Causal Reasoning in Graphics

Overview

Most data graphics describe; few argue. The difference is whether the display is organized around the causal variable or merely around time and sequence. Tufte's chapter "Visual and Statistical Thinking" in Visual Explanations establishes the standard through two paired case studies: John Snow's 1854 cholera map, which correctly displays a causal argument and helps end an epidemic, and the 13 Morton Thiokol charts faxed to NASA the night before the Challenger launch, which rested on the right causal theory but selected and arranged the data in ways that concealed the causal signal and contributed to seven deaths. The lesson is not stylistic: how data is arranged determines whether a causal relationship is visible or invisible, and that invisibility can be fatal.

§1. The Fundamental Question: Compared with What?

Every causal claim requires a comparison. Without a baseline, a count is only a count.

Tufte identifies "Compared with what?" as the foundational question in statistical analysis. In Visual Explanations (p. 30), he argues that studying only cholera victims provides only half the evidence — a complete causal investigation requires equally rigorous analysis of those who did not contract the disease.

Snow had 83 deaths mapped. The map's causal argument depended equally on showing the spaces with no deaths — the brewery (70+ workers, no cholera; they drank malt liquor and never used the Broad Street pump) and the workhouse (535 inmates, only 5 deaths; they had their own well and never sent to Broad Street for water). Both anomalies are visible only because they appear on the same map as the deaths.

The Thiokol engineers committed the mirror failure. Pre-launch, their damage-history chart listed the damaged flights with no temperatures attached, and their temperature chart covered just two launches plus four test motors (p.43) — the 17 flights without damage, almost all at warm temperatures, never entered the evidence. (The familiar 7-damaged-vs-17-undamaged split describes the post-accident 48-rocket chart, pp.46–47.) Those undamaged flights are the statistical leverage that reveals the temperature-damage correlation.

Tufte draws the parallel directly in Visual Explanations (p. 44): the Thiokol engineers' data selection was equivalent to Snow having mapped only a subset of cholera deaths while ignoring all the disease-free areas and their pumps. The undamaged flights carry the statistical leverage that makes the temperature pattern visible — numbers become evidence only when placed in relation to each other.