Data Analysis And Experimental Uncertainty
Prepared by David B. Pengra, University of Washington, and L. Thomas Dillman, Ohio Wesleyan
University
This set of notes has been adapted from ones given to Ohio Wesleyan University physics students
in the introductory laboratories. Although they are pitched at a relatively elementary level, they
contain many hints that may be useful even to advanced students.
The topics discussed below may be supplemented with pertinent sections in the references listed at
the end of the article; the text by Bevington and Robinson (see reference [1]) gives a good account
of basic statistical theory and practical computer methods most often used in analyzing data from
physics experiments.
1 Types of Uncertainty
There are two basic kinds of uncertainties, systematic and random uncertainties. Systematic un-
certainties are those due to faults in the measuring instrument or in the techniques used in the
experiment. Here are some examples of systematic uncertainty:
⢠If you measure the length of a table with a steel tape which has a kink in it, you will obtain
a value which will appear to be too large by an amount equal to the loss in length resulting
from the kink. On the other hand, a calibration error in the steel tape itselfâ"an incorrect
spacing of the markingsâ"will produce a bias in one direction.
⢠If you measure the period if a pendulum with a clock that runs too fast, the apparent period
will be systematically too long.
⢠The stiï¬ness of many springs depends on their temperature. If you measure the stiï¬ness of
a spring many times, by compressing and decompressing it, the internal friction inside the
spring may cause it to warm. You may see this by a systematic trend in your data set; for
example, each data point in a data set will be smaller than the previous one.
Random uncertainties...
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