A Minimal Book Example
1
Introduction
2
Categorizing and Summarizing Information
2.1
How to Tell a Story
2.2
Types of Data
2.2.1
Statistics and Parameters
2.2.2
Scales of Measurement
2.2.3
Dependent and Independent Variables, Predictor Variables and Predicted Variables
2.3
Summary Statistics
2.3.1
A Brief Divergence Regarding Histograms
2.3.2
Central Tendency
2.3.3
Quantiles
2.3.4
Spread
2.3.5
Skew
2.3.6
Kurtosis
2.4
R Commands
2.4.1
mean
2.4.2
median
2.4.3
mode
2.4.4
quantiles
2.4.5
range
2.4.6
variance
2.4.7
standard deviation
2.4.8
Skewness and kurtosis
2.5
Bonus Content
2.5.1
The mathematical link between mean, variance, skewness, and kurtosis
3
Visual Displays of Data
3.1
About this Page
3.1.1
Packages Used to Make The Figures in This Chapter
3.1.2
Datasets Created for the Figures in This Chapter
3.2
Making the Audience Smarter
3.3
Essentials of Good Visualization
3.3.1
Maximize the Data-ink Ratio
3.3.2
When
Not
to Visualize Data
3.3.3
Lines and Angles
3.3.4
Ducks
3.3.5
Annotations
3.3.6
Lying
3.3.7
Colors
3.3.8
Fonts
3.4
Types of Visualization
3.4.1
Boxplots
3.4.2
Bar Charts
3.4.3
Histograms
3.4.4
Combining Histogram Elements with Bar Chart Elements
3.4.5
Scatterplots
3.4.6
Line Charts
3.4.7
Pie Charts
3.4.8
Forestplots
3.4.9
Heatmaps
3.4.10
Choropleth maps
3.4.11
Alluvial Diagrams (
aka
Sankey Plots,
aka
Riverplots,
aka
Ribbonplots)
3.4.12
Small Multiples
3.5
Closing Remarks
3.6
The Worst Data Visualization Ever Made
4
Probability Theory
4.1
Probability, Statistics, and Scientific Inquiry
4.2
The Three Kolmogorov (1933) Axioms
4.2.1
1. Non-negativity
4.2.2
2. Normalization
4.2.3
3. Finite Additivity
4.3
Methods of Assigning Probability
4.3.1
Objective Methods
4.3.2
Subjective Probability
4.4
Intersections and Unions
4.4.1
Intersections
4.4.2
Unions
4.5
Expected Value and Variance
4.5.1
Probability Trees
4.6
Elementary and Compound (or Composite) Events
4.7
Permutations and Combinations
4.7.1
Permutations
4.7.2
Combinations
4.8
Odds
4.8.1
Odds in Favor/Against
4.8.2
Odds Ratios
4.9
Conditional Probability
4.9.1
Binomial Probability
4.9.2
Bayes’s Theorem
4.10
Monte Carlo Methods
4.10.1
Random Walk Models
4.10.2
Markov Chain Monte Carlo (MCMC)
4.11
Summary Information
4.11.1
Glossary
4.11.2
Formulas
4.12
Bonus Content
4.12.1
Why is the factorial of zero equal to one?
4.12.2
Excerpts from
Statistics for Everybody
by D. Barch, reprinted with permission from the author
5
Probability Distributions
5.1
Weirdly-shaped Jars and the Marbles Inside
5.2
The Binomial Distribution
5.2.1
Discrete Probability
5.2.2
Features of the Binomial Distribution
5.2.3
Sufficient Statistics for the Binomial
5.2.4
Cumulative Binomial Probability
5.2.5
Finding Binomial Probabilities with R Commands
5.3
The Normal Distribution
5.3.1
The Standard Normal Distribution
5.3.2
Features of the Normal Distribution
5.3.3
The Cumulative Normal Distribution
5.3.4
Percentiles with the Normal Distribution
5.3.5
The Connections Between the Normal and the Binomial
5.4
the
\(t\)
distribution
5.4.1
The Central Limit Theorem
5.5
The
\(\chi^2\)
Distribution
5.6
Other Probability Distributions
5.6.1
Uniform distribution
5.6.2
the
\(\beta\)
distribution
5.6.3
The Logistic Distribution
5.6.4
The Poisson Distribution
5.7
Interval Estimates
6
Classical and Bayesian Inference
6.0.1
Different Approaches to Analyzing the Same Data
6.0.2
The Essential Difference
6.0.3
Consequences of the Difference
6.1
Examples of Classical and Bayesian Analyses
6.1.1
Classical Null Hypothesis Testing
6.1.2
The Six (sometimes Five) Step Procedure
6.1.3
Confidence Intervals
6.2
Bayesian Inference
6.2.1
Posterior Probabilities
6.2.2
Bayesian Interval Estimates
6.2.3
Bayes Factor
7
Correlation and Regression
7.1
Correlation Does Not Imply Causation…
7.1.1
…but it Doesn’t Imply NOT Causation either
7.2
Correlation
7.2.1
The Product Moment Correlation Coefficient
\(r\)
7.2.2
Parametric Correlation Example
7.2.3
Nonparametric correlation
7.2.4
Nonlinear correlation
7.3
Regression
7.3.1
The Least-Squares Regression Line
7.3.2
The Proportionate Reduction in Error (
\(r^2\)
)
7.3.3
Prediction Errors,
a.k.a.
Residuals
7.4
Bonus Content
7.4.1
Correcting the Kendall’s
\(\tau\)
Software Estimate
8
Signal Detection Theory
8.1
Detecting Signals
8.1.1
Hits, Misses, False Alarms, and Correct Rejections
8.2
The Signal Detection Metaphor
8.2.1
Limits of the Signal-Detection Metaphor
8.2.2
Signal + Noise and Noise Distributions
8.3
Distinguishing Signal from Noise
8.3.1
\(d'\)
8.3.2
\(\beta\)
8.3.3
C-statistic
8.4
Doing the Math
8.4.1
Assumptions of Variances
8.4.2
SDT with Unequal Variances
8.4.3
Equal Variance Assumption
References
Published with bookdown
Advanced Statistics
References