Sunday, May 11, 2008

Wattage debate (isn't there always!)

Debate currently raging over on Wattage as to how to derive some statistical measure of significance on the results. Hmmn, opened a can-o-worms...

[quote]From: Robert Chung
Date: Wed, 7 May 2008 11:09:10 -0700 (PDT)
Local: Thurs, May 8 2008 4:09 am
Subject: Re: Aero Testing Sheets - Update (Chung & Regression Methods)

> On May 7, 12:04 pm, Robert Chung wrote:

> > Andy (Coggan): with the regression method, using the proper model specification
> > always dominates.

> But (somewhat rhetorically) what is the "proper model specification"?
> The two alternatives are mathematically equivalent, the physics don't
> really help you decide, and the argument could be made that a power
> meter is just as much a force (torque) meter. To me, then, it comes
> down to how errors in the underlying measurements impact the precision
> of the CdA estimate, and that's what I can't decide (since the noise
> isn't necessarily "white", I don't think that a simple uncertainty
> analysis will suffice).

Since this is rhetorical, you almost surely already know the answer
but for those who don't, Andy's right, the physics models don't help,
and the mathematics are equivalent. What's not equivalent is the
statistical model. The underlying linear regression model is unbiased
and efficient (i.e., lowest variance) when the Gauss-Markov
assumptions are met. The "usual" regression model (where one regresses
W/v on v^2) will produce inefficient (though consistent aka
asymptotically unbiased) estimates because of heteroscedasticity.
However, over the range of v we usually see for these kinds of field
tests, I expect the efficiency loss will be relatively small. The
bottom line is that it's slightly better to use whatever the PM
reports rather than to transform the variables, though only very
slightly.

BTW, you're right that the errors aren't "white." Note, for example,
systematic holes in the SRM's speed reporting. [/quote]

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