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A Statistical Guide for the Ethically Perplexed

Table of Contents

Preamble

Introduction
The (Questionable) Use of Statistical Models

TOOLS FROM PROBABILITY AND STATISTICS
Probability Theory: Background and Bayes’ Theorem
The (Mis)assignment of Probabilities
The Probabilistic Generalizations of Logical Fallacies Are No Longer Fallacies
Using Bayes’ Rule to Assess the Consequences of Screening for Rare Events
Bayes’ Rule and the Confusion of Conditional Probabilities
Bayes’ Rule and the Importance of Base Rates

Probability Theory: Application Areas
Some Probability Considerations in Discrimination and Classification
Probability and Litigation
Betting, Gaming, and Risk

Correlation
Illusory Correlation
Ecological Correlation
Restriction of Range for Correlations
Odd Correlations
Measures of Nonlinear Association
Intraclass Correlation

Prediction
Regression toward the Mean
Actuarial Versus Clinical Prediction
Incorporating Reliability Corrections in Prediction
Differential Prediction Effects in Selection
Interpreting and Making Inferences from Regression Weights
The (Un)reliability of Clinical Prediction

The Basic Sampling Model and Associated Topics
Multivariable Systems
Graphical Presentation
Problems with Multiple Testing
Issues in Repeated-Measures Analyses
Matching and Blocking
Randomization and Permutation Tests
Pitfalls of Software Implementations
Sample Size Selection

Psychometrics
Traditional True Score Theory Concepts of Reliability and Validity
Test Fairness
Quotidian Psychometric Insights
Psychometrics, Eugenics, and Immigration Restriction

DATA PRESENTATION AND INTERPRETATION
Background: Data Presentation and Interpretation
Weight-of-the-Evidence Arguments in the Presentation and Interpretation of Data

(Mis)reporting of Data
The Social Construction of Statistics
Adjustments for Groups Not Comparable on a Variable, Such As Age

Inferring Causality
Casuistry
The Bradford-Hill Criteria for Determining a Causal Connection
Some Historical Health and Medical Conceptions of Disease Causality
Medical Error as (the) Causative Factor

Simpson’s Paradox

Statistical Sleuthing and Explanation
Sleuthing Interests and Basic Tools
Survival Analysis
Statistical Sleuthing and the Imposition of the Death Penalty: McCleskey v. Kemp (1987)

EXPERIMENTAL DESIGN AND THE COLLECTION OF DATA
Background: Experimental Design and the Collection of Data
Observational Studies: Interpretation
Observational Studies: Types
Observational Studies: Additional Cautions
Controlled Studies
Controlled Studies: Additional Sources of Bias
The Randomized Response Method

Ethical Considerations in Data Collection
The Nazi Doctor’s Trial and the Nuremberg Code
The National Research Act of 1974
The Declaration of Helsinki

The Federal Rules of Evidence
Junk Science
The Consequences of Daubert and the Data Quality Act (of 2001)

Some Concluding Remarks

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