- CFA Exams
- 2021 Level I
- Study Session 2. Quantitative Methods (1)
- Reading 7. Statistical Concepts and Market Returns
- Subject 2. Measurement Scales
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Subject 2. Measurement Scales PDF Download
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.
Learning Outcome Statementsa. 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® 2021 Level I Curriculum, , Volume 1, Reading 7
User Contributed Comments 10
|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.|