We measure data on different scales:
- nominal scales,
- ordinal scales,
- interval scales, and
- ratio scales.
On nominal scales, data can only be categorized; it cannot be ranked. In other words, there are differences on nominal scales, but no ranking is possible.
Example:
There are differences between different nationalities, but there is no way to rank them. Nationality A is not better than nationality B, only different. Therefore, nationalities are measured on nominal scales.
On ordinal scales, we can sort data into categories (something we can not do on nominal scales).
Example:
Four students sit a math exam at their school and get grades of D, C, B, and B.
The grades can be ordered, e.g. as B, B, C, D or as D, C, B, B. But the distances are not comparable: the distance between grade D and C is much greater than that between C and B.
On interval scales, the distances between scale values are equal. The properties of nominal and ordinal scales are also found on interval scales.
Example:
Temperatures in °F and °C are measured on interval scales.
Ratio scales have all the characteristics of the other scales; they also have a true zero point.
Example:
Distances measured in miles or kilometers have a true zero point, because we cannot change them.
THE LAMBERT METHOD
It’s very important to understand the differences between the various scales, because the type of analysis performed on the data differs from one scale to the next. Put differently, measurement scales are vital, because using the right mean, dispersion and correlation differs on different scales:
| Scale | Mean | Dispersion | Correlation |
|---|---|---|---|
| nominal scale | mode | not relevant | not relevant |
| ordinary scale | median | range | Spearman correlation coefficient |
| interval scale | arithmetic mean | variance, standard deviation | correlation coefficient of Bravais and Pearson |
| ration scale | arithmetic mean | variance, standard deviation | correlation coefficient of Bravais and Pearson |
The important aspects of Statistical Concepts and Market Returns can be seen on this MindMap (click on it to get a larger picture).
Did you find the Mindmap helpful? All of Lambert Education’s MindMaps for CFA Level I and CFA Level II can be found here:
https://daniel-lambert.de/produkt-kategorie/chartered-financial-analyst/
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