Quantitative

A quantitative property can be meaningfully measured using numbers; properties which aren't quantitative are called qualitative. Examples of quantitative properties include:

• the number of grains of sand on a beach,
• the width of a hair, and
• the time for a hammer to fall a certain distance.

An observation isn't necessarily quantitative just because it's been recorded using numbers. Any measurement can be made using numbers; a researcher recording names, for instance, could assign the number 1 to mean "Susan", 2 to mean "Michael", and so on. This, however, is not a meaningful use of numbers: the researcher can arbitrarily reassign the numbers (so that 1 means "Michael" and 2 means "Susan") without losing any information. Put another way, facts about numbers (for example, that 2 is greater than 1, that 5 is two more than 3, and that 8 is twice 4) don't mean anything about the names corresponding to those numbers. Because of this, a person's name is not a quantitative property.

On the other hand, suppose a researcher is counting the grains of sand on a beach. The researcher could assign the number 7 to mean "41 grains of sand" and the number 4 to mean "78 grains of sand", but this loses information: even though 7 is greater than 4, 41 grains are still fewer than 78 grains. Put another way, the researcher can assign numbers to observations so that facts about those numbers will correspond to facts about the observed property. Therefore, the number of grains of sand on a beach is a quantitative property.

Statisticians typically don't use the terms "quantitative" and "qualitative", and have instead developed more sophisticated categories of scale.

• A nominal scale allows distinction between different points of data, but not necessarily anything else; names are an example of a nominal scale. Nominal scales are always qualitative.
• An ordinal scale has an inherent system of ordering; the ratings "bad", "mediocre", and "good" are organized on an ordinal scale. Some ordinal scales are quantitative.
• A constant distance on an interval scale means the same thing everywhere on the scale. An extra 5 kilograms is an extra 5 kilograms, whether it's on top of 7 kilograms or 207 — but an extra point on the logarithmic Richter scale is a much larger difference for an 8.0 than for a 2.0. All interval scales all quantitative.
• A ratio on a ratio scale means the same thing everywhere on the scale. 2 meters is twice as far as 1 meter, but 40 degrees Celsius is not twice as hot as 20 degrees Celsius (since 0 degrees Celsius is not Absolute Zero). All ratio scales are quantitative.

Use in debate

SATs are often accused of attempting to put a quantitative measure (the SAT score) to something that is fundamentally qualitative (education and human intelligence).

Particularly in political debate, it can be an effective tactic to dismiss an observation as qualitative rather than quantitative; this is seen as undermining the legitimacy of that observation. This may be related to the common perception of quantitative data as more objective than qualitative data.