ErrorAnalysis_Handout_1

ErrorAnalysis_Handou - An Introduction to Error Analysis for Chemical Engineers Nathan W Moore Presented to Chemical Engineering Laboratory(ECH155A

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1 Nathan W. Moore An Introduction to Error Analysis for Chemical Engineers Presented to: Chemical Engineering Laboratory (ECH155A) University of California at Davis October 2005 Overview Identifying error Quantifying error Confidence intervals Error propagation Uncertainties in best-fit lines Reporting uncertainties
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2 The Sources of Error The two kinds of error Systematic error ...occurs in a predictable way. ...results from imperfect instrumentation or procedures. ...tells you how accurate your data is. Random error ...occurs unpredictably. ...results from unrepresentative samples. ...tells you how precise your data is.
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3 Sources of systematic error Inaccurate calibration (or wrong model used) Bias (measurement consistently high or low of actual value) Drift (operating parameters changing over time) Hysteresis (reading depends on history of measurement, i.e., from mechanical manipulation) Incorrect model used for analyzing relationships between data Propagation of errors through calculation Reducing systematic error Goal: Make Systematic Error less than Random Error Improve the skill of the person making measurements. Compare measurements to standards and controls. Measure bias, drift, and nonlinearity and adjust your data accordingly. Redesign the procedure to avoid known hysteresis. If the experiment cannot be redesigned, randomize the order of measurements.
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4 Sources of random error Sample properties not uniform in time and space usually from uncontrollable interactions with environment (e.g. air temperature fluctuations) Measurement device not consistent in time and space e.g. voltage fluctuations in a thermocouple Reducing random error Goal: measure “representative samples” Repeat measurements Repeat measurements Repeat measurements
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5 Confidence Intervals (a quick review) Random errors ...occur from unrepresentative samples. Measured values Count Guess for true mean
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6 Random errors ...occur from unrepresentative samples. Infinitely large samples usually have a Gaussian distribution: Measured values Count or Probability Student’s t-distributions Better description when N<30 (sample size) Still works when N>30 can use all the time! Measured values Probability student t-distribution is broader than Gaussian dist’ more uncertainty in smaller sample sizes Gaussian distribution
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7 Confidence intervals Given spread in data, what is the range of values in which the true mean is likely to be found? Measured values Probability true mean is somewhere in here Estimating confidence intervals .. t CI N σ ⎛⎞ = ⎜⎟ ⎝⎠ standard deviation of data number of data points t-value Depends on: confidence level (usually 95%) degrees of freedom (N-1 in this case).
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This note was uploaded on 09/30/2011 for the course ECH 155A taught by Professor Kuhl during the Summer '11 term at UC Davis.

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ErrorAnalysis_Handou - An Introduction to Error Analysis for Chemical Engineers Nathan W Moore Presented to Chemical Engineering Laboratory(ECH155A

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