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Index
Statistics in a Nutshell
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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
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
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
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
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
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
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
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
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
9. Factorial ANOVA and ANCOVA
Factorial ANOVA
Interaction
Two-Way ANOVA
Three-Way ANOVA
ANCOVA
Exercises
10. Multiple Linear Regression
Multiple Regression Models
Dummy Variables
Methods for Building Regression Models
Forward entry
Backward removal
Exercises
Example 1
Example 2
11. Logistic, Multinomial, and Polynomial Regression
Logistic Regression
Converting Logits to Probabilities
Multinomial Logistic Regression
Polynomial Regression
Overfitting
Exercises
12. Factor Analysis, Cluster Analysis, and Discriminant Function Analysis
Factor Analysis
Cluster Analysis
Discriminant Function Analysis
Exercises
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
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
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
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
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
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
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
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
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 Equalities
Fractions, Decimals, and Percents
Factorials, Permutations, and Combinations
Answers
Laws of Arithmetic and Real Numbers
Exponents, Roots, and Logarithms
Natural Logarithms
Solving Equations for x
Solving Systems of Linear Equations
Linear Equations and Cartesian Coordinates
Linear Equalities
Fractions, Decimals, and Percents
Factorials, Permutations, and Combinations
B. Introduction to Statistical Packages
Minitab
SPSS
SAS
R
Microsoft Excel
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
D. Probability Tables for Common Distributions
The Standard Normal Distribution
The t-Distribution
The Binomial Distribution
The Chi-Square Distribution
E. Online Resources
General Resources
Glossaries
Probability Tables
Online Calculators
Online Textbooks
F. Glossary of Statistical Terms
Index
About the Author
Colophon
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