Home » Measurement Scales: Nominal, Ordinal, Interval and Ratio
Statistics For Economists

# Measurement Scales: Nominal, Ordinal, Interval and Ratio

## Measurement Scales:

By measurement, we usually mean the assigning of numbers to observations or objects and scaling is a process of measuring. The four scales of measurement are briefly mentioned below:

## Nominal Scale:

The classification or grouping of the observations into mutually exclusive qualitative categories or classes is said to constitute a nominal scale. For example, students are classified as male and female. Number 1 and 2 may also be used to identify these two categories. Similarly, rainfall may be classified as heavy, moderate and light. We may use number 1, 2 and 3 to denote the three classes of rainfall. The numbers when they are used only to identify the categories of the given scale carry no numerical significance and there is no particular order for the grouping.

## Ordinal or Ranking Scale:

It includes the characteristic of a nominal scale and in addition has the property of ordering or ranking of measurements. For example, the performance of students (or players) is rated as excellent, good, fair or poor, etc. Number I, 2, 3, 4, etc. are also used to indicate ranks. The only relation that holds between any pair of categories is that of greater than (or more preferred).

## Interval Scale:

A measurement scale possessing a constant interval size (distance) but not a true zero point, is called an interval scale. Temperature measured on either the Celsius or the Fahrenheit scale is an outstanding example of interval scale because the same difference exists between 20°C (68°F) and 30°C (86°F) as between 5°C (41°F) and l5°C (59°F). It cannot be said that a temperature of 40 degrees is twice as bot as a temperature of 20 degree, i.e. the ratio 40/20 has no meaning. The arithmetic operation of addition, subtraction, etc. are meaningful.

An interval scale variable satisfies the last two properties of the ratio scale variable but not the first. Thus, the distance between two time periods, say (2000–1995) is meaningful, but not the ratio of two time periods (2000/1995). At 11:00 a.m. PST on August 11, 2007, Portland, Oregon, reported a temperature of 60 degrees Fahrenheit while Tallahassee, Florida, reached 90 degrees. Temperature is not measured on a ratio scale since it does not make sense to claim that Tallahassee was 50 percent warmer than Portland. This is mainly due to the fact that the Fahrenheit scale does not use 0 degrees as a natural base.

## Ratio Scale:

It is a special kind of an interval scale where the scale of measurement has a true zero point as its origin. The ratio scale is used to measure weight, volume, length, distance, money, etc. The key to differentiating interval and ratio scale is that the zero point is meaningful for ratio scale. For a variable X, taking two values, X1 and X2, the ratio X1/X2 and the distance (X2 – X1) are meaningful quantities. Also, there is a natural ordering (ascending or descending) of the values along the scale. Therefore, comparisons such as X2 ≤ X1 or X2 ≥ X1 are meaningful. Most economic variables belong to this category. Thus, it is meaningful to ask how big this year’s GDP is compared with the previous year’s GDP. Personal income, measured in dollars, is a ratio variable; someone earning \$100,000 is making twice as much as another person earning \$50,000.