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Re: [Phys-l] propagation of error (or not)



On 06/01/2009 01:55 PM, alex brown wrote:
I require a book on lab\practical practises and techniques including
error propagation at under graduate level.

On 06/02/2009 04:39 AM, Richard L. Bowman wrote:
Alex, I have found the book by D. C. Baird, "Experimentation: An
Introduction to Measurement Theory and Experiment Design," 3rd ed.

Well, if anyone finds Baird useful, that's good ... and I don't want
to dispute questions of taste.

However, I feel obliged to point out that not everyone finds Baird
to be particularly helpful for improving experimental technique.

In the context of error propagation: Baird derives the general
formula for mathematical propagation of error:

σz^2 = (dz/dx)^2 σx^2 + (dz/dy)^2 σy^2 [1]

Question: How many of your students, after reading Baird, would be
able to explain the conditions for validity of equation [1]?

I'd wager not many, because Baird doesn't say much about it, and
what he does say isn't entirely true.


Rather than asking students to buy Baird, I would skip equation [1]
entirely and proceed directly from basic probability to Crank
Three Times and thence to Monte Carlo, as previously discussed.
Baird doesn't review probability and doesn't mention Crank Three
Times or Monte Carlo. If somebody forced me to mention equation [1],
I still wouldn't rely on Baird; I would prepare a handout, using
1/3rd of a page to derive equation [1] and using the rest of the
page (and the back side) to elucidate its limits of validity.


In the section on least squares fitting, Baird says almost nothing
about the principles underlying the technique, and then asserts
"This is really all one can say ..." Hogwash. There is a great
deal more one could say, if one had any reasonable understanding of
curve fitting in particular or data analysis in general. (It turns
out that the probabilistic underpinnings of least squares are not
particularly sound, but we should at least get this out on the table
for discussion.)


Some chapters of Baird have equations in them, but others have few
or none, offering long philosophical discussions instead.


My favorite sentence in the book says "Because of this range, the
advice which could be given to help a student is likely to be so
generalized and vague as to be of very little practical assistance."

On the plus side, this sentence earns the author credit for an
exceptional degree of self-awareness and frankness.

Alas, the book then proceeds to meet this very low standard: "so
generalized and vague as to be of very little practical assistance."
It might prepare you to go to a fancy tea party where lords and
ladies talk-talk-talk about experimentation ... but it's not much
help for actually doing experimentation.


To put this in perspective, Baird ranks in the middle:

-- Taylor : Appalling, worse than useless.
-- Baird : Useless, soporific.
-- Bevington : Useful but heavily flawed.