# A Halloween chocolate lesson in nominal, ordinal, interval, and ratio data #MRX

If you want to choose the right statistic for the numbers in your dataset, you need to know what kind of numbers you’re dealing with. This handy table will help you differentiate between nominal, ordinal, interval, and ratio data. Enjoy, but don’t lick the screen!

# The LoveStats Award Program #MRX

Image by chooyutshing via Flickr

Everybody deserves a little recognition once in a while. Many of us do good deeds on a regular basis and are never recognized for those accomplishments. Today, however, is your chance to shine.

Do you qualify for any of these awards? Then be proud and claim them! Copy the link and post the awards on your website. But be honest. Falsely claiming awards will result in your name being published on Santa Clause’s naughty list. Just sayin.

# Really Simple Statistics: What is Interval Data? #MRX

Image via Wikipedia

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.

Ready? Today we tackle interval data. Unlike nominal data which has no real relationship with numbers, and ordinal data which shows orders among numbers, interval data can show specific relationships among numbers.

Examples of interval data include:

• Yesterday is exactly one day away from today and exactly two days away from tomorrow. A day is the same no matter which day of the week you look at. But, you can’t say that tomorrow is twice as far from yesterday as it is from today. (Woh! That’s confusing!)
• 20 degrees Celsius is exactly one degree different from 21 degrees and exactly 10 degrees different from 30 degrees. A degree is the same no matter where you measure it. But, you can’t say that 30 degrees is 50% hotter than 20%.

The important distinction with interval data is this:

• The numbers have real meaning
• The numbers have a real order
• The differences between the numbers are measurable

And that’s all there is to it!

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# Really Simple Statistics: What is Ordinal Data? #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.

Today we tackle another kind of number. Unlike nominal numbers, ordinal numbers have real meaning behind them. The name itself hints at the meaning. Ordinal numbers portray ordered numbers.

But, the only thing we know about the numbers is that there is an order to them. For example, there are more cookies in the first picture than there are in the second. But, we can’t see the whole picture, so we don’t know how many more cookies are in the first picture. We could assign a a 2 to the first picture and a 1 to the second picture, but we wouldn’t be able to say that there are twice as many cookies in the first picture. Just that there are more. Here are some examples of ordinal data.

• A big handful of rice vs a small handful of rice. Why: We don’t know how much rice is in each hand but we can see there is more in one than the other.
• Someone who is a bit shy vs someone who is really shy. Why: We don’t how much more shy the really shy person is, but we know they are more shy.
•  Questions on surveys where the answers look like: Strongly agree, somewhat agree, somewhat disagree, strongly disagree. Why: We don’t know how much more “strongly” is compared to “somewhat” but we do know it’s more.
• This is more than that. This is lighter than that. This is heavier than that. This is taller than that. This is bluer than that. This is tastier than that. This feels more rough than that. This smells worse than that. This is longer than that. This is earlier than that. This is faster than that.
The key indicators are these:
1. Something is more or less than the other thing
2. We don’t know how much more or less it is
It’s just that simple!

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# Really Simple Statistics: What is Nominal Data? #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.

One of the first things people learn in statistics class is that there are different kinds of numbers. We’ve gotten so used to treating all numbers the same but many people find the concept difficult to grasp. It’s important to understand the differences because you can’t choose the right statistical test unless you know what kind of data you’re working with. So let’s start with the most basic kind of number: the nominal number.

The word nominal is a hint in itself. Nominal means name so we’re actually starting with a number that really isn’t a number. Nominal numbers are numbers that get assigned to things where the number has no real meaning. You could call a couch Arnold or Triangle or 7 or Blue but it’s still just a couch. 7 might be a number, but it is being used as a name. Here are some examples of nominal data and variables.

• A variable that lists out people’s names. If you think about an Excel spreadsheet listing your friends and family names and addresses, the column that includes their name is nominal. “John” isn’t twice as much as “Mary” and “Harold” isn’t larger than “Earnest.” Each word is simply a name.
• Gender: Even if you assign the number “1” to women and the number “2” to men, there is no meaning behind those numbers. Women aren’t twice as human as men. Men aren’t half as alive as women. The numbers are just a convenient way to code or name the two options in a dataset.
• Region: You might have a variable that identifies whether people live in the city or the country. For convenience sake, you might decide to code people who live in the city as “1” and people who live in the country as “2.” But, we know that cities aren’t half as liveable as the countryside and the countryside isn’t twice as fun as living in the city.
• Other nominal variables: Flavours of cookies (chocolate, oatmeal), types of furniture (couch, chair), types of animals (dog, cat, goat), names of cities (london, paris, athens), shapes (circle, square, triangle), days of the week (friday, wednesday), months of the year (october, april), personality characteristics (shy, creative, intelligent),  brand used (ford, toyota)

The rule of thumb is that if you can figure out a legitimate reason for assigning a specific number to something, it is no longer a nominal variable. It’s that simple.

# 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.

# Thanksgiving for Research

[tweetmeme source=”lovestats” only_single=false]I am thankful for pie charts that are used to represent percentages out of 100 as opposed to numbers summing to 217.63.

I am thankful for bar charts that reflect quantities of categorical data not trends over time.

I am thankful for knowing whether a rating scale reflects an ordinal or interval scale.

I am thankful for 3.1415927 and chocolate.

I am thankful for loving the work I do and wanting to go to work, for I know that is a rare occurrence.