Levels of Measurement

We can classify data into 1 of 4 levels of measurement. These levels of measurement will be important, because certain calculations can be done with only certain kinds of data. How's that for vague?

The first (and weakest) level of data is called nominal level data. Nominal level data is made up of values that are distinguished by name only. There is no standard ordering scheme to this data.

Ex. The colors of M&M candies is an example of nominal level data. This data is distinguished by name only. There is no agreed upon ordering of this data, although we each may have an opinion about which should be listed first. I'm partial to brown and may feel that brown should always be listed first, but you may like green and feel it should go first.

The second level of data is called ordinal level data. Ordinal level data is similar to nominal level data in that the data is distinguished by name, but it is different than nominal level data because there is an ordering scheme.

Ex. Movies on a certain TV show are classified as 2 thumbs up, 1 thumb up, or 0 thumbs up. There is an order here. A movie that receives 2 thumbs up is better that a movie that receives 1 thumb up (supposedly anyway). How much better is a movie that receives 2 thumbs up than a movie that receives 1 thumb up? Is it 1 thumb better? What exactly does that mean?

Ex. Voters are classified as low-income, middle-income, or high-income. This is an example of ordinal level data. We do know that people in the low-income bracket earn less than the people in the middle-income bracket, who in turn earn less than the people in the high-income bracket. So there is an ordering scheme to this data.

The thing that ordinal level data lacks is that you can't measure the difference between two pieces of data. We know that high-income people earn more than low-income people, but how much more. This is where the third level of data comes in. Interval level data is similar to ordinal level data in that it has a definite ordering scheme, but it is different in the fact the differences between data is meaningful and can be measured.

Ex. The boiling temperatures of different liquids are listed. This is an example of interval level data. We can tell whether a temperature is higher or lower than another, so we can put them in an order. Also, if water boils at 212 degrees and another liquid boils at 284 degrees, the second temperature is 72 degrees higher than the first. So the differences between data are measurable and meaningful.

The one thing that interval data lacks is a zero starting point. Is 0 degrees the absolute lowest temperature? As anyone from Hibbing, Minnesota will tell you, temperatures go below 0 degrees on a regular basis. Because there is no zero starting point, ratios between 2 data values are meaningless. Is 75 degrees three times as hot as 25 degrees? No, because the ratio of 75 to 25 (i.e. 3 to 1) is meaningless here. Think about the following cooking example.

Ex. A brownie recipe calls for the brownies to be cooked at 400 degrees for 30 minutes. Would the results be the same if you cooked them at 200 degrees for 60 minutes? How about at 800 degrees for 15 minutes? I think we would get 3 different types of brownies : just right, awful gooey, and awful crunchy. The problem is that 200 degrees is not half as hot as 400 degrees, and 800 degrees is not twice as hot as 400 degrees.

This is where Ratio level data comes in. Ratio level data is just like interval level data, except that ratios make sense. I guess it's pretty well named.

Ex. Four people are randomly selected and asked how much money they have with them. Here are the results : $21, $50, $65, and $300.

Is there an order to this data? Yes, $21 < $50 < $65 < $300.

Are the differences between the data values meaningful? Sure, the person who has $50 has $29 more than the person with $21.

Can we calculate ratios based on this data? Yes because $0 is the absolute minimum amount of money a person could have with them. The person with $300 has 6 times as much as the person with $50.

Other examples of ratio level data would be ages of people, scores on exams (graded from 0 to 100), and hours of study for a test.

Practice Questions

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