**Quantitative Methods: Basic Concepts**

**Reading 7. Statistical Concepts and Market Returns**

**Learning Outcome Statements**

a. distinguish between descriptive statistics and inferential statistics, between a population and a sample, and among the types of measurement scales;

b. define a parameter, a sample statistic, and a frequency distribution;

*CFA Curriculum, 2020, Volume 1*

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**Subject 2. Measurement Scales**

**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.

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**User Contributed Comments**
10

You need to log in first to add your comment. ###### beatjeff

Nominal scale is the weakest value

###### rainatt

ratio scale has true zero point and allows the computation of meaningful ratios.

interval scale has no true zero point,and differences between scales are equal

###### achu

"NOIR" nominal (nothing but a label) ordinal (only a relative rank) interval, ratio.

###### rethan

Why cannot speed be ratio? It meets the criterion mentioned for answer A- a) the numbers have meaning (speed has meaning. ex a car is traveling at 60 mph)& cant go below 0 (BTW,

A car can have 0 speed i.e it could be stationary)

###### rethan

BTW, speed also has a true zero point. For example, you can make make such statments as a car, moving at 60mph, is moving at speeds TWICE its speed when it was moving at 30 mph (you cant say that if speed was interval)

###### thekid

rethan ---> NO ONE said speed CANT be a ratio scale.... Look at the above exercise 4.

###### VikramJ

So the answer for Exercise 2 says temperature is always measured on the interval scale. Yet, Kelvin Temperature is a Ratio Scale..

###### ColonelCFA

It says "Fahrenheit scale for temperature" not all temperature systems. Which makes their statement true.

###### 2014

U see '0"rdinal "0" in the begining means no true zero point. Ordinal name itself suggest ranking

As the name suggest "NO"minal Measurement as u see "NO" in the beginging it means it is not quantitative so by that it is categorical. (Minal is girl name and thats destructive statistic)

so remove Minal from Nominal Measurement so it is now No measurement.

Ordinal is which girl u like most rank in order .... 1,2,3

Interval is how fast the aircondition would be in the exam .... temperature. I heard in exams ACs are very fast be jackets

Interval and Ordinal share similar characteristics: Ranking and no true zero point.

###### kseeba17

stattrek(dot)co(m)/statistics/measurement-scales.aspx?Tutorial=AP. < this is a much better explanation.