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Terminology of Measurement & Variables

posted Apr 16, 2011, 7:15 PM by Prof Kiernan   [ updated Apr 16, 2011, 7:16 PM ]
I had several students come in last week looking for help understanding what their professors were explaining in class. Most of the students were saying things like 
"So, I just left my class and the instructor wasn't speaking English. I could understand some words, but every other word out of the prof's mouth was variable... discrete variable, quantitative variable, qualitative variable and so on. Isn't there some law about cruel and unusual punishment?" 

This is what helped this student make some sense out of the variables, maybe it will help you:

1. There are two types of variables Quantitative and Qualitative. First thing you need to do is figure out if the problem is using a measured amount (Quantity) or some category/description (Quality).

Quantitative variables use measurements that are often Numbers
Qualitative variables describe variables using words.  

2. The next question is what level of measurement is the problem using? Well, Qualitative variables can be Nominal or Ordinal levels of measurement while Quantitative variables can be measured through Interval or Ratio levels of measurement

Nominal Level of Measurement: qualitative that cannot be put in a universal, meaningful order.  
For those of you who, like myself, need the English translation: The Nominal level of measurement is another way of saying the info you gather is all about thenames or symbols that can be put into any order you want. Watch out for the trick questions for this category like phone numbers or zip codes, they are numbers, but the numbers are not measurable. That is, someone with the area code 732 isn't any cooler than someone with the area code 908. These numbers are really just categories that identify a certain phone.

Ordinal Level of Measurement: qualitative data that can be put in an order, but any numerical
differences are meaningless.

Why does it feel like a vocabulary lesson instead of a statistics lesson? English translation: The ordinal level of measurement describes information that is gathered that can be arranged into some sort of order. Ok this one can be difficult, what you're looking for is a series of words that can be ordered but the order isn't specific to everyone. For example, drink sizes: there's small, medium, large or tall, venti, and grande. Everyone knows that small and tall are the lowest level, but a small coffee might be 8 oz. or 12 oz. depending if you went to DD or Starbucks.

Interval Level of Measurement: quantitative data with no natural starting point.
I thought I was taking a math course... I'm soo confused. Fear not, here's the English translation: The Interval level of measurement is a number that can be negative. When I'm stuck with this type of problem I ask myself "Can a (insert category here) be negative?" For example, when measuring the average body temperature of a college student. I ask myself "Can a temperature be negative?" The answer, of course, is yes (it felt like it was -30 degrees while I was chipping the ice off my car this morning). So the body temperature is an interval level of measurement.  

Ratio Level of Measurement: quantitative data with a natural starting point.
No panicking! It does get easier. Here's the English translation: You are working with information that are numbers and cannot be negative... ask yourself the "Can a (insert category here) be negative?" question. 
An example would be height of college students, can you have a negative height? Since the obvious answer is no, the height is a the ratio level of measurement.