Determining the appropriate level of measurement for Olympic years

Intro

Howdy!  I'm Professor Curtis of Aspire Mountain Academy here with more statistics homework help.  Today we're going to learn how to determine the appropriate level of measurement for Olympic years.  Here's our problem statement: Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate for the data below: Years in which an Olympics was held.

Solution - Example 1

OK, we're given four different answer options here, each one corresponding to the different levels of measurement.  And what's interesting here is that we've got definitions of each of the different levels to help us select the right answer.  So we look at the definitions here --- the ordinal level of measurement --- and this says that "the data can be ordered but differences cannot be found or are meaningless."  Well, we can find differences between different years, so that's obviously not going to be the right answer.  "The nominal level of measurement is most appropriate because the data cannot be ordered."  Well, yeah, the data actually can be ordered.  That's the whole point of having years.  We can order them from low to high or high to low.

That's the interval level of measurement.  It "is most appropriate because the data can be ordered" --- that's true.  "Differences can be found and are meaningful" --- that's true.  And "there's no natural starting zero point" --- that's true.  The zero point for years is just an arbitrarily chosen value, so it's just something that's accepted by convention.  There's no natural point for zero, and so the interval level of measurement is what we have.  And when you see years, you need to think interval level of measurement because the two pretty much go together.  The final answer --- ratio level of measurement --- would not be correct because it says here "the data can be ordered," which is true.  "Differences can be found or are meaningful" --- that's true.  "There is a natural starting point," and that's what we don't have with the years.  So the correct answer here is the interval level of measurement.  Fantastic!

Solution - Example 2

Let's go through one more example just to illustrate what we've got here.  So now we've got the number of houses that people own.  Well, the number of houses people own, would that be the ratio level of measurement?  Yeah, probably, because look, the data can be ordered, the differences can be found and are meaningful.  I mean, you've got one person who's got two houses, and one person's got one.  That extra house --- that's a meaningful difference.  There is a natural starting zero point.  It's like you got zero houses.  That's a natural place to start counting something.  So ratio level of measurement is what we would select here.  Fantastic!

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