Main description:

This book was written with two specific goals in mind. The first is as a resource for graduate students who are pursuing an advanced degree in medical physics who are also required to take a course in statistics. This text includes many practical medical physics problems which would be ideal for this course. Although there are a number of statistics books available, there are no books which present statistics in a context that has applications important to medical physics and medicine. Most medical physicists are familiar with the very basics of statistical analysis like mean and standard deviation: however their ability to analyze data and design statistically valid experiments may be limited. The second goal, therefore, is for the book to serve as a key resource on statistical analysis for senior medical physicists or clinical researchers.

The book includes 11 chapters, beginning with very basic topics like Binomial, Poisson, and Normal probability distributions and gradually progressing to more advanced topics.

This book will be a valuable addition to any library due to the wide range of statistical topics and the many practical applications that are provided throughout the text. Medical physics graduate students would benefit from a book which addresses practical clinical topics while learning statistics rather than abstract statistical analysis that is the approach of many other statistics books.

Contents:

1 Fundamental Concepts and Their Applications
1.1 Permutations
1.2 Combinations
1.3 Frequency Distribution
1.4 Median, Mode, and Mean
1.5 Quartiles
1.6 Cumulative Frequency Distribution
Useful References
Practice Exercises
2 Probability Distribution
2.1 Introduction to Characteristics of Probability Distributions
2.2 Binomial Probability Distribution
2.2.1 Fundamentals
2.2.2 Application A
2.2.3 Application B
2.2.4 Application C
2.3 Poisson Probability Distribution
2.3.1 Fundamentals
2.3.2 Applications
2.4 Normal Probability Distribution
2.4.1 Fundamentals
2.4.2 Application A
2.4.3 Application B
2.5 Log Normal Probability Distribution
2.5.1 Fundamentals
2.5.2 Application
2.6 Error Function
2.6.1 Basics
2.6.2 Application
Useful References
Practice Exercises
3 More Details about the Normal Probability Distribution
3.1 The Mean
3.2 The Standard Deviation
3.3 Statistical Sampling
3.4 Applications of Mean and Standard Deviation
3.4.1 Estimation of the Standard Deviation
3.4.2 Relative Standard Deviation
3.5 Standard Deviation for Addition and Subtraction Operations
3.6 Standard Deviation for Multiplying or Dividing Operations
3.7 Standard Error of the Mean
3.8 The Cumulative Normal Probability Distribution
3.9 Approximation to the Cumulative Normal Probability Distribution
3.10 Confidence Intervals
3.11 Logit Transforms
3.12 Applications
Useful References
Practice Exercises
4 Separation of Two Statistical Populations
4.1 Variation of Sample Mean
4.2 Separation of Two Different Normal Population Distributions
4.3 The Decision Matrix
4.4 Receiver Operating Characteristic (ROC) Graphs
4.5 Student's T-Test
4.6 Required Sample Size
4.7 Chauvenet's Criterion
4.8 Chi-Square Test for""Goodness of Fiti""
4.9 Applications
Useful References
Practice Exercises
5 Bayes' Theorem
5.1 Basics
5.2 Patient Population Characteristics
5.3 Applications
Useful References
Practice Exercises
6 Graphical Fits to Measured Data
6.1 Basics of Linear Regression
6.2 Inverse Matrix Approach to Linear Regression
6.3 Polynomial Fit to Data
6.4 Exponential Functions
6.5 Logarithmic Functions
6.6 Power Functions
6.7 Standard Error of the Estimate (SE)
Useful References
Practice Exercises
7 Correlation Function
7.1 Linear Correlation Coefficient
7.2 Alternate Form for Linear Correlation Coefficient
7.3 How Significant Is the R2 Value?
7.4 Terminology for Correlation
7.5 Correlation for Nonlinear Functions
Useful References
Practice Exercises
8 Fractals and Their Applications
8.1 Basic Concepts
8.2 Examples of Fractals in Nature
8.3 Applications of Fractals to Human Anatomy
8.4 Mandelbrot Sets
Useful References
Practice Exercises
9 Monte Carlo Methods
9.1 Random Numbers
9.2 Random Walk
9.3 Illustrations of Monte Carlo Process
9.3.1 Application Using First Monte Carlo Example
9.3.2 Application Using a Second Monte Carlo Example
9.4 Monte Carlo Analysis of X-Ray Photon Interactions
Useful References
Practice Exercises
10 Application of Statistics to Image Quality Measurements
10.1 Signal-to-Noise Ratio (SNR)
10.2 Contrast-to-Noise Ratio (CNR)
10.3 Contrast-Detail Diagrams
10.4 Detective Quantum Efficiency (DQE)
10.5 Noise Equivalent Quanta (NEQ)
10.6 Digital Subtraction Angiography (DSA)
Useful References
Practice Exercises
11 Misuse of Statistics
11.1 Introduction
11.2 Categories for Misuse of Statistics
11.2.1 Sampling Error
11.2.2 Influence of Bayes' Theorem
11.2.3 Spurious Correlations
11.2.4 Discarding Unfavorable Data
11.2.5 Mining Data
11.2.6 Ambiguous Evaluations
11.2.7 Systematic Errors
11.2.8 Verbal Context
11.3 Summary
Useful References
Appendix A: Normal Probability Distribution Tables
Appendix B: Two-Tailed Cumulative Normal Probability About the Mean Value Table
Appendix C: Lower One-Tailed Cumulative Normal Probability from -8 to X Table
Appendix D: Student's T-Test Value for Various Degrees of Freedom Table
Appendix E: Significance of the Correlation""Ri"" Value Table
Index
About the Author