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measurement scale

Which measurement scale we have to use?

During the statistical observations we get results that we have to present on the decent way. The method of the presentation depends on various things like the type of the observed thing (discrete or contionous random variables).
Level of measurement or scale of measure is a classification that describes the nature of information within the numbers assigned to variables. An American Psychologist Stanley Smith Stevens developed the most popular classification, with four levels: nominal, ordinal, interval and ratio.

Properties of measurements scales, that we examine at the different scales:

  • Indentity: 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. So some elements are bigger and some elements are smaller than the other.
  • Equal units: the units are equally divided along the scale. This means that the difference between 2 and 4 is equal with difference between 6 and 8.
  • Location of zero: is the zero element is the minimum value?

In this article we will deal with the classic measurement scale by Stevens. Lets talk about the 4 categories that he described:

Nominal

This is the easisest of all and the lowest measurement level by statistical viewpoint. There is no any mathematical relation between the scale values. Sometimes in the case of Nominal scales we order numbers to objects as a label. It is not the measure of quantity, it measures indentity and difference.

 

Properties of Nominal scale
Identity Magnitude Equal units True zero
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Here is some example for the use of this scale:

nominal_scale-600x150

Nominal scale illustration

Ordinal

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

 

Properties of Ordinal scale
Identity Magnitude Equal units True zero
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Example: rank of a race, size of clothes etc…

ordinal_illsutration

Ordinal scale illustration

Interval

The scale values have an own identity, magnitude and the scale units are equal. 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 between 10 degrees F and 20 degrees F is the same as the difference between 35 degrees F and 45 degress F.

 

Properties of 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

Interval scale illustration

Ratio

It also has equally spaced units along the scale with an absolute zero point. Zero is the first element of the scale, this type are widely used in physical sciences (mass, length, duration, etc..,). This scale has all the properties that we described at the beginning of this document. This properties are ensure us to execute all the operations that include, addition, substraction, multiplication and division. The absolute zero point allow us to define how many times greater value A than value B.

 

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

ratio_illustration-600x170

Ratio scale illustration

Summary table

Comparison of the different scales to each other for the 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 substract values like-icon like-icon
Multiply and divide values like-icon
Absolute zero point like-icon
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