Nominal Scale

Key Concepts

The nominal scale, which is often referred to as the unordered categorical or discrete scale, is used to assign individual datum into categories. Categories in the nominal scale are mutually exclusive and collectively exhaustive. They are mutually exclusive because the same label is not assigned to different categories and different labels are not assigned to events or objects of the same category. Categories in the nominal scale are collectively exhaustive because they encompass the full range of possible observations so that each event or object can be categorized. The nominal scale holds two additional properties. The first property is that all categories are equal. Unlike in other scales, such as ordinal, interval, or ratio scales, categories in the nominal scale are not ranked. Each category has a unique identifier, which might or might not be numeric, which simply acts as a label to distinguish categories. The second property is that the nominal scale is invariant under any transformation or operation that preserves the relationship between individuals and their identifiers.

Some of the most common types of nominal scales used in research include sex (male/female), marital status (married or common-law/widowed/ divorced/never-married), town of residence, and questions requiring binary responses (yes/no).

Stevens's Hierarchy

In the mid-1940s, Harvard psychophysicist Stanley Stevens wrote the influential article “On [Page 903]the Theory of Scales of Measurement,” published in Science in 1946. In this article, Stevens described a hierarchy of measurement scales that includes nominal, ordinal, interval, and ratio scales. Based on basic empirical operations, mathematical group structure, and statistical procedures deemed permissible, this hierarchy has been used in textbooks worldwide and continues to shape statistical reasoning used to guide the design of statistical software packages today.

Under Stevens's hierarchy, the primary, and arguably only, use for nominal scales is to determine equality, that is, to determine whether the object of interest falls into the category of interest by possessing the properties identified for that category. Stevens argued that no other determinations were permissible, whereas others argued that even though other determinations were permissible, they would, in effect, be meaningless. A less argued property of the nominal scale is that it is invariant under any transformation. When taking attendance in a classroom, for example, those in attendance might be assigned 1, whereas those who are absent might be assigned 2. This nominal scale could be replaced by another nominal scale, where “1” is replaced by the label “present” and “2” is replaced by the label “absent.” The transformation is considered invariant because the identity of each individual is preserved. Given the limited determinations deemed permissible, Stevens proposed a restriction on analysis for nominal scales. Only basic statistics are deemed permissible or meaningful for the nominal scale, including frequency, mode as the sole measure of central tendency, and contingency correlation. Despite much criticism during the past 50 years, statistical software developed during the past decade has sustained the use of Stevens's terminology and permissibility in its architecture.

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