# Four Statistical Scales of Measurement

To measure appropriately 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 the four statistical scales of measurement and what variables do these measure? The following article enumerates and describes the four statistical scales of measurement 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 that you have identified in your conceptual framework. Further, once you make the variables quantifiable, application of the appropriate statistical test is possible.

I previously discussed the role that variables play in the conduct of research, i. e., it primarily serves as the focal points of the whole research process because the phenomenon is abstract in nature. It takes some skill to isolate such research variables, but with constant practice and familiarity, the identification of these variables becomes easy.

How can you say that the factors studied are variables?

One of the primary attributes of variables is that these lend themselves to statistical scales of measurement. Research variables must be measurable. Statisticians devised four statistical scales of measurement. These are nominal or categorical, ordinal, interval and ratio statistical scales.

### The Four Major Statistical Scales of Measurement

#### 1. Nominal or categorical

The nominal or categorical statistical scale of measurement is used to measure those variables that can be broken down into groups. Each group has attributes distinctly different from the other. The most commonly used nominal or categorical variables measured using this research scale of measurement are gender, civil status, nationality, or 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. These are mainly classifications that separate one group from the other.

The nominal scale of measurement is referred to by statisticians as the crudest statistical scale of measurement. While this may be the crudest, this 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.

### 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 now an equal spacing between the different groups that composes 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 absence, week 2 absence, week 3 absence
• water volume in 5 milliliter increments – 5 ml, 10 ml, 15 ml, 20 ml

### 4. Ratio

The ratio scale of measurement works similarly with the interval scale. In fact, in using statistical tests, these two statistical scales of measurement are not treated differently from the other. The only difference between the ratio and the 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

### Exercises

To test your skill at this point, identify which statistical scale of measurement applies for the following variables. Compare your answer with your classmates to confirm.

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

Enjoy!

© 2012 December 16 P. A. Regoniel

## 9 thoughts on “Four Statistical Scales of Measurement”

1. N. P. Liyanage says:

really usefull

2. Yana Z. says:

This really helped me to untangle the four scales. Wow. Just… wow. Thanks!

3. SIMON D. FWACHANO says:

Very informative. Thanks

4. ketchup says:

i had an exam today and i HOPE this will help me score good marks…….. tq;-)

5. landseac says:

“number of student absences in one week” and “water volume in 5 milliliter increments” – both should be ratio scales, not interval scales, right?
Water volume, for example, does have a absolute and meaningful zero point, which corresponds to no volume at all. And it makes perfect sense to say that 10ml is twice the volume of 5ml.

6. Prof Dr. G . Azam says:

It is a a useful material for a researcher.

7. vishnu Narayan says:

beauty of contestants
light intensity
water turbidity
environmental awareness
emotional intelligence
number of accidents
vehicle speed
allowance of students
brand of cellphone
softdrink preference

8. Darayola says:

1- Ordinal
2- Ordinal
3- Ordinal
4- interval
5- Ordinal
6- Nominal/Interval (depending)
7- Interval
8- interval
9- Nominal
10- Nominal

9. Lucky says:

Can you give me the answer of below question:

A researcher collected the following data about different points of households. Determine
whether the data thus obtained come under nominal, ordinal, interval or ratio scale. The
caste of the family residing in a household
i) Number of members in a household
ii) Age of the oldest person of a household
iii) Highest education of the family members of a household
iv) Monthly income of a household
v) Number of mobile phones in a household
vi) Length of the longest long-distance call made in a month
vii)Whether there is a landline telephone in a household
viii) Whether there is a high-speed internet connection in the household.
ix) Monthly mobile bill of a household
x) Monthly Expenditure on the Medicines.