A Modern Statistical Re-Analysis of John Snow’s 1854 South London ‘Grand Experiment’

Abstract

Cholera is a horrible and often deadly disease and was a scourge of mid-19th century London, visiting in 1831, 1849, 1854, and for the last time in 1866. John Snow proposed in 1849 that cholera was a gastrointestinal disease that was transmitted via ingestion of contaminated fecal matter (known today as the fecal-oral route), a theory we now know is correct. At the time, however, there was considerable uncertainty and competition among alternative theories. Snow is well-known for his accumulation of evidence in support of his theory, but William Farr, John Simon, and others contributed to the evidence and debate over competing theories.This paper focuses on one particular strand of Snow’s evidence, his south London "Grand Experiment" - analyzing mortality for a population of nearly half a million. Snow’s analysis was innovative - he is credited with the first application of both randomization as an instrumental variable (IV) and differences-in-differences (DiD). I undertake a re-analysis of the south London evidence, casting Snow’s analysis in the modern forms of DiD and randomization as IV. The re-examination supports Snow’s claims that the south London data demonstrated water as the primary causal factor, providing strong evidence against alternative theories. For modern practitioners Snow’s analysis provides a valuable example and template for "good design, relevant data, and testing predictions against reality in a variety of settings" (Freedman, 1991).

Keywords: John Snow, Cholera, Causal Inference, Epidemiology, Statistical Methodology, History of Science

JEL Classification: C18, N33, N93, B40, C52