Lesson 1: Discrete and Continuous variables

Researchers collect many types of data, and there are several ways we can categorize this data. Data can be quantitative or it can be qualitative. Quantitative data is data that involves quantities or measurements, i.e. numbers. These data often address questions of how many/much, when, or where. Qualitative data is data that involves descriptions of the qualities. These data often address questions of what or how. Some types of information can be collected qualitatively or quantitatively. Let's look at a few examples:

This family owns 2 cats.	Quantitative
Sara-Liz ran 4.5 miles...	Quantitative
in 32:46...	Quantitative
on 11/13/2014.	Quantitative
The patient had a broken arm.	Qualitative
My car is red.	Qualitative
The lion was last seen near mile marked 15 on I-20.	Qualitative
The lion was last seen at 33°38'02.2"N 81°46'25.5"W.	Quantitative

Now that we've settled that, let's get to discrete vs continuous variables. Continuous variables are data that can have any value within a range; most quantitative data are continuous. Discrete variables are data that can only have certain integer or category values; some quantitative and all qualitative data are discrete. Let's look at those examples again:

This family owns 2 cats.	Quantitative	Discrete
Sara-Liz ran 4.5 miles...	Quantitative	Continuous
in 32:46...	Quantitative	Continuous
on 11/13/2014.	Quantitative	Discrete
The patient had a broken arm.	Qualitative	Discrete
My car is red	Qualitative	Discrete
The lion was last seen near mile marked 15 on I-20.	Qualitative	Discrete
The lion was last seen at 33°38'02.2"N 81°46'25.5"W.	Quantitative	Continuous

Of course the number of cats, while a quantitative measure of cat-ownership, is discrete because you can have 0, 1, 2...50, etc cats, but you cannot have 2.5 cats. Unless you are Schrodinger, it which case you shouldn't be allowed any cats. The date example is a little bit funny. As expressed it's discrete; It's Nov 13th or it's Nov 14th. But time is a continuous variable; it can be 6:15am on Nov 13, 6:15am on Nov 14, or any moment in between. Color is likewise; the car is red or blue...until it's purple (for color we can use wavelength or hue as a continuous variable). Which is to say, sometimes data can be recorded as either a continuous or discrete variable.

Of course, the question "why was this lesson 1?" needs to be answered. Simply, I started here because it's important to know which type of data we are working with. Different types of data call for different types of statistical analyses. And when I explain these analyses I want to be sure we're all on the same page regarding how and when they are used (and not used).

On to lesson 2...