Can an Ordinal Variable Be Measured on a Continuous Scale

Scales of Measurement

There are four scales of measurement in statistics which are nominal scale, ordinal scale, interval scale, and ratio scale. Scales of measurement are defined as the ways to collect and analyze data. It depends on the purpose of the study and the type of data (qualitative or quantitative) on which the selection of an appropriate scale is being dependent.

1.	What are Scales of Measurement in Statistics?
2.	Nominal Scale of Measurement
3.	Ordinal Scale of Measurement
4.	Interval Scale of Measurement
5.	Ratio Scale of Measurement
6.	FAQs on Scales of Measurement

What are Scales of Measurement in Statistics?

When data is collected for a study, the next step is to analyze it which depends on the tools that we used for data collection. For example, if we want to collect qualitative data, then we can use certain labels (nominal scale) from which the respondents will select their option. For quantitative data, interval scales and ratio scales can be used which makes it possible for the researcher to represent the data using numbers. Let us take an example of data collection to find out the nature of cars people prefer to drive. This type of data can be collected using a scale with certain labels like electric cars, diesel cars, hybrid cars, etc. So, a nominal scale of measurement will be used for this purpose. Similarly, if the researcher wants to find out the weight of people in a town, then a ratio scale of measurement can be used. We will be learning about the properties of all four scales of measurement in this article in the sections below.

The four scales of measurement in statistics are listed below:

• Nominal
• Ordinal
• Interval
• Ratio

These scales of measurement are written in a fixed order which specifies that the ordinal scale contains properties of a nominal scale as well, the interval scale has properties of both nominal and ordinal scales, and at last, the ratio scale has properties of all the above three scales of measurement.

Let us learn about each measurement scale one by one.

Nominal Scale of Measurement

A nominal scale of measurement is used for qualitative data. It does not give any numerical meaning to the data. Using the nominal scale of measurement, the data can be classified but cannot be added, subtracted, multiplied, or divided. It can cover a wide variety of qualitative data. Some of the situations where nominal measurement scale can be used are given below:

• Study to find the country of birth of people in a town
• In collecting data on the eye color of people
• Classifying people into categories like male/female, working-class population/unemployed, vaccinated/unvaccinated people, etc.

Some of the properties of the nominal scale of measurement are given below:

1. It can categorize variables but does not put them in any order.
2. It does not show any numerical value.
3. It is used for qualitative data.

Ordinal Scale of Measurement

The ordinal scale of measurement groups the data into order or rank. It contains the property of nominal scale as well, which is to classify data variables into specific labels. And in addition to that, it organizes data into groups though it does not have any numerical value. For example, the study of people's satisfaction with a company's product on a scale of #1 - Very happy, #2 - satisfactory, #3 - neutral, #4 - unhappy, and #5 - extremely dissatisfied. This is an example of an ordinal scale of measurement. This measurement scale can be used for the following purposes:

• Ranks of players in a race.
• Data collection on variables such as hottest to coldest, richest to poorest, etc.
• Data on people's satisfaction with any product, person, or government.

Some of the properties of the ordinal measurement scale are listed below:

1. It displays the order or rating of the variables.
2. It does not give any numerical value to the data. So, it is also used for qualitative data as similar to nominal measurement scale.
3. It contains variables that can be placed in order like heaviest to lightest, ranks of players or students, etc.

Interval Scale of Measurement

The interval scale of measurement includes those values that can be measured in a specific interval, for example, time, temperature, etc. It shows the order of variables with a meaning proportion or difference between them. For example, on a temperature scale, the difference between 20 °C and 30 °C is the same as the difference between 50°C ad 60°C. It is an example of an interval measurement scale. On the other hand, the difference between the scores of the first two rankers in a race and the two runner-ups will be different, which is an example of an ordinal scale.

Some of the properties of the interval scale of measurement are listed below:

1. It includes the properties of both nominal and ordinal scales.
2. It shows meaningful divisions between variables.
3. The difference between the variables can be presented in numerical terms.
4. It includes variables that can be added or subtracted from each other.
5. It gives a meaning to 'Zero" which was not possible in the above two scales. For example, zero degrees of temperature.

Ratio Scale of Measurement

The ratio scale is the most comprehensive scale among others. It includes the properties of all the above three scales of measurement. The unique feature of the ratio scale of measurement is that it considers the absolute value of zero, which was not the case in the interval scale. When we measure the height of the people, 0 inches or 0 cm means that the person does not exist. On the interval scale, there are values possible on both sides of 0, for example, temperature could be negative as well. While the ratio scale does not include negative numbers because of its feature of showing absolute zero. An example of the ratio measurement scale is determining the weight of people from the following options: less than 20 kgs, 20 - 40 kgs, 40 - 60 kgs, 60 - 80 kgs, and more than 80 kgs.

Some of the properties of the ratio scale of measurement are listed below:

1. It is used for quantitative data.
2. It shows the absolute value of zero which means if the value is 0, it's nothing.
3. The variables can be added, subtracted, multiplied, or divided. In addition to these, calculation of mean, median, and mode is also possible with this scale.
4. it doesn't include negative numbers because of the feature of true zero value.

Look at the table below showing the properties of all four scales of measurement.

Properties	Nominal	Ordinal	Interval	Ratio
Labeled variables	✔	✔	✔	✔
Meaningful order of variables	✖	✔	✔	✔
Measurable difference	✖	✖	✔	✔
The absolute value of zero	✖	✖	✖	✔

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Scales of Measurement Examples

1. Example 1: The order in which athletes cross the finish line in a race is an example of which of the scales of measurement?

   Solution: The order in which athletes cross the finish line in a race is an example of the ordinal scale. It is because here we are placing the variables as per their ranks (in a specific order). There is no numerical attribute attached to it. For an instance, we do not know the time taken by individual runners to finish the race. Therefore, it is an example of the ordinal measurement scale.

2. Example 2: Amount of calories in a pack of cheese is an example of which of the measurement scales?

   Solution: It is an example of the ratio scale as here the number of calories is considered which is quantitative or has a numerical value. Therefore, the amount of calories in a cheese pack is an example of the ratio scale of measurement.

3. Example 3: Children in a primary school are evaluated and classified as #0 - non-readers, #1 - beginners, #2 - grade level readers, or #3 - advanced readers. Which of the four scales of measurement is used in this evaluation?

   Solution: Here, we are classifying children into reading groups based on their ranks scored in a reading evaluation. There are no quantitative scores given. Therefore, it is an example of the ordinal scale.

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Practice Questions on Scales of Measurement

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FAQs on Scales of Measurement

What are the Scales of Measurement?

The scales of measurement are the ways or a specific attribute of data collection related to its purpose and analyses. For qualitative data, nominal and ordinal scales are preferred to use, while for quantitative data, interval and ratio scales are preferred. It depends on the data variables as to which scale has to be used. For example, for determining gender, favorite color, types of bikes preferred, etc the nominal scale is used.

What Differentiates Interval from Ratio Scales of Measurement?

There is a small difference in the interval and the ratio scales of measurement which is the absolute value of zero. The interval scale does include zero but fails to represent its true value. For example, on a temperature scale which is an example of an interval scale, 0 degrees has a specific value. There are values present to both sides of zero. On the other hand, on the ratio scale, for example, height, weight, etc, 0 means nothing. If the height or weight is 0, it means that the person does not exist. If the number of cars sold by XYZ enterprises is 0 on a particular day, it means there is no car sold by them. This is the basic difference between the interval and the ratio scales of measurement.

What are the 4 Scales of Measurement?

The four measurement scales are given below:

• Nominal
• Ordinal
• Interval
• Ratio

How Many Scales of Measurement are there in Research?

There are four scales of measurement in research which are nominal scale, ordinal scale, interval scale, and ratio scale.

How Many Scales of Measurement Exist?

Four measurement scales exist in math which are used for research purposes. Those scales are nominal, ordinal, interval, and ratio scales.

Why are Scales of Measurement Important?

Scales of measurement help us to interpret the numbers or variables in a detailed manner. Each scale provides a different type of information that can be kept in mind while interpreting or analyzing the data.

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Source: https://www.cuemath.com/measurement/scales-of-measurement/

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