Types of Variables

Note that there is something different about the values that different variables can take on. The values for the political party are categories (Republican, Democrat). Moreover, these are categories that cannot be ranked in any specific order. Being a Republican is not “higher” than being a Democrat. This means that the political party is a nominal variable.

Nominal variables come in categories that cannot be ranked. Additional examples include the presidential election winner in a state (Joe Biden, Donald Trump), a person’s race (Asian, Black, White), and whether a school is public or private.

The values for the level of education are categories (High School Degree, Bachelor’s Degree, and Master’s Degree). Moreover, these values are categories that can be ranked: a Master’s degree is higher than a Bachelor’s degree, which is higher than a High School degree. This means that the level of education is an ordinal variable.

Ordinal variables come in categories that can be ranked in a specific order. Additional examples include a student’s letter grade in an exam (A+, A-, B+), how likely a student is to recommend an instructor (very likely, somewhat likely, unlikely) and a person’s military rank (Liutenant, Captain, General).

Now let’s take a look at the year of birth. As with the highest degree earned, we can rank these values: a person born in 1970 is older than a person born in 1990, and a person born in 1990 is older than a person born in 2002. But note how this is different from ordinal variables: now we can exact the differences between the values: a person born in 1970 is 20 years older than a person born in 1990. Moreover, year of birth is a variable that doesn’t have a true zero. The year “zero” only reflects a convention for how we count years in our calendar. All of this means that the year of birth is an interval variable.

Interval variables come in numeric quantities that allow us to calculate the differences between values, and have no true zero. Additional examples include a person’s body temperature (measured in Fahrenheit) or a person’s credit score (which varies between 300 and 850).

Now look at the unemployment rate. As with the year of birth, we can calculate the numeric difference between states: a 3% unemployment rate is 7 percentage points lower than a 10% unemployment rate. But note how the unemployment rate is different from a person’s year of birth as the unemployment rate has a true zero: a state could have zero unemployment in a given year. This means that the unemployment rate is a ratio variable.

Ratio variables come in numeric quantities and have a true zero. Additional examples include a person’s annual income (50k, 70k, 100k) and the percentage of votes for a candidate in a given election (40%, 50%, 55%).