[spam] Re: Re.: Traditional Statistics

CSGnet Archive CSG2006
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[Martin Taylor 2006.12.17.22.26]

[From Rick Marken (2006.12.17.1455)]

Bill Powers (2006.12.17.1350 Mst)--

My basic objection to the uses of statistics is not the statistical calculations themselves, but the way people let themselves settle for statistical truths when, with a little more effort, they could be aspiring to obtain real knowledge. It's too easy to blame fuzzy results on nature ("behavior is inherently variable") when the real problem is an inadequate theory. But getting clear results often means keeping the subject matter simple, and that just isn't sexy enough for many people.

I, of course, completely agree.

Of course. And I partially agree. I would agree completely if we insert the word "often" in the end of Bill's 3rd last line, after "the real problem".

Even a perfectly complete and correct theory will lead to variable (not "fuzzy", which has a different technical meaning) results if not all the boundary conditions are precisely specified.

If the effects on X are completely specified by X = ax + by +cz, and you can only measure x and y precisley, the variation in the unobservable values of z will lead to variation in X, despite that the theory is perfect. The same applies if the parameter values a, b, c aren't precisely known.

I do agree, however, with a lot of the time "people let themselves settle for statistical truths when, with a little more effort, they could be aspiring to obtain real knowledge".

Martin

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[From Bill Powers (2006.12.17.1150 MST)]

Martin Taylor 2006.12.17.22.26 --

Even a perfectly complete and correct theory will lead to variable (not "fuzzy", which has a different technical meaning) results if not all the boundary conditions are precisely specified.

If the effects on X are completely specified by X = ax + by +cz, and you can only measure x and y precisley, the variation in the unobservable values of z will lead to variation in X, despite that the theory is perfect.

But if the theory is perfect, z will be part of it. If z can't be observed or measured, the the theory can't be perfect. I'm sure that there are unmeasurable and unidentified z's in every theory, but in a good theory they produce only very small unpredictable variations in X. All the major causes are accounted for, which is why good theories are associated with very high correlations.

All I'm really saying that if your model gives 1- or 2-sigma precision, it's worth while trying to get that up to 4 sigmas, because then you can forget about the possibility that the predicted behavior could have occurred by chance, and you can forget about correlations, too. In my tracking experiments the model commonly achieves 10- to 30-sigma precision (prediction errors of 3 to 10 per cent RMS).

The same applies if the parameter values a, b, c aren't precisely known.

If they aren't precisely known, my advice would be to try to get to know them better.

I do agree, however, with a lot of the time "people let themselves settle for statistical truths when, with a little more effort, they could be aspiring to obtain real knowledge".

My definition of real knowledge is signal 4 sigma above the noise. For lesser precision, I would make lesser claims and use a term more modest than "knowledge."

No doubt I would be considered peculiar in many circles.

Best,

Bill P.