Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: Semi-log and log graphs - Leigh's response





On Wed, 11 Mar 1998, Allen Brown wrote:

Attempting to do do a
linear fit on suspected exponential data that have been transformed by
logarithm violates the principles used - "maximum likliehood" I believe it
is - because the distribution underlying each data point is no longer
normal. On a semi-log plot, especially when uncertainties may be largish,
you can really see the effect of the skewing. The use of a least squares
algorithm is not just a matter of aesthetic choice.
.....
using a linear fit to
logarithmized data invalidates the mathematical statistics underlying the
procedure.

That's the heart of the matter. *If* repeated measurements have a normal
distribution, the transformed measurements generally don't have a normal
distribution. Students generally do not realize that

The statistics of the formulae and procedures elementary students use for
'error analysis' are based on the assumptions that.

1. The uncertainties are relatively small (small percent).
2. The error distributions are normal (Gaussian), or close enough to
normal that it doesn't affect the results. The hypothesis of the normal
distribution is often called "robust" because if it isn't quite true, it
often doesn't matter much. (But the kind of transformations one uses to
"linearize" a graph are often severe enough to matter).

Students don't realize that transforming a variable can take a data
set with a normal error distribution into one with a markedly non-normal
distribution, thus making the simple rules of combinations of
uncertainties simply wrong. Example: transform X to 1/X.

Thoughtful error analysis includes examination of the data to see whether
the uncertainties are consistent in size over the whole range of data. If
the uncertainties are constant, the relative (percent) uncertainties
aren't--and vice versa.

Now, how many of you use a screwdriver for purposes other than driving
screws? Personally, I plead guilty :-)

Allen


I've sometimes used sledgehammers to crack walnuts. Does that count?

-- Donald

......................................................................
Dr. Donald E. Simanek Office: 717-893-2079
Professor of Physics FAX: 717-893-2048
Lock Haven University, Lock Haven, PA. 17745
dsimanek@eagle.lhup.edu http://www.lhup.edu/~dsimanek
......................................................................