The 4 Measurement Scales for the CFA Exam (NOIR)
Within the Quantitative methods study session on the CFA Level 1 exam there is a pivotal reading around statistical concepts and market returns.
One testable part of this reading centers around the four main types of measurement scales and there differences.
There are four different measurement scales that are used to create either order or rankings. They are:
- Nominal Scales
- Ordinal Scales
- Interval Scales
- Ratio Scales
To help with memorization you can group them by remembering that the first letter of each forms the French word NOIR (meaning black).
Now let's dive into each of the four scales starting with the least descriptive and ending with the most descriptive/ordered.
Nominal scales refer to randomly assigning numbers to different groups to act as a descriptive category. For example, we might group a set of hedge funds into different groups consisting of Group 1, 2, 3 and so on. While these funds are grouped and separated, there is no numerical significance or relationship between the groupings. Thus of all four rankings nominal scales contain the least amount of information and are thus considered the weakest level of measurement.
Ordinal scales contain more information than nominal scales because each group now has an ordered relationship with one another. For example, we could assign the best 10% of managers to Group 1, the second best 10% to Group 2 and so on. With ordinal scales, however, the intervals separating the ordinal groupings are not directly comparable. For example, while we could say Group 1 (the top 10% of managers) has better performance than Group 2, we cannot say anything about the magnitude of the difference in their performance. We also cannot say if the difference between Group 1 and 2 is the same as the difference between Group 2 and 3.
Interval scales have the same ranking information as ordinal groups, but they also introduce the idea of equal differences (scale) in value. A key example would be temperature. For example, we not only know that 70 degrees is hotter than 60 degrees, we also have a precise context for just how much hotter. Put simply, with interval scales we not only get the ordered relationship of different categories to figure out which is bigger or smaller, but we also understand how much bigger or smaller a value is.
Ratio scales are the most refined level of measurement. Ratio scales not only order categories and have defined differences in value—the same as interval scales—but they also have a true, meaningful zero point. A key example here is weight or money. If you have $10 you have 10 times the purchasing power as if you had zero dollars. This is not true of an interval scale like temperature: 0 degrees is not the absence of temperature it is just one more value. Because there is a true zero point with ratio scales we can compute ratios and add and subtract amounts within the scale.
Summarizing the CFA Level 1 Measurement Scales
NOIR describes four ways of grouping data, from least descriptive to most descriptive. For the L1 exam, expect a question to test your ability to distinguish which convey the most info, key characteristics of each (e.g. which scale allows for use the use of ratios), and the ability to compare and contrast them.