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Error on Measurement

  1. Mar 15, 2007 #1
    I did an experiment on the Hall Effect, and found the voltage for the Hall "probe" (it was a strip of bismuth) as a function of a current magnetizing the B-field. Anyway, I did a least squares fit to find the regression line with A^T A = A^T b, and found four lines for each of my four data sets. I also found the uncertainties on the each of the four with [tex]\sigma = \sqrt{\frac{1}{N-2} \sum_{i=1}^N (y_i - A -Bx_i)^2}[/tex].

    My question is that if I find the average regression line, using [tex]\sum_{i=1}^N \frac{y_i}{N}[/tex], would I simply take the mean of errors since they will all be dependent on the same factors? Should I add the errors in quadrature since they were all errors would be random, and dependent on different random factors?
  2. jcsd
  3. Mar 15, 2007 #2


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    You are asking the right questions! The answer depends on how you made your measurements. Are the uncertainties uncorrelated? If one is a voltage and another is a dimension, for instance, then you can assume no correlation = rms. If they are related, for instance the same meter is used separately to measure current and voltage, and there's a systematic error (meter calibration is off), then you might need to sum the errors.
  4. Mar 15, 2007 #3
    They are correlated, though I haven't actually done a correlation test, because all I did was increase the magnetic field until the galvanometer measuring the voltage hit its sensitivity peak, and then I turned the current back to zero (to get rid of remanent magnetization) and did the test all over again.

    At the same time, I could see how since any error on the measurements will be a random error, as any systematic error would repeatedly show in every test, why they would be uncorrelated. Random events can't really correlate together.

    Ultimately, I guess that simply adding the uncertainties will make the most since though.
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