ME365chap4_Stats

ME365chap4_Stats - Error Analysis Statistics Accuracy and...

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KARTIK B. ARIYUR PURDUE UNIVERSITY Error Analysis - Statistics Accuracy and Precision Individual Measurement Uncertainty Distribution of Data Means, Variance and Standard Deviation Confidence Interval Uncertainty of Quantity calculated from several Measurements Error Propagation Least Squares Fitting of Data 1 Statistics
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KARTIK B. ARIYUR PURDUE UNIVERSITY Some Intuition for Statistics: Throwing Horseshoes 2 Statistics 0 5 10 15 20 25 30 0 5 10 KBA inches 5 10 15 20 25 30 35 40 45 0 5 10 JW inches 0 10 20 30 40 50 60 0 5 10 RW inches 0 5 10 15 20 25 30 35 0 5 10 MW inches 0 10 20 30 40 50 60 0 0.5 1 inches KBA 0 10 20 30 40 50 60 0 0.5 1 inches JW 0 10 20 30 40 50 60 0 0.5 1 inches RW 0 10 20 30 40 50 60 0 0.5 1 inches MW Histograms Cumulative Distributions
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KARTIK B. ARIYUR PURDUE UNIVERSITY Horseshoes Accuracy over Time 3 Statistics 0 20 40 60 0 5 KBA -1 inches 0 20 40 60 0 5 KBA -2 inches 0 20 40 60 0 5 JW -1 inches 0 20 40 60 0 5 JW -2 inches 0 20 40 60 0 5 RW -1 inches 0 20 40 60 0 5 RW -2 inches 0 20 40 60 0 5 MW -1 inches 0 20 40 60 0 5 MW -2 inches 0 20 40 60 0 0.5 1 inches KBA -1 0 20 40 60 0 0.5 1 inches KBA -2 0 20 40 60 0 0.5 1 inches JW -1 0 20 40 60 0 0.5 1 inches JW -2 0 20 40 60 0 0.5 1 inches RW -1 0 20 40 60 0 0.5 1 inches RW -2 0 20 40 60 0 0.5 1 inches MW -1 0 20 40 60 0 0.5 1 inches MW -2 Histograms Cumulative Distributions
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KARTIK B. ARIYUR PURDUE UNIVERSITY Accuracy and Precision Accuracy Closeness of the data (sample) to the “true value.” Precision Closeness of the grouping of the data (sample) around some central value. 4 Statistics
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KARTIK B. ARIYUR PURDUE UNIVERSITY Accuracy and Precision Inaccurate & Imprecise Precise but Inaccurate Relative Frequency X Value True Value Relative Frequency X Value True Value 5 Statistics
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KARTIK B. ARIYUR PURDUE UNIVERSITY Accuracy and Precision Accurate but Imprecise Precise and Accurate Relative Frequency X Value True Value Relative Frequency X Value True Value 6 Statistics
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KARTIK B. ARIYUR PURDUE UNIVERSITY Accuracy and Precision Q: How do we quantify the concept of accuracy and precision? -- How do we characterize the error that occurred in our measurement? 7 Statistics
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KARTIK B. ARIYUR PURDUE UNIVERSITY Individual Measurement Statistics Take N measurements: x 1 , . . . , x N Calculate mean and standard deviation: What to use as the “best value” and uncertainty so we can say we are Q% confident that the true value lies in the interval x best ± D x. Need to know how data is distributed. x N x i i N 1 1 S N x x i x i N 2 2 1 1 8 Statistics
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KARTIK B. ARIYUR PURDUE UNIVERSITY Population and Sample Parent Population The set of all possible measurements. Sample A subset of the population - measurements actually made. Population Bag of Marbles Handful of marbles from the bag Samples 9 Statistics
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KARTIK B. ARIYUR PURDUE UNIVERSITY Histogram (Sample Based) Histogram A plot of the number of times a given value occurred.
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