Statistics for Physical Sciences - 1st Edition - ISBN: 9780123877604, 9780123877659

Statistics for Physical Sciences

1st Edition

An Introduction

Authors: Brian Martin
eBook ISBN: 9780123877659
Hardcover ISBN: 9780123877604
Imprint: Academic Press
Published Date: 19th January 2012
Page Count: 320
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Statistics for Physical Sciences is an informal, relatively short, but systematic, guide to the more commonly used ideas and techniques in statistical analysis, as used in physical sciences, together with explanations of their origins. It steers a path between the extremes of a recipe of methods with a collection of useful formulas, and a full mathematical account of statistics, while at the same time developing the subject in a logical way. The book can be read in its entirety by anyone with a basic exposure to mathematics at the level of a first-year undergraduate student of physical science and should be useful for practising physical scientists, plus undergraduate and postgraduate students in these fields.

Key Features

  • Offers problems at the end of each chapter
  • Features worked examples across all of the chapters
  • Provides a collection of useful formulas in order to give a detailed account of mathematical statistics


Graduate and undergraduate students in the physical sciences. Physicists, astronomers, chemists, earth scientists and others.

Table of Contents


Chapter 1. Statistics, Experiments, and Data

1.1. Experiments and Observations

1.2. Displaying Data

1.3. Summarizing Data Numerically

1.4. Large Samples

1.5. Experimental Errors

Chapter 2. Probability

2.1. Axioms of Probability

2.2. Calculus of Probabilities

2.3. The Meaning of Probability

Chapter 3. Probability Distributions I

3.1. Random Variables

3.2. Single Variates

3.3. Several Variates

3.4. Functions of a Random Variable

Chapter 4. Probability Distributions II

4.1. Uniform

4.2. Univariate Normal (Gaussian)

4.3. Multivariate Normal

4.4. Exponential

4.5. Cauchy

4.6. Binomial

4.7. Multinomial

4.8. Poisson

Chapter 5. Sampling and Estimation

5.1. Random Samples and Estimators

5.2. Estimators for the Mean, Variance, and Covariance

5.3. Laws of Large Numbers and the Central Limit Theorem

5.4. Experimental Errors

Chapter 6. Sampling Distributions Associated with the Normal Distribution

6.1. Chi-Squared Distribution

6.2. Student's t Distribution

6.3. F Distribution

6.4. Relations Between χ2, t, and F Distributions

Chapter 7. Parameter Estimation I

7.1. Estimation of a Single Parameter

7.2. Variance of an Estimator

7.3. Simultaneous Estimation of Several Parameters

7.4. Minimum Variance

Chapter 8. Parameter Estimation II

8.1. Unconstrained Linear Least Squares

8.2. Linear Least Squares with Constraints

8.3. Nonlinear Least Squares

8.4. Other Methods

Chapter 9. Interval Estimation

9.1. Confidence Intervals: Basic Ideas

9.2. Confidence Intervals: General Method

9.3. Normal Distribution

9.4. Poisson Distribution

9.5. Large Samples

9.6. Confidence Intervals Near Boundaries

9.7. Bayesian Confidence Intervals

Chapter 10. Hypothesis Testing I

10.1. Statistical Hypotheses

10.2. General Hypotheses: Likelihood Ratios

10.3. Normal Distribution

10.4. Other Distributions

10.5. Analysis of Variance

Chapter 11. Hypothesis Testing II

11.1. Goodness-of-Fit Tests

11.2. Tests for Independence

11.3. Nonparametric Tests

Appendix A. Miscellaneous Mathematics

Appendix B. Optimization of Nonlinear Functions

Appendix C. Statistical Tables

Appendix D. Answers to Odd-Numbered Problems




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About the Author

Brian Martin


"Martin (physics and astronomy, U. College London) has produced an undergraduate textbook that is more thorough than the drivel of statistics that physical science students get — usually as part of some other course — but still not the full theoretical and practical treatment that most students do not have time for and most schools do not teach. He assumes a knowledge of calculus and matrices the level of first-year undergraduate physical science student."--Reference and Research Book News, Inc.