The purpose of this text is to provide an introduction to the techniques of data reduction and error analysis commonly employed by individuals doing research in the physical sciences and to present them in sufficient detail and breadth to make them useful for students throughout their undergraduate and graduate studies. The presentation is developed from a practical point of view, including enough derivation to justify the results, but emphasizing the methods more than the theory.
The level of primary concern is that of junior and senior undergraduate laboratory where a thorough study of these techniques is most appropriate. The treatment is intended to be comprehensive enough to be suitable for use by graduate students in experimental research who would benefit from the generalized methods for linear and nonlinear least-squares fitting and from the summaries of definitions and techniques.
At the same time, the introduction of the material is made self-supporting in that no prior knowledge of the methods of statistical evaluation is assumed; the meterial of each section is developed from first principles. A discussion of differential calculus and manipulation of matrices and determinants is included in the appendixes to supplement their use in the text.
1. Uncertainties in Measurements
2. Probability Distributions
3. Error Analysis
4. Estimates of Mean and Errors
5. Monte Carlo Techniques
6. Least-Squares Fit to a Straight Line
7. Least-Squares Fit to a Polynomial
8. Least-Squares Fit to an Arbitrary Function
9. Fitting Composite Curves
10. Direct Application of the Maximum-Likelihood Method
11. Testing the Fit