Guss said:
>
>No. You said yourself that you are _selecting_ the x1 and x2 to be
>uniform.
Yes, we do this so that we will have examples of all combinations of x1 and
x2,as we would do when using a factorial anova design. But such uniform
sampling does not make the variables into causes, Adding x1 to x2 causes y,
We do not infer that x1 and x2 are the causes because they are uniformly
sampled. We infer they are the causes because their correlations polarize
across the ranges of the dependent variable y,
>Of course the Y you generate by adding them will then be triangular. Of
>course
>the correlations will come out the way you want them to. But does that
>prove
>causality? Of course not. Look at your model in the opposite direction:
>Y is caused by x1 and x2, but I want to prove it isn't, that the
>causality
>effect is y, x2 => x1. What do I do? I follow your recommendations and
>select
>the y uniformly and presto: causality goes the other way.
>
No it does not, You do not infer that the uniformly sampled variable is the
cause, You sample the variables you think may be the causes uniformly and
then see if you get the polarization effect across the ranges of any other
variables, whether they are uniform or triangular, You are being misled I
think by Gottfried's speculations about distributions, But Gottfried and I
have long had a friendly disagreement about this, He sees the presto in the
distributions, I do not, My point is supported by the fact that you could
have two variables that are uniformly distributed and a third that is
triangular and (according to both reality and corresponding
correlations/regressions) there be no causal relationship between the
variables. Furthermore, if you convert the data to ranks after generating
the y=x1+x2 model based on interval data, then CR still reveals the causal
pattern. CR does not "know" the data you pass to it are not all uniform,
It simply looks for the polarization, not for the distribution,
Let's focus this conversation, What do you think about the polarization
effect, assuming for the moment that it is wise to sample factors uniformly,
in the way experimenters do in ANOVA designs?
Bill
>Again I ask: What did I miss?
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