Subject 2. Measurement Scales
Measurement is the assignment of numbers to objects or events in a systematic fashion. To choose the appropriate statistical methods for summarizing and analyzing data, we need to distinguish between different measurement scales or levels of measurement.
- Nominal Scale
- Nominal measurement represents the weakest level of measurement.
- It consists of assigning items to groups or categories.
- No quantitative information is conveyed and no ordering (ranking) of the items is implied.
- Nominal scales are qualitative rather than quantitative.
- Ordinal Scale
- Measurements on an ordinal scale are categorized.
- The various measurements are then ranked in their categories.
- Measurements with ordinal scales are ordered with higher numbers representing higher values. The intervals between the numbers are not necessarily equal.
- Interval Scale
- Ratio Scale
Note that as you move down through this list, the measurement scales get stronger.
Hint: Remember the order of the different scales by remembering NOIR (the French word for black); the first letter of each word in the scale is indicated by the letters in the word NOIR.
Before we move on, here's a quick exercise to make sure that you understand the different measurement scales. In each case, identify whether you think the data is nominal, ordinal, interval or ratio:
- The number of goals scored by a soccer player in a season.
- The temperature in Fahrenheit.
- The relative positions of contestants in a beauty pageant.
- The speed at which a vehicle travels.
- The allocation of the number "1" to boys and "2" to girls in a class.
Answers and Explanations
- Ratio: numbers have meaning and can't go below 0.
- Interval: temperature is always measured on the interval scale.
- Ordinal: relative positions are ranks, so this data has been ranked.
- Ratio: speed is a meaningful number and cannot be negative.
- Nominal: the numbers are labels, and have no other meaning.
Practice Question 1The following chart illustrates the breakdown of a survey of 300 bachelors, living in Florida, as to their favorite fast food restaurant.
Favorite Fast Food Restaurant
Burger King ================= 51
Hardee's =============== 45
McDonald's ====================== 66
Taco Bell ========== 30
Wendy's ============================ 84
Other ======== 24
What level of data is the number of bachelors?
C. ordinalCorrect Answer: A
Practice Question 2A student's score on the ACT test would be what level of measurement?
C. ratioCorrect Answer: B
Practice Question 3If thirty students listed the distance that they drive to school, this data would be what level of measurement?
C. ratioCorrect Answer: C
Practice Question 4If an administrator had someone count the number of people in each room of an office building, this data would be what level of measurement?
C. ratioCorrect Answer: C
Practice Question 5The years in which the U.S. gross domestic product decreased would be an example of which level of measurement?
C. ordinalCorrect Answer: B
The correct answer is interval because it makes sense to talk about differences between years (1984 - 1963 = 21 years); ratios are meaningless since time did not begin in year 0.
Study notes from a previous year's CFA exam:
2. Measurement Scales