You will be using error analysis throughout your whole university physics career, starting from your first lab, and if you continue your life in any scientific discipline, error analysis will continue to play an important role. As an aid to you, to test your understanding of errors, as a small part of our evaluation of your work and also to introduce you to the lab computer, you are required to do a exercise in error analysis which is done on the lab computer. You may take this test at any time that you can gain access to a terminal -- with the exception of those times during which regular labs are in session. Click on the Faraday X terminal icon on the desktop, or use the X-terminals in MP257, MP125 or MP126; then follow the Test item on the menu. (Note that ERRTST is not available by remote-modem-login)
If you wish credit for your mark on ERRTST, you must complete the assignment by the posted due date. After that date, you are free to try the exercise on the computer, but it will not be credited to your mark. The test consists of four questions to be done in 45 minutes.
You are permitted a maximum of four attempts at the test. After the first
attempt, the computer will ask you if you wish the test to count in your
mark. If you type " no " then the first attempt will be ignored. (This
gives you a chance to become accustomed to being tested by a computer).
Each attempt at the test is averaged with your previously accumulated mark
to produce a new mark.
Make sure you do ERRTST by the appropriate deadline!! Absolutely no
extensions will be granted. Please don't wait until the day of your
deadline to do ERRTST you'll be confronted by huge lineups if you do!
The test on error analysis, ERRTST, generates four questions on error analysis for you to answer. Here we describe how the test works.
You have 45 minutes to complete each attempt of the test; experience has shown that this is much more time that most students need. You may take the test four times for credit, and the mark for the test is the most recent attempt and the previous mark averaged equally. Thus, you can rapidly increase your mark. For your first attempt, you may choose to count it or not; the program will ask you after you have completed the attempt.
There are ten topics of error analysis that can be examined, and the computer program chooses four of the ten at random; this means that there exist 84 different combinations of topics that you could be asked about. For each topic, a number of versions exist, each relating that topic to a measurement done for an existing experiment in the laboratory; the program chooses a version at random. Then, the program randomly generates numerical data within realistic ranges. The topics and number of versions are:
| Topic | Number of Versions |
|---|---|
| Calculating the standard deviation | 3 |
| Calculating the standard error of the mean | 3 |
| Choosing between the standard deviation and the reading error | 3 |
| Accuracy does not increase with repeated measurements | 2 |
| Propagation of errors for addition and subtraction | 3 |
| Propagation of errors for multiplication and division | 2 |
| Propagation of errors for powers | 2 |
| Propagation of errors for addition and multiplication | 2 |
| Propagation of errors for multiplication and powers | 2 |
| Rejection of measurements | 3 |
For example, for the topic of Calculating the standard deviation, the number of repeated measurements is chosen randomly to be between 4 and 8. One version randomly generates values of the time for a metal hoop to undergo 20 oscillations; the second version generates values for the thickness of a metal hoop as measured by a micrometer; the third version generates values for the width of a metal hoop as measured by a vernier caliper.
Here is a question from a particular test:
Using a vernier caliper, you have repeated measurements of the width w of a metal hoop 4 times.
You estimate that your reading error in reading the vernier is plus or minus 0.002 centimeters.
You calculate that the standard deviation of your sample of measurements is 0.001 centimeters.
What is the error, in centimeters, in each individual measurement of the width w (no units please)?
The correct answer to this question is 0.002 centimeters. If you enter that answer, the program will congratulate you and go on to the next question. If you give a wrong answer the program will state:
No. The correct answer is numerically: 0.002
This question involved the topic:
"Choosing between std. dev. and reading error"
If you wish to take some notes on this question before continuing, I have
stopped the clock.
Press RETURN to restart the clock and continue ...
N.B. Finally, the questions are such that the correct answer should have only one significant figure. The program will silently accept two significant figures, but then deducts 5% for each additional insignificant digit.
Here is another question:
You are measuring the wavelength L of a particular line in the spectra experiment using the equation:
L = [ m/(y - b) ] + L0.
You are given that L0 = 284.8 plus or minus 0.5 nm (nanometers).
The results of your calibration of your spectrometer give the slope as m = 4606 plus or minus 30 nm-units and the intercept as b = 3.82 plus or minus 0.02 units. 'units' is the units of the scale of the spectrometer.
For the particular line you are measuring, the scale on the spectrometer reads y = 15.43 units and you estimate your reading error of this scale to be plus or minus 0.02 units.
What is the error, in nm (nanometers) in your measurement of the wavelength L?
I'll leave the working out of the answer up to you!! -
A suggestion - work it out in your head first, then check it the stupid way.