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There are a total of only four ways that you can
obtain a quantity in lab. It might help you to see this laid
out:
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You can obtain a quantity by… |
… for which the uncertainty is given by… |
| 1) |
… making one or two measurements, |
… estimation. |
| 2) |
… calculation from other numbers using a theoretically
based formula, |
… propagation of uncertainty rules. |
| 3) |
… averaging many values which ideally should be the same
(e.g., measurements), |
… calculating the standard deviation. |
| 4) |
… obtaining parameters from a least-squares fit of a
graph…
a) … using linear regression…
b) … using non-linear |
a) …the output of Excel's LINEST(), Mathematica's
LinearModelFit(), or equivalent.
b) … the output of Mathematica's NonlinearModelFit(), the
Solver procedure in Excel, or equivalent. |
Methods 4a and 4b are conceptually the same, but
require different handling due to the mathematical relationships.
Sometimes methods 3 or 4 can free you from having to
do methods 1 or 2. That is…
- … if you can obtain a bunch of values that you expect to be
the same, then you can skip estimation or propagation of
uncertainty and use standard deviation instead.
- … if you can obtain a bunch of values, use them to make a
graph, and then get parameters from a fit, then you can skip
estimation or propagation of uncertainty and use LINEST()
instead.
On the other hand, when you are being extremely
careful, uncertainties from methods 1 or 2 can be used as part of
the calculation process for methods 3 or 4. That level of
care is not expected in any but the most advanced Geneseo course
work.
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