The Order of the Statistical Jedi
Preface
Introduction
The power of repetition (and my…umm…
complicated
history with statistics)
But there’s a better way
Ethics
The Scientific Method
Univariate Distributions
Categorical Variables
Column Sorting
Visualizing
Pie Charts
Bar Charts
Interpreting Bar Charts
Example one
Example two
Univariate Estimates
Bivariate Visualizations
Bivariate Estimates
Diagnostics
Models are tools. And they don’t have feelings.
Residuals
Diagnostic tool # 1: Histogram of the residuals
Sensitivity Analyses
Diagnostic tool # 2: Residual Dependence (RD) Plot for Linearity
Statistical Models are Lazy
Residual Dependence Plots
How to Fix Nonlinearity
How to tell if nonlinearity is a problem?
How much nonlinearity is too much?
Diagnostic tool # 3: Scale-Location (SL) Plots for Homoscedasticity
Spread-Location (SL) Plots
Outliers
Independence
Why do models assume independence?
What happens if you violate the independence assumption?
How to detect and handle dependent data?
Summary
Probability
Why and when we need probability?
Finite Samples
Infinite sets
Infinite Sets and Sampling
How to ensure a representative sample
Probability Density Functions
Computing Probabilities From PDFs
Chapter Summary
Probability Two: Bayesian Versus Frequentist Approaches
A Tale of Two Roomates
Tom’s Approach
Egon’s Approach
What do they conclude?
The Bayesian Approach
Strengths of the Bayesian approach
Weaknesses/Objections to the Bayesian Approach
Frequentist/Likelihood Description
Strengths
Weaknesses
Probability 3: The Central Limit Theorem
The General Linear Model
Changes to make
Wax on, wax off
What is a model
What is the general linear model
What makes a good statistical model?
Categorical GLMs for Two Groups (t-test)
Out with the old, in with the shiny
Converting Categorical Variables to Numeric Variables
Categorical GLMs for Three + Groups (ANOVA)
Converting Three + Categories to Numeric Variables
Multivariate General Linear Models
What is a multivariate relationship?
Reasons to use multivariate GLMs
Multivariate GLMs: Conditioning Effects
Multicollinearity
Controlling by conditioning
Conditioning is just residualizing
All the ways of thinking about “conditioning”
Be careful about conditioning! (And using multiple regression)
1. Conditioning will not prove causation.
2. Be Careful what you condition on
3. Only study and interpret the effects of the interest variable
4. Conditioning with interaction effects.
Additional Estimates of Interest
Slopes
R squared.
Semi-Partial
\(R^2\)
Applied Analyses
ANCOVA
Multiple Regression
Multivariate GLMs: Interaction Effects
The language of interaction effects
Visualizing interaction effects
A simple visual trick to tell if there’s an interaction
The GLM for interaction effects
Main effects when interactions exist
Estimates for interactions
Applied Analyses
Factorial ANOVA
Multiple Regression
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The Order of the Statistical Jedi:
Responsibilities, Routines, and Rituals
The Order of the Statistical Jedi:
Responsibilities, Routines, and Rituals
Dustin Fife
2020-04-17
Preface