
Statistics in a Nutshell
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Content
- Intro
- Table of Contents
- Preface
- OK, Just What Is Statistics?
- The Focus of This Book
- Statistics in the Age of Information
- Organization of This Book
- Conventions Used in This Book
- Using Code Examples
- Safari® Books Online
- How to Contact Us
- Acknowledgments
- Chapter 1. Basic Concepts of Measurement
- Measurement
- Levels of Measurement
- Nominal Data
- Ordinal Data
- Interval Data
- Ratio Data
- Continuous and Discrete Data
- Operationalization
- Proxy Measurement
- True and Error Scores
- Random and Systematic Error
- Reliability and Validity
- Reliability
- Validity
- Triangulation
- Measurement Bias
- Bias in Sample Selection and Retention
- Information Bias
- Exercises
- Chapter 2. Probability
- About Formulas
- Basic Definitions
- Trials
- Sample Space
- Events
- Union
- Intersection
- Complement
- Mutual Exclusivity
- Independence
- Permutations
- Combinations
- Defining Probability
- Expressing the Probability of an Event
- Conditional Probabilities
- Calculating the Probability of Multiple Events
- Union of mutually exclusive events
- Union of events that are not mutually exclusive
- Intersection of independent events
- Intersection of nonindependent events
- Bayes' Theorem
- Enough Exposition, Let's Do Some Statistics!
- Dice, Coins, and Playing Cards
- Exercises
- Closing Note: The Connection between Statistics and Gambling
- Chapter 3. Inferential Statistics
- Probability Distributions
- The Normal Distribution
- The Binomial Distribution
- Independent and Dependent Variables
- Populations and Samples
- Nonprobability Sampling
- Probability Sampling
- The Central Limit Theorem
- Hypothesis Testing
- Confidence Intervals
- p-values
- The Z-Statistic
- Data Transformations
- Exercises
- Chapter 4. Descriptive Statistics and Graphic Displays
- Populations and Samples
- Measures of Central Tendency
- The Mean
- The Median
- The Mode
- Comparing the Mean, Median, and Mode
- Measures of Dispersion
- The Range and Interquartile Range
- The Variance and Standard Deviation
- Outliers
- Graphic Methods
- Frequency Tables
- Bar Charts
- Pie Charts
- Pareto Charts
- The Stem-and-Leaf Plot
- The Boxplot
- The Histogram
- Bivariate Charts
- Scatterplots
- Line Graphs
- Exercises
- Chapter 5. Categorical Data
- The R×C Table
- Measures of Agreement
- The Chi-Square Distribution
- The Chi-Square Test
- Fisher's Exact Test
- McNemar's Test for Matched Pairs
- Proportions: The Large Sample Case
- Correlation Statistics for Categorical Data
- Binary Variables
- The Point-Biserial Correlation Coefficient
- Ordinal Variables
- The Likert and Semantic Differential Scales
- Exercises
- Chapter 6. The t-Test
- The t Distribution
- The One-Sample t-Test
- Confidence Interval for the One-Sample t-Test
- The Independent Samples t-Test
- Confidence Interval for the Independent Samples t-Test
- Repeated Measures t-Test
- Confidence Interval for the Repeated Measures t-Test
- Unequal Variance t-Test
- Exercises
- Chapter 7. The Pearson Correlation Coefficient
- Association
- Scatterplots
- Relationships Between Continuous Variables
- The Pearson Correlation Coefficient
- Testing Statistical Significance for the Pearson Correlation
- The Coefficient of Determination
- Exercises
- Chapter 8. Introduction to Regression and ANOVA
- The General Linear Model
- Linear Regression
- Assumptions
- Analysis of Variance (ANOVA)
- One-Way ANOVA
- Post Hoc Tests
- Calculating Simple Regression by Hand
- Exercises
- Regression
- ANOVA
- Chapter 9. Factorial ANOVA and ANCOVA
- Factorial ANOVA
- Interaction
- Two-Way ANOVA
- Three-Way ANOVA
- ANCOVA
- Exercises
- Chapter 10. Multiple Linear Regression
- Multiple Regression Models
- Dummy Variables
- Methods for Building Regression Models
- Forward entry
- Backward removal
- Exercises
- Example 1
- Example 2
- Chapter 11. Logistic, Multinomial, and Polynomial Regression
- Logistic Regression
- Converting Logits to Probabilities
- Multinomial Logistic Regression
- Polynomial Regression
- Overfitting
- Exercises
- Chapter 12. Factor Analysis, Cluster Analysis, and Discriminant Function Analysis
- Factor Analysis
- Cluster Analysis
- Discriminant Function Analysis
- Exercises
- Chapter 13. Nonparametric Statistics
- Between-Subjects Designs
- The Wilcoxon Rank Sum Test
- The Sign Test
- The Median Test
- Kruskal-Wallis H Test
- Within-Subjects Designs
- Wilcoxon Signed Ranks Test
- Friedman Test
- Exercises
- Chapter 14. Business and Quality Improvement Statistics
- Index Numbers
- Time Series
- Decision Analysis
- Minimax, Maximax, and Maximin
- Decision Making under Risk
- Decision Trees
- Quality Improvement
- Run Charts and Control Charts
- Exercises
- Chapter 15. Medical and Epidemiological Statistics
- Measures of Disease Frequency
- Ratio, Proportion, and Rate
- Prevalence and Incidence
- Crude, Category-Specific, and Standardized Rates
- The Risk Ratio
- Attributable Risk, Attributable Risk Percentage, and Number Needed to Treat
- The Odds Ratio
- Confounding, Stratified Analysis, and the Mantel-Haenszel Common Odds Ratio
- Power Analysis
- Sample Size Calculations
- Confidence Interval for a Proportion
- Power for the Test of the Difference between Two Sample Means (Independent Samples t-Test)
- Exercises
- Chapter 16. Educational and Psychological Statistics
- Percentiles
- Standardized Scores
- Test Construction
- Classical Test Theory: The True Score Model
- Reliability of a Composite Test
- Measures of Internal Consistency
- Split-Half Methods
- Coefficient Alpha
- Item Analysis
- Item Response Theory
- Exercises
- Chapter 17. Data Management
- An Approach, Not a Set of Recipes
- The Chain of Command
- Codebooks
- The Rectangular Data File
- Spreadsheets and Relational Databases
- Inspecting a New Data File
- String and Numeric Data
- Missing Data
- Chapter 18. Research Design
- Basic Vocabulary
- Observational Studies
- Quasi-Experimental Studies
- Experimental Studies
- Ingredients of a Good Design
- Gathering Experimental Data
- Identifying Experimental Units
- Identifying Treatments and Controls
- Specifying Treatment Levels
- Specifying Response Variables
- Blinding
- Retrospective Adjustment
- Blocking and the Latin Square
- Example Experimental Design
- Chapter 19. Communicating with Statistics
- General Notes
- Writing for a Professional Journal
- Writing the Article
- The Peer Review Process
- Writing for the General Public
- Writing for Your Workplace
- Chapter 20. Critiquing Statistics Presented by Others
- Evaluating the Whole Article
- The Misuse of Statistics
- Common Problems
- Quick Checklist
- Issues in Research Design
- Variation
- Population
- Sampling
- Controls
- The Power of Coincidence
- Descriptive Statistics
- Measures of Central Tendency
- Standard Error and Confidence Intervals
- Graphical Presentation of Data
- Extrapolation and Trends
- Inferential Statistics
- Assumptions of Statistical Tests
- t-tests
- ANOVA
- Linear regression
- Appendix A. Review of Basic Mathematics
- Laws of Arithmetic
- Order of Operations
- Properties of Real Numbers
- Exponents and Roots
- Properties of Roots
- Solving Equations
- Systems of Equations
- Graphing Equations
- Linear Inequalities
- Fractions
- Factorials, Permutations, and Combinations
- Exercises
- Laws of Arithmetic and Real Numbers
- Exponents, Roots, and Logarithms
- Natural Logarithms
- Solving Equations for x
- Systems of Linear Equations
- Linear Equations and Cartesian Coordinates
- Linear Inequalities
- Fractions, Decimals, and Percents
- Factorials, Permutations, and Combinations
- Answers
- Laws of Arithmetic and Real Numbers
- Exponents and Roots
- Logarithms
- Solving Equations for x
- Solving Systems of Linear Equations
- Linear Equations and Cartesian Coordinates
- Linear Inequalities
- Fractions, Decimals, and Percents
- Factorials, Permutations, and Combinations
- Appendix B. Introduction to Statistical Packages
- Minitab
- SPSS
- SAS
- R
- Microsoft Excel
- Appendix C. References
- Preface and General Sources
- Chapter 1
- Chapter 2
- Chapter 3
- Chapter 4
- Chapter 5
- Chapter 6
- Chapter 7
- Chapter 8
- Chapter 9
- Chapter 10
- Chapter 11
- Chapter 12
- Chapter 13
- Chapter 14
- Chapter 15
- Chapter 16
- Chapter 17
- Chapter 18
- Chapter 19
- Chapter 20
- Appendix D. Probability Tables for Common Distributions
- The Standard Normal Distribution
- The t-Distribution
- The Binomial Distribution
- The Chi-Square Distribution
- Appendix E. Online Resources
- General Resources
- Glossaries
- Probability Tables
- Online Calculators
- Online Textbooks
- Appendix F. Glossary of Statistical Terms
- Index
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