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Categorical (Qualitative) vs. Quantitative

Quantitative variables have direct measurements and have scale. Examples include temperature, pressure, humidity, weight, height, and width.

Categorical (also called Qualitative) variables are classified into categories. Examples include pass/fail, vendor, color, day of week, and gender.

Typically, it is quite easy to identify a variable as Categorical or Quantitative. A good rule is "does a half a unit make sense"? For example, if the variable is temperature then 2.5, 5.5, and 100.5 degrees are all quite possible. Thus temperature is quantitative. If the variable is gender then the notion of "half a gender" no longer makes sense. Thus the variable is qualitative.

Most of the confusion between categorical and quantitative variables revolves around discrete quantitative and ordinal data.

Discrete Quantitative: Many people associate quantitative with continuous, which would be incorrect. The question is "does half a unit make sense" not "is half a unit possible". A good example of a discrete quantitative variable is the volume on a television. Most modern TVs have discrete steps for volume. You press the up button and the volume increases by a set amount. You can't set the volume at a value between the settings (unless you have the old knob style TV). This makes the volume discrete; however, it is still Quantitative. Why? The underlying measurement is volume measured in decibels. Values of 30.5, 50.5, and 100.5 are all possible. Thus the variable is quantitative. Our world is filled with examples of discrete quantitative variables.

Examples of Discrete Quantitative:

Gear on a car: Possible values are 1^st^ gear, 2^nd^ Gear…. The underlying metric is gear ratio which is quantitative.

Digital Clocks: Values are displayed in minutes, 5:02, 5:03…. The underlying metric is time which is quantitative.

Digital Thermostat: Values are displayed in degrees, 69, 70, 71…. The underlying metric is temperature which is quantitative.

Ordinal Data: Ordinal data is typically "count" data which can only take on integers. An example of ordinal data is the number of defects in a product. The number of possible defects can be 0, 1, 2, 3 … infinity. Ordinal data doesn't have to be numbers. For example, survey results from "Strongly Disagree", "Disagree", "Neutral", "Agree", and "Strongly Agree" are also ordinal. The key to identifying ordinal data is that the variable has scale but a half of one isn't possible.

Ordinal data walks a fine line between Categorical and Qualitative. These variables have scale but are only available at unique points. If the number of observed levels is very small, then the data will act very much like categorical data. For example, if a scale has three possible values "Disagree", "Neutral", and "Agree", then the data acts very much like Categorical. However, if many levels are observed, then the data starts to respond much like quantitative data. For example, if the output is the number of pages that jam when printing from a laser printer and you regularly see 0 to 20 jams depending on the conditions, then your data will respond very much like discrete quantitative (and you need a new printer). You must use your judgment when classifying ordinal data.