In Exercises 21–28, determine which of the four levels of measurement (nominal, ordinal, interval, ratio) best describes the given data.
College Students In order to better plan for the incoming freshman class, a college dean asks each newly admitted student to identify their likely major (physics, business, math, psychology, engineering, law, etc.).

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Understand the four levels of measurement: Nominal, Ordinal, Interval, and Ratio. Nominal involves categories without a specific order, Ordinal involves categories with a specific order, Interval involves numerical scales with equal intervals but no true zero, and Ratio involves numerical scales with a true zero.

Identify the type of data being collected. In this case, the data consists of categories of college majors such as physics, business, math, etc.

Determine if there is any inherent order to the categories. College majors do not have a natural order; one major is not inherently 'higher' or 'lower' than another.

Since the data consists of categories without a specific order, it fits the definition of the nominal level of measurement.

Conclude that the level of measurement for the given data (college majors) is nominal, as it involves categorizing students into groups without any ranking or order.

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주요 개념

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Levels of Measurement

The levels of measurement refer to the different ways data can be categorized and quantified. They include nominal, ordinal, interval, and ratio scales. Each level has distinct characteristics that determine how data can be analyzed and interpreted, influencing the types of statistical tests that can be applied.

Nominal Scale

The nominal scale is the simplest level of measurement, used for categorizing data without any order or ranking. In this scale, data is classified into distinct categories that are mutually exclusive, such as names of majors (e.g., physics, business). The only permissible operation is counting the frequency of each category.

Ordinal Scale

The ordinal scale involves categorizing data into ordered categories, where the order matters but the differences between the categories are not quantifiable. For example, if students were ranked by their preference for majors, the order would indicate preference but not the degree of difference between them. This scale allows for comparisons in terms of greater or lesser but not precise measurements.