Paul, No, I do not know the type I and type II error rates. They would be interesting to know, however. I think they will differ according to the level of correlation between the variables, the number of intervals, the sample size, etc. I suggest that such an inquiry begin with manifolds. These are the errorless cases that we approximate using samples. There are no end to the variations of samples but the manifolds are written in stone and represent the ceiling on error rates... there should be none but rde, C or what ever is used will vary by sample size and other factors that are not errors. Manifolds will allow many different variations of these nonerror determinants.
To create a manifold simply use the ranges of the presumed causes as factors in a factorial anova pattern. Thus if we are interested in two causes, one having ten levels, the other five, then the manifold will have five columns and ten rows. At the head of each row and column is listed the appropriate level of its factor, i.e 1,2,3...10 (rows) and 1,2,3...5 (columns). In each cell where the row and column cross, put their sum y (if creating an additive manifold). If creating a subtractive, enter y as the difference. Or the product if creating multiplicative manifolds etc. We can also easily geneate three, four and higher dimensional causal spaces as manifolds. These manifolds should serve as home base. Distortions from these patterns can thus be compared with the manifold. Manifolds are the theoretical limit on valid inference, since they contain no error. Each application of CR should include the manifold model as the source of rejection/acceptance criteria inferences. Hope this helps. Best, Bill "Paul Bernhardt" <[EMAIL PROTECTED]> wrote in message [EMAIL PROTECTED]">news:[EMAIL PROTECTED]... > It seems to me that some things that need to be known about the CR method > is how well it theoretically works. For this we have to agree that a > Pearson/Nyman truth table analog applies to this method. That is, given a > method of detecting causation (in this case, CR), what is it's type 1 and > type 2 error rates? (This ignores the possibility that the whole question > of asking to show causation with correlational data may be a type 3 > error, the error of asking the wrong question.) What characteristics of > data does those error rates depend upon? Is the method actually sensitive > to uniform vs normal vs skewed, etc. distribution? Is the method > sensitive to failures of homoscedacity? etc. > > Monospace that font!! > > True Causality > Decision Exists Doesn't Exist > ------------------------ > CR Says | Correct |Type 1 Error| > Exists |Decision | | > ------------------------ > CR Says | Type 2 | Correct | > Not Exist| Error | Decision | > ------------------------ > > Bill, Do you know the type 1 and type 2 error rates for your method? > > Paul > . > . > ================================================================= > Instructions for joining and leaving this list, remarks about the > problem of INAPPROPRIATE MESSAGES, and archives are available at: > . http://jse.stat.ncsu.edu/ . > ================================================================= . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
