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Notes on Uncertainty Analysis

Notes on Uncertainty Analysis. a.k.a. Error Analysis. Uncertainty. Any measured or calculated value has some level of uncertainty Not due to mistakes Unavoidable due to the nature of the experiment Consider measuring a grape Uncertainties usually reported to 1 significant figure

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Notes on Uncertainty Analysis

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  1. Notes on Uncertainty Analysis a.k.a. Error Analysis

  2. Uncertainty • Any measured or calculated value has some level of uncertainty • Not due to mistakes • Unavoidable due to the nature of the experiment • Consider measuring a grape • Uncertainties usually reported to 1 significant figure • Use several significant figures while calculating the uncertainty • When complete, report it to one significant figure • Two ways to represent uncertainty • Absolute uncertainty (AU): same units as reported value • Relative uncertainty (RU): represents AU as a fraction/percentage

  3. Absolute Uncertainty • Example: measurement = (23.27 ± 0.01) grams • Two primary contributions to AU • Accuracy • Precision • Accuracy (systematic error) • Reported for instruments • ACME Temperature Probe claims accuracy to ± 0.03º C • AJAX Analytical Balance claims accuracy to ± 0.0001 g • Precision (reproducibility error) • Ability to read an instrument • The ten-thousandths digit of the AJAX balance is fluctuating between 1 and 5 • Reproducibility error would be ± 0.0002 • Multiple measurements • Reproducibility approximated by standard deviation of average • AU = systematic error + reproducibility error • AUAJAXBalance = 0.0001 g + 0.0002 g = 0.0003 g • AUs are positive with one significant figure

  4. Accuracy and Precision Inaccurate (systematic error) Accurate Precise xxx xx xx x xxx xx xx x Imprecise (reproducibility error) x x xx x xx x x x x x x xx x xx x x x xx x

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