There are four levels of measurement. Nominal, Ordinal, Interval, and Ratio. And as we will see each higher level builds upon the prior level. Levels of measurement are important because the type of measurement used determines what kind of statistical analysis you can perform.
Higher levels of measurement can be compressed to lower levels, for example you can change a ratio level measurement to an ordinal level. However, you cannot transform a lower level measurement to a higher level, for example, you cannot change an ordinal level measurement to an interval level. For most measurement we do in this course you should try and use ratio or interval level measurement.
Levels of measurement are listed in order of Nominal, Ordinal, Interval, and Ratio.
From this slide you can review more information about each of the four levels of measurement. Start with nominal and then see how each level of measurement builds upon the prior level. For each level I provide the abstract definition and then concrete examples of that type of measurement.
Nominal Level, Ordinal Level, Interval Level, Ratio Level.
Nominal Level
A nominal level of measurement contains two things 1) It is exhaustive and 2) It is mutually exclusive. What do these mean? Exhaustive means there are enough categories that all observations fit into the available categories. Mutually exclusive means no observation can fit in to more than one category. Or put another way each observation fits in to only one category. The nominal level is the most basic level of measurement and establishes only that observations can be categorized differently. This level is more to do with quality than quantity.
For example if asking about participant sex we could have response options of males and females and have males represented as 1 and females represented as 2. Assigning the number 1 to males and 2 to females does not mean anything. It does not mean males come before females or that females are twice as good as males. We simply choose the arbitrary numbers 1 and 2. I could have named females 1 and males 2, or males as 15 and females as 26. The numbers are simply tags or labels.
Another example is eye color, we might have participants with only green, blue, or brown eyes and need to code their eye color. I might assign 1 to green, 2 to blue, and 3 to brown. Again the numbers do not mean anything I simply chose them. Other examples of nominal measurement are car license plate numbers or social security numbers in the vast majority of cases a car license plate or social security number does not tell you anything informative about someone.
What is your sex?
What is your sex?
Ordinal Level
An ordinal level of measurement contains the same two things as the nominal level of measurement - exhaustive and mutually exclusive but now an additional characteristic is added. In an ordinal level of measurement the values can be rank ordered. Rank ordered means we can place participants in order of how much of the attribute they possess, for example most to least.
Exhaustive
Mutually exclusive
Values rank ordered
For example, we know someone who finished 2nd in the race ran faster than someone who finished 3rd. But with the ordinal level, we cannot tell the precise difference or distance between the ranks. For example how much faster was the person who finished 2nd than the person who finished 3rd? Was it one second, one minute, or one hour?
Another example is an individual's vegetable preference. Suppose someone ranked the following four vegetables –Broccoli, Cauliflower, Cabbage, Turnip- for how much they liked each one. We might end up with a result like this. What we do not know though is whether the individual likes any of the vegetables, perhaps they hate them all but hate Turnips the least, or perhaps they love Turnips and Broccoli, slightly dislike Cauliflower, and hate Cabbage. We just do not know.
Interval Level
An interval level of measurement builds on the characteristics of the ordinal level. It is therefore again 1) exhaustive, 2) mutually exclusive, and 3) values can be rank ordered. but now two additional characteristics are added. In an interval level of measurement we know the distance between values and the scale lacks a true zero. Again let us talk about what these two new characteristics mean.
Knowing the distance between values means we believe the distance between two adjacent points on the scale is the same as the distance between two different adjacent points. Or put another way the distances between each interval on the scale are equal. Lacking a true zero means there is no point on the scale where the attribute is completely absent. In other words even if the scale has a zero it does not mean a complete absence of the attribute. In other words if there is a zero there is still some of the thing being measured present when a zero value is used.
For example, agreement with a statement, such as:
“Earthworms are likeable.” Strongly disagree (1), Disagree (2), Neutral (3), Agree(4), Strongly agree (5).
Here, we can know the distance between different values.
Difference between “5” and “3” is the same as the difference between “4” and “2”.
So, we can start to perform subtraction and addition.
Lack of a true zero means that you cannot meaningfully say that “4” is twice as much as “2”. Indicating a 1 Strongly disagreeing that earthworms are likeable does not necessarily mean you have a complete absence of liking of earthworms.
Another example of interval measurement is temperature.
80 ̊F is not twice as hot as 40 ̊F because 0 ̊F does not mean lack of heat. The zero was arbitrarily placed.
Another example is IQ, someone with an IQ of 120 is not twice as smart as someone with an IQ of 60 this is again due to the IQ scale not having a true zero.
Ratio Level
A ratio level of measurement builds on the characteristics of the ordinal level. It is therefore again 1) exhaustive, 2) mutually exclusive, 3) values can be rank ordered, 4) we know the distance between values. However, a ratio measure has a true zero whereas the interval measure did not. So, what is a true zero? A true zero means the zero value on a measure indicates a complete lack of the attribute measured.
An example of a ratio level of measurement is weight because of the true zero, zero weight means a complete absence of weight and so it is meaningful to say that a 50kg bag is 5 times as heavy as a 10kg bag
Another example is income, here zero income is a true zero and means no financial income. This allows us to state someone with a $100,000 income has twice the income of someone with a $50,000 income
Activity
Test your understanding of the four levels of measurement by dragging the level of measurement to the appropriate example.
Choose the appropriate level of measurement for the examples. First you will be presented with the example. Next, is the list of possible answers. Correct answers are provided after each question.
1. How would you describe your color of hair?
This is an example of which level of measurement?
Correct answer: Nominal level
2. What is your University Class Rank?
This is an example of which level of measurement?
Correct Answer: Ordinal level
3. Distance from home.
This is an example of which level of measurement?
Correct Answer: Ratio level
4. How often do you study?
This is an example of which level of measurement?
Correct answer: Interval level
Test your knowledge by dragging the Examples to the appropriate level of measurement
Choose the appropriate example for each level of measurement listed. You will be presented with the level of measurement and a list of possible examples.
There will be more than one answer. Correct answers are provided after each question.
1. Nominal level
Correct answer: Eye Color, Place of Birth, Religious preference.
2. Ordinal level
Correct answer: National Rank of a Sports Team, Ranks in the army, Letter grades assigned in a course.
3. Interval level
Correct answer: Score on a standardized test, Temperature, IQ
4. Ratio level
Correct answer: Height , Number of times married, Time to complete a test
Overview Table
| Level of Measurement | Description | Examples |
|---|---|---|
| Nominal Level | Exhaustive, mutually exclusive | Hair color, gender, SSN, License plate, place of birth |
| Ordinal Level | Exhaustive, mutually exclusive, values are rank ordered | Position in a race, hardness of an object, ordinal vegetable preference, university class rank |
| Interval Level | Exhaustive, mutually exclusive, values rank ordered, know distance between values, lack of a true zero | Likert scale, temperature, GPA |
| Ratio Level | Exhaustive, mutually exclusive, values rank ordered, know distance between values, has a true zero | Age in years, income, number of times married, weight |
End of activity.