The following represent examples of the use of nominal scales in measurement, except for a. ethnic group. b. SAT scores. c. hair color. d. gender
The correct answer and explanation is:
The correct answer is b. SAT scores.
Nominal scales are used for measurement when data are categorized without any quantitative value or order. They simply label or name categories that are mutually exclusive and collectively exhaustive. Examples include ethnic group, hair color, and gender. These categories identify groups but do not imply any rank or numeric relationship between them.
Ethnic group, hair color, and gender are classic examples of nominal data because they classify individuals into distinct groups. For example, ethnic group categories might include “Asian,” “African,” and “Caucasian.” Hair color might be categorized as “blonde,” “brown,” or “black.” Gender is often categorized as “male,” “female,” or other identities. None of these categories have an inherent order or value; they only serve as labels.
SAT scores, however, are measured on an interval or ratio scale rather than a nominal scale. SAT scores are numeric values assigned based on a standardized test, and these numbers have meaning in terms of quantity and order. A higher SAT score indicates better performance than a lower score. The scores can be compared, ranked, and used for meaningful arithmetic operations such as calculating averages or differences. This kind of measurement allows more complex statistical analysis beyond simple categorization.
In summary, nominal scales categorize without any order or numerical value. Ethnic group, hair color, and gender fit this definition perfectly because they assign categories or names. SAT scores do not fit this definition since they are numeric values that convey magnitude and rank. Therefore, SAT scores are an example that does not belong with the nominal scale examples.