Advanced Physics Laboratory PHY 326/327 and PHY 426/427/428/429

Lectures on Error Analysis in Scientific Measurement:

Part 1: The meaning and calculation of uncertainty Part 2: The least-squares method of fitting data

J. H. Thywissen September 12, 2006.

Outline: 1.1 Illegitimate Errors 1.2 Accuracy versus Precision 1.3 Recording Error 1.4 What is meant by statistical uncertainty? 1.5 Error propagation 1.6 Examples of error propagation 1.7 The Normal distribution 1.8 Weighted average & standard deviation of the mean 2.1 Fitting a function to data 2.2 Definition of χ2 2.3 Finding the best fit 2.4 Uncertainty in fit parameters 2.5 Linear and polynomial fit solutions 2.6 Including x uncertainty 2.7 Goodness of fit 2.8 Summary

References: J. R. Taylor, An Introduction to Error Analysis (University Science Books, 1982) P. R. Bevington & D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill) J. Orear, Notes on Statistics for Physicists, revised (unpublished, 1982) online: http://nedwww.ipac.caltech.edu/level5/Sept01/Orear/Orear.html

Part 1: The meaning and calculation of uncertainty

Outline: 1.1 Illegitimate Errors 1.2 Accuracy versus Precision 1.3 Recording Error 1.4 What is meant by statistical uncertainty? 1.5 Error propagation 1.6 Examples of error propagation 1.7 The Normal distribution 1.8 Weighted average & standard deviation of the mean

Part 2: The least-squares method of fitting data

Outline: 2.1 Fitting a function to data 2.2 Definition of χ2 2.3 Finding the best fit 2.4 Uncertainty in fit parameters 2.5 Linear and polynomial fit solutions 2.6 Including x uncertainty 2.7 Goodness of fit 2.8 Summary