Which scale of measurement includes categories without any numerical value?

The nominal scale of measurement is characterized by its use of categories that do not have inherent numerical values or a specific order. This type of scale is often utilized to classify data into distinct groups based on qualitative traits or characteristics. For example, categories such as gender, hair color, or types of pets fall under the nominal scale because they differentiate between groups without indicating any rank or quantity. Each category is unique and there is no mathematical relationship between them.

In contrast, the ordinal scale does involve an order to its categories but does not specify the degree of difference between them. Interval and ratio scales both incorporate numerical values where meaningful calculations can be performed, including addition and subtraction for interval scales, and multiplication and division for ratio scales, which provide additional context and detail regarding the relationships of the values measured. Thus, the distinction of the nominal scale is its focus on simple classification without quantitative implications.