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

[Allen Brown <brownan@educ.queensu.ca>]

I disagree.

On Tue, 10 Mar 1998, Leigh Palmer wrote:

> > Having read what others are saying about logarithmic graphs, I just wanted
> > to point out (and I'm sure that they know this) that it is incorrect to do
> > a linear fit on the transformed (i.e., "logarithimized") data, in any
> > case.  It is incorrect even when the uncertainties are weighted, a.k.a.
> > weighted least-squares or equivalent.
>
> May I point out here that "incorrect" is too strong a term? The fitting
> of a curve to data is a process which is used "to guide the mind". The
> use of a least squares algorithm is entirely a matter of aesthetic
> choice; no specific fitting algorithm is mandated by Nature.

Incorrect is correct ;-)  Most frequently, the objective in fitting a
curve is (given that you believe the relationship that you are fitting
against) parameter estimation.  Even ignoring that, and assuming that the
fitting is an exploratory exercise to judge appropriateness of
relationship, regardless of what was said about Nature here, the fitting
algorithm is based on mathematical principles.  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.

Gee Leigh, it surprises me that you would say this because you are usually
such a stickler for detail, and this is not just a detail, but the basis
on which the procedure is carried out.

> Thus, if one makes it clear that the fit made to data in a given case
> is a linear fit to a logarithmic series derived from the data, then
> that is perfectly correct. It would also be correct to fit an
> exponential to the data by a least squares method and specify that it
> was done that way. That would likely give a different fit, but the fit
> would not be in any way intrinsically superior to the first one. In
> order to make a judgment of relative merit one would need more
> information about the object of the measurements.

Again, I disagree.  There is nothing "perfectly correct" about it.  The
fit to the exponential would be correct, though, and as such would be
superior.  It would likely be different.  You don't need anything else to
make a judgment of relative merit here;  using a linear fit to
logarithmized data invalidates the mathematical statistics underlying the
procedure.

What is that saying about the right tool for the right job?  This may be a
case where people just get a little bit careless and don't think as much
as they should about their procedures (i.e., "let's just transform it and
run it through this handy linear LSF package").  Some of this is a result
of the fact that linear LSF's are among the most popular and easily
available software packages.

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

Allen