When your work involves using data to help organizations make informed decisions, an appreciation for data types, their strengths, and their limitations is imperative. In this post, we describe some of the data that we use in our line of work at Social Scientific.

Measurement Is The Assignment of Values to Things To Represent Facts Or Conventions About Them

As we explained in this post, a variable is an aspect of an idea that can be measured. And it is so-called because the measured value can vary for each instance of the variable. What, then, is measurement? Measurement is the assignment of values (i.e. numbers, text, etc.) to things so as to represent facts and conventions about them. For example, people often operationalize the concept of race using an aspect of race such as skin color because it is readily observable (of course, whether skin color reflects race more than, say, last name, country of origin, etc. is a discussion for another day). When they see skin that is very light-brown (because of low levels of melanin), they assign the value of “white”. On the other hand, when they see skin that is very dark brown (because of high levels of melanin), they assign the value of “black”.

Scale Is A Description Of The Nature Of The Values Assigned During Measurement 

Measurements are meaningful only when we understand, consciously or subconsciously, the nature of the values assigned to things. More often than not, assigned values/data are qualitative or quantitative. Qualitative values are values that reflect categories. Going back to our example, the value of “black” is a category under which people usually place skin that is dark brown. Another example is “food” which is a category under which people place, say, anything that is comestible and nourishing to the body. Or “spicy”, a category for food that leaves a burning sensation in the mouth. Quantitative values, on the other hand, are values that reflect magnitude or extent. For example, the value “14” could reflect how many years a human has spent on earth, how many months a couple has been married, or even how many days to your birthday.

A brief side note. Just because you assign numbers to a qualitative value doesn’t make it quantitative. Indeed, doing so may make it easier to work with data. However, as long as those numbers reflect categories, they are qualitative.

There Are Two Types Of Qualitative Scales: Nominal and Ordinal

There are two types of qualitative scales: nominal scale and ordinal scale. Nominal scale describes data for which you can neither measure the difference between the categories nor order and rank them. Suppose there are 4 colored soccer balls (red, black, green, blue) in a basket. The values assigned to ball color are on a nominal scale because while you know that blue is different from green, you cannot measure (i.e. assign a value to) this difference. Furthermore, you cannot rank the colors and say that blue is higher than red, which is higher than black and green. Perhaps, under certain criteria (such as brightness or ability to absorb heat) you could. Without a criterion, however, the data doesn’t readily subject itself to ordering/ranking, making such ranking/ordering not meaningful.

Like nominal scale, ordinal scale describes data for which you can’t measure the differences between the categories. However, the distinguishing feature is that the categories naturally subject themselves to ordering or ranking. Suppose you ask your business customers whether a product or service is useful and they have to select a level of agreement that is either “strongly disagree”, “disagree”, “neutral”, “agree”, and “strongly agree”. Level of agreement is on an ordinal scale because while you can’t assign a value to the difference between, say, “strongly disagree” and “agree”, you can tell that they are on opposing ends of some spectrum. Thus, there is an ordering of the categories.

There Are Two Types Of Quantitative Scales: Interval and Ratio 

Zeros in interval data have no meaning

Interval scale and ratio scale are the two types of quantitative scales. Interval scale describes data for which the values are ordered and equidistant from each other, and any value of 0 is arbitrary and therefore not meaningful. An example of data on an interval scale is temperature. Temperature values are ordered in the sense that 50 degrees is higher than 40 degrees and -40 degrees is colder than -20 degrees or 40 degrees. Also, values are equidistant from each other in the sense that the difference between 10 degrees and 20 degrees is the same as the difference between 30 degrees and 40 degrees, or between 80 degrees and 90 degrees. Furthermore, a temperature of 0 degrees Fahrenheit is meaningless because it doesn’t reflect a complete absence of heat. Rather it tells us that the temperature is 10 degrees less than 10.

In fact, because 0 degrees is arbitrary, we can perform addition and subtraction but not multiplication and division operations with the values. Here is why. An arbitrary 0 means that we could assign temperature values such that -5 degrees becomes the new 0 degrees, 40 degrees becomes 35 and 20 becomes 15. The result of this is that dividing 40 degrees by 20 degrees will not produce the same result (2) as dividing 35 by 15 (0.0667). In other words, because a meaningful and non-arbitrary zero is needed to interpret double, and a value of 0 is meaningless and arbitrary on an interval scale, we cannot say that a temperature of 40 degrees is twice as hot as 20 degrees. Other examples of data on an interval scale are credit scores, IQ scores, GMAT scores, etc.

Zeros in ratio data have meaning

Finally, ratio scale has all the properties of interval scale except one. That is, it has a meaningful, non-arbitrary zero. In other words, a value of 0 actually reflects an absence of the property under consideration. For example, a weight of 0 means no weight. Because of this, multiplication and division operations can be conducted on such data. For example, a height of 180m is twice a height of 90m. Other examples of data on a ratio scale are length, height, length of time/duration.

Conclusion

This classification of data into nominal, ordinal, interval and ratio was pioneered by an American psychologist named Stanley Smith Stevens in the 1940s. While some have questioned this classification, it has enjoyed considerable staying power in the social sciences. We hope you found this blog informative.

References

On the Theory of Scales of Measurement. Author(s): S. S. Stevens. Source: Science, New Series, Vol. 103, No. 2684 (Jun. 7, 1946), pp. 677-680

What is interval data? examples & definitions. Code Institute Global. (2022, August 9). Retrieved September 30, 2022, from link

Jansen, D. (2022, September 27). Nominal, ordinal, interval & ratio: Explained simply. Grad Coach. Retrieved September 30, 2022, from link

Data levels and measurement. Statistics Solutions. (2021, August 10). Retrieved September 30, 2022, from link

Blog, F. (2019, October 23). What is interval data? + [examples, variables & analysis]. Formplus. Retrieved September 30, 2022, from https://www.formpl.us/blog/interval-data

Seraf Fej (https://stats.stackexchange.com/users/213434/seraf-fej), Why are multiplication and division not allowed when using the interval scale?, URL (version: 2018-08-14): https://stats.stackexchange.com/q/362135