Talk:Regression toward the mean
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I'm not sure this page explains "regression to the mean" very well.
- I agree; it's lousy. Michael Hardy 23:26, 2 Feb 2004 (UTC)
F. Galton's use of the terms "reversion" and "regression" described a certain, specific biological phenomenon, and it is connected with the stability of an autoregressive process: if there is not regression to the mean, the variance of the process increases over time. There is no reason to think that the same or a similar phenomenon occurs in, say, scores of students, and appealing to a general "principle of regression to the mean" is unwarranted.
- I completely disagree with this one; there is indeed such a general principle. Michael Hardy 23:26, 2 Feb 2004 (UTC)
I guess I could be convinced of the existence of such a principle, but something more than anecdotes is needed to establish that.
- Absolutely. A rationale needs to be given. Michael Hardy 23:26, 2 Feb 2004 (UTC)
Regression to the mean is just like normality of natural populations: maybe it's there, maybe it isn't; the only way to tell is to study a lot of examples.
- No; it's not just empirical; there is a perfectly good rationale.
I'll revise this page in a week or two if I don't hear otherwise; the page should summarize Galton's findings,
- I don't think regression toward the mean should be taken to mean only what Galton wrote about; it's far more general. I'm really surprised that someone who's edited a lot of statistics articles here does not know that there is a reason why regression toward the mean in widespread, and what the reason is. I'll return to this article within a few days. Michael Hardy 23:26, 2 Feb 2004 (UTC)
connect the biological phenomenon with autoregressive stability, and mention other (substantiated) examples. Wile E. Heresiarch 15:00, 2 Feb 2004 (UTC)
In response to Michael Hardy's comments above --
- Perhaps I overstated the case. Yes, there is a class of distributions which show regression to the mean. (I'm not sure how big it is, but it includes the normal distribution, which counts for a lot!) However, if I'm not mistaken there are examples that don't, and these are by no means exotic.
- There is a terminology problem here -- it's not right to speak of a "principle of r.t.t.m." as the article does, since r.t.t.m. is a demonstrated property (i.e., a theorem) of certain distributions. "Principle" suggests that it is extra-mathematical, as in "likelihood principle". Maybe we can just drop "principle".
- I had just come over from the Galton page, & so that's why I had Galton impressed on my mind; this article should mention him but need not focus on his concept of regression, as pointed out above.
regards & happy editing, Wile E. Heresiarch 22:57, 3 Feb 2004 (UTC)
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Small change to the historical background note.