his definition was true.
Don suggests that mine works well for the case when variable X can take
only two values. But that is not how I meant it, nor how I stated it.
My definition captures the continuous case too.
Now let's talk examples. Don offers the following:
For example, after several visits to a new bank a
person may observe, "The earlier in the morning I go to the
bank, the less time I have to wait to be served." ("Duration
of waiting time" is the response variable and "bank arrival
time" is the predictor variable.)
Don concludes that his definition better suits this example. But I
disagree. Or I just think of things differently. The key is this.
When the person concludes that they have to wait less time in the
morning, what are they comparing that to?
.
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Your supposed to be answering this question
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If they are comparing that to when they go at a time other than the
morning, the example follows my definition. x' versus x'' -- morning
versus not morning -- 10:00 versus 2:00. To fit Don's definition, they
would have to be comparing that to the average time they wait, overall,
including morning.
Now, to me, it makes more sense to compare morning to not-morning; the
comparison from morning to overall is not how I think.
Or maybe I didn't understand this either. It's just my thought. But I
think this is an important topic -- how basic ideas of statistics are
defined, and how to define them in terms of how people think. I like
Don's work a lot, because he addresses these issues, has useful things
to say, and makes me think.
Bob Frick
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