Scales of Measurements

There are four scales on which a given variable can be measured – Nominal, Ordinal, Interval, Ratio.

Statistical Concepts
Scales of Measurements
Nominal Scale

Chintu has built several apps. All these apps have names. To handle the hosting, each app has also been allotted unique ID numbers. These apps cater to specific industries. 

These three variables (name, ID, and industry) cannot be compared. They are simply tags. The names DuoLingo and AmongUs are not inherently comparable. We could probably rate them based on UX and design but otherwise, the names are merely labels. Similarly, Analytics and Consulting are industries that cannot be compared on the basis of the tag itself. Even the unique ID, which can be recorded in numerals, is acting as a label. 

On nominal scale, we measure these kinds of variables that act as a tag or a label.

Formally, a nominal scale is the 1st level of measurement scale in which the records serve as “tags” or “labels” to classify or identify the objects. A nominal scale usually deals with the non-numeric variables or the numbers that do not have any value.

Characteristics of Nominal Scale

  • It is qualitative. The numbers are used here to identify the objects.
  • The numbers don’t define the object characteristics. The only permissible aspect of numbers in the nominal scale is “counting.”

Example: The names of ice creams available at a counter.

Ordinal Scale

Chintu released one of his apps on Google Play Store. Very soon, it ranked 3rd in the Top-grossing charts after Free Fire and Call of Duty. 

Here, it is very clear that there is an inherent ordering in the variable called Top-grossing. Free Fire has earned the most, followed by Call of Duty and then Chintu’s app. Yet, we cannot clearly interpret the difference between the order of these apps. We fail to answer questions such as by how much a second-ranked app is behind the top-ranked one.

Such a variable is measured on an ordinal scale.

Formally, the ordinal scale is the 2nd level of measurement that reports the ordering and ranking of data without establishing the degree of variation between them. 

Characteristics of the Ordinal Scale

  • The ordinal scale shows the relative ranking of the variables
  • Along with the information provided by the nominal scale, ordinal scales give the rankings of those variables

Example: NIRF rankings of colleges and universities; the CAT percentile.

Interval Scale

Example 1 – Looking at Chintu’s success, Chutki also released an app on Google Play Store. She asked her friends to rate the app. The rating menu had an option of 1-5 stars. 

In this case, the ratings are measured on an interval scale as the difference between the rating stars is meaningful and the presence of zero is arbitrary (zero does not exist).

Example 2 – Sensing competition from Chutki, Chintu started working harder. This caused him to develop a high fever. He was advised to rest. Bored, he started switching the measurement unit on his thermometer from Celsius to Fahrenheit and vice-versa.

Both these measures of temperature have meaningful differences that can be compared. However, the zero is arbitrary in both cases since it doesn’t denote the absence of heat. 

Formally, the interval scale is the 3rd level of measurement scale. It is defined as a quantitative measurement scale where there is order, the difference between the two variables is meaningful and equal, and the presence of zero is arbitrary. It measures variables that exist along a common scale at equal intervals.

Characteristics of Interval Scale:

  • The interval scale is quantitative as it can quantify the difference between the values
  • To understand the difference between the variables, we can subtract the values between the variables

Example: On a scale of 1 to 10, how likely you might recommend this article or blog to your friends, classmates (This is known as Net Promoter Score or NPS).

Ratio Scale

Chutki’s app received a great response from people. Within a month, the downloads crossed a thousand while also receiving great reviews.

The number of downloads is an example of measurement of the ratio scale. Here, there is a natural order, the differences have meaningful interpretations and the presence of zero is not arbitrary – it truly denotes the absence of the quantity, here downloads.  

Formally, the ratio scale is the 4th level of measurement scale. It allows us to compare the differences or intervals. The ratio scale has a unique feature. It possesses the character of the origin or zero points.

Characteristics of Ratio Scale:

  • Ratio scale has a feature of absolute zero
  • It doesn’t have negative numbers, because of its zero-point feature
  • We can orderly add, subtract, multiply, divide the variables.

Example: We measure height, weight on a ratio scale.

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