Table of 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