De Veaux Map

From Sean_Carver
Revision as of 19:31, 19 November 2018 by Carver (talk | contribs) (→‎Chapter 15: Random Variables)
Jump to: navigation, search

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
Formulas for variance and standard deviation
Thinking about variation
  • 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
Working with pictures of the Normal curve
Inflection points at mean +/- one standard deviation
Interpretation of area under Normal curve as proportion of observations in interval (implied by pictures and exposition)
  • 5.4: Finding Normal Percentiles
Normal percentiles
Other models
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

Chapter 12: Experiments and Observational Studies

  • 12.1: Observational Studies
Observations studies
Retrospective studies
Prospective studies
  • 12.2: Randomized, Comparative Experiments
Random assignment of subjects to treatments
Explanatory variables, factors and levels
Response variables
  • 12.3: The Four Principles of Experimental Design
Principle 1: Control
Principle 2: Randomize
Principle 3: Replicate
Principle 4: Block
Diagramming experiments
Statistically significant differences between groups
Contrasting experiments and samples
  • 12.4: Control Treatments
Blinding (single and double)
Placebos
  • 12.5: Blocking
Matched participants
  • 12.6: Confounding
Lurking or confounding

Part IV: Randomness and Probability

Chapter 13: From Randomness to Probability

  • 13.1: Random Phenomena
"A random phenomenon is a situation in which we know what outcomes can possibly occur, but we don't know which particular outcome will happen"
Trials
Outcomes
Sample space
Events
The law of large numbers
Empirical probability
The nonexistent law of averages
  • 13.2: Modeling Probability
Theoretical probability
Personal probability
  • 13.3: Formal Probability
The five rules of probability
Rule 1: A probability must be a number between 0 and 1
Rule 2: Probability assignment rule: The probability of a the sample space must be 1
Rule 3: The complement rule
Rule 4: The addition rule
Rule 5: The multiplication rule

Chapter 14: Probability Rules!

  • 14.1: The General Addition Rule
  • 14.2: Conditional Probability and the General Multiplication Rule
  • 14.3: Independence
  • 14.4: Picturing Probability: Tables, Venn Diagrams, and Trees
  • 14.5: Reversing the Conditioning and Bayes' Rule

Chapter 15: Random Variables

  • 15.1: Center: The Expected Value
Computation of expected value for discrete random variables
  • 15.2: Spread: The Standard Deviation
Computation of variance and standard deviation for discrete random variables
  • 15.3: Shifting and Combining Random Variables
E(X +/- c)
Var(X +/- c)
E(aX)
Var(aX)
E(X +/- Y)
Var(X +/- Y), when X and Y are independent
  • [Unnumbered section, labeled optional]: Correlation and Covariance
Covariance of two random variables
Var(X +/- Y), when X and Y covary
Correlation of two random variables
  • 15.4: Continuous Random Variables
The Normal random variable as an example of a continuous random variable
Caption to Figure 15.1: Interpretation of area under Normal curve as probability of finding an observation in the interval.
How can every value have a probability 0?
Sums of independent Normal random variables are Normal.

Chapter 16: Probability Models

  • 16.1: Bernoulli Trials
  • 16.2: The Geometric Model
  • 16.3: The Binomial Model
  • 16.4: Approximating the Binomial Model
  • 16.5: The Continuity Correction
  • 16.6: The Poisson Model
  • 16.7: Other Continuous Random Variables: The Uniform and the Exponential
Retrieved from "https://seancarver.org/index.php?title=De_Veaux_Map&oldid=3487"