Chapter Eight
Measurement and Scaling:
Fundamentals and
Comparative Scaling
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Measurement and Scaling
Measurement means assigning numbers or other
symbols to characteristics of objects according to
certain pre-specified rules.
•
•
•
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.
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Scale Characteristics
Description
By description, we mean the unique labels or
descriptors that are used to designate each value
of the scale. All scales possess description.
Order
By order, we mean the relative sizes or positions
of the descriptors. Order is denoted by
descriptors such as greater than, less than, and
equal to.
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Scale Characteristics
Distance
The characteristic of distance means that
absolute differences between the scale
descriptors are known and may be expressed in
units.
Origin
The origin characteristic means that the scale has
a unique or fixed beginning or true zero point.
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Measurement and Scaling
Scaling involves creating a continuum upon
which measured objects are located.
Consider an attitude scale from 1 to 100. Each
respondent is assigned a number from 1 to 100,
with 1 = Extremely Unfavorable, and 100 =
Extremely Favorable. Measurement is the actual
assignment of a number from 1 to 100 to each
respondent. Scaling is the process of placing the
respondents on a continuum with respect to their
attitude toward department stores.
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Primary Scales of Measurement
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Primary Scales of Measurement
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Primary Scales of Measurement
Scale Fig. 8.1
Nominal
Numbers
Finish
Assigned
to Runners
Ordinal
7
8
3
Rank Order
of Winners
Interval
Performance
Rating on a
0 to 10 Scale
Ratio
Time to Finish
in Seconds
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Finish
Third
place
Second
place
First
place
8.2
9.1
9.6
15.2
14.1
13.4
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Primary Scales of Measurement
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Primary Scales of Measurement
Nominal Scale
• Nominal scale is a naming scale, where variables are simply
“named” or labeled, with no specific order as gender, place of
residence.
• 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.
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Primary Scales of Measurement
Nominal Scale
Example:
“Which brand of smartphones do you prefer?” Options :
1- “Apple”
2- “Samsung”
3- “OPPO”
In the above example, when a survey respondent selects
Apple as their preferred brand, the data entered and
associated will be “1”.
This helped in quantifying and answering the final question –
How many respondents selected Apple, how many selected
Samsung, and how many went for OnePlus – and which one is
the highest.
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Primary Scales of Measurement
Ordinal Scale
• A ranking scale in which numbers are assigned to
objects to indicate the relative extent to which the
objects possess some characteristic.
• Can determine whether an object has more or less of
a characteristic than some other object, but not how
much more or less.
• Ordinal scale data can be presented in tabular or
graphical formats for a researcher to conduct a
convenient analysis of collected data.
• In addition to the counting operation allowable for
nominal scale data, ordinal scales permit the use of
statistics based on centiles, e.g., percentile, quartile,
median.
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Primary Scales of Measurement
Ordinal Scale
Example: A semantic differential scale question such as:
Q- How satisfied are you with our services?
12345-
Very Unsatisfied
Unsatisfied
Neutral
Satisfied
Very Satisfied
This scale not only assigns values to the variables but also measures
the rank or order of the variables, such as:
• Grades
• Satisfaction
• Happiness
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Primary Scales of Measurement
Interval Scale
• Interval scale contains all the properties of the
ordinal scale, in addition to which, it offers a
calculation of the difference between variables.
• For instance, consider a Celsius/Fahrenheit temperature scale –
• 80 degrees is always higher than 50 degrees and the difference between
these two temperatures is the same as the difference between 70 degrees
and 40 degrees.
• Interval scale is often chosen in research cases
where the difference between variables is a mandate
– which can’t be achieved using a nominal or ordinal
scale.
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Primary Scales of Measurement
Interval Scale
• Example:
Q- Please state your annual income
1.
2.
3.
4.
5.
Below $40,000
$40,000- $59,999
$60,000- $79,999
$80,000- $99,999
Above $100,000
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Primary Scales of Measurement
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.
• All statistical techniques can be applied to ratio data.
• Because of the existence of true zero value, the
ratio scale doesn’t have negative values.
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Primary Scales of Measurement
Ratio Scale
• Example:
Q- What is your daughter’s current height?
a)
b)
c)
d)
Less than 5 feet.
5 feet 1 inch – 5 feet 5 inches
5 feet 6 inches- 6 feet
More than 6 feet
Q- What is your weight in kilograms?
a)
b)
c)
d)
e)
Less than 50 kilograms
51- 70 kilograms
71- 90 kilograms
91-110 kilograms
More than 110 kilograms
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Primary Scales of Measurement
Table 8.1
Scale
Nominal
Ordinal
Interval
Ratio
Basic
Characteristics
Numbers identify
& classify objects
Common
Examples
Social Security
nos., numbering
of football players
Nos. indicate the Quality rankings,
relative positions rankings of teams
of objects but not in a tournament
the magnitude of
differences
between them
Differences
Temperature
between objects (Fahrenheit)
Zero point is fixed, Length, weight
ratios of scale
values can be
compared
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Marketing
Permissible Statistics
Examples
Descriptive
Inferential
Brand nos., store Percentages,
Chi-square,
types
mode
binomial test
Preference
Percentile,
rankings, market median
position, social
class
Rank-order
correlation,
Friedman
ANOVA
Attitudes,
opinions, index
Age, sales,
income, costs
Productmoment
Coefficient of
variation
Range, mean,
standard
Geometric
mean, harmonic
mean
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Primary Scales of Measurement Versus Data Type
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Summary – Levels of Measurement
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