Paul and Gus, The point of finding a subsample is to get rid of the normal distribution and replace it with a uniform sample that allows the concurrence of similar extremes of both causes. If we start with a normal distribution and want a uniform, then a random subsample will NOT do. All that would do is give us back a picture of the same original normal sample, but with smaller sample size.
I can not seem to communicate that normal distributions are not better than others, just because we often get normal distributions from snap shots. Just going out and taking a snap shot of some phenomenon is likely to leave us with the extremes of the causes under sampled... a normal distribution. I know this statement challenges a very large number of studies in many disciplines. But I was not the first to so challenge. Nunnally called normally sampled causes "dead data." Only the effects should be sampled as normal or triangular. Sampling is a type of perception and like all perception, the instrument is a construction. The eyes do not allow us to see many wave lengths. We are subject to certain illusions. The eyes are not perfect. No sampling strategy is perfect either. Only God in his omniscience has perfect perception. We ain't him. Neither is the normal distribution. When we collect an approximately equal number AND a sufficient number of observations so that we can see the combinations of all the possible values of the causes, then we get a less distorted view of how those causes can combine. The manifold is a map or prototype of such structure. A cause can be expressed in data but unless we can see it, we can not make much sense of it. This is why scientists search long and hard to fill out the ranges of their observations in experimental science. Normal distributions do not reflect the combinations of the similar extremes of causes. You do not see normally distributed cell sizes across the factors of an ANOVA. We need something else to see what happens in the extremes of the cross-tabulation/conjunction of causes. This something else is a manifold, which is approximated by uniform samples of the causes. Bill "Paul Bernhardt" <[EMAIL PROTECTED]> wrote in message [EMAIL PROTECTED]">news:[EMAIL PROTECTED]... > Gus Gassmann said on 9/30/02 7:35 AM: > > > > >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! > > Maybe some slight rewording will help both of you get to the same page. > > Maybe the question should be, "Does causation transfer to a > representative subest?" Representative needs to be defined, but is > probably best defined as a simple random sample of the original data used > to investigate causation (which was, presumably, collected using rational > methods). If a simple random sample of the original data to create a > subset is an insufficient definition, Bill, please offer what it needs to > be. A simple random sample to create the subset would typically have the > same distribution as the original data which you've already used to > investigate causation or lack thereof, therefore already has > characteristics you favor. > > 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/ . =================================================================
