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Dichotomous Variable

A dichotomous variable, a special case of categorical variable, consists of two categories. The particular values of a dichotomous variable have no numerical meaning. A dichotomous variable can either be naturally existing or constructed by a researcher through recoding a variable with more variation into two categories. A dichotomous variable may be either an independent or a dependent variable, depending on its role in the research design. The role of the dichotomous variable in the research design has implications for the selection of appropriate statistical analyses. This entry focuses on how a dichotomous variable may be defined or coded and then outlines the implications of its construction for data analysis.

Identification, Labeling, and Conceptualization of a Dichotomous Variable

Identification and Labeling

A dichotomous variable may also be referred to as a categorical variable, a nonmetric variable, a grouped dichotomous variable, a classification variable, a dummy variable, a binary variable, or an indicator variable. Within a data set, any coding system can be used that assigns two different values.

Natural Dichotomous Variables

Natural dichotomous variables are based on the nature of the variable and can be independently determined. These variables tend to be nominal, discrete categories. Examples include whether a coin toss is heads or tails, whether a participant is male or female, or whether a participant did or did not receive treatment. Naturally dichotomous variables tend to align neatly with an inclusive criterion or condition and require limited checking of the data for reliability.

Constructed Dichotomous Variables

Dichotomous variables may be constructed on the basis of conceptual rationalizations regarding the variables themselves or on the basis of the distribution of the variables in a particular study.

Construction Based on Conceptualization

While studies may probe the frequency of incidence of particular life experiences, researchers may provide a conceptually or statistically embedded rationale to support reducing the variation in the range of the distribution into two groups. The conceptual rationale may be rooted in the argument that there is a qualitative difference between participants who did or did not receive a diagnosis of depression, report discrimination, or win the lottery. The nature of the variable under study may suggest the need for further exploration related to the frequency with which participants experienced the event being studied, such as a recurrence of depression, the frequency of reported discrimination, or multiple lottery winnings. Nonetheless, the dichotomous variable allows one to distinguish qualitatively between groups, with the issue of the multiple incidence or frequency of the reported event to be explored separately or subsequently.

Construction Based on Distribution

The original range of the variable may extend beyond a binomial distribution (e.g., frequency being recorded as an interval such as never, sometimes, often, or with an even broader range when a continuous variable with possible values of 1–7 may be reduced to two groups of 1–4 and 5–7). An analysis of the standard deviation and shape of the frequency distribution (i.e., as represented through a histogram, box-plot, or stem-and-leaf diagram) may suggest that it would be useful to recode the variable into two values. This recoding may take several forms, such as a simple median split (with 50% of scores receiving one value and the other 50% receiving the other value), or other divisions based on the distribution of the data (e.g., 75% vs. 25% or 90% vs. 10%) or other conceptual reasons. For example, single or low-frequency events (e.g., adverse effects of a treatment) may be contrasted with high-frequency events. The recoding of a variable with a range of values into a dichotomous variable may be done intentionally for a particular analysis, with the original values and range of the variable maintained in the data set for further analysis.

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