Dichotomous Variables

A dichotomous variable is one that takes on one of only two possible values when observed or measured. The value is most often a representation for a measured variable (e.g., age: under 65/65 and over) or an attribute (e.g., gender: male/female).

If the dichotomous variable represents another variable, that underlying variable may be either observed or unobserved. For example, a dichotomous variable may be used to indicate whether a piece of legislation passed. The dichotomous variable (pass/fail) is a representation of the actual, and observable, vote on the legislation. In contrast, each legislator's vote is the result of an individual, and unobserved, probability distribution between voting either for or against the legislation.

Dichotomous variables are most commonly measured using 1 and 0 as the two possible values. The use of 1 and 0 usually has no specific meaning relating to the variable itself. One could just as easily choose 2 and 0, or 1 and −1 as the two values. Even so, the 1, 0 coding does have the advantage of showing, when cases are summed and averaged, the proportion of cases with a score of 1. The choice and assignment of 1 and 0 is usually based on ease of interpretation and the nature of the specific research question.

Dichotomous variables may be used as either dependent (endogenous)or independent (exogenous) variables. Many research questions in the social sciences use dichotomous dependent variables. Such questions often involve individual binary choices or outcomes (e.g., to purchase or not, to vote for or against, to affirm or reverse). Estimating models with dichotomous dependent variables often requires the use of nonlinear techniques because linear models (such as ordinary least squares) may be unrealistic on a theoretical level and produce inefficient or inconsistent results.

When used as independent variables, dichotomous variables are often referred to as “controlling” or “dummy” variables. Unfortunately, referring to dichotomous independent variables in this way may lead to inadequately justifying the measurement of the variable or its inclusion in the model. As with any other variable, a dichotomous independent variable should have a sound theoretical basis and be properly operationalized.

As a cautionary note, one must not be overly eager to “dichotomize” variables (i.e., convert a measurable underlying variable to dichotomous form) for three reasons. First, such conversions may not be theoretically justifiable. The popularity of estimation techniques such as probit analysis and logit caused some to unnecessarily convert continuous dependent variables to dichotomous form. Second, even when theoretically justified, such conversions necessarily result in a loss of information. It is one thing, for example, to know that the Supreme Court affirmed a decision, but quite another to know whether it did so by a 9–0 or 5–4 vote. Third, forcing a variable into just two categories may not always be easy or appropriate if there is a nontrivial residual category. For example, if one measures handedness dichotomously (left/right), the number of ambidextrous individuals or those with arm injuries that required converting to their other hand may pose coding or analytical problems.