In our previous article, we learned that data were primarily divided into two main types: categorical and numerical data. However, we also learned that categorical data can be further subdivided into nominal and ordinal data. In addition, numerical data can be further subdivided into interval and ratio data. Let’s learn about each of these four types of data that we encounter in data science. Nominal DataNominal data are a type of categorical data. That is, they are used to represent named qualities. However, nominal data have no natural rank order to them (they differ by their name only). For example, the colors red, green, and yellow all describe the color of apples. However, no one color is greater than or less than another color. Other examples of nominal data include: your name, your credit card number, and the name of the city where you were born. The key distinction is that nominal values have no natural order to them. However, they can still be sorted alphabetically. There are a limited number of mathematical operations that we can perform on nominal data. We can test two nominal values for equality (i.e. we can determine if they are the same named category). In addition, we can determine their mode (i.e. we can get the most frequently occurring category in a set of nominal values). Ordinal DataOrdinal data are a type of categorical data. That is, they describe named qualities of things. However, ordinal data do have a natural rank order to them. So they can be sorted in order by their rank. For example, we could group apples into small, medium, and large sizes. Medium apples are larger than small apples, and large apples are larger than medium apples, so they do have a natural rank order. Other examples of ordinal data include: bronze, silver, and gold medals in the Olympics, assigning letter grades for student test scores, and low, medium, and high speeds on a portable fan. The key distinction is that ordinal values do have a natural order to them, so we can sort them in a natural way. We can perform a few more mathematical operations on ordinal data than on nominal data. In addition to testing for both equality and determining the mode. We can also test two ordinal values for their order (by determining if one value is ranked greater than or less than another). In addition, we can determine the median (i.e. the middle most value in a list of sorted values). Interval DataInterval data are a type of numerical data. That is, they represent measured quantities of things. Interval data allow for a degree of difference between two values (i.e. we can add or subtract the values in meaningful ways). However, interval scales have an arbitrary zero point on their scale For example, imagine a thermometer measuring outdoor temperature. The zero point on a Celsius thermometer represents the temperature where water freezes. This is simply for convenience zero on this scale does not represent absolute zero heat, as it does on the Kelvin scale. The difference between 20°C and 30°C (which is a 10° change) is the same difference in temperature as a change from 40° to 50° (also a 10° change). So we can perform addition and subtraction with this interval scale. However, it doesn’t make sense to say that 20°C is half as hot as 40°C or that 40°C is twice as hot as 20°C. This is because 0°C isn’t the absence of all heat but rather was an arbitrarily chosen point on the scale where water freezes. So it simply doesn’t make sense to discuss ratios, multiplication, or division with the Celsius temperature scale or other interval scales. Other examples of interval data include: IQ scores, dates on a calendar, and longitudes on a map. The key distinction is that the zero point on an interval scale is arbitrarily chosen; it doesn’t represent a natural minimum quantity of the thing being measured. We can perform a few more mathematical operations on interval data than we can on nominal and ordinal data. In addition to testing for equality, sorting by order, and determining both the mode and the median. We can also add or subtract interval data. In addition, we can also determine the arithmetic mean (i.e. average value in a set of interval values). Ratio DataRatio data are a type of numerical data. That is, they represent measured quantities of things. Ratio data allow for a degree of difference between two values, just like interval data. However, unlike interval data, ratio scales do have a natural (non-arbitrarily chosen) zero point. So the concept of a ratio, and multiplying or dividing two values make perfect sense. For example, imagine we have two apples: One has a mass of 100 grams and the other has a mass of 200 grams. Unlike an interval scale, it make perfect sense to say that a 100-gram apple is half the mass of a 200-gram apple. This is because zero grams on this scale represents a natural minimum quantity (i.e. no mass at all). So 200 grams of mass is twice as much mass as 100 grams of mass. Other examples of ratio data include: the distance between two points, income from your job, and elapsed time. The key distinction (once again) between interval and ratio scales is that the zero point on a ratio scale represents a natural zero quantity of the thing being measured. It can be difficult to recognize the subtle yet important difference between interval scales and ratio scales. So if you’re having difficulty understanding, you may want to research this topic further. We can perform a few more mathematical operations on ratio data than we can on nominal, ordinal, and interval data. In addition to all of the operations we’ve seen so far, we can also multiply and divide ratio data. In addition, we can determine the geometric mean, which is a method of averaging used for values with widely varying ranges. To learn more about the types of data in data science, please see my latest course Intro to Data for Data Science.
If you’re new to the world of quantitative data analysis and statistics, you’ve most likely run into the four horsemen of levels of measurement: nominal, ordinal, interval and ratio. And if you’ve landed here, you’re probably a little confused or uncertain about them. Don’t stress – in this post, we’ll explain nominal, ordinal, interval and ratio levels of measurement in simple terms, with loads of practical examples.
When you’re collecting survey data (or, really any kind of quantitative data) for your research project, you’re going to land up with two types of data – categorical and/or numerical. These reflect different levels of measurement. Categorical data is data that reflect characteristics or categories (no big surprise there!). For example, categorical data could include variables such as gender, hair colour, ethnicity, coffee preference, etc. In other words, categorical data is essentially a way of assigning numbers to qualitative data (e.g. 1 for male, 2 for female, and so on). Numerical data, on the other hand, reflects data that are inherently numbers-based and quantitative in nature. For example, age, height, weight. In other words, these are things that are naturally measured as numbers (i.e. they’re quantitative), as opposed to categorical data (which involves assigning numbers to qualitative characteristics or groups). Within each of these two main categories, there are two levels of measurement:
Let’s take look at each of these, along with some practical examples.
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As we’ve discussed, nominal data is a categorical data type, so it describes qualitative characteristics or groups, with no order or rank between categories. Examples of nominal data include:
In all of these examples, the data options are categorical, and there’s no ranking or natural order. In other words, they all have the same value – one is not ranked above another. So, you can view nominal data as the most basic level of measurement, reflecting categories with no rank or order involved.
Ordinal data kicks things up a notch. It’s the same as nominal data in that it’s looking at categories, but unlike nominal data, there is also a meaningful order or rank between the options. Here are some examples of ordinal data:
As you can see in these examples, all the options are still categories, but there is an ordering or ranking difference between the options. You can’t numerically measure the differences between the options (because they are categories, after all), but you can order and/or logically rank them. So, you can view ordinal as a slightly more sophisticated level of measurement than nominal.
As we discussed earlier, interval data are a numerical data type. In other words, it’s a level of measurement that involves data that’s naturally quantitative (is usually measured in numbers). Specifically, interval data has an order (like ordinal data), plus the spaces between measurement points are equal (unlike ordinal data). Sounds a bit fluffy and conceptual? Let’s take a look at some examples of interval data:
Importantly, in all of these examples of interval data, the data points are numerical, but the zero point is arbitrary. For example, a temperature of zero degrees Fahrenheit doesn’t mean that there is no temperature (or no heat at all) – it just means the temperature is 10 degrees less than 10. Similarly, you cannot achieve a zero credit score or GMAT score. In other words, interval data is a level of measurement that’s numerical (and you can measure the distance between points), but that doesn’t have a meaningful zero point – the zero is arbitrary. Long story short – interval-type data offers a more sophisticated level of measurement than nominal and ordinal data, but it’s still not perfect. Enter, ratio data…
Ratio-type data is the most sophisticated level of measurement. Like interval data, it is ordered/ranked and the numerical distance between points is consistent (and can be measured). But what makes it the king of measurement is that the zero point reflects an absolute zero (unlike interval data’s arbitrary zero point). In other words, a measurement of zero means that there is nothing of that variable. Here are some examples of ratio data:
In all of these examples, you can see that the zero point is absolute. For example, zero seconds quite literally means zero duration. Similarly, zero weight means weightless. It’s not some arbitrary number. This is what makes ratio-type data the most sophisticated level of measurement. With ratio data, not only can you meaningfully measure distances between data points (i.e. add and subtract) – you can also meaningfully multiply and divide. For example, 20 minutes is indeed twice as much time as 10 minutes. You couldn’t do that with credit scores (i.e. interval data), as there’s no such thing as a zero credit score. This is why ratio data is king in the land of measurement levels.
At this point, you’re probably thinking, “Well that’s some lovely nit-picking nerdery there, Derek – but why does it matter?”. That’s a good question. And there’s a good answer. The reason it’s important to understand the levels of measurement in your data – nominal, ordinal, interval and ratio – is because they directly impact which statistical techniques you can use in your analysis. Each statistical test only works with certain types of data. Some techniques work with categorical data (i.e. nominal or ordinal data), while others work with numerical data (i.e. interval or ratio data) – and some work with a mix. While statistical software like SPSS or R might “let” you run the test with the wrong type of data, your results will be flawed at best, and meaningless at worst. The takeaway – make sure you understand the differences between the various levels of measurement before you decide on your statistical analysis techniques. Even better, think about what type of data you want to collect at the survey design stage (and design your survey accordingly) so that you can run the most sophisticated statistical analyses once you’ve got your data.
In this post, we looked at the four levels of measurement – nominal, ordinal, interval and ratio. Here’s a visual summary of each.
Remember, the level of measurement directly impacts which statistical techniques you can use in your analysis, so make sure you always classify your data before you apply any given technique.
This post is part of our research writing mini-course, which covers everything you need to get started with your dissertation, thesis or research project. |
When the data have the properties of interval data and the ratio of two values is meaningful the variable has which scale of measurement nominal ordinal interval ratio?
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