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Statistics - Measurement Levels


Different data types have different measurement levels.

Measurement levels are important for what types of statistics can be calculated and how to best present the data.


Measurement Levels

The main types of data are Qualitative (categories) and Quantitative (numerical). These are further split into the following measurement levels.

These measurement levels are also called measurement 'scales'

Nominal Level

Categories (qualitative data) without any order.

Examples:

  • Brand names
  • Countries
  • Colors

Ordinal level

Categories that can be ordered (from low to high), but the precise "distance" between each is not meaningful.

Examples:

  • Letter grade scales from F to A
  • Military ranks
  • Level of satisfaction with a product

Consider letter grades from F to A: Is the grade A precisely twice as good as a B? And, is the grade B also twice as good as C?

Exactly how much distance it is between grades is not clear and precise. If the grades are based on amounts of points on a test, you can say that there is a precise "distance" on the point scale, but not the grades themselves.

Interval Level

Data that can be ordered and the distance between them is objectively meaningful. But there is no natural 0-value where the scale originates.

Examples:

  • Years in a calendar
  • Temperature measured in fahrenheit

Note: Interval scales are usually invented by people, like degrees of temperature.

0 degrees celcius is 32 degrees of fahrenheit. There is consistent distances between each degree (for every 1 extra degree of celcius, there is 1.8 extra fahrenheit), but they do not agree on where 0 degrees is.

Ratio Level

Data that can be ordered and there is a consistent and meaningful distance between them. And it also has a natural 0-value.

Examples:

  • Money
  • Age
  • Time

Data that is on the ratio level (or "ratio scale") gives us the most detailed information. Crucially, we can compare precisely how big one value is compared to another. This would be the ratio between these values, like twice as big, or ten times as small.