Levels of Measurement

Categorical vs. quantitative measures

Quantitative measures

In essence, quantitative measures are numbers and counts that have quantitative interpretations.

e.g., What is our forecast for the new product's earnings in year 1?

This could be any number, positive or negative, so it's a quantitative variable.

e.g., How many times has this customer purchased our product?

Count variables like this can't have negative values. In that sense, count variables have a "range restriction." Nonetheless, they're still quantitative variables.

Categorical measures

In essence, a categorical measure refers to "types" or "categories" that don't have a quantitative relationship to one another.

e.g., To which customer segment does this customer belong? (referring to, say, three segments: (1) prestige buyers, (2) price buyers, (3) convenience buyers)

These segments have no quantitative relationship with one another. They could have been listed in another order. They're merely types.

e.g., In what state does the customer live? (1 = Alabama, 2 = Alaska, etc.)

This example used numbers to represent the states, so it might appear to be quantitative. However, the variable is categorical because the numbers refer to different types or categories. There is no true quantitative relationship between the states as they are listed. In this example, the numbers referred to simple alphabetical order, and that's not meaningful.

Please note:

Some measures could go either way, depending on our intended meaning. For example, a manager looking back at sales over time might ask, "What discounts were we offering during these weeks?" The answer is a quantitative variable if it's referring to a discount measured in dollars. The answer is a categorical variable if it's referring to, say, three different types discounts such as (1) 25% off this purchase, (2) 25% off your next purchase, and (3) Buy three, get one free.

Some constructs are inherently quantitative but we measure them in a less-than-ideal way that turns them into a categorical variable.

For example, household income is an inherently quantitative construct. However, if we measure income as ...
     (1) less than $50k, (2) $50k to $150k, and (3) greater than $150k,
     ... we have taken the inherently quantitative construct and transformed it into a categorical variable.