Statistics in a Nutshell by Boslaugh, Sarah -- Read -- Imperial Library of Trantor

Index

Statistics in a Nutshell SPECIAL OFFER: Upgrade this ebook with O’Reilly 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 SPECIAL OFFER: Upgrade this ebook with O’Reilly Copyright

← Prev
Back
Next →

← Prev
Back
Next →