Statistical Techniques
MAR 6648: Marketing Research
February 1, 2011
Overview
• We’ll talk about basic statistical tools
– T-tests, crosstabs, and regression are useful tools
• We’ll talk about what they can and can’t do
• More sophisticated tools can give a deeper
view of your customers
– Conjoint analysis, cluster analysis, and factor
analysis can help you understand who your
customers are and what they like
A Quick Note on Data Analysis
• Statistics are just one part of an argument
• People are easily persuaded by numbers and statistics
– The more complicated the analysis, the less likely it is to be
challenged
• The strongest challenge to many statistical arguments
is not in how the data are analyzed, but in how the
data are collected
– Methodological expertise always trumps data analytic
experience
– Data analytic knowledge allows for more careful
consideration of methodology
Really Basic: Comparing Groups
• In marketing we often have a need to understand
differences between groups
– Segmentation
• Are two or more segments really different along some
dimension of behavior or attitude?
– Experiments
• Did the treatment work?
• We need a systematic approach that allows us to
say when two (or more) groups of customers,
companies, markets, etc. really are different
Most Basic: t-tests
• Do web shoppers pay a different price for cars
than dealership shoppers?
• Do a hypothesis test:
Null Hypothesis:
=
Alternative:
≠
T-test Results
• “Customers who bought their new vehicles on the Auto
Online website report having paid less for their vehicles
than did customers who purchased their vehicles at the
dealership (Monline = $11,582 vs. Mdealer = $13,594),
t(1398) = -6.14, p < .001).”
– If the p-value of the test is “small” we reject the null
hypothesis
– Here “small” typically means less than 5% (p = .05)
• Now try answering a different question:
– Are customers who purchase a car online more likely to
buy their next car online as well?
Understanding Associations
• One of the most common questions in
Marketing Research:
– Are two (or more) variables associated?
Customer type
Subsequent
transaction
Tools for Analyzing Associations
• Cross tabulation
• Regression
– Only for two categorical
variables
– Easy to understand
Online 1st
Online 2nd
Dealer 1st
– Applies to any number
of variables
– Not necessarily
categorical variables
– Slightly harder to
understand
Dealer 2nd
1400
1200
1000
Sales
800
600
400
200
0
0.75
1.25
1.75
2.25
Price
2.75
3.25
Χ2-test for Association
• We can do a statistical test here
• The null hypothesis is that there is no
association between method of first purchase
and method of subsequent purchase
– This means that the percentage of people their
next car online is the same regardless of how they
purchased their previous car
• Again, if the p-value of the test is less than .05,
we reject the null hypothesis
Intuition for Χ2-test
• The Χ2-test is based on comparing the actual
cell counts to what we would expect them to
be if there was no association
1
2
= 333/500
= 154/500
3
4
= 0.692*0.666
= 0.231*500
We would expect
the table to look
like this if there
was no association
Intuition for Χ2-test
• The Χ2-test is based on comparing the actual
cell counts to what we would expect them to
be if there was no association
Actual
Expected
Conclusion: Based on this data, it looks like customers who purchase
a car online are no more likely to buy their next car online than
customers who bought their initial car from a dealer.
Χ2 (1, N = 500) = 3.002, p = .08
Crosstabs
• Crosstabs is a quick and easy tool for analyzing
the association between two categorical
variables
• Caveats:
– You find associations – not causations
• An observed association may be driven by a third variable
not captured in the analysis
• In crosstabs we cannot control for other variables – we
need regression for this
– Warning: Be careful when cell counts are low. The
test does not work well in this case (stats programs
should tell you)
Key Points
• T-tests:
– Good for analyzing data with a continuous dependent
variable and a 2-level categorical variable
– Does not allow for a more complex design
– Does not allow the analysis to control for the
presence of another known variable
• Crosstabs
– An easy method for describing categorical data
– Easily analyzed using simple non-parametric tests
(e.g., chi-square)
– Poorly suited for handling non-categorical data
– But often unable to isolate causation in data
Regression
• Regression analysis is widely used in
Marketing Research
– It can detect associations between variables
– It can help make forecasts
– It can test Marketing Mix models: Impact of
marketing mix variables on sales
– It can analyze results of experiments
Example: Minute Maid Sales
• Imagine that you’ve been hired as a consultant
for the Minute Maid Company
• Before going for an important meeting with
senior management, you have been asked to
analyze the sales data for MM orange juice for
the Southern California market
• To assist in your deliberations, some data have
become available from one of your key accounts
(the largest grocery chain in the market)
Example: Minute Maid Sales
• The database was collected from weekly store
scanner data that captures information such
as sales (# of cartons sold), price, and other
promotion information for each product
• Management is particularly interested in
understanding how different pricing strategies
affect sales
The data
week
Total OJ Sales(00 cartons)
Minute Maid-Sales (00 cartons)
Price-MM
1
1029
66
2.99
2
350
89
2.99
3
802
565
2.59
4
701
50
2.99
5
484
186
2.99
6
763
334
2.39
7
848
57
2.99
8
957
732
1.99
.
.
.
.
.
.
.
.
115
1296
88
2.53
116
1472
760
2.19
Weekly Minute Maid Sales and Price
A Linear Sales Model
• We wish to explain variation of sales as a function of price
• Assume that sales and price are related as:
St =β0 + β1Pt + εt
• We have now assumed that sales in week t is a linear function
of price plus a random component
• We need to find β0
and β1
SPSS Regression output
t-statistic
b0
b1
Standard errors of b0 and b1
≈ uncertainty associated with
b0,b1
St =β0 + β1Pt + εt
p-value
Test of
H0: β1=0
Ha: β1 ≠0
What does this mean?
Key Points
• Regression:
– Generates a specific equation describing the
relationship between a specific predictor (e.g.,
prices) and a specific outcome variable (e.g., sales)
– The results can offer precise (if imperfect)
prescriptions for managers
Example: Minute Maid Sales
• We previously identified a relationship
between Minute Maid prices and Minute
Maid sales
– Essentially, Sales = 1093 + (-377 x price)
• This model seems a little simplistic
– What about accounting for the behavior of
competitors?
– Regression is good at that too
• St =β0 + β1Pmm + β2Ptp + β3Ptr + β4Psb + ε
Sales = 289 + (-479 × MMprice) + (131 ×
TPprice)
+ (175 × TRprice) + (144 × SBprice)
These are dummy coded variables
representing the presence or
absence of specific product
promotions in the OJ market.
Question:
Did our Minute Maid promotions positively
influence sales? (controlling for the presence
of other known variables)?
Multiple Regression
Controlling for everything else, the
advertisement was still effective.
An ad increased sales by 202 units. (Now,
given the cost of advertising, you can make a
recommendation about whether advertising
is a good idea.)
Multiple Regression
What else can we learn?
Tropicana Ads do not influence Minute
Maid sales, but Store Brand ads do.
It looks like ads generally decrease
price sensitivities. (We would need to
test interactions to learn more about it)
Multiple Regression
• Conceptually, the procedure allows you to
track multiple variables at once
– Track the influence of competition
– Control for exogenous factors (e.g., weather,
seasonality, etc.)
• Every added variable improves the fit of the
model to the given data
Multiple Regression
• Pitfalls:
– That does not necessarily make it better at
predicting the future. You can “overfit” the data
– Bad things happen when the predictors are
strongly related to each other
– It intrinsically assumes that a linear model is a
pretty good approximation
• It often is
• But not always…
Key Points
• Regression not only helps make precise
predictions, it can simultaneously account for
multiple influences
• In so doing, it gets much closer to causal
inferences (and good market researchers are
after causal inferences)
• Nevertheless, regression is not a panacea, and
should be used as a tool, not the only tool
• Nothing fixes poor research design
Specialized Techniques
• Research for segmentation decisions
– Segmentation is an essential part of the marketing
plan, but how do we actually find the segments
• Demographics?
– Sometimes useful, but demographics are often a poor predictor
of behaviors and attitudes
• Attitudes
– Segment customers based on attitudinal info (e.g., “optimists vs.
“pessimists”, “leaders” vs. “followers”)
• Benefits
– Segment customers based on benefits sought from
product/service
• Behavior
– Segment customers based on similar behavior (e.g., “heavy
users”, “light users”)
• Cluster analysis is a
technique used to
identify groups of
‘similar’ customers in a
market (i.e., market
segmentation).
• If some customers are
very similar to one
another but different
from other (groups of)
customers, cluster
analysis can help you
identify these (multiple)
segments.
Brand Loyalty
Cluster Analysis
Price sensitivity
Cluster Analysis
• What is it actually doing?
• The algorithm measures the “distance” between
every point and generates a solution which
minimizes distances within a cluster and
maximizes distances between clusters
– Note that this language is very close to how you were
taught to think about the attributes of good
segmentation
• What, exactly, is “distance”?
– A rare literal example
Cluster Analysis: Baseball
• Baseball batters attempt to
hit balls to parts of the
field without any defensive
players.
• Baseball coaches have
seven players to distribute
wherever they want on the
field.
• Despite this general
flexibility, fielders are
almost uniformly
distributed in the same
locations.
• Is that where batted balls
tend to land?
Let’s look at clustering of batted balls
for a single player.
Chase Utley
Example: Shopping Attitudes
•
•
•
•
•
•
V1: Shopping is fun
V2: Shopping is bad for your budget
V3: I combine shopping with eating out
V4: I try to get the best buys while shopping
V5: I don’t care about shopping
V6: You can save a lot of money by comparing
prices
Example: Shopping
• Cluster 1: _______________
• Cluster 2: _______________
• Cluster 3: _______________
Key Points
• Cluster Analysis allows us to simplify across
respondents
• When used effectively, it can guide marketing
strategy
• Nevertheless, it is by no means pure
computational science. Identifying and
labeling clusters requires some interpretation
– This is a strength (in flexibility)
– And a weakness
Clusters versus Factors
Factor
Analysis
V1 V2 V3 V4 V5
Cluster
Analysis
Data
…..
V20
Factor Analysis
• Factor Analysis can be used for data reduction
(i.e., to reduce the number of variables).
• Factor analysis: Summarize the information
contained in a larger number of variables into
a smaller number of ‘factors’ without
significant loss of information.
– Data reduction is important when you need to measure
“fuzzy” concepts like “love,” “trust,” or “satisfaction
– Ask a series of questions that tap into the different
components of the concept
– Too many variables! Factor analysis can help to reduce
this dimensionality problem
Factor Analysis: Intuition
• Factor analysis assumes that the correlation
between a large number of variables is due to
them all being dependent on the same small
number of “factors”
• Example: Choice of movies
– Suppose individuals choose movies based on two
main attributes:
• Plot/story line (A1)
• Production quality (A2)
– Each individual has a preference for A1 and A2
Example: Choice of Movies
A1 Weight
A2 Weight
I can relate to the characters
0.81
-0.02
The movie is visually pleasing
0.07
0.92
Set and costume design are an
important part of a movie
-0.13
0.85
Movie features major stars
0.09
0.16
Movie has first-rate special
effects
-0.08
0.69
Engaging story-line
0.76
0.12
I feel “transported” while
watching
0.72
-0.18
Key Points
• Factor Analysis allows us to simplify across
measures
• It helps hone in on large difficult concepts that
a single item measures poorly
• It has a set of guidelines for interpretation and
use (e.g., Eigenvalues > 1, KMO > .6), but it is
only slightly less flexible than Cluster Analysis
Key Points
• Market Research data is often extremely bulky and
complicated. We need tools simply to make it
comprehensible
– Cluster Analysis helps with complexity across consumers,
Factor Analysis helps with complexity across measures,
Perceptual maps can helpfully present this information
• These analytic tools are well suited to basic strategic
concerns
– Identifying segments and matching them to preferences
and brand perceptions
– In combination they are even better
• Use these tools carefully: Because there is room for
interpretation, there is also room for clumsiness (or
deceptiveness)
How do individuals form
preferences over a large
selection of different brands
within a product category?
.
.
.
.
.
.
Think of different brands
as different combinations
of attributes!
.
.
.
Engine Size HP
Type #Doors Brand Price
2.5L
184 Sedan
4
BMW $27,800
4.0L
203 SUV
2
Ford $21,715
6.0L
316 SUV
4
Hummer $48,455
3.0L
215 Sedan
.
.
.
2.4L
.
.
.
4
.
.
.
157 Sedan
Lexus $29,435
.
.
.
4
.
.
.
.
.
.
Toyota $18,970
Attribute based approach
• Think of a product (a certain car) as a bundle of
attributes.
• A consumer prefers a certain car, car A, to another, car
B, because the attributes of car A are more appealing
to the consumer than the attributes of car B.
• Suppose we assume that consumers form preferences
over brands implicitly by forming preferences for the
attributes of which the brands consists.
• So if we present certain lists of attributes the consumer
can rank these.
Conjoint Analysis
• Conjoint Analysis: A technique that enables a
researcher to estimate consumers’ valuations
of different attributes
– Allows us to understand how consumers make
trade-offs among attributes/characteristics of
products and services
– How much are consumers willing to pay/give up to
get/avoid different attributes?
Uses of Conjoint Analysis: New
Products
• Estimate market share of brands that differ in
attribute levels
Uses of Conjoint Analysis:
Pricing/Valuation
• Use information about customers’ valuation of
attributes to guide pricing strategy for a
product line
Uses of Conjoint Analysis: Brand Equity
• Brand name equity
• How much is a brand really worth?
or
Assumption of Part-Worth’s
• Total utility = sum of utilities of each attribute
U(
U(
U(
)=
) =
) =
u(motorola) + u(pink) + u($149) + u(flip format)+…
u(motorola) + u(grey) + u($149) + u(flip format)+…
u(nokia) + u(black) + u($129) + u(candy bar format)+…
Example: New Job
Salary
$100 K
Location
$150 K
Example: New Job
Prospective
Employee 1
City
Salary
New York
0.0 (w11)
San Francisco
0.75 (w12)
$100,000
0.0 (w21)
$150,000
0.25 (w22)
Now we can rank jobs for this person:
U(NY,$100K)=0
U(NY,$150K)=0.25
U(SF,$100K)=0.75
U(SF,$150K)=0.25+0.75=1.0
Example: New Job
Prospective
Employee 1
City
Salary
New York
0.0 (w11)
San Francisco
0.75 (w12)
$100,000
0.0 (w21)
$150,000
0.25 (w22)
Now we can rank jobs for this person:
U(NY,$100K)=0
U(NY,$150K)=0.25
U(SF,$100K)=0.75
U(SF,$150K)=0.25+0.75=1.0
Example: New Job
City
Salary
Prospective
Employee 1
Prospective
Employee 2
New York
0.0 (w11)
0.0 (w11)
San Francisco
0.75 (w12)
0.25 (w12)
$100,000
0.0 (w21)
0
$150,000
0.25 (w22)
0.75 (w22)
(w21)
Now we can rank jobs for this person, and compare it to this person:
U(NY,$100K)=0
U(NY,$150K)=0.25
U(SF,$100K)=0.75
U(SF,$150K)=0.25+0.75=1.0
U(NY,$100K)=0
U(NY,$150K)=0.75
U(SF,$100K)=0.25
U(SF,$150K)=0.25+0.75=1.0
Example: New Job
City
Salary
Prospective
Employee 1
Prospective
Employee 2
New York
0.0 (w11)
0.0 (w11)
San Francisco
0.75 (w12)
0.25 (w12)
$100,000
0.0 (w21)
0
$150,000
0.25 (w22)
0.75 (w22)
(w21)
Now we can rank jobs for this person, and compare it to this person:
U(NY,$100K)=0
U(NY,$150K)=0.25
U(SF,$100K)=0.75
U(SF,$150K)=0.25+0.75=1.0
U(NY,$100K)=0
U(NY,$150K)=0.75
U(SF,$100K)=0.25
U(SF,$150K)=0.25+0.75=1.0
How do we get the part-worths?
• This is very nice but we don’t know consumers’ valuations of
attributes…
• …and consumers probably don’t know their own valuations
either!
• A solution: Force consumers to rank different bundles of
attributes (i.e., “brands”)
1.
C
2.
E
C
3.
A
D
4.
F
5.
B
6.
D
A
B
E
F
Conjoint Analysis: Approaches
• Traditional Conjoint: Have respondents directly rank or rate
a series of product profiles
Conjoint ≈Consider Jointly
• Discrete Choice Models (allows for non-choice)
– Also called “Choice Based Conjoint”
• (from Sawtooth Software’s web-site:
http://www.sawtoothsoftware.com/conjoint-analysissoftware)
Standard Conjoint Analysis: Process
• Develop the set of attributes
• Select the levels of each attribute
• Obtain an evaluation (rating or ranking) of the product
profiles from respondents
• Estimate the part-worths values for each level of each
attribute
• Compute importance weights for each attribute
(normalized range)
• Aggregation of results across consumers
• Evaluate the tradeoffs among attributes
• Market simulations
• Evaluate accuracy of results
From Preference to Choice
• Conjoint model predicts utility, not choice
• Utility is a continuous, relative measure of preference
for each alternative. Choice is a discrete outcome.
• Need a rule to translate preferences to choices:
– First choice rule: Respondent chooses the profile with the
highest predicted utility score
– Share of preference rule: Predictions of choice
probabilities sum to 1 over the set of stimuli tested.
• First choice rule usually more appropriate for sporadic,
non-routine purchases.
• However, both rules are ad hoc
Conjoint Pluses and Minuses
• When to use CA:
– Can the product be seen as a bundle of attributes?
• Avoid using CA for “image” products
– Are the respondents familiar with the category?
• Avoid using CA for new-to-the-world products
– Must know relevant attributes (exploratory research)
• Warnings
– CA will not indicate the absence of an important attribute
– Attributes should be actionable to the firm
– Interpolation between attribute levels ok – but do not
extend beyond the range selected
Key points
• Conjoint is a very popular and frequently
useful tool for identifying the underlying
utilities of consumers.
• It details the relative value of product
attributes and guides product development
and competitive pricing.
• Nevertheless, its application is deeply
contingent on both the consumer and the
product category.
Summary
• There are a number of useful statistical
techniques that can help you understand your
data
– T-tests, crosstabs, and regression are basic tools
that can make comparisons and show
relationships between marketing variables
– Cluster, factor, and conjoint analysis can help you
understand your customers’ traits and preferences
• These tools are only effective if you have good
research design to start