lec07_handout

lec07_handout - Error Analysis - Statistics Accuracy and...

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ME365 Statistics 1 Error Analysis - Statistics Accuracy and Precision Individual Measurement Uncertainty – Distribution of Data – Means, Variance and Standard Deviation –C o n f i d e n c e I n t e r v a l Uncertainty of Quantity calculated from several Measurements – Error Propagation Least Squares Fitting of Data Hypothesis Testing - χ 2 Test ME365 Statistics 2 From Last Time Confidence interval
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ME365 Statistics 3 General Formula Suppose that y is related to n independent measured variables { x 1 , x 2 , …, x n } by a functional representation: Given the uncertainties of x’ s around some operating points: The expected value of ݕ and its uncertainty Δ y are: Propagation of Error ME365 Statistics 4 Propagation of Error Proof: Assume that the variability in measurement y is caused by k independent zero-mean error sources: e 1 , e 2 , . . . , e k . Then, ( y - y true ) 2 = ( e 1 + e 2 + . . . + e k ) 2 = e 1 2 + e 2 2 + . . . + e k 2 + 2 e 1 e 2 + 2 e 1 e 3 + . . . E [( y - y true ) 2 ] = E [ e 1 2 + e 2 2 + . . . + e k 2 + 2 e 1 e 2 + 2 e 1 e 3 + . . .] = E [ e 1 2 + e 2 2 + . . . + e k 2 ] [] σσ σ σ yk k Ee =+ + + = + + + 1 2 2 22 1 2 2 LL
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ME365 Statistics 5 Example (Standard Deviation of Sampled Mean) Given Use the general formula for error propagation: Propagation of Error ME365 Statistics 6 Propagation of Error Ex: What is the uncertainty in calculating the kinetic energy ( mv 2 / 2 ) given the uncertainties in the measurements of mass (m) and velocity (v)?
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ME365 Statistics 7 Best Linear Fit –How do we characterize “ BEST ”?
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lec07_handout - Error Analysis - Statistics Accuracy and...

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