Comments on Seeing and Doing

I am grateful to Professor Lindley for taking the time to study my book Causality, and for summarizing its main ideas so crisply and lucidly to the readers of this Journal. I would like to comment on a couple of issues that I believe warrant further emphasis in discussing causality. The first concerns the importance of mathematical notation for distinguishing causal from associational relationships, the second deals with the theoretical foundations of causality. It is true that many members of Lindley's generation were not tormented by causal questions but, still, one should not take lightly the frustration of those who tried to tackle such questions and who could not find any mathematical machinery for solving, or even posing those questions. Having been part of this frustrated generation, I remember quite clearly how, even ten years ago, we could not express mathematically the simple fact that symptoms do not cause diseases, let alone draw mathematical conclusions from such facts. Asking for the probability that one event "caused" another was considered an ill-posed, metaphysical question that lies outside the province of statistical analysis. Statisticians who had to interface with researchers in other disciplines have encountered many barriers of confusion and miscommunication, all rooted in causation. The main users of statistical methods: economists, biologists, and health and social scientists, brought with them a wealth of substantive, do(x)-type information (also called "assumptions"), which they were unable to incorporate into statistical methods and techniques. Likewise, these users expected statistical methods to produce meaningful do(x)-type conclusions, but all statistics could deliver were study-specific associations of the see(x) variety. In some applications (e.g., epidemiology), the absence of notational distinction between do(x) and see(x)-type dependencies seemed unnecessary, because investigators were able to keep such distinctions implicitly in their heads, and managed to confine the mathematics to strictly conventional, see(x)-type expressions. In others, as in economics and the social sciences, investigators rebelled against this notational restriction by leaving mainstream statistics and constructing their own mathematical machinery (called Structural Equation Models). This machinery has remained a mystery to outsiders, and eventually became a mystery to insiders as well. "Every science is only so far exact as it knows how to express one thing by one sign," said Augustus de Morgan in 1858, and the results of not having the signs for expressing causality reached a critical point in the 1980-90's. Problems such as the control of confounding, the estimation of treatment effects, the distinction between direct and indirect effects, the estimation of probability of causation, and the combination of experimental and nonexperimental data became a source of endless disputes among the users of statistics, and statisticians could not come to the rescue. Causality describes several such disputes, and why they could not be resolved by conventional statistical methodology.