[EMAIL PROTECTED] wrote:
> Gus,
>
> You need to explain what you did. You keep changing your story or expressing
> it in such abstract terms that it is not clear what you did.
>
> > >
> > > If you simply counted every 5th or tenth value then you are collecting
> > > uniform subsamples of a normal distribution. This will not work because
> you
> > > are not allowing for coincidences of the extremes of x1 and x2. They are
> > > still very rare and do not tend to occur together. Thus you are merely
> > > subsampling uniformly from normal distributions! In doing so, you are
> not
> > > filling out the corners of the cross tabulation of x1 and x2. There will
> > > still not be data in which similar values of x1 and x2 are crossed in
> their
> > > extremes. So we need to talk about what we mean by uniform
> distributions.
> >
>
> > That is not what I meant, so let's back up. What I mean by a uniform
> random
> > variable in one dimension is something that has the probability density
> > 1/(b-a) I_{b-a}(x), that is, the probability that a realization of this
> random
> > variable falls into any subinterval of [a,b] of length delta depends only
> on
> > delta,
> > not on the endpoints of the subinterval. The excel function rand() spits
> out
> > such uniformly distributed random variables (on [0,1]).
>
> Gus, it is not so complicated as you are making it. A uniform distribution
> is simply a range from which each interval is sampled an equal number of
> times. The point of using uniform distributions is to allow the extremes of
> y to be determined by the conjunction of the most extreme similar values of
> x1 and x2. When this occurs, as in a manifold, then the highest values of y
> will happen when the highest values of x1 and x2 are added. The lowest
> values of y will occur when the lowest values of x1 and x2 occur together.
> If you sample enough to allow this to happen, then x1 and x2 will be
> positively correlated in the extremes of y. It is simple logic.
>
> >
> > Let's say I collect a sample of size 100 from the two uniformly
> distributed
> > random variables x1 and x2 and I compute y = x1 + x2. In this sample y is
> > caused by x1 and x2, the way I understand it. (Do you agree?)
>
> Yes, this is the model of causation. y=x1+x2 where x1 and x2 are uniformly
> distributed. We expect therefore to have incidents in which the extreme
> similar values of x1 and x2 are paired to produce the theoretical highest
> and lowest values of y that are possible. If not enough data is gathered to
> allow x1 and x2 to be crossed at all their levels, then CR will not work
> because the extremes of x1 and x2 are not paired. This would be a case of
> sloppy sampling, not of invalidation of CR.
>
> >
> > I don't want to give the entire sample here, but let's say it looks like
> this:
> >
> > Row x1 x2 y
> > 1 0.47 0.15 0.62
> > 2 0.71 0.43 1.14
> > 3 0.77 0.87 1.64
> > ...
> > 100 0.50 0.74 1.24
>
> Ok.
>
> >
> > Now suppose I take a subsample from this, for instance,
> > I select rows 2, 7, 16, 33, 39, 54, 66, 71, 90, 99.
> > In this subsample, is y still caused by x1 and x2 or not?
>
> I ask AGAIN... on what basis are chosing to select rows 2,7,16, 33.... 99?
Look, why would that matter? I am _not_ asking will CR stiill work, I am
only asking, is y still caused by x1 and x2? And are x1 and x2 the causes?
> I know for sure that if you simply trim the sparsely elaborated tails off y,
> that CR works on average. If all you are doing is chosing ten rows out of
> 100, I must ask why those ten? Why cut the data down from 100 observations
> to just 10? Do not try to snowball me with abstractions. I am far to old to
> be fooled by that kind of sophistiry. Anyway, I am not that stupid with
> mathematics. I will trace down your abstractions to their roots. How do you
> think I managed to discover CR? You still do not seem to understand that the
> point of trimming and the point of uniform causes is to allow for
> combinations of the extrems of x1 and x2. Normal distributions do not allow
> for such extremes. Using them is to use a rigged test. If there is no or
> very slim possibilities of the pairing of extremes of x1 and x2 then they
> can not be correlated. REAL scientists can ask the question, would I expect
> the causal pattern to occur if I paired like extremes of the causes. All
> honest scientists would say yes! Does your mysterious subsampling procedure
> allow us to pair like extremes of x1 and x2 enough times to see the
> correlation that I predict. If not, your test is rigged and you are cheating
> or ignorant of what you do. Which is it?
Evidently I am either ignorant of what I am doing or using a different
definition
of causality. I ask again: Does causation transfer to a subset? And please try
to answer this question without reference to CR. That has nothing to do with it!
.
.
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