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: Quantitative, identifier, ordinal, categorical (categorical & nominal considered synonyms)

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

Recognizing when a re-expression can help

• 9.2: Finding a Good Re-Expression

Plan A: The ladder of powers

Re-expressing to straighten a scatterplot

Comparing re-expressions

Plan B: Attack of the logarithms

Multiple benefits to re-expressions

Why not just fit a curve?

Part III: Gathering Data

Chapter 10: Understanding Randomness

• 10.1: What Is Randomness?

Meaning of the word "random"

Discussion of the process of generating random numbers

• 10.2: Simulating by Hand

Basic terminology: Simulations, trials, components, response variable

Chapter 11: Sample Surveys

• 11.1: The Three Big Ideas of Sampling

Idea 1: Examine a part of the whole

Population versus sample

Bias

Idea 2: Randomize

Idea 3: It's the sample size

Sample size

Does a census make sense

• 11.2: Populations and Parameters
• 11.3: Simple Random Samples

Sampling frame

Sampling variability

• 11.4: Other Sampling Designs

Stratified sampling

Cluster sampling

Multistage sampling

Systematic sampling

• 11.5: From the Population to the Sample: You Can't Always Get What You Want
• 11.6: The Valid Survey

Know what you want to know

Tune your instrument

Ask specific rather than general questions

Ask for quantitative results when possible

Be careful in phrasing questions

Pilot studies

• 11.7: Common Sampling Mistakes or How to Sample Badly

Mistake 1: Sample volunteers

Mistake 2: Sample convieniently

Mistake 3: Use a bad sampling frame

Mistake 4: Undercoverage

Nonresponse bias

Response bias

How to think about biases

Look for biases in any survey you encounter

Spend your time and resources reducing biases

Think about the members of the population who could have been excluded from your study

Always report your sampling methods in detail