Statistics: Overview

Empirical work is about estimating the relationships among variables and then, based on the values of and confidence in those estimates, discussing their substantive implications. These relationships are expressed as a model relating some outcome or set of outcomes, the endogenous variable or variables, denoted by Y, to a set of explanatory variables, conventionally denoted by X and referred to as the exogenous or causal variables. The models may be explicitly referred to as causal models, but the term causal is frequently treated as implicit.

The current commonly used definition of causation, referred to as the Neyman-Holland-Rubin (NHR) model, is based on how one might expect Y to be different if there were a different value for X in an otherwise identical world. A second view is that causation is a process of interactions that connect values of X to values of Y and that this process depends on the context being studied. For example, being female might be the “cause” of women's wages being lower than wages for men with the same education and experience because of the chain of actions that occur in the labor market, not because an additional X chromosome affects wages. An important research objective is elaborating and examining empirically the components of this chain in their sequential order. All views of causation imply a temporal sequence, where a change in X must occur, or have a very strong likelihood of occurring, prior to the change in Y even if the time lag is smaller than the intervals at which one observes X and Y. An important requirement for models and empirical work is that they improve our understanding of this causal process.

Causal models and thinking are a central part of our personal and professional lives. If you hit your thumb with a hammer, it will hurt and you will at a minimum get a bad bruise. More abstractly, social scientists talk regularly in causal terms: Will mailings increase voter turnout? Will reducing class size improve student learning? Will more on-the-job training raise wages? Will economic sanctions bring a nation to the bargaining table? These examples involve a chain of reasoning underlying the causal statement connecting the change in one variable to the change in the other. The hammer hitting a thumb does not directly cause the bruise, [Page 2525]pain, and swelling. Post cards, smaller classes, job training, and sanctions per se do not cause voters to turn out, students to get higher test scores, wages to increase, or countries to bargain, but we proceed as if we believe they do.

Causal statements vary in the confidence one has in the causal logic or in the chain of events linking Y to X and therefore in the prediction of how Y is likely to be different if X is different. For example, one can confidently predict that your thumb will hurt, swell, and turn purple if you hit it with a hammer. There is less confidence in the prediction that turnout will increase if all potential voters receive a mailing or a phone call before election day. And there is far, far less confidence in the prediction that economic sanctions will lead a rogue state to negotiate. This entry provides a brief introduction to the types of data and statistical methods used in the social sciences to try to reduce this uncertainty about causal arguments and to estimate the magnitude of the relationship between Y and the X.

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