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July 03, 20167 min read

Which Measurement Scale Should We Use?

During statistical observations, we get results that we have to present on the decently. The method of the presentation depends on various factors such as the type of the observed data (discrete or continuous random variables). The level of measurement or scale of measure is a classification that describes the nature of information within the numbers assigned to variables. American Psychologist Stanley Smith Stevens developed the most popular classification with four levels: nominal, ordinal, interval, and ratio.

The properties of measurements scales that we examine at different scales are the following:

  • Identity: Each value on the scale has a unique meaning (e.g. 0 false , 1 true)
  • Magnitude: There is an ordered relationship between the scale values. Some elements are bigger, and some elements are smaller than others.
  • Equal Units: The units are equally divided along the scale. For example, the difference between 2 and 4 is equal to the difference between 6 and 8.
  • Location of Zero: Is the zero element the minimum value?

In this article, we will deal with Steven’s classic measurement scale. Let’s talk about the four categories he described:

Nominal

Nomial is the easiest of all the categories and the lowest measurement level by statistical viewpoint. There are no mathematical relations between the scale values. Sometimes, in the case of nominal scales, we assign numbers to objects as a label. It is not the measure of quantity rather, it measures the identity and difference.

Properties of a Nominal Scale
Identity Magnitude Equal Units True Zero
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Here is an** example** of the use of this scale:

nominal_scale

Figure 1. Nominal scale illustration

Ordinal

In the case of the ordinal scale, we can order the measurements in terms of “greater than”, “less than” or “equal to”. The ordinal scale is based on rankings. The order matters, but the differences between the variables do not. In the case of ordinal scales, we can use a median, but never use the mean because it is meaningless.

Properties of an Ordinal Scale
Identity Magnitude Equal Units True Zero
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An ordinal scale can be used for placing winners of a race, sizes of clothing and so on. Here is an example of the use of this scale:

ordinal_illsutration

Figure 2. Ordinal scale illustration

Interval

The interval scale values have an own identity and magnitude, and the scale units are equal. An interval scale is equally divided along the scale without a predefined zero point. The zero is not the minimum value of the scale. The difference between the neighboring points are measurable, so the difference in temperature for example between 10° F and 20° F is the same as the difference between 35° F and 45° F.

Properties of an Interval Scale
Identity Magnitude Equal Units True Zero
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The most frequently used interval scales are the Celsius scale and the Fahrenheit scale.

interval_scale

Figure 3. Interval scale illustration

Ratio

The ratio scale also has equally spaced units along the scale but with an absolute zero point. Zero is the first element of the scale. This type of scale is widely used in the physical sciences to measure mass, length, duration, and so on. This scale has all the properties that we described at the beginning of this document. These properties ensure that we execute all the operations, which includes addition, subtraction, multiplication, and division. The absolute zero point allows us to define how many times greater Value A is than Value B.

Properties of a Ratio Scale
Identity Magnitude Equal Units True Zero
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The Kelvin temperature scale has a true zero point:

ratio_illustration

Figure 4. Ratio scale illustration

Summary Table

Comparing of the different scales to each other makes them easier understand.

Comparison Table
Identity Nominal Ordinal Interval Ratio
Frequency (Countable) like-icon like-icon like-icon like-icon
Ordered (<, =, > ) like-icon like-icon like-icon
Difference between Values like-icon like-icon
Add or Subtract Values like-icon like-icon
Multiply and Divide Values like-icon
Absolute Zero Point like-icon

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