Table of Contents

1. Introduction to Statistics and Statistical Thinking

1.1 Overview

1. Collecting and Measuring Data
2. What Is Statistics?
3. The Purpose of Statistics
4. Inferential Statistics
5. Types of Data
6. Applications of Statistics
7. Fundamentals of Statistics
8. Critical Thinking
9. Experimental Design
10. Random Samples
11. Attributions

2. Statistics in Practice

2.1 Observational Studies

1. What are Observational Studies?
2. The Clofibrate Trial
3. Confounding
4. Sex Bias in Graduate Admissions
5. Attributions

2.2 Controlled Experiments

1. The Salk Vaccine Field Trial
2. The Portacaval Shunt
3. Statistical Controls
4. Attributions

3. Visualizing Data

3.1 The Histogram

1. Cross Tabulation
2. Drawing a Histogram
3. Recognizing and Using a Histogram
4. The Density Scale
5. Types of Variables
6. Controlling for a Variable
7. Selective Breeding
8. Attributions

3.2 Graphing Data

1. Statistical Graphics
2. Stem-and-Leaf Displays
3. Reading Points on a Graph
4. Plotting Points on a Graph
5. Slope and Intercept
6. Plotting Lines
7. The Equation of a Line
8. Attributions

4. Frequency Distributions

4.1 Frequency Distributions for Quantitative Data

1. Guidelines for Plotting Frequency Distributions
2. Outliers
3. Relative Frequency Distributions
4. Cumulative Frequency Distributions
5. Graphs for Quantitative Data
6. Typical Shapes
7. Z-Scores and Location in a Distribution
8. Attributions

4.2 Frequency Distributions for Qualitative Data

1. Describing Qualitative Data
2. Interpreting Distributions Constructed by Others
3. Graphs of Qualitative Data
4. Misleading Graphs
5. Do It Yourself: Plotting Qualitative Frequency Distributions
6. Summation Notation
7. Graphing Bivariate Relationships
8. Attributions

5. Describing, Exploring, and Comparing Data

5.1 Central Tendency

1. Mean: The Average
2. The Average and the Histogram
3. The Root-Mean-Square
4. Which Average: Mean, Mode, or Median?
5. Averages of Qualitative and Ranked Data
6. Attributions

5.2 Measures of Relative Standing

1. Measures of Relative Standing
2. Median
3. Mode
4. Attributions

5.3 The Law of Averages

1. What Does the Law of Averages Say?
2. Chance Processes
3. The Sum of Draws
4. Making a Box Model
5. Attributions

5.4 Further Considerations for Data

1. The Sample Average
2. Which Standard Deviation (SE)?
3. Estimating the Accuracy of an Average
4. Chance Models
5. The Gauss Model
6. Comparing Two Sample Averages
7. Odds Ratios
8. When Does the Z-Test Apply?
9. Attributions

6. Measures of Variation

6.1 Describing Variability

1. Range
2. Variance
3. Standard Deviation: Definition and Calculation
4. Interpreting the Standard Deviation
5. Using a Statistical Calculator
6. Degrees of Freedom
7. Interquartile Range
8. Measures of Variability of Qualitative and Ranked Data
9. Distorting the Truth with Descriptive Statistics
10. Exploratory Data Analysis (EDA)
11. Attributions

7. Sampling

7.1 Populations and Samples

1. Populations
2. Samples
3. Random Sampling
4. Random Assignment of Subjects
5. Surveys or Experiments?
6. Attributions

7.2 Sample Surveys

1. The Literary Digest Poll
2. The Year the Polls Elected Dewey
3. Using Chance in Survey Work
4. How Well Do Probability Methods Work?
5. The Gallup Poll
6. Telephone Surveys
7. Chance Error and Bias
8. Attributions

7.3 Sampling Distributions

1. What Is a Sampling Distribution?
2. Properties of Sampling Distributions
3. Creating a Sampling Distribution
4. Continuous Sampling Distributions
5. Mean of All Sample Means (μ x)
6. Shapes of Sampling Distributions
7. Sampling Distributions and the Central Limit Theorem
8. Attributions

7.4 Errors in Sampling

1. Expected Value and Standard Error
2. Using the Normal Curve
3. The Correction Factor
4. A Closer Look at the Gallup Poll
5. Attributions

7.5 Sampling Examples

1. Measuring Unemployment
2. Chance Models in Genetics
3. Attributions

8. Probability

8.1 What Are the Chances?

1. Fundamentals of Probability
2. Conditional Probability
3. Unions and Intersections
4. Complementary Events
5. Attributions

8.2 Probability Rules

1. The Addition Rule
2. The Multiplication Rule
3. Independence
4. Counting Rules and Techniques
5. Bayes’ Rule
6. The Collins Case
7. Attributions

8.3 More About Chance

1. The Paradox of the Chevalier De Méré
2. Are Real Dice Fair?
3. Attributions

Appendix

Glossary of Key Terms