Four Essential Scales of Measurement in Statistics Every Student Should Know

What are the four scales of measurement in statistics?

This article discusses these measurement scales, which are crucial for the correct analysis of data and making sound conclusions. An interactive quiz is available to test your knowledge after reading this article.

Introduction

To appropriately measure the research variables identified and reflected in the conceptual framework, a budding researcher must be very familiar with the four statistical scales of measurement.

What are these four statistical scales of measurement, and what variables do they measure? The following article enumerates and describes these scales and provides examples with exercises.

In the course of gathering your data, you should be very well familiar with the different statistical scales of measurement. This knowledge will help you adequately and appropriately measure the variables you have identified in your conceptual framework. Furthermore, once you make the variables quantifiable, applying the appropriate statistical analysis becomes possible.

I previously discussed the role that variables play in the conduct of research, specifically as the focal points of the entire research process because the phenomenon is abstract in nature. You may read them in my post titled “What are examples of variables in research?“

It takes some skill to isolate such research variables, but with constant practice and familiarity, identifying these variables becomes easier.

How can you tell if the factors studied are variables?

One primary attribute of variables is that they lend themselves to statistical scales of measurement. Research variables, particularly in quantitative research, must be measurable.

Statisticians devised four statistical scales of measurement: nominal or categorical, ordinal, interval, and ratio statistical scales. Let me explain the difference between these scales in the next section.

The Four Scales of Measurement in Statistics

1. Nominal or categorical

The nominal, or categorical, statistical scale of measurement is used to measure variables that can be divided into groups, with each group having attributes distinctly different from the others. The most commonly used nominal variables measured using this research scale are gender, civil status, nationality, and religion.

These variables and their corresponding categories are as follows:

• gender – male or female
• civil status – single or married
• nationality – Filipino, Chinese, Singaporean, Malaysian, Indonesian, Vietnamese
• religion – Muslim, Christian, Buddhist, Shinto

Notice that the categories of each nominal variable do not indicate that one is superior or greater than the other. They are primarily classifications that separate one group from another.

Statisticians refer to the nominal scale of measurement as the crudest statistical scale of measurement. While it may be the crudest, it is a powerful statistical scale of measurement when correlating two nominal variables, like gender and reproductive health bill position. The statistical question in this instance is “Is there a correlation between gender and reproductive health position?” Chi-square is the appropriate statistical test for this question.

Thus, when the correct scale of measurement is applied and the correct statistical question is asked, the appropriate statistical test is easily identified.

2. Ordinal

The ordinal statistical scale of measurement applies to variables that signify, as the root word suggests, “order” of the different groups. It is possible to rank order the different groups because each group shows attributes that are convincingly superior or greater than the other or vice-versa.

To illustrate this statistical scale simply and clearly, examples of variables that are measured using this scale of measurement are the following:

• order of child in the family – eldest, second eldest … youngest
• socioeconomic status of families – upper, middle, lower
• educational attainment – elementary, high school, college, graduate
• size – small, medium, large

Notice that while the different groups follow an order of magnitude, there is no discernible distance between them or that the distances could vary between each group. Say, the eldest child may be older by two years to the next eldest child, but the second eldest child may be three years older than the next child, and so on. No specific income difference describes the socioeconomic status, and so on. The number of years spent in the elementary is not the same as the number years in high school or the graduate school. The size difference between small, medium and large can vary widely.

3. Interval

The interval scale of measurement measures variables better than the rank order mode of the ordinal scale of measurement. There is an equal spacing between the different groups that compose the variable.

Examples of variables that can be measured using this statistical scale of measurement are the following:

• household income in PhP5,000 brackets – 1st group: earns up to PhP5,000, 2nd group: PhP10,000, 3rd group: PhP15,000
• temperature in 5 degree intervals – 5, 10, 15, 20
• number of student absences in one week – week 1 absences, week 2 absences, week 3 absences
• water volume in 5 milliliter increments – 5 ml, 10 ml, 15 ml, 20 ml

4. Ratio

The ratio scale of measurement works similarly to the interval scale. In fact, when using statistical tests, these two statistical scales of measurement are not treated differently from each other. The only difference between the ratio and interval scale is that the former (i.e., the ratio scale) has an absolute zero point.

Examples of ratio variables are the following:

• weight in kilograms or pounds
• height in meters or feet
• distance of school from home
• amount of money spent during vacation

Make sure that you thoroughly remember and learn how to apply the knowledge of the four scales of measurement to measure variables. This understanding is crucial for identifying the specific statistical tests that will most appropriately apply to the data you gathered in the field. This information can also assist you in preparing your interview or survey questionnaire, especially if you use a quantitative research design where quantification of variables is an essential requirement.

Now, if you are confident that you have fully absorbed the contents of this article, you may take the 10-item quiz I prepared to assess your understanding. See if you can perfect the test.

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How Well Do You Understand this Article?

Test your knowledge of the four scales of statistical measurement by answering the quiz below.

Quiz: Four Scales of Measurement

Submit Answers

Refresh (F5) to try again until you perfect this quiz.

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Activity to Further Strengthen Your Understanding

To further test your knowledge and skills at this point, identify which statistical scale of measurement applies for the following variables. Compare your answers with your classmates.

1. beauty of contestants
2. light intensity
3. water turbidity
4. environmental awareness
5. emotional intelligence
6. number of accidents
7. vehicle speed
8. allowance of students
9. brand of cellphone
10. softdrink preference

Justify your answer if there is a discrepancy or re-read the article for a better understanding.

Enjoy!

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FAQ: Four Scales of Measurement in Statistics

1. What are the four statistical scales of measurement?

The four statistical scales of measurement are nominal, ordinal, interval, and ratio. Each plays a unique role in measuring research variables accurately.

2. What defines the nominal scale of measurement?

The nominal scale categorizes variables into distinct groups without implying any order or hierarchy. Common examples include gender, nationality, and civil status.

3. How does the ordinal scale of measurement function?

The ordinal scale ranks variables into an order based on magnitude or significance but doesn’t measure the exact difference between ranks. Examples include educational attainment levels and socioeconomic status.

4. What distinguishes the interval scale from other scales?

The interval scale provides equal spacing between measurements, allowing for meaningful comparison of differences. However, it lacks a true zero point. Examples are temperature scales and income brackets.

5. What is the unique feature of the ratio scale of measurement?

The ratio scale includes all properties of the interval scale but also has an absolute zero. This allows for meaningful calculations of ratios and rates. Examples include weight, height, and distance.

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