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Re: [Phys-l] calibration



Jeff,
Thanks for the shared reference:

Thank you for introducing such a worthwhile topic.


http://www.chem.utoronto.ca/coursenotes/analsci/StatsTutorial/
ErrRegr.html

I like it, except for one detail. The predicting variable y (what is
measured is fluorescence) was plotted vertically while the inferred
variable (concentration) is plotted horizontally. Their formula to
calculate standard deviation of the inferred variable contains the
slope of the line, b.

My predicting (independent) variable, r, is plotted horizontally while
the inferred (dependent) variable is plotted vertically. That seems to
be more logical.

In creating the calibration curve, it makes more sense to me to plot p
horizontally and r vertically. One prepares six samples of an alloy,
each with a fixed value of p. The resistivity of a sample depends on
the percentage p of zinc in the sample. Having prepared each sample,
one then measures the resistivity. You can tell by the regular spacings
of the values of p that it was the values of p that were chosen
independently by the experimenter. The experimenter did not, for each
data point, decide on a value of resistivity and then add zinc to the
copper until the sample had that resistivity. It would seem that this
is an important point in that the actual value of p, not just its
standard deviation, depends on which variable is treated as the
independent variable and which variable is treated as the dependent
variable.

But that is not the main point. I think that what
they call slope b (in the formula for the standard deviation of the
predicted concentration) should be replaced by 1/b', where b' is the
slope of my line. I will try to do this later and see if our results
agree. What was the numerical value of b that you used in their
formula? _______________________________________________________


I used the applet at
<http://espse.ed.psu.edu/edpsych/faculty/rhale/Statistics/statlets/free/
calib.htm>
(in which the formulas used are not made known to the user) to get the
values in my last post which means I did not necessarily use the formula
(of which you speak) provided in the University of Toronto Stats
Tutorial at:
<http://www.chem.utoronto.ca/coursenotes/analsci/StatsTutorial/ErrRegr.h
tml>
In response to your question just above however, I did type the data and
mathematical expressions into a spreadsheet. See:
<http://www.anselm.edu/internet/physics/phys-l/zincStats.xls>
The value of b in that analysis is: 1.132 nano-ohm meter/percent.

Note that the standard deviation of the final result for p in the
spreadsheet is different from the one yielded by the applet. The result
I got using the formulas in the University of Toronto Stats Tutorial
was:
p = (33.1 +/- 9.5) %

Note that the +/- 9.5 % was arrived at using the expression for an
extrapolated value rather than the expression for an interpolated value.
This is appropriate because the resistivity 62 nano-ohm meters is
greater than the maximum value of resistivity used in the calibration
curve. The handwritten expression for the standard deviation in the
predicted value for p that you show on your web page looks more like the
interpolated value expression provided in the University of Toronto
Stats Tutorial.