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Course: ENGR 431, Fall 2009
School: Wisconsin
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Measurements CEE Course Lecture &amp; Laboratory Assessing Experimental Data (Part 1) Common Types of Error Uncertainty Estimation of Precision Uncertainty Theory based on Population and Sample Goodness of Fit Line Fitting &amp; Method of Least Squares Common Types of Error Error is the difference between the measured value and the true value. Minimizing error is important in experimental design....

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Measurements CEE Course Lecture & Laboratory Assessing Experimental Data (Part 1) Common Types of Error Uncertainty Estimation of Precision Uncertainty Theory based on Population and Sample Goodness of Fit Line Fitting & Method of Least Squares Common Types of Error Error is the difference between the measured value and the true value. Minimizing error is important in experimental design. Once the data has been collected, estimating a bound on error is important. This bound generally looks like: where u is the uncertainty estimated at odds of n:1. u +u (n :1) Classes of Error Bias (systematic) errors Precision (random) errors Illegitimate error Loading error Backlash, friction, and drift cause hysteresis in error Total error is the sum of all errors Instrumentation Rating Terms Accuracy: difference between the measured and true values. Generally equal to maximum error (99.9%) though not always stated. Precision: difference between reported values during repeated measurements of the same quantities. Resolution: smallest increment of change in the measured value. Sensitivity: change in output per unit change in measured quantity. Uncertainty Uncertainty is the estimate of the amount of error in our measurement. Combining two sources of uncertainty is done using a rms approach: U x = (B + P 2 x 2 0.5 x ) Estimation of Precision Uncertainty Using an assumed Gaussian or normal distribution model for errors, an estimate of the probably difference (confidence interval) between measures and true values may be obtained. Sample vs Population Probability Distributions Theory based on Population Idealistic in the most commonly we have a sample, not full population Probability Density Function (PDF) Gaussian (normal), average, std. dev. Table 3.1 Z-distribution Theory based on Sample Modified average and std. dev. Denominator is called number of degrees freedom. of Estimate of uncertainty of good sample means, std dev match? Confidence Intervals: Large Samples:Eq 3.19, Eq 3.21 Small Samples: Eq 3.23 Goodness of Fit Does the data represent a certain distribution? Only look at Gaussian. Eyeball: histogram, normal prob. plot see Fig 3.14 for results Assessing Experimental Data (Part 2) Statistical Analysis by Computer Propagation of Uncertainty Examples of Uncertainty Analysis Minimizing Error in Designing Experiments Statistical Analysis by Computer Data 2 100 Minitab SPSS Statview 90 80 Total 70 60 50 40 30 .01 .1 X1 : Total Variance: 138.834 Sum: 5199 # < 10th %: 7 # > 90th %: 6 1 5 10 2030 50 7080 9095 99 99.999.99 Percent Mean: 73.225 Minimum: 34 t 95%: 2.789 50th %: 74 Har. Mean: 70.995 Std. Dev.: 11.783 Maximum: 98 95% Lower: 70.436 75th %: 81 Kurtosis: .889 Std. Error: 1.398 Range: 64 Coef. Var.: 16.091 Sum of Sqr.: 390417 10th %: 58.6 Mode: Count: 71 # Missing: 0 25th %: 67 Geo. Mean: 72.187 95% Upper: 76.015 90th %: 87 Skewness: -.467 Normal Probability Plot Deviations Propagation of Uncertainty Usually experimentation is carried out in...

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Wisconsin - ENGR - 431
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