2. A Few Keywords and Definitions for Understanding Statistics – III (contd.)

(6 minutes read)

    - By Dr. Prafulla Dikshit

2.7  Four Levels of Measurement

So far, we have seen how the continuity versus disjointedness of data points, can be the greatest differentiator between different types of data. We can also look at types of data from a measurement level perspective to get a very relevant view of data types. There are broadly four levels of measurement:

            2.7.1  Nominal – A nominal level of data measurement is at the most a categorization. Importantly, the categories are not ordered. For example, if 'place of birth' is a variable we are interested in, the data we collect is nominal, since we may categorize the participants by place of birth, but we can't order it to say that this one, say London, or that, like Tokyo, is the best 'place of birth' and then another one, and then another and so on. Similarly, we can categorize people by race or color of skin but can’t say this one is the top race and then another one and so on. So, at a nominal level, we can say the measurement is almost negligible since there is hardly any differentiation in terms of value. Since there is no value differentiator, we also can’t perform any mathematical operations on nominal data.  

       

2.7.2  Ordinal – The data that exists at an ordinal level, can be categorized and ordered, but the differences between such ordered categories of data are meaningless. A good example is a Rank. We can, for instance, rank schools by their academic performance, however, the difference between rank 1 and rank or rank 2 and rank 4, or any other sets of ranks does not convey meaningful information. So, a school with rank 2 is not necessarily 2 units better than a school B with rank 4. Another example of an ordinal variable could be the categorization of people's preferences, for example, let's say a set of personal care products may be ranging from skincare creams to high-end perfumes, on a comparative level such as essential, necessary, or desirable. The categorization may indicate essential at a basic or lower-level whereas desirable at a higher level or vice-versa as per preferences. However, the difference between the 'essential' and the 'necessary' and that between the 'necessary' and the 'desirable' could not be construed as the same, or even equivalent, thus has no meaning in measurable terms. 

My Insight 1 =>

One may argue that the difference in the rank indicates how much better or worse off, a school is. However, on a closer look rank difference of 2 between let's say school A and school B on academic performance may not mean the same thing as a 2-rank difference between school B and school C. This is because the underlying trait, property, or characteristic is more subjective and qualitative. In this case, 'academic performance' is a subjective and qualitative property based on several different qualitative aspects. If, however, we were to assume that academic performance would simply be represented by average marks of students (an objective measure of academic performance) and base the rank on the same, we might say that rank difference conveys some meaning. However, in such cases, rank becomes redundant, since we have 'marks' as a direct and objective measure of academic performance. In such a case, we would prefer using marks directly rather than ranks to classify or compare performance.   

My insight 2=>

Nominal versus ordinal categorization may also depend on the context and objectives of the research. For example, 'place' of birth may be ordered by temperature, though not by whether it is the 'best place' to be born.  

 

2.7.3 Interval – Interval data is categorical, ordered, and has meaningful differences, but it has no – 'natural zero'. Now, what's a natural zero? I will explain that in a bit, but first, let's consider an example of money in your bank account and your bank statement says zero, which means there is an 'absence' of any money in your bank account. Or if a water glass is empty, we can say that there is an 'absence' of water, or to be more precise there is zero ml of water in the glass. However, what if the temperature on a Celsius thermometer says zero? does it really mean the absence of any heat or temperature in the room? The answer is no because if it were so, there would be no heat, and we'd all be dead as soon as the temperature reaches 0 degrees. So, in this case, we do have a zero on the temperature scale, but it is not a 'natural' zero, while in the case of money there is a natural zero, since money in the bank account, implies an absence of any money there.   

            2.7.4  Ratio – The ratio scale or level of measurement is just like the interval level, except that it has a natural zero unlike for interval scale. We already considered the example of money in a bank account, and water in a glass, wherein the absence of something upon measuring it implies a real absence of the measured item or entity. Most of the obvious and tangible quantities are measured on a ratio scale. Such as height, weight, pulse, drug dose, etc. Notably, temperature when measured on a Kelvin scale instead of Celsius also has a natural zero, and thus, is categorized as being on a ratio scale in this case.

That’s it for now folks! Questions and comments are most welcome. If you feel this knowledge can be useful for others you know, do share it.  In the next post, we will talk about data sampling and sampling techniques. Till then - take care!

***