[proFit-list] feature request--calculate-Data Transform with errors

[pro Fit Support]

Andrew

Disclaimer: I am not a statistics expert. The following is based on a  
cursory review of some literature regarding this topic. Maybe there is  
someone more knowledgeable on this list to correct me.

As far as I understand, what you need is to calculate the "Prediction  
Interval" or "Confidence Interval" of the interpolated values. These  
two intervals differ in their definition:

* When you calculate the 95% Confidence Interval you can say the  
following: "I am 95% confident that the average of all future values  
yp at a given xp will be within the Confidence Interval.

* When you calculate the 95% Prediction Interval you can say the  
following: "I am 95% confident that an individual value yp measured  
at  a given xp will be within the Prediction Interval.

As follows from the above, the Confidence Interval will, by its  
nature, be more narrow than the Prediction Interval.

There is no built-in way within pro Fit to to calculate the Confidence  
Interval or Prediction Interval. However, out of interest, I have  
prosecuted the topic further, and have found the following:

1) Calculating the Prediction Interval or Confidence Interval for  
arbitrary functions, even non-linear polynomials, is not for the faint  
of heart.

2) Calculating the Prediction Interval or Confidence Interval for  
linear regression is fairly well documented, but only for data sets  
where the error of the y-values is equal for all data points. In that  
case, the standard algorithms calculate the errors from how well the  
data fits the line, i.e. any specifically given error values are  
ignored.

I have tried to write a pro Fit script that takes your data (in  
columns 1 and 2 of your data set), fits them to a straight line  
(linear regression), and tabulates a list of interpolated values in a  
new data window. The new data window contains height in column 1, the  
interpolated value in column 2, and its 95% prediction interval in  
column 3, its 95% confidence interval in column 4.

To set the start, end and step width of the resulting table, edit the  
constants xpMin, xpMax and xpStep at the beginning of the script.

To run the script, compile it. Then bring your data window to the  
front, and run the script from the Prog menu.


Best regards

Kurt Sutter
QuantumSoft

-------------- next part --------------
A non-text attachment was scrubbed...
Name: ConfidenceIntervals
Type: application/octet-stream
Size: 33397 bytes
Desc: not available
Url : http://quantum-soft.com/pipermail/profit-list_quantum-soft.com/attachments/20080818/6ecedd37/attachment-0001.obj 
-------------- next part --------------



On 15.08.2008, at 07:32, Andrew Calvert wrote:

> Hi Kurt,
>
> I've attached an example of the data and plot.  I have a vial of  
> rock samples.  Standards (minerals of known age) are arranged at  
> heights of 1.25, 23.4, 42 and 55.8 mm above the base.  Measurements  
> and errors of these standards are plotted with small circles.   
> Between those standards I have unknowns (rocks of unknown age)  
> arranged at heights of 5.35, 13.05, 19.75, 27.3, 34, 39.7, 45.75,  
> and 52.45 mm.  I need to assign a "J" and error to each of the  
> unknowns.  (J is an irradiation parameter used in 40Ar/39Ar  
> geochronology).
>
> So, I plot the data, fit them with a polynomial, load the fitted  
> parameters into the Parameter Sets (Func menu).  Then I choose  
> Calc>Data Transform and select my unknown's heights as column X and  
> the Calculated J for column Y, then choose Y = Polynomial (X) under  
> Various Functions.  This calculates a nice J for my unknowns  
> (plotted as +), but I would also like an error.  Is there a simple  
> way to do that?
>