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Q1. Differentiate between nominal, ordinal, interval and ratio scales, with an example of each.


Answer:
 1. Nominal measurement
This level of measurement consists in assigning numerals or symbols to different categories of a variable.

The example of male and female applicants to an MBA program mentioned earlier is an example of nominal measurement. The numerals or symbols are just labels and have no quantitative value. The number of cases under each category are counted.

Nominal measurement is therefore the simplest level of measurement. It does not have characteristics such as order, distance or arithmetic origin.

2. Ordinal measurement
In this level of measurement, persons or objects are assigned numerals which indicate ranks with respect to one or more properties, either in ascending or descending order.

Example
Individuals may be ranked according to their “socio-economic class”, which is measured by a combination of income, education, occupation and wealth.
The individual with the highest score might be assigned rank 1, the next highest rank 2, and so on, or vice versa.
The numbers in this level of measurement indicate only rank order and not equal distance or absolute quantities. This means that the distance between ranks 1 and 2 is not necessarily equal to the distance between ranks 2 and 3.

Ordinal scales may be constructed using rank order, rating and paired comparisons. Variables that lend themselves to ordinal measurement include preferences, ratings of organizations and economic status.

Statistical techniques that are commonly used to analyze ordinal scale data are the median and rank order correlation coefficients.
3. Interval measurement
This level of measurement is more powerful than the nominal and ordinal levels of measurement, since it has one additional characteristic – equality of distance. However, it does not have an origin or a true zero. This implies that it is not possible to multiply or divide the numbers on an interval scale.

Example
The Centigrade or Fahrenheit temperature gauge is an example of the interval level of measurement. A temperature of 50 degrees is exactly 10 degrees hotter than 40 degrees and 10 degrees cooler than 60 degrees.
Since interval scales are more powerful than nominal or ordinal scales, they also lend themselves to more powerful statistical techniques, such as standard deviation, product moment correlation and “t” tests and “F” tests of significance.

4. Ratio measurement
This is the highest level of measurement and is appropriate when measuring characteristics which have an absolute zero point. This level of measurement has all the three characteristics – order, distance and origin.

Examples
Height, weight, distance and area. Since there is a natural zero, it is possible to multiply and divide the numbers on a ratio scale. Apart from being able to use all the statistical techniques that are used with the nominal, ordinal and interval scales,
techniques like the geometric mean and coefficient of variation may also be used.

The main limitation of ratio measurement is that it cannot be used for characteristics such as leadership quality, happiness, satisfaction and other properties which do not have natural zero points.

The different levels of measurement and their characteristics may be summed up.

In the table below –
Levels of measurement
Characteristics
Nominal
No order, distance or origin
Ordinal
Order, but no distance or origin
Interval
Both order and distance, but no origin
Ratio
Order, distance and origin

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