In physical experiments it occurs often, that you make several measurements on the same experimental arrangement. Usually you fit each data set separately, due to experimental circumstances, which disallow the use all data points in one fit. In my PhD-thesis I described a way to fit these data in a single run, thus having more data points for the estimation of fit parameters of interest.

In my PhD-thesis I worked on light scattering at binary liquid mixtures with a miscibility gap. I used this method to fit the experimental data from turbidity measurments. The fit method is decribed in one of the appendices of my thesis. I wrote a special fit program to perform the fit, but I pointed out, that it should be possible with a standard (well not too standard, BMDP could do it) data processing program. The results between the standard program and my program were nearly the same.

In brief I will show If you're interested in this method of data processing, just let me know and drop me an email. Now you can read on or return to the start.
You have a nice formula which describes the relation between two
physical properties. You make your measurements in several separated
runs, but when you plot your data, you will see, that each series has
slight variations to the other, while each serie gives comparable good
results on the parameters in your formula. The error on the parameters
depends on the number of data points in each serie. If you could
combine all series together you have more data points and the
signal noise ratio would improve. But, the design of the experiment leads to
these damn differences between each serie, so that a fit with all data
gives results with a *worse* quality. There are some parameters which
depend on the experiment *condition* rather than the
underlying physical relationship.

is to separate the parameters in the formula which are related to the
physical concept (p-parameters) from
those parameters which are related to the condition of the
experiment (e-parameters). In my fit of *all* data points in a
*single* run the p-parameters are estimated only once, thus using
all data points, while the e-parameters are estimated for each serie,
thus using only the data points in the distinct serie. The signal
noise ratio of the p-parameters is obviously better than the one for
the e-parameters. But only the p-parameters are of interest.

Realization of this page Franz-Josef Wirtz (nospam-contact@gut-wirtz.de). Copyright Notice:

All material within this webspace is copyrighted to F.-J. Wirtz, except where declared otherwise. You are allowed to use and distribute this information as long as it's for free, since you got it for free too.

Last edited on: September, 9th 1999