De Veaux Map

Part I: Exploring and Understanding Data

Chapter 1: Exploring and Understanding Data =

• 1.1: What is Statistics?
• 1.2: Data
• 1.3: Variables

Types of Variables: Categorical, Quantitative, Identifier, Ordinal

Chapter 2: Displaying and Describing Categorical Data

• 2.1: Summarizing and Displaying a Single Categorical Variable

The area principle

Frequency tables

Bar charts

Pie charts

• 2.2: Exploring the Relationship Between Two Categorical Variables

Contingency tables

Conditional distributions

Independence

Plotting conditional distributions (with pie charts, bar charts and segmented bar charts)

Chapter 3: Displaying and Displaying Quantitative Data

• 3.1: Displaying Quantitative Variables

Histograms

Stem and leaf displays

Dotplots

• 3.2: Shape

Unimodal, bimodal or multimodal

Symmetric or skewed

Outliers

• 3.3: Center

Median

• 3.4: Spread

Range, min, max

Interquartile range, Q1, Q3

• 3.5: Boxplots and 5-Number Summaries
• 3.6: The Center of a Symmetric Distribution: The Mean

Mean or Median?

• 3.7: The Spread of a Symmetric Distribution: The Standard Deviation
• 3.8: Summary---What to Tell About a Quantitative Variable

Chapter 4: Understanding and Comparing Distributions

• 4.1: Comparing Groups with Histograms
• 4.2: Comparing Groups with Boxplots
• 4.3: Outliers
• 4.4: Timeplots
• 4.5: Re-Expressing Data: A First Look

...To improve symmetry

...To equalize spread across groups

Chapter 5: The Standard Deviation as a Ruler and the Normal Model

• 5.1: Standardizing with z-Scores
• 5.2: Shifting and Scaling

Shifting to adjust the center

Rescaling to adjust the scale

Shifting, scaling and z-Scores

• 5.3: Normal Models

The "nearly normal condition"

The 68-95-99.7 Rule

• 5.4: Finding Normal Percentiles

Normal percentiles

From percentiles to scores: z in reverse

• 5.5: Normal Probability Plots

Part II: Exploring Relationships Between Variables

Chapter 6: Scatterplots, Association, and Correlation

• 6.1: Scatterplots

Direction (negative or positive)

Form

Strength

Outliers

Explanatory and response variables

• 6.2: Correlation

Formula

Assumptions and conditions for correlation, including...

"Quantitative variables condition,"

"Straight enough condition,"

"No outliers condition"

• 6.3: Warning: Correlation Does Not Equal Causation
• 6.4: Straightening Scatterplots

Chapter 7: Linear Regression

• 7.1 Least Squares: The Line of "Best Fit"

The linear model

Predicted values and residuals

The least squares line and the sense in which it is the best fit

• 7.2 The Linear Model

Using the linear model to make predictions

• 7.3 Finding the Least Squares Line

Formulas for slope and intercept

• 7.4 Regression to the Mean

Etiology of the word "Regression"

Math Box: Derivation of regression formula

• 7.5 Examining the Residuals

Formula for residuals

Appropriate (lack of) form of Residuals versus x-Values plot

The residual standard deviation

• 7.6 R^2---The Variation Accounted For by the Model

How big should R^2 be?

Predicting in the other direction---A tale of two regressions

• 7.7 Regression Assumptions and Conditions

"Quantitative variable" condition

"Straight enough" condition

"Outlier" condition

"Does the plot thicken?" condition

Judging the conditions with the residuals-versus-predicted-values plot

Chapter 8: Regression Wisdom

• 8.1: Examining Residuals

Getting the "bends": When the residuals aren't straight

Sifting residuals for groups

Subsetting with a categorical variable

• 8.2: Extrapolation: Reaching Beyond the Data

Warning with extrapolation

Warning with predicting what will happen to cases in the regression if they were changed

• 8.3: Outliers, Leverage, and Influence
• 8.4: Lurking Variables and Causation
• 8.5: Working with Summary Values

Chapter 9: Re-expressing Data: Get It Straight!

• 9.1: Straightening Scatterplots -- The Four Goals

Goal 1: Make the distribution of a variable more symmetric.

Goal 2: Make the spread of several groups more alike, even if their centers differ

Goal 3: Make the form of a scatterplot more nearly linear

Goal 4: Make the scatter in a scatterplot spread out evenly rather than thinkening at one end

• 9.2: Finding a Good Re-Expression

The ladder of powers