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:
â¢ 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.
â¢ If you measure the period if a pendulum with a clock that runs too fast, the apparent period
will be systematically too long.
â¢ 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 are associated with unpredictable variations in the experimental conditions
under which the experiment is being performed, or are due to a deï¬ciency in deï¬ning the quantity
being measured. Here are some examples of random uncertainty:
Changes in room temperature, electrical noise from nearby machinery, or imperfect connec-
tions to the voltmeter probes may cause random ï¬uctuations in the magnitude of a quantity
measured by a voltmeter
The length of a table may depend on which two points along the edge of the table the
measurement is made. The "lengthâ is imprecisely deï¬ned in such a case.
Repeated measurements of the period of a pendulum which are made with a stopwatch vary
because it is hard for a person to start and stop the watch at exactly the same point in the
pendulum's swing. Note, however, that if the experimenter always starts the watch late, but
stops it early, this will lead to a systematic error.
Of these two types of uncertainties, random uncertainties are much easier to deal with and to
quantify. There is no general procedure for estimating the magnitude of systematic uncertainties
as there is for random uncertainties. Only an experimenter whose skill has come through long
experience can consistently detect systematic uncertainties and prevent or correct them.
If an experiment has low systematic uncertainty it is said to be accurate. If an experiment has low
random uncertainty it is said to be precise. Obviously an experiment can be precise but inaccurate
or accurate but imprecise. When thinking about uncertainty, it is important to remember these
associations, so they are worth repeating:
Random uncertainty decreases the precision of an experiment
Systematic uncertainty decreases the accuracy of an experiment
These distinctions are illustrated in Fig. 1. You should avoid...