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Set05_6 - Error Error Analysis Statistics Accuracy and...

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Error Analysis - Statistics Statistics Accuracy and Precision Individual Measurement Uncertainty Distribution of Data Means, Variance and Standard Deviation ME365 Statistics Slide 1 Galen King Purdue University Confidence Interval Uncertainty of Quantity calculated from several Measurements Error Propagation Least Squares Fitting of Data Hypothesis Testing - χ 2 Test
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Accuracy and Precision Accuracy Closeness of the data (sample) to the “true value.” Precision ME365 Statistics Slide 2 Galen King Purdue University Closeness of the grouping of the data (sample) around some central value.
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Accuracy and Precision Inaccurate & Imprecise Precise but Inaccurate ME365 Statistics Slide 3 Galen King Purdue University Relative Frequency X Value True Value Relative Frequency X Value True Value
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Accuracy and Precision Accurate but Imprecise Precise and Accurate ME365 Statistics Slide 4 Galen King Purdue University Relative Frequency X Value True Value Relative Frequency X Value True Value
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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? ME365 Statistics Slide 5 Galen King Purdue University
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Individual Measurement Statistics Take N measurements: x 1 , . . . , x N Calculate mean and standard deviation: x N x i N = 1 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 ∆∆ x. Need to know how data is distributed. i = 1 ( 29 S N x x i x i N 2 2 1 1 = - = μ ±
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Population and Sample Parent Population The set of all possible measurements. Sample Handful of marbles from the bag Samples ME365 Statistics Slide 7 Galen King Purdue University A subset of the population - measurements actually made. Population Bag of Marbles
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Histogram (Sample Based) Histogram A plot of the number of times a given value occurred. Relative Frequency A plot of the relative number of times a given value occurred. Histogram Relative Frequency Plot ME365 Statistics Slide 8 Galen King Purdue University 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 X Value (Bin) Number of Measurements 0 0.05 0.1 0.15 0.2 0.25 0.3 30 35 40 45 50 55 60 65 70 75 80 X Value (Bin) Relative Frequency
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Probability Distribution Function ( P(X) ) Probability Distribution Function is the integral of Probability Distribution (Population Based) Probability Density Function (pdf) ( p(x) ) Describes the probability distribution of all possible measures of x . Limiting case of the relative ( P X x X = the probability that ME365 Statistics Slide 9 Galen King Purdue University the pdf, i.e. Q: Plot the probability distribution function vs X.
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