How things are measured in research is very important as it provides information about how to interpret those measurements. ‘Scales of measurement’ is a classification that describes the nature of the information within the values assigned to variables. That is, measurement is generally described as the assignment of numbers or labels to a variable. To refresh our memory, measurement is simply the process of assigning numbers or labels to variables that represent attributes or properties of subjects or treatments. It is important to note that researchers do not assign numbers or labels randomly. It is rather done based on some set rule that provides consistency and helps to compare variables that are measured by other researchers. In 1946, Stanley Stevens introduced four scales or levels of measurement stating what is required to be measured at each level and what statistical processes can be performed to get meaningful results. These scales are: , , , and .
Different types of scales of measurement
Nominal scale
Nominal scale measures provide labels to the observations. Originating from the Latin word nomin, meaning name, it assigns classification or labels or names to observations so that it can be categorized. It is the simplest type of measurement that identifies types rather than the amount of something. Labels can be symbols, words, or even numbers to classify observations.
For example, jersey numbers in basketball are measures at the nominal level, as numbers do not necessarily have any significance. Other examples are zodiac signs, gender, ethnicity, political affiliation.
You can either keep the labels as is or the researcher can code them.
is the process of converting a categorical variable to numeric values. For example, the variable gender can be coded as, male=1 and female =2, LGBTQ=3. These scores (1, 2, or 3) have no inherent meaning. They are just for convenience. At the same time, an important characteristic of these labels is that they are discrete or mutually exclusive. That is, one observation cannot belong to more than one category/label. This measurement scale is considered to be basic as the scores or observations cannot be meaningfully arranged from lowest to highest. It is primarily used for classification.
Ordinal scale
Also known as the rank order scale, it ranks the observations on given quality and categorizes them. Originating from the Latin word ordin, meaning order, it allows observations to be ranked but the distance between these ranks is not equal.
For example, grocery stores generally rank their hot sauce as, “mild”, “medium”, and “spicy”. We know which one is the hottest and which one is less hot, but we don’t know whether the increase in hotness from “mild” to “medium” is the same as it is from “medium” to “spicy.”
We can easily know this for temperature, for instance. The difference between 60 and 70 degrees is the same as the difference between 40 and 50 degrees Fahrenheit. But with ordinal scales that is not possible. Ordinal measures are often used in ‘Likert scales’, which are commonly used to measure beliefs and opinions.
An example of a Likert scale can be, “Strongly Disagree”, “Disagree”, “Neutral”, “Agree”, and “Strongly Agree”.
Researchers code the observations or responses by assigning numerical values (scores) so that scores can be classified and meaningfully arranged from lowest to highest. Since these numerical values are more meaningful than a simple representation of categories, it allows researchers to perform some statistical tests. However, we cannot perform any other mathematical operations other than ranking, such as addition and/or subtraction.
Interval scale
It inherits all the characteristics of the ordinal scale and has a meaningful distance between adjacent scores. Originating from the Latin words inter meaning between and vallum meaning ramparts, it provides a meaningful interval between the scores.
For example, the difference between $21 and $22 is the same as $45 and $46.
That makes it easy for the researchers to say who earns more and by how much. This opens up the possibility of additional mathematical and statistical calculations one can perform. But it still lacks one property. It lacks a true zero.
For example, we can measure IQ scores, depression, temperature, years on the timeline, but all of these lack a true zero. An IQ score of zero is meaningless the same way as a depression score of zero, or year zero.
There is no true zero for temperature as well. Age is another example. We can categorize people based on age, rank them, know exactly who is older and by how much. But do we have an age zero? What would that be? The day a child is born or the day they are conceived? So the interval scale lacks a true and meaningful zero, but it has all the properties of the ordinal scale in addition to equal distance between adjacent scores.
Ratio scale
It inherits all the characteristics of an interval scale in addition to having a true zero. Originating from the Latin word ratio meaning calculations, it is the highest level of scales of measurement where the researchers can perform mathematical and statistical operations. Examples of ratio scale are, the number of children, weight, height, response time, income, etc. Many social science and educational variables cannot be measured using this scale. It is impossible to have zero self-esteem, intelligence, compassion, spelling ability, etc.
To summarize the scales of measurement, here are their properties.
| Level of Measurement | Can categorize data? | Can order/rank data? | Can add or Subtract data? | True or Meaningful Zero? | Preciseness |
| Nominal | Yes | No | No | No | Least precise |
| Ordinal | Yes | Yes | No | No | Little precise |
| Interval | Yes | Yes | Yes | No | Precise |
| Ratio | Yes | Yes | Yes | Yes | Most precise |
Many students also learn about the . For statistical purposes, these variables are measured at the ordinal scale but treated as an interval scale, so that more advanced statistical operations can be performed. Many social science researchers use ordinal scales and combine the results of all these questions to make a composite interval scale. They are also referred to as composite scales. For example, the Centers for Epidemiologic Studies Depression Scale (CESD) is made up of 20 questions (https://cesd-r.com/cesdr/) or (https://link.springer.com/content/pdf/10.1007%2F978-3-319-69892-2_416-1.pdf). Each question is an ordinal scale. But combining scores of all the questions can get us a range of scores that is an interval scale.
Each ordinal scale (question) is then scored from 0 to 4 and all the scores are added up giving a possible range of final score from 0-60. Composite scales thus combine scores from ordinal scales and treat them as interval scales. Depression is also a complex concept measure through nine related concepts of sadness (dysphoria), loss of interest (anhedonia), appetite, sleep, thinking / concentration, guilt (worthlessness), tired (fatigue), movement (agitation), and suicidal ideation.
Bibliography
Christensen, L. B., Johnson, B., & Turner, L. A. (2020). Research methods, design, and analysis (Thirteenth edition. ed.). Upper Saddle River, New Jersey: Pearson Education, Inc.
Salkind, N. J. (2010). Encyclopedia of research design. Thousand Oaks, Calif.: SAGE Publications.
Stevens, S. (1946). On the theory of scales of measurement. Science, 103(2684), 677-680. Retrieved November 10, 2020, from http://www.jstor.org/stable/1671815
Cite this article (APA)
Trivedi, C. (2020, November 21). What are the scales of measurement? ConceptsHacked. https://conceptshacked.com/scales-of-measurement/
