# Mathematical Scales of Measurement

Nominal Ordinal Interval Ratio
Principles
People or objects with the same scale value are the same on some attribute.

The values of the scale have no 'numeric' meaning in the way that you usually think about numbers.

People or objects with a higher scale value have more of some attribute.

The intervals between adjacent scale values are indeterminate.

Scale assignment is by the property of "greater than," "equal to," or "less than."

Intervals between adjacent scale values are equal with respect the the attribute being measured.

E.g., the difference between 8 and 9 is the same as the difference between 76 and 77.

There is a rationale zero point for the scale.

Ratios are equivalent, e.g., the ratio of 2 to 1 is the same as the ratio of 8 to 4.

Examples
Gender.

Ethnicity.

Marital Status.

Movie ratings (0, 1, or 2 thumbs up).

SES.

USDA quality of beef ratings (good, choice, prime).

The rank order of anything.

Degrees F.

Most personality measures.

WAIS intelligence score.

Degrees K.

Annual income in dollars.

Length or distance in centimeters, inches, miles, etc.

Operations
Counting Greater than or less than operations. Addition and subtraction of scale values. Multiplication and division of scale values.

Louis Guttman, Scales and the Structures of Social Life, American Sociological Review 9:139-150, 1944

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