First, we do not do percent error calculations, but % difference calculations. I believe Hugh's comments are more directly applicable to percent error calculations. I might be wrong.
My students are to determine why the two values might be different. I specifically state that we should not hold textbook values in too high of a regard. They must state what might cause these differences, how their laboratory procedure might have caused these differences, and what could be done to change the procedure to limit the error involved. I do not give them the 'accepted' values of these substances. Kids today will google or Wikipedia the value. If I don't ask them to do a % diff, some (not all) will attempt to fudge data to match the internet value. I've done labs along these lines to determine an unknown item in the past (maybe use n or C to determine what solution or metal sample you have been handed).
None of my labs are cookbook recipe labs. I rarely conduct verification labs. However, students are becoming very adept at finding some of the information that I ask them to determine. Years ago I would ask them to use a double slit to find the wavelength of a laser. Then kids could more easily find the wavelength. I switched to find the slit separation. Now kids google the little CAS image on the Cornell slides I've got and they know the openings on the slides. I now have to find a new version of Young's Double slit. Don't know what that will be, but it has never been a verification lab.
I never spoke of using human error as a source of uncertainty. I wouldn't accept it any more than you would. I do things very similar to what you suggest:
" It is much better to design experiments that have no pre-known answer, and show them how to 1) estimate a statistical uncertainty value, and 2) look critically at the experimental setup and try to figure out what, if any, systematic error might be present due to the experimental design."
However, we do not estimate a statistical uncertainty value, we do your item 2). In the beginning of the year they do this as a reflection at the end of the lab. By the third lab, they are to think about these things before they conduct the lab. They should then plan their lab in a manner that reduces as many systematic errors as possible.
I understand the point that these values (index of refraction) can be calculated with one measurement of incidence and refraction. However, a plot of sin(theta-i) vs sin(theta-r) yields a nice y=mx plot. This is, in my opinion, a nice way to get the kids to understand some of the ways in which mathematical models are applied and created. The students must justify if the y-intercept should be zero or not. They can then determine what the slopes might represent. This becomes more obvious if different groups are conducting the lab with different solutions. If I have each group conduct the lab with a different solution, they *should* all be able to get plots of similar quality. The linear best-fit lines (Excel best-fit lines as opposed to true regression lines) with R^2 values should have R^2 values in the same general neighborhood. If so, then we can compare slopes etc... Many of the labs that one requires students to plot data and analyze values could be done with one data point or two. That doesn't make one-data point labs preferable. Just quicker.
I am not sure what Hugh means by an accepted value of 0.
p.s.
A nice way to conduct the resonance lab without a 0.4 multiplier to correct for end effects: Find the first & second points of constructive interference (n=1, n=3). The distance btn these two points is 1/2 wavelength. When the kids ask why they can't use 4*L(1), you have a nice discussion on your hands and the opportunity to have some students conduct the lab each way. Then compare results.
Paul Lulai (where I'm attempting to listen and stand my ground while not stepping on toes).
Physics Instructor, Science Olympiad Coach,
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