lec05_handout

# lec05_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 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.

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ME365 Statistics 3 Accuracy and Precision Inaccurate & Imprecise Precise but Inaccurate Relative Frequency X Value True Value X Value True Value ME365 Statistics 4 Accuracy and Precision Accurate but Imprecise Precise and Accurate X Value True Value X Value True Value
ME365 Statistics 5 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 6 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 ݔ ௕௘௦௧ േΔݔ .

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ME365 Statistics 7 Population and Sample Parent Population The set of all possible measurements.
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lec05_handout - Error Analysis Statistics Accuracy and...

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