Module 3: The Analysis of 2× 2× 2 (Multiway) Contingency Tables: Explaining Simpson’s Paradox and Demonstrating Racial Bias in the Imposition of the Death Penalty

This module discusses the two major topics of Simpson’s paradox and the Supreme Court decision in McCleskey v. Kemp (1987). Simpson’s paradox is ubiquitous in the misinterpretation of data; it is said to be present whenever a relationship that appears to exist at an aggregated level disappears or reverses when disaggregated and viewed within levels. A common mechanism for displaying data that manifests such a reversal phenomenon is through a multiway contingency table, often of the 2× 2× 2 variety. For example, much of the evidence discussed in McCleskey v. Kemp was cross-categorized by three dichotomous variables: race of the victim (black or white), race of the defendant (black or white), and whether the death penalty was imposed (yes or no). Despite incontrovertible evidence that the race of the victim plays a significant role in whether the death penalty is imposed, the holding in McClesky v. Kemp was as follows: Despite statistical evidence of a profound racial disparity in application of the death penalty, such evidence is insufficient to invalidate defendant’s death sentence.