Chapter 1 Variables and Their Measurement
1.6 Creating Variables
If you ever find yourself in need of creating your own variables (perhaps, in creating a questionnaire), this brief final note is for you. As well, you can learn to evaluate whether an existing variable has been operationalized properly.
To properly create a variable, its categories need to satisfy two requirements: they need to be collectively exhaustive and mutually exclusive. The first condition, collectively exhaustive, refers to the requirement that the categories cover all possible ways the variable can vary (or all posisble answers to a questionnaire question) — none can be excluded. The second condition, mutually exclusive, adds the logical necessity that a specific variation (or an answer to a questionnaire question) can exist in one and only one category.
This is simpler than the definition makes it sound to be. The following example illustrates.
Example 1.4. Logical Requirements to Operationalizing Variables
Imagine you are filling out a questionnaire and one of the questions is about age, like this:
Q1. What is your age?
a) 20-29
b) 30-39
c) 40-49
d) 50-59
What if you are 18 or 19? Which answer would you pick? How about if the person filling out the questionnaire is 60 or older? As stated, the Q1 question (i.e., the way the variable age is operationalized by it) violates the first requirement, that of providing an exhaustive list of all possibilities. All possible variations need to be covered by the variable’s categories, otherwise the variable is incomplete.
Now consider another hypothetical way to ask the same questionnaire question:
Q2. What is your age?
a) 18-25
b) 25-30
c) 30-35
d) 35-40
e) 40-45
f) 45-50
g) 50+
Assuming the questionnaire is administered only to adults, Q2 provides a collectively exhaustive list of possible answers; the variable’s categories are too collectively exhaustive.
They are, however, misleading as they are not mutually exclusive. Which answer do you pick if you are 25 — a) or b)? Which answer do you pick if you are 40 — d) or e)? Logically, one and the same possible variation cannot fall into two or more categories; it can only fall in one of the variable’s categories.
Thus, one proper way to operationalize age is something like this:
Q3. What is your age?
a) 18-25
b) 26-30
c) 31-35
d) 36-40
e) 41-45
f) 46-50
g) Above 50
See if you can spot and fix violations of the two logical operationalization requirements in the exercise below.
Do It! 1.6. What is Wrong with These Variables’ Operationalizations?
Q4. What year in college are you?
a) First-year
b) Second-year
Q5. How many siblings do you have?
a) 0
b) 1
c) 1-2
d) 3-4
e) 4 or more
Q6. How do you commute to your institution’s campus?
a) Car
b) Public transit
c) Bus
d) Bike
Now that we’ve covered the theoretical preliminaries, go see what working with actual data is like, in Chapter 2.