Errors of Measurement: Dichotomization of a Continuous Variable

A variable is any concept that has more than one possible value. This is contrasted with a constant whose value never changes (e.g., pi, the speed of light). A variable, at a minimum, must have two possible values (e.g., gender has male or female). A variable, at the other end, can have an unlimited set of potential values (distance between two places measured in meters). The question is how to organize or set up the measurement of some quantity using an operationalization. This entry introduces dichotomization of a continuous variable as one approach to addressing errors of measurement, paying specific attention to the justifications for and costs of deploying this method.

An operationalization takes the conceptual variable and provides a means of measurement using some device. When measuring an attitude toward chocolate, for example, the device could be as simple as (a) like and (b) dislike. A more sophisticated measurement may involve a number of choices and a person could rate the degree of preference (like or dislike) on a 1–3, 1–5, 1–7 basis, for instance. Essentially, one can use a simple dichotomous measure or use a more refined measurement tool.

What typically happens is that measurements use more than one instance, particularly in the case of a Likert statement. For example, one could rate the desire for chocolate using a Likert statement (e.g., where 1 refers to very much agree and 5 to very much disagree) as a response to the statement, “Chocolate is my favorite food.” Then, the participants are asked a second item, such as, “Chocolate is a great treat to eat.” Basically, one can add a series of statements and then create a scale to measure the attitude. The usual practice is to add up the individual scores from each statement to form a composite score to represent the attitude (usually after a variety of measurement tests examining the factor structure and/or reliability evaluations).

The use of such approaches generates a set of scores that form a continuous variable with a potential range. The expectation is that the estimates of the mean (as well as other measures of central tendency) and the measures of variability (variance, range, standard deviation) reflect the assumption of a normal distribution (bell-shaped curve).