Scales of Measurement: Nominal, Ordinal, Interval, and Ratio, Lecture notes of Business Systems

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Module 3

Measurement and Scaling

Objects or individuals are

not measured

• but some characteristic

or feature of the same are

measured.



One-to-one correspondence between the numbers and the

characteristics being measured



The rules for assigning numbers should be standardized

and applied uniformly



Rules must not change over objects or time

Measurement

the process or result of

observing an event or object

in order to determine its extent or quantity

by comparison with a known unit and

then assigning numbers or any other symbols to

characteristic or feature

according to some pre-specified formal rules

No.7 No. 8 No. 3

Primary Scales of Measurement

Nominal Numbers

Assigned

to Runners

Ordinal Rank Order

of Winners

Interval Performance

Rating on a

0 to 10 Scale

Ratio Time to

Finish, in

3rd

2nd 1st

Nominal Scale



The numbers serve only as labels or tags for identifying

and classifying objects.



When used for identification, there is a strict one-to-one

correspondence between the numbers and the objects.



The numbers do not reflect the amount of the

characteristic possessed by the objects.



The only permissible operation on the numbers in a

nominal scale is counting.



Only a limited number of statistics, all of which are based

on frequency counts, are permissible, e.g., percentages,

and mode.

Interval Scale



Numerically equal distances on the scale represent equal

values in the characteristic being measured.



It permits comparison of the differences between objects.



The location of the zero point is not fixed. Both the zero

point and the units of measurement are arbitrary.



Any positive linear transformation of the form y = a + bx

will preserve the properties of the scale.



It is meaningful to take ratios of scale values.



Statistical techniques that may be used include all of those

that can be applied to nominal and ordinal data, and in

addition the arithmetic mean, standard deviation, and other

statistics commonly used in marketing research.

Ratio Scale



Possesses all the properties of the nominal, ordinal, and

interval scales.



It has an absolute zero point.



It is meaningful to compute ratios of scale values.



Only proportionate transformations of the form y = bx,

where b is a positive constant, are allowed.



All statistical techniques can be applied to ratio data.

Classification of Scaling Techniques

Likert

Semantic

Differential

Stapel

Scaling Techniques

Noncomparative

Scales

Comparative

Scales

Paired

Comparison

Rank

Order

Constant

Sum

Q-Sort and

Other

Procedure

s

Continuous

Rating Scales

Itemized

Rating

Scales

Comparison of Scaling Techniques



Comparative scales involve the direct comparison of

stimulus objects. Comparative scale data must be

interpreted in relative terms and have only ordinal or rank

order properties.



In noncomparative scales, each object is scaled

independently of the others in the stimulus set. The

resulting data are generally assumed to be interval or ratio

scaled.



A respondent is presented with two objects and asked to

select one according to some criterion.



The data obtained are ordinal in nature.



Paired comparison scaling is the most widely used

comparative scaling technique.



With n brands,

n

C

2

paired comparisons are required.

Paired comparison scales

Obtaining Shampoo Preferences - Using Paired Comparisons

For each pair of shampoo, please indicate which one of the

two brands of shampoo you would prefer for personal use.

1 in a particular box means that the brand in that column was preferred

over the brand in the corresponding row.

0 means that the row brand was preferred over the column brand.

The number of times a brand was preferred is obtained by summing the

1s in each column.

Preference for Toothpaste Brands

using Rank Order Scaling

Rank the various brands of toothpaste in order of preference.

Begin by picking out the one brand that you like most and

assign it a number 1. Then find the second most preferred

brand and assign it a number 2. Continue this procedure until

you have ranked all the brands of toothpaste in order of

preference.

The least preferred brand should be assigned a rank of 10.

No two brands should receive the same rank number.

The criterion of preference is entirely up to you. There is no

right or wrong answer. Just try to be consistent.

Constant Sum Scaling



Respondents allocate a constant sum of units, such as 100

points to attributes of a product to reflect their importance.



If an attribute is unimportant, the respondent assigns it

zero points.



If an attribute is twice as important as some other attribute,

it receives twice as many points.



The sum of all the points is 100. Hence, the name of the

scale.

Responses of 3 Segments of Consumers

Attribute Ladies

Gentlemen Children

1. Mildness
2. Lather
3. Shrinkage
4. Price
5. Fragrance
6. Packaging
7. Moisturizing
8. Cleaning Power

Importance of Bathing Soap Attributes

Using a Constant Sum Scale

Also called the graphic rating scale

respondents are asked to rate each variable on a

continuous scale that runs from one end to the other

the mark can be put at any place on line

sometimes a supporting scale with numbers or grades is

provided just below the continuous line to facilitate the

answering by the respondent

Example – How would you rate the overall performance Sony

TV on the following scale?

Continuous rating scale

I I I I I

BAD 10 20 30 40 50 SUPERB