Causal Inference in Statistics: A Primer

If you have taught an introductory statistics course, you have probably uttered the phrase “correlation is not causation” many times. While most textbooks include that idea, fewer explain when it is relevant. Generally, a carefully designed experiment in which we control extraneous variables and randomly assign subjects to treatments allows us to reach causal conclusions, at least for the subjects at hand. The mantra is relevant primarily to situations where we take a survey of a randomly selected sample, or to observational studies where no randomization is applied. In these situations we cannot control any of the variables involved, and so it is hard to be sure of their effect.

Unfortunately, there are many research questions that are not amenable to a designed experiment. The variables may be intrinsically beyond our control, like the weather, or there may be ethical considerations when the subjects are human beings. We would like very much to be able to untangle causes in these situations, and statisticians have addressed that desire for decades. The earliest firm guidelines are known as “Hill’s Criteria.” These were formalized in part during a debate over the harmful effects (if any) of smoking. They are well worth discussing in a first course because most of the statistics our students will see in later life will not be from controlled experiments.

Hill’s Criteria are methodological principles described in words. In recent years, there have been attempts to devise mathematical techniques that help us assess causes in observational data. Judea Pearl, first author of the book at hand, has been prominent among those making this attempt. A mathematician who considers phrases like “causal chain” or “causal connections” will not be surprised to learn that Pearl’s work has involved the use of graph theory. A graph can be made of associational interconnections in a particular situation. We can focus on the directionality of the edges and the effects of cutting an existing edge or the implications of the existence of an edge we observe.

The work at hand offers a list of about sixty references for those wanting details, but the back cover describes this book as a “beginner-level book” that is “accessible… to the interested layperson.” Clearly the blurb writer has not read the book! The chapter template begins with a verbal explanation that tries to characterize the problem at hand. These are well-written and would be accessible to the intended audience. But nothing in these introductory explanations would allow anyone to understand or use the techniques. After these few words, the exposition becomes very mathematical. Reasonable prerequisites might be a year-long introductory statistics course, a mathematical statistics course (which would presuppose multi-variable calculus), and a basic familiarity with graph theory. So in fact the book is not likely to be accessible to a lay person or a beginner or even to most social scientists.

For those who do have the real prerequisites, however, this book serves the valuable purpose of gathering material scattered through the research literature into a single source.

After a few years in industry, Robert W. Hayden (bob@statland.org) taught mathematics at colleges and universities for 32 years and statistics for 20 years. In 2005 he retired from full-time classroom work. He now teaches statistics online at statistics.com and does summer workshops for high school teachers of Advanced Placement Statistics. He contributed the chapter on evaluating introductory statistics textbooks to the MAA's Teaching Statistics.