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**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.

*Example 1**Example 2***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 1

The 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?

A. ratio

B. nominal

C. ordinalCorrect Answer: A

#### Practice Question 2

A student's score on the ACT test would be what level of measurement?A. ordinal

B. interval

C. ratioCorrect Answer: B

#### Practice Question 3

If thirty students listed the distance that they drive to school, this data would be what level of measurement?A. ordinal

B. interval

C. ratioCorrect Answer: C

#### Practice Question 4

If an administrator had someone count the number of people in each room of an office building, this data would be what level of measurement?A. nominal

B. interval

C. ratioCorrect Answer: C

#### Practice Question 5

The years in which the U.S. gross domestic product decreased would be an example of which level of measurement?A. ratio

B. interval

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