March 13, 2021
University of California, Los Angeles
Computer Science Department
Los Angeles, CA, 90095-1596, USA (310) 825-3243 / [email protected]
To students of causality, the writings of William Cochran provide an excellent and intriguing vantage point for studying how statistics, lacking the necessary mathematical tools, managed nevertheless to cope with increasing demands for policy evaluation from observational studies. Cochran met this challenge in the years 1955-1980, when statistics was preparing for a profound, albeit tortuous transition from a science of data, to a science of data generating processes. The former, governed by Fisher’s dictum (1922) “the object of statistical methods is the reduction of data” was served well by the traditional language of probability theory. The latter, on the other hand, seeking causal effects and policy recommendations, required an extension of probability theory to facilitate mathematical representations of generating processes.
No such representation was allowed into respectable statistical circles in the 1950-60s, when Cochran started looking into the social effects of public housing in Baltimore. While data showed improvement in health and well-being of families that moved from slums to public housing, it soon became obvious that the estimated improvement was strongly biased; Cochran reasoned that in order to become eligible for public housing the parent of a family may have to possess both initiative and some determination in dealing with the bureaucracy, thus making their families more likely to obtain better healthcare than non-eligible families.1 This led him to suggest “adjustment for covariates” for the explicit purpose of reducing this causal effect bias. While there were others before Cochran who applied adjustment for various purposes, Cochran is credited for introducing this technique to statistics (Salsburg, 2002) primarily because he popularized the method and taxonomized it by purpose of usage.
Unlike most of his contemporaries, who considered cause-effect relationships “ill-defined” outside the confines of Fisherian experiments, Cochran had no qualm admitting that he sought such relationships in observational studies. He in fact went as far as defining the objective of an observational study: “to elucidate causal-and-effect relationships” in situations where controlled experiments are infeasible (Cochran, 1965). Indeed, in the paper before us, the word “cause” is used fairly freely, and other causal terms such as “effect,” “influence,” and “explanation” are almost as frequent as “regression” or “variance.” Still, Cochran was well aware that he was dealing with unchartered extra-statistical territory and cautioned us:
“Claim of proof of cause and effect must carry with it an explanation of the mechanism by which this effect is produced.”