De Veaux Map
From Sean_Carver
Contents
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
- 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
- Idea 1: Examine a part of the whole
- 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