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Physics I Lab Manual 2011 109

# Physics I Lab Manual 2011 109 - would say the measurements...

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APPENDIX B. AN INTRODUCTION TO ERROR ANALYSIS is “known” that means the uncertainty is negligible) we can say the measured values “agree” if the range of values for the two measurements overlap, that is if there is one possible value that falls within the uncertainty of both measurements. Thus if we compare a quantity a ± δa to another quantity A ± δA we say they agree if | a - A | < δa + δA (i.e. the quantities differ by less than the total uncertainty, so they could be a measure of the same value. When the above criteria is not met, i.e. | a - A | > δa + δA the measurements “do not agree” within the experimental uncertainty. It is useful to describe how much disagreement there is, one meaningful way of doing this is to state how far they were apart relative to the uncertainty relative error = | a - A | δa + δA σ, where σ is the greek letter sigma and stands for “standard deviation”. We can think of it as just our unit of relative uncertainty just as the percent sign is our unit of percent error. For example if two measurements have a difference that is twice the total uncertainty we
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Unformatted text preview: would say the measurements diﬀered by 2 σ . Another method is to describe the percent error between the values percent error = | a-A | ( a + A ) / 2 × 100% and also express the total uncertainty as a percentage for comparison percent uncertainty = δa + δA ( a + A ) / 2 × 100% These types of objective statements about the measurement and uncertainty are an important part of a report. Subjective statements such as “the measured value was 0.2% oﬀ form the expected value so the measurement was successful” are not useful and often lead to incorrect conclusions - without knowledge of the uncertainty it is impossible to tell if an error is signiﬁcant, even if it seems small. Scientiﬁc reports have no room for subjective interpretation of what is signiﬁcant and what is not. With the tools for error analysis presented here there is no reason for such subjective statements. 99...
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