Error analysis and uncertainty

Jun 17th, 2015
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In making physical measurements, one need to keep in mind those measurements is not completely accurate. Each measurement will have some number of significant figures and should also have some indication as to how much we can “trust” it (i.e. error bars).

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Error analysis and uncertaintyIn making physical measurements, one need to keep in mind those measurements is not completely accurate. Each measurement will have some number of significant figures and should also have some indication as to how much we can trust it (i.e. error bars). Thus in order to reliably interpret experimental data, we need to have some idea as to the nature of the errors associated with the measurements.A systematic error is when measurements are incorrect in some consistent fashion.The consistency of the erroris the key point. There has to be a system to what has gone wrong.This is the opposite of a random error.Systematic errors are caused by some consistent fault. This is going to be either - a fault with the apparatus - a faulty technique (but one that is consistently applied)Apparatus faultsA common fault with certain apparatus is a zero error, where the instrument does not measure zero correctly.E.g. a newton meter spring has slipped a little, so that the meter reads 0.3N before any force is applied. Every reading that you take with this newton meter will be 0.3N too large.A similar fault might be if the spring in the newton meter had started to weaken with age. If the spring was (for example) twice as easy to stretch as it should be, every force reading would be twice the true value. Technique faultsIf you consistently do the wrong thing, this may cause a systematic error.E.g.

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