Really Simple Statistics: Nominal Ordinal Interval and Ratio Numbers #MRX

Welcome to Really Simple Statistics (RSS). There are lots of places online where you can ponder over the minute details of complicated equations but very few places that make statistics understandable to everyone. I won’t explain exceptions to the rule or special cases here. Let’s just get comfortable with the fundamentals.

What? There are different kinds of Numbers?

In statistics, the type of number you use determines the type of statistic you can use. Learn these and you’ll have an easier time deciding what statistic makes more sense to use. There are four basic types of numbers that we consider in statistics.

What are Nominal Numbers?

Nominal numbers make the least sense because they aren’t really numbers. Nominal numbers are simply numbers that are different. 1 is not 2. 3 is not 9. It really makes more sense to think of things like apples and oranges, or cookies with green sprinkles vs cookies with red sprinkles. There is no reason to assign apples to the number 1 or 3 nor does it make any sense to assign oranges to the number 2 or 9. We just assign numbers to things because it makes doing statistics and creating charts easier. It’s like a check all that apply question on a survey.

What are Ordinal Numbers?

With ordinal numbers, we have a little bit more information about the numbers. When we use ordinal numbers, we know that one of the numbers is bigger than another number. We know that 2 is bigger than 1, and 7 is bigger than 3. And it works the other way too. 1 is smaller than 2 and 3 is smaller than 7. We know which number is bigger, we just don’t know by how much bigger. One cookie is simply bigger than the other cookie. And I’ll have the bigger one. Like you could even yank it out of my hand. These types of numbers show up when we use Likert scale questions on a survey.

What are Interval Numbers?

Now let’s add in another piece of information. Interval numbers tell us everything we learned above, AND they tell about the spacing between the numbers. For instance, the amount of space between 1 and 2 is the same as the amount of space between 6 and 7. Or, the difference between 1 and 2 cookies is the same as the difference between 2 and 3 cookies. The difference in both cases is exactly one cookie. My cookie.

What are Ratio Numbers?

And lastly, this is where we thank Muhammad ibn Ahmad al-Khwarizmi. Ratio numbers incorporate the number zero. Now we know which number is bigger, and we know how much bigger, and we also know how to create none of it. This would be a survey question where you ask people to make sure their numbers add up to 100%. But I don’t dare illustrate what zero cookies looks like. The shock of it might kill me.

13 responses

  1. My book describes the interval level as not having a meaningful 0 and ratio level as having a meaningful 0, can you provide an example of that and what that means? Thanks!

    1. Think of a meaningful zero as when you can hold zero in your hands. A few people could each have a few cookies. You have 2. John has 3. I have zero. That zero actually means I have no cookies.

      However, let’s say we’re talking celcius temperature. When it’s ten degrees celcius outside, that is exactly 1 degree warmer than nine degrees celcius. But, zero degrees celcius doesn’t mean there is zero temperature. That zero simply reflects a point along the range from really really hot to really really cold.

      Does that help?

  2. Hi
    I really like your explanations.
    I’ve just posted a YouTube video about this that you might like.

  3. Hi! I’m in a Probs and Stats class at my college and this blog entry helped me quite a bit with my homework. Thank you for posting.

    1. I’m glad to hear it. Good luck with your class!

  4. Hello…new to this site and my first comment. I’m 46 and a new student in college. The last time I took math, I was 18, and I nowhere NEAR even learned about all these statistics terms I’m learning now…for the first time!!!!…I’m hazy on ordinals, nominals, intervals, and ratios. Though I printed out some helpful stuff from here, my BIGGEST question so far… I don’t know how to articulate the question I want to even ask!!!!!’s like being confused but not knowing where to begin the process to gain clarity!!!….any ideas?

    1. It’s never too late to learn something new. 🙂

      And that in itself is a tough question! Something I usually do is pretend I’m explaining my problem to someone who knows less than I do. Perhaps your mom or dad or kid or never took those kinds of courses so you can try to articulate something to them. And do remember, statistics aren’t learned instantly – they sink in slowly over time and then suddenly, out of nowhere, you go, oooohhhhhh that’s what it all means!

      Good luck with your classes!

  5. Your post helped me so much. I went to class and i read the book and i still could not really understand the terms but now thanks to you i feel more confident about it. If only my instructor would have put it this way.

    1. Glad to hear it. Good luck!

  6. thank you if only they said it like that in the lectures.

    1. You’re welcome 🙂

  7. This was great. I would like to see the “error” side of this, which explains why it is important to understand your scales and not confuse (for example) interval and ordinal data.

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