Ordinal Scale

In the hierarchy of measurement levels, the ordinal scale is usually considered the second lowest classification order, falling between the nominal and interval scales. An ordinal scale is a measurement scale that allocates values to variables based on their relative ranking with respect to one another in a given data set. Ordinal-level measurements indicate a logical hierarchy among the variables and provide information on whether something being measured varies in degree, but does not specifically quantify the magnitude between successive ranks. The measurement taxonomy, including the ordinal scale terminology, was first brought forth by psychologist Stanley Smith Stevens in his 1946 seminal paper and has subsequently guided the selection of appropriate statistical techniques despite debates on its limitations, data exceptions, and contemporary relevance.

Ordinal-scale variables may be further classified as strongly ordered or weakly ordered (as presented by J. Chapman McGrew, Jr., and Charles Monroe) depending on the ranking scheme. A strongly ordered variable is one in which the measurements [Page 976]are continuous, sequentially ordered, and not strictly categorically dependent. For example, a list of the 10 most populous countries in the world receive rankings based on their relative population size to one another, demonstrating an order then from highest to lowest; however, as with all ordinal-level data, the exact difference in population between successive rankings would be unknown. On the other hand, a weakly ordered variable is based on nominal-level groups that are then rank-ordered in a meaningful arrangement. These groups represent frequency counts and do not display individual rankings of the aggregated data, thus limiting the amount of information conveyed when compared with strongly ordered variables. Categories showing country population as low (less than 1 million), medium (between 1 million and 100 million), and high (greater than 100 million), for instance, are weakly ordered because rankings within the ordered categories cannot be differentiated.

Numeric measurements on ordinal scales are ordered such that higher (lower) rankings are associated with larger (smaller) values. A common ordinal scale frequently employed in social and behavioral research is the Likert scale, which uses a hierarchical ranking system to indicate comparative levels of satisfaction, confidence, agreement, and so on, about a subject. Many mental constructs in psychology cannot be observed directly; therefore, these measures tend to be ordinal (e.g., Likert scaling). Opinions, attitudes, level of anxiety, specific personality characteristics, and so on, are all constructs that are regarded as varying in degree among individuals but tend to allow only indirect ordinal measurements. These are generally self-report measures. For example, a subject might be asked to rate the level of satisfaction he or she experiences with his or her current job on a Likert scale from 1 (extremely dissatisfied) to 5 (extremely satisfied). It cannot be assumed that a person assigning a rating of “4” to that question is exactly twice as satisfied with his or her job as a co-worker who answers the question with a “2.” However, it is clear that the first person feels more satisfied with his or her job than the co-worker.

Providing rankings is also a common type of ordinal scale. For example, a subject might be asked to rank a list of values according to what is most important to him or her. Another example is a faculty search committee asked to rank-order a list of job candidates based on the overall qualifications in the areas of teaching ability, research skills, and so on. The candidate ranked “1” will be perceived by the committee as better than the candidate ranked “2,” but not how much better. A special case of the ordinal scale occurs when data are used to classify individuals into two categories (a dichotomy), but the variable itself is assumed to be normally distributed with underlying continuity. For example, a psychological test might classify individuals into the categories normal (1) or abnormal (0). There is an implied order in the presence or absence of a characteristic.

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