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Perceptual Mapping
This module introduces two perceptual mapping
methodologies: attribute rating and overall similarity.
Authors: Ron Wilcox and Stu James
© 2013 Ron Wilcox, Stu James and Management by the Numbers, Inc.
There are two primary methods of constructing perceptual
maps from consumer-level data:
Attribute
Rating
Method
PERCEPTUAL MAPPING
Perceptual Mapping
Overall
Similarity
Method
Insight
“Simple Graphics are often the most powerful way to communicate
complicated statistical information.”
- Edward R. Tufte, The Visual Display of Quantitative Information
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The Market for Sports Utility Vehicles (circa 2005)
Prestigious
Cadillac
Escalade
Hummer
H2
Jeep
Grand
Cherokee
Chevy
Tahoe
Nissan
Pathfinder
Toyota
4Runner
Not Rugged
Rugged
Ford
Explorer
Jeep
Cherokee
SAMPLE PERCEPTUAL MAP (ATTRIBUTE RATING METHOD)
Sample Perceptual Map (Attribute Rating)
Not Prestigious
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Direct measurement of consumer perceptions of attributes
and products based on the following question format:
[Insert product name] is a [insert attribute] [insert product category].
Strongly
Agree
Agree
Neither Agree
Nor Disagree
Disagree
Strongly
Disagree
One question for each attribute for each product
HOW IS THIS PERCEPTUAL MAP CREATED?
How is this Perceptual Map Created?
I believe [insert product name] is an excellent [insert product category].
Strongly
Agree
Agree
Neither Agree
Nor Disagree
Disagree
Strongly
Disagree
One question for each product
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Next, calculate the average attribute rating for each vehicle
based on the survey population (summarize 1st question)
Product 1
Product 2
………..
Product N
Attribute 1
Attribute 2
[average rating]
………….
Attribute M
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HOW IS THIS PERCEPTUAL MAP CREATED?
How is this Perceptual Map Created?
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Then, calculate the Avgerage Preference Rating score for
each product based on the survey population (summarize
2nd question)
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HOW IS THIS PERCEPTUAL MAP CREATED?
How is this Perceptual Map Created?
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Next, run a regression analysis of the data such that the
attribute ratings for each product are the independent
variables and the product preference is the dependent
variable.
Overall Preferencein = α + β1 Attrib1in + β2 Attrib2in + …+βM AttribMin + εin
For example, the results of the regression analysis for the
vehicles in this study might be:
HOW IS THIS PERCEPTUAL MAP CREATED?
How is this Perceptual Map Created?
Overall Preference = -2.7 + 1.25 * Prestige + 2.5 * Ruggedness +...
Insight
The coefficients that are the greatest in absolute value will form the
axis of your perceptual map.
Note: This presumes all of the survey questions are on the same 1-5 scale. If the scale
is not the same for all measures, this would not necessarily be true.
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Sports Utility Vehicles with Average Ratings
Prestigious
Cadillac
Escalade (1.2, 4.7)
Hummer
H2 (4.5, 4.6)
Jeep
Chevy
Tahoe (1.9, 3.8) Grand
Cherokee
(2.5, 3.8)
Nissan
Pathfinder (3.6, 4)
Toyota
4Runner (3.5, 3.3)
Not Rugged
Rugged
Ford
Explorer (2.1, 2)
Jeep
Cherokee (4, 1.7)
Insight
Not Prestigious
Now we also know that
Prestigious / Not Prestigious
and Rugged / Not Rugged had
the highest absolute value
coefficients in the regression.
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SAMPLE PERCEPTUAL MAP (ATTRIBUTE RATING METHOD)
Sample Perceptual Map (Attribute Rating)
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Overall Preferencein = α + β1 Attrib1in + β2 Attrib2in + …+βM AttribMin + εin
Can we get anymore information from this regression?
YES!
Overall Preference = -2.7 + 1.25 * Prestige + 2.5 * Ruggedness +…
CONSTRUCTING AN IDEAL VECTOR
Constructing the Ideal Vector
• Take the ratio of the coefficient of the second-most important
perceptual attribute to the most important. In this case we would
have 1.25 / 2.5 = ½.
• Plot the ideal vector with slope defined by this ratio and whose
beginning point is at the origin of the graph (assumes most
important attribute is on the X axis) as shown on the following slide.
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The Market for Sports Utility Vehicles (circa 2005)
Prestigious
Cadillac
Escalade
Hummer
H2
Jeep
Grand
Cherokee
Chevy
Tahoe
To more
preferred
(slope = ½)
Nissan
Pathfinder
Toyota
4Runner
Not Rugged
From less
preferred
CONSTRUCTING AN IDEAL VECTOR
Constructing the Ideal Vector
Rugged
Ford
Explorer
Jeep
Cherokee
Insight
By drawing lines perpendicular
to the ideal vector to each
product we can “order” the
vehicles from least preferred
to most preferred.
Not Prestigious
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Now let’s move to the Overall Similarity Method of creating perceptual
maps. Here, rather than comparing products on particular attributes,
we instead measure their overall similarity using a scaled method or by
ranking products from most similar to least similar. While the
methodologies are different, they offer similar interpretive challenges.
On a scale from 1 (very different) to 5 (very similar), please compare
[Product NameA] with [Product NameB].
Very Different
(1)
(2)
(3)
(4)
Very Similar
(5)
MULTI-DIMENSIONAL SCALING (MDS)
Multi-Dimensional Scaling (MDS)
One question for each product pair
Insight
Notice how the question does not care why the responder rates the products as
similar or different only the degree to which the responder perceives them to be.
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Here is a sample similarity matrix for a set of movies that corresponds
to the average similarity ratings for a population based on the question
from the previous slide.
Movie Similarity Matrix
About
Schmidt
Lord of
Rings
Gangs
of NY
Maid in
Manhattan
A Guy
Thing
About Schmidt
5.0
Lord of Rings
4.2
5.0
Gangs of NY
3.0
4.0
5.0
Maid in Manhattan
2.0
1.5
1.7
5.0
A Guy Thing
1.0
2.0
3.4
2.1
5.0
Bowling for Columbine
3.5
2.5
2.2
1.9
1.2
Bowling for
Columbine
MULTI-DIMENSIONAL SCALING
Multi-Dimensional Scaling
5.0
Using this data, we can use a MDS program to plot these products in a
two-dimensional space that best maintains their relative similarities as
shown on the next slide.
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MULTI-DIMENSIONAL SCALING
Multi-Dimensional Scaling
MDS for Movie Data
Final Configuration, dimension 1 vs. dimension 2
1.0
MAID
0.8
BOWL
0.6
Dimension 2
0.4
0.2
SCHMIDT
0.0
-0.2
RINGS
-0.4
AGUY
-0.6
-0.8
-1.0
NYGANGS
-0.6
-0.2
0.2
0.6
1.0
1.4
Dimension 1
Notice that the axes are not defined on this map due to the nature of
how the data is collected. Also, recognize that we are attempting to
describe products that have an unknown number of perceived
attributes in a two dimensional space. Does this impact our ability to
use the map? Possibly. Let’s explore this further.
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One way to aid our interpretation of the map is to include some
additional questions in the survey which can be used to enhance the
MDS analysis. In effect, we are adding additional “products” that are
pure perceptions.
Very
Different
Nissan Pathfinder and
Rugged
1
[ ]
Very
Similar
2
[ ]
3
[ ]
4
[ ]
Very
Different
Reliable and
Hummer
1
[ ]
Very
Similar
2
[ ]
3
[ ]
4
[ ]
Very
Different
Rugged and
Reliable
1
[ ]
5
[ ]
5
[ ]
OVERALL SIMILARITY WITH PERCEPTUAL ATTRIBUTES
Overall Similarity with Perceptual Attributes
Very
Similar
2
[ ]
3
[ ]
4
[ ]
5
[ ]
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Luxurious
Cadillac
Escalade
Chevy
Tahoe
Ford
Explorer
Hummer
H2
Nissan
Pathfinder
Jeep
Toyota
Grand
Cherokee 4Runner
Reliable
Good Value
Rugged
Jeep
Cherokee
Insight
SAMPLE PERCEPTUAL MAP (ATTRIBUTE RATING METHOD)
MDS with Non-Product Perceptions
Notice that the position of the brands, though similar to the attribute rating method, is
different. This is due to different methodology used in MDS which captures overall perception
of the brands rather than the direct measurement of an attribute such as ruggedness. There
are no axes for guidance, only relative positioning to the perceptions.
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Another approach for creating perceptual maps using the overall
similarity method is to have study participants rank each pair of
products from most similar to least similar. One could also use the
same data collected in the prior example to create this rank order. In
addition to ranking each pair, one could also collect rank order or
ratings on various perceptions (such as ruggedness, good value, etc.)
and preference or sales data to aid in interpretation of the perceptual
map as we’ll see in the following example.
MULTI-DIMENSIONAL SCALING (MDS)
Multi-Dimensional Scaling (MDS)
The following screen shows a perceptual map created from a survey
from a particular target market segment in an automobile simulation.
In this example, sales data was also collected for this segment, and
brands were rated on three dimensions: Price, size, and dealer
service. Finally, data was also collected about the characteristics of
their ideal brand. Let’s take a look at this perceptual map and attempt
to interpret the information provided.
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MDS EXAMPLE WITH VECTORS AND STRESS
MDS Example with Vectors and Stress
Before considering the vector and ideal brand information, let’s look at
the relative positioning of the brands themselves. We could say that
brands A and B are perceived as being fairly similar (and brands E, G
and I as well). We could also say that brand F is perceived as very
different from all other brands in the study. Take a moment to consider
what underlying factors might be driving the positioning of the vehicles.
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Stress is a measure
of how well the map
captures the brand
relationships in two
dimensions. Lower is
better. Under .20 is
good, .20 - .40 is
acceptable, over .40
means that the map
is struggling to
capture the
relationships in 2
dimensions.
r2 measures how
well the position of
the vector on the
map reflects the
ratings data
collected
(1.0 means perfectly
correlated).
Estimated
preferred,
expected or
ideal position
for the
customer is
marked by the
“*”
Top 10 brands
for customer
are listed in
order of sales
to the target
customer
segment
MDS EXAMPLE WITH VECTORS AND STRESS
MDS Example with Vectors and Stress
With this additional information, what
can we say about the map?
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First we can say that this map does a good job capturing the relative
positioning of the brands in a two dimensional space (stress = .17).
Next we can say that as we move from left to right on the map, we’re
generally going from lower priced brands to higher priced brands and
that it appears that this customer prefers a lower priced brand. We
can also say that as we move from the bottom left to the top right
brands are going from small to large (in size). Since the r2 is fairly
high on these two dimensions (and the stress is low), these
relationships are fairly accurate.
MULTI-DIMENSIONAL SCALING (MDS)
Multi-Dimensional Scaling (MDS)
As we might expect, since brands A and
B are closest to the ideal, their sales are
the highest. We could also say that
despite the relatively good positioning of
brand J, something is keeping it from
achieving higher sales that is not
captured on the map (distribution,
advertising, etc.)
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Dolan, Robert J. "Perceptual Mapping: A Manager's Guide."
Harvard Business School Background Note 590-121, July
1990.
FURTHER REFERENCE
Further Reference
Michael Deighan, Stuart W. James, and Thomas C. Kinnear,
StratSimMarketing: The Marketing Strategy Simulation,
Interpretive Software, 2011
Sawtooth Technologies
http://www.sawtooth.com
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