# Difference between "interval" and "ratio" variable: How to explain?

I am grateful to anyone who can give me practical, non-theoretical examples to help guide me and my class as to how to split hairs between ordinal, interval, and ratio data classification.

UPDATE 5/24/2013

Thank you all for your helpful answers. Of course, everything you are saying is correct, and as you know, I am looking for a way that really resonates (at least with me) so I can use that to explain to my students. Taking into account your thoughtful answers, here are my challenges on the periphery:

In interval vs. ratio, imagine a person has $0. Is this interval or ratio? $0 is having no money. However, people can have bank accounts that are -$100. You could say it is interval, like Celcius temperature, or you could say it is ratio, like height - a person with no height is at 0, and a person with no money has $0.

Another challenge comes to bear with units. Let's say I have schools A, B, and C, and they have 100, 600, and 1,000 students respectively. A new school, school D, has 0 students until they open, so these units could be ratio. However, students are not equal because people are all different. If school A is a high school and B is a pre-school, then adding a unit to A is not the same kind of unit as adding it to B. Therefore, the intervals are not equal. This can also be said with age, or years of education. Yes, you can have 0 years and 0 years of education, but is your first year anything like your 16th year? Can they be counted on the same scale?

In ordinal vs. interval (which I admittedly did not ask but unfortunately is relevant), imagine I give a test worth 100 points. The nuance is that questions 1-50 are difficult essays and 51-100 are simple multiple choice. Many would call this interval, because it does not matter which 90 points a student gets, if s/he gets 90 points, I will give him/her an A. On the other hand, getting points on the first part vs. the second part is different amounts of effort, suggesting ordinal. This is why I do not like to use rank examples in ordinal - anyone in high school knows/feels that if s/he is ranked 12 and his/her friend is ranked 6 that s/he is twice the distance from her friend from the top. The fact that the intervals between rank 1 (valedictorian) and rank 2 (salutatorian) and all the other ranks are technically different is lost on any high school student because they do not see it that way, and that is how most people encounter rank in daily life.

I especially like Jochen's example of degrees in terms of color - or even, a circle or an arc. We all know that an angle or arc of 0 degrees does not mean there is no angle or arc, just that it is at 0 degrees. This one I will use as a good difference between "interval" and "ratio". However, the class will challenge me with the above and I want to have some better answers.

Thanks again, and I will keep reading as I'm working on my materials for my stats class in fall.

UPDATE 5/29/2013

Clerot, Venkata, and Mohammad: You have convinced me NOT to use temperature as an example! I think it tries to be a good example, but has too many grey areas around the edges.

Charles: I love No Oil In Rivers! I will add that!

I am still really liking Jochen's example of degrees in terms of a color or an arc. Are there any more similar to that that can really illustrate when something is interval but NOT ratio?

## All Answers (16)