How to do physics practicals properly? (error analysis help needed)

[-Vitaly-]

Hello, I just need some help about doing university 1st year practicals. Particularly error analysis, what's the easiest way to do it? We were given huge formulas on how to work out the errors, but I can't understand anything. At high school we used to do things like
error=(instrument uncertainty)/(measurement). So can I still use this?
What about standard deviation? I was told sd is roughly = error.
so the true value X=measurement+-error (stated above)?

And then usually in practicals we have things like functions of x -> f(x). And we need to calculate the error in the f(x). Again from high school I remember that when we add, subtract, multiply, ?divide? values, the errors add up. But what if we have something like
f(x)=square root(x)? then what's the value of the error in f(x)
I had a similar function at my last practical and I couldn't work out the error on f(x). The demonstrator first told me something about derivaties and errors, then gave a huge formula to try as a different method, then I understood that he didn't really know what he was doing (because eventually he said a computer software could have worked it out from the graph of f(x), but I was supid to use excel that doesn't do it...). And after a day long practical I got average mark, instead of a good one because of this minor slip.

Anyway, how do YOU work with errors? I'm particularly interested in opinions of people who have done many practicals and can suggest an easy to understand way (or even algorithm: 1) 2) 3)... in working out errors or tips).
Thank you

 

[physics girl phd]

There are two main points here that you seem to have confused (perhaps because of or in spite of your demonstrator):
(1) When you talk about graphing and using software to find errors (via linear regressions, least squares fitting and other errors found statistically through a "fit" of data), you are talking about discovering the statistical error of the measurement technique and eliminating this error as much as possible (within a given time frame) by making multiple measurements, then using statistics to help you estimate the error in the average value (or perhaps the constants of the fit) based on the spread of the data.

(2) When you talk about f(x) and derivatives, etc, you are talking about "propagation of error" -- i.e. taking the measurements from (1) with their statistical errors and then doing math with these measurements to find results for other, ultimately more interesting things that are perhaps difficult to measure separately and easier to determine by knowing somethings about physics and some things about math. These new derived quantities have error too... which is where the propagation of errors techniques come into play. There are a number of good texts and websites out there discussing "propagation of error" (also known as 'propagation of uncertainty."

It's good to have practice with both statistical error and propagation of error. In some of my research work, I programmed my devices to take multiple measurements until a certain statistical error was achieved, and then I carried error through to my final interesting quantities so my results in my publications (material constants) had meaning for other people who might eventually be interested in those material properties. Some peoples' research even works on measuring fundamental constants to smaller and smaller error.

 

[-Vitaly-]

Thank you very much, I have a practical tomorrow, will try to read more about the propagation of errors and stuff :)