Statistics in Theory and Practice
About this book
Aimed at a diverse scientific audience, including physicists, astronomers, chemists, geologists, and economists, this book explains the theory underlying the classical statistical methods. Its level is between introductory "how to" texts and intimidating mathematical monographs. A reader without previous exposure to statistics will finish the book with a sound working knowledge of statistical methods, while a reader already familiar with the standard tests will come away with an understanding of their strengths, weaknesses, and domains of applicability. The mathematical level is that of an advanced undergraduate; for example, matrices and Fourier analysis are used where appropriate.
Among the topics covered are common probability distributions; sampling and the distribution of sampling statistics; confidence intervals, hypothesis testing, and the theory of tests; estimation (including maximum likelihood); goodness of fit (including c2 and Kolmogorov-Smirnov tests); and non-parametric and rank tests. There are nearly one hundred problems (with answers) designed to bring out points in the text and to cover topics slightly outside the main line of development.
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Information
Table of contents
- Cover page
- Half-title page
- Title page
- Copyright page
- Contents page
- Preface
- 1. Introduction
- 2. Preliminaries
- 3. Some Common Probability Distributions
- 4. Distributions Related to the Gaussian
- 5. Sampling
- 6. Distributions of Sample Statistics
- 7. Bayes' Theorem and Maximum Likelihood
- 8. Confidence Intervals
- 9. Hypothesis Testing
- 10. The Theory of Maximum Likelihood Estimators
- 11. Least Squares Fitting for Linear Models
- 12. Hypothesis Testing in the Linear Model
- 13. Rank Correlation Coefficients
- 14. Tests of Fit
- 15. Robust Tests for Means
- Epilogue
- Some Numerical Exercises
- References
- Answers
- Symbol Index
- Problem Index
- Index