The Statistical Analysis of Data.
Thomas L. Moore, T. W. Anderson, Stanley L. Sclove, Warren Chase, Fred Brown, A. S. C. Ehrenberg, James T. McClave, Frank H. Dietrich, Larry E. Toothaker · Journal of the American Statistical Association · 1989
This book was written for students in an upper-division physics laboratory course.It covers propagation of error, regression analysis, and related topics.The linearity in the book title is between the variations that can be expected in each input datum and the resulting variations in the output parameters derived from that input.Covariance matrices describe the input and output variations while first-order Taylor expansions and Jacobian matrices describe the linear relationships involved.Linearity is guaranteed when firstorder Taylor expansions provide accurate input-output relationships over the range of typical input errors, such as when the relationships are linear or when the input errors are kept small enough.Moreover, even when the input errors begin contributing nonlinearly, an analysis based on linearity typically provides a good first approximation.Microsoft Excel is an excellent platform for demonstrating the material.The final chapter shows how to use it for the procedures presented here and several spreadsheet examples can be found on the lab website.Only Excel's Regression and Solver add-ins are used.No other add-ins are needed.A few exercises are scattered throughout the book to fill in various steps in the logic and to provide practice with the equations and procedures.Two noteworthy results are presented in the chapter on regression analysis.One shows how a least squares solution is equivalent to a maximum likelihood solution not only for Gaussian-distributed data, but for Poissonand binomial-distributed data as well.The other shows how the uncertainty in an instrument calibration propagates to the uncertainty in any results obtained using that instrument.Hopefully, the reader will find these and other topics treated rigorously and clearly, but also practically, with formulas and procedures applicable to many everyday data analysis tasks.