What is a Cardinal Scale? Definition and Example

With different scale levels in empirical research, different properties of the examined object are measured. Non-metric nominal and ordinal scales provide us with simpler response options such as gender, education, or professional affiliation. Metric cardinal scales, on the other hand, allow us to make more complex statements about the frequency or intensity of our everyday behaviors.

General Definition of Cardinal Scale

A cardinal scale or metric scale (English: "metric scale") refers to such scale levels that, in contrast to nominal or ordinal scales, have a defined metric or numerical distance between two variables (e.g., 5°C between 15 and 20°C in temperature measurement). The response options for all metric scales have a directly usable numerical value.

These three types of scale levels are counted as cardinal scales:

1. Interval scale
2. Ratio scale
3. Absolute scale

 

 

 

1. Interval Scale

With this, not only can a ranking be established between the individual elements, but the concrete difference is also measured. The intervals between two elements must be equal in size – or at least are considered to be so!

A typical example of an interval-scaled variable is the Celsius temperature: On the corresponding scale, the interval between answer A (15°C) and answer B (20°C) is exactly as large as between answer C (25°C) and answer D (30°C). In empirical research, interval scales are very frequently used to measure attitudes or opinions of respondents (= rating scale).

 

2. Ratio Scale

With this, differences between individual elements or variables can be measured at equal intervals, similar to the interval scale. Additionally, however, all ratio-scaled variables have a physically defined lower limit, the natural zero point, which cannot be exceeded.

These include variables such as body height or weight: The natural point means that there is no person who is physically smaller than 0 centimeters or weighs less than 0 grams (= no negative number possible). In contrast, the Celsius temperature does have a zero point (0°C), but this number was chosen arbitrarily at some point and can be exceeded (= negative degrees are possible).

 

3. Absolute Scale

This is a subcategory of the ratio scale, where there is not only a natural zero point, but additionally a natural unit (typically a count) is specified. While temperature can be measured in Celsius or Fahrenheit, the units of measurement of the absolute scale are not freely selectable.

A typical example is the inhabitants of a country, which on the scale can only be specified in fixed numerical values (1 inhabitant = "1 unit"). In empirical research and statistics, the absolute scale plays an insignificant role because it provides the same data as the ratio scale.