USING BAYESIAN ANALYSIS TO ASSESS THE VALUE OF CONDUCTING
MARKETING RESEARCH
It makes business sense for managers to assess the value of conducting research. If the cost
exceeds the value, then the manager shouldn’t conduct the research. After all, why pay more for
something than it’s worth! That said, Mike can attest that in all the research he conducted for the
hospitality industry, not once did a client ask him to show that the value of his proposed study
exceeded the price being charged. Typically, those hospitality managers relied on an informal
process for assessing net worth. Instead, we suggest that you rely on a more formal procedure.
Specifically, we recommend that you use a Bayesian approach, which is a more formal way to
assess likely value.
Although helpful, Bayesian analysis is not a panacea for assessing the value of marketing
research. Certainly, such analyses are susceptible to the GIGO—garbage in, garbage out—
problem. If estimates based on historical data and managerial intuition are inaccurate, then a
formal procedure for combining those estimates will produce poor forecasts. Like all marketing
research, Bayesian analysis is only as valuable as the data on which it’s based; regardless of
method, you can’t make a good decision based on bad data. (Of course, you can always make a
‘lucky’ decision.) Hence, it’s vital that you plug well-founded estimates into your analysis.
Guessing or forecasting the likelihood of alternative outcomes may help you to make the most
appropriate decision. Secondary data can assist in assigning a probability of a particular event or
outcome. As such, you can calculate the expected value of an outcome by multiplying the
probability of that outcome by its associated payoff (or loss). In essence, Bayesian analysis
revises prior probabilities based on new information.
The following two examples show Bayesian analyses. The first example shows how marketing
research can revise a basic pricing decision, and the second example shows how to assess the
value of conducting marketing research. The Excel spreadsheet included with this CD will allow
you to conduct an analysis similar to the second example.
Example 1
Here’s an example of using Bayesian analysis and marketing research to make a basic pricing
decision. Assume you’re a marketing manager who must decide about a pricing strategy for a
new product. Table 1 indicates the payoff table for that pricing decision: the likely profits for
each pricing strategy (high, intermediate, and low) related to each possible level of demand
(light, moderate, and heavy). The probability of light demand, all else being equal, is 0.5 (50%);
the probability of moderate demand is 0.3 (30%); and the probability of heavy demand is 0.2
(20%). (Remember, probabilities may be expressed as percentages summing to 100% or decimal
fractions summing to 1.0.) These are prior probabilities, in the sense that no research has been
done to improve these estimates and the assumption is that they are based on historical data
and/or managerial intuition.
Page | 1
Combining pricing strategies and possible levels of demand, you can compute the expected value
(EV) for each strategy (noted beneath Table 1). The EV is what you would expect to occur ‘on
average’, which is another way to say that you’re summing all possible outcomes after weighting
them for their likelihood of occurrence. By adding these weighted profits and losses together,
these calculations show that the high-price strategy is optimal, as you would expect the highest
profit ‘on average’ from that strategy.
Table 1
Payoff Table for Pricing Decision
(Numbers in each cell in thousands of dollars)
Alternative
A1: High Price
A2: Intermediate Price
A3: Low Price
S1: Light Demand
P (S1) = 0.5
$100
$60
-$40
State of Nature
S2: Moderate Demand
P (S2) = 0.3
$55
$95
$0
S3: Heavy Demand
P (S3) = 0.2
-$55
-$30
$70
EV (A1) = (0.5) ($100) + (0.3) ($55) + (0.2) (-$55) = $55.5 (optimal choice)
EV (A2) = (0.5) ($60) + (0.3) ($95) + (0.2) (-$30) = $52.5
EV (A3) = (0.5) (-$40) + (0.3) ($0) + (0.2) ($70) = -$6.0
Now, let’s assume that you can purchase marketing research prior to deciding on a high,
intermediate, or low pricing strategy for this new product. Table 2 indicates the likelihood of
each test market result given that ultimately what will occur is light demand, moderate demand,
or heavy demand. In other words, how accurate is the research in forecasting eventual demand
(or assuming a certain outcome, what is the likelihood of each research result.) Notice that the
numbers in each column sum to 1.0, but they don’t sum to 1.0 across rows. The reason: once
light demand has occurred, then the probability is 1.0 (100%) that the test market result—
assuming a test market has been conducted—was either mildly or moderately or highly
successful. If demand is moderate, there’s a 100% chance that the test market result would have
been one of these three outcomes. If demand is ultimately heavy, there’s also a 100% chance that
the test market result would have been one of these three outcomes. (Don’t be disappointed if
you need to read this paragraph a few times.)
Assuming demand ultimately will be light, there’s a 0.6 (60%) chance that a test market to
predict demand will be mildly successful, a 0.3 (30%) chance that a test market to predict
demand will be moderately successful, and a 0.1 (10%) chance that a test market to predict
demand will be highly successful. The third result—the highly successful test market—is a very
erroneous prediction of demand because demand ultimately will be light, and yet the test market
results suggest that demand will be heavy. For another similar example, consider the last column
in Table 2. If you ran a test market to predict demand and it predicts demand will be heavy, then
there’s only a 0.1 (10%) chance that the test market will be mildly successful, a 0.2 (20%)
chance that the test market will be moderately successful, and a 0.7 (70%) chance that the test
market will be highly successful.
Page | 2
Table 2
Conditional Probability of Getting Each Test Market Result Given Each State of Nature
Test Market Result
Z1: Mildly Successful
Z2: Moderately Successful
Z3: Highly Successful
S1: Light
0.6
0.3
0.1
Σ=1.0
Level of Demand
S2: Moderate
0.1
0.6
0.3
Σ=1.0
S3: Heavy
0.1
0.2
0.7
Σ=1.0
Although Table 2 contains useful information—in this case, the historical accuracy of a test
market for predicting ultimate demand—it’s merely an intermediate step. If the potential
marketing research supplier has conducted many past test markets, then this table could be
constructed based on the previous accuracy of those test markets to forecast demand. However,
what you really want to know is the probability of a certain level of demand given a certain test
market result. In other words, given a certain level of demand will occur, what is the probability
of each test market prediction? Table 3 shows how to determine those probabilities.
In Table 3, Column #1 and #2 list the test market success and three different levels of demand,
respectively. Column #3 and Column #4 list prior and conditional probabilities, respectively.
Column #5 reflects the joint probability of demand and success (derived from multiplying
column 3 and 4). To calculate joint probabilities, think about the odds associated with flipping a
coin. The odds of ‘heads’ on a single coin flip are 50%; the odds of heads on two consecutive
coin flips are 25% (that is, 50% x 50%). If the coin and flipper are ‘fair’—the heads-versus-tails
odds are equal and the coin flips are independent—then you multiply the probabilities of each
outcome to determine the probability of those outcomes occurring jointly. Note that the three
probabilities for each type of test market result need not sum to 1.0, although they may by
coincidence. Therefore, the probabilities sum to 1.0 down a column but not across a row.
The values in Columns #3 through #5 are intermediate values. The probability of interest in
Table 3 is found in Column #6; specifically, you want to know the probability of a certain level
of demand (state of nature) given that you receive a certain test market result (rather than the
probability of a certain test result given an eventual level of demand, as in Column #4). To
calculate this probability, you must standardize the numbers in Column #5; in other words, you
must force the probabilities associated with all possible levels of demand under each test market
result to sum to 1.0. You make this calculation by taking the three probabilities grouped under
each test market result in Column #5 and dividing them by the sum of those three probabilities.
For example, there’s a 35% (0.35) chance of the mildly successful test market result (Z1). So,
take 0.30, 0.03, and 0.02 and divide each one by 0.35 to calculate those first three probabilities in
Column #6. Note that those probabilities—0.857, 0.086, and 0.057—sum to 1.0. The results of
the same calculations for a moderately successful test market result and a highly successful test
market result produce the remaining probabilities listed in Column #6.
It’s important to recognize the degree to which each research result revises initial estimates about
probabilities for the different levels of demand. Before you commission any research, you are
50% confident that demand will be light, 30% confident that demand will be moderate, and 20%
Page | 3
confident that demand will be heavy. Those probabilities appear in Column #3. Now combine
those initial probability assessments with the test market results. If the result is mildly successful
(Z1), then you’ve only reinforced your initial assessment: you’re now 85.7% rather than 50%
certain that demand will be light, 8.6% rather than 30% certain demand will be moderate, and
5.7% rather than 20% certain that demand will be heavy. So, if you commission a test market,
given your prior beliefs, and the result is only mildly successful, then all you’ve done is reinforce
those beliefs.
Table 3
Revision of Prior Probabilities in Light of Possible Test Market Results
Test Market
Result
ZK
(1)
Level of
Demand
SJ
(2)
Prior
Probability
P(SJ)
(3)
Conditional
Probability
P(ZK|SJ)
(4)
Joint
Probability
P(ZKSJ)
(5)=3x4
Posterior
Probability
P(SJ|ZK)
(6)=5/Σ of 5
Z1: Mildly
Successful
S1: Light
S2: Moderate
S3: Heavy
0.5
0.3
0.2
0.6
0.1
0.1
0.30
0.03
0.02
Σ=0.35
0.857
0.086
0.057
Σ=1.000
Z2: Moderately
Successful
S1: Light
S2: Moderate
S3: Heavy
0.5
0.3
0.2
0.3
0.6
0.2
0.15
0.18
0.04
Σ=0.37
0.405
0.486
0.108
Σ=1.000
Z3: Highly
Successful
S1: Light
S2: Moderate
S3: Heavy
0.5
0.3
0.2
0.1
0.3
0.7
0.05
0.09
0.14
Σ=0.28
Σ=1.00
0.179
0.321
0.500
Σ=1.000
However, if you commission a test market and it’s highly successful, then your assessment
changes markedly. You’ve gone from 50%—30%—20% (0.5—0.3—0.2) probabilities to
17.9%—32.1%—50.0% (0.179—0.321—0.500) probabilities for light, moderate, and heavy
demand, respectively. So, if the test market is mildly successful, given your prior beliefs, then
you’d probably be comfortable assuming light demand and choosing a high pricing strategy. In
contrast, if the test market is highly successful, then you’re far less certain about the likely level
of demand and optimal course of action. In this latter case, you’d probably want to conduct
additional research to forecast the level of demand.
Table 4 summarizes the expected value calculations with revised probabilities for the ultimate
level of demand based on managerial intuition plus the research results. If the test market results
are mildly successful, then the expected value is recalculated accordingly and the expected value
is even higher—$87,000 versus $55,500 in Table 1—for the high-price strategy. If the test
market is mildly successful, then a high-price strategy remains the optimal decision. However,
the expected value calculation shows that the optimal strategy shifts if the test market results are
Page | 4
either moderately or highly successful; instead, the optimal decision is the intermediate-price
strategy (A2) for a moderately successful test market and the low-price strategy (A3) for a highly
successful test market. The post-research EV calculation shows that the test market result doesn’t
encourage a strategy change if the test market is mildly successful; however, if it’s either
moderately or highly successful, then you are well-advised to shift from a high-price strategy to
an intermediate-price and low-price strategy, respectively.
Table 4
Expected Value (EV) of Each Alternative Given Each Research Outcome
(Numbers in thousands of dollars)
Z1: Mildly Successful (Disappointing) Test Market
Revised Probabilities: P(S1) = 0.857; P(S2) = 0.086; P(S3) = 0.057
EV(A1) = [($100) x 0.857)] + [($55) x (0.086)] + [(-$55) x (0.057)] = $87.2 (Best choice)
EV(A2) = [($60) x (0.857)] + [($95) x (0.086)] + [(-$30) x (0.057)] = $57.8
EV(A3) = [(-$40) x (0.857)] + [($0) x (0.086)] + [($70) x (0.057)] = -$30.2
Z2: Moderately Successful Test Market
Revised Probabilities: P(S1) = 0.405; P(S2) = 0.486; P(S3) = 0.108
EV(A1) = [($100) x (0.405)] + [($55) x (0.486)] + [(-$55) x (0.108)] = $61.2
EV (A2) = [($60) x (0.405)] + [($95) x (0.486)] + [(-$30) x (0.108)] = $67.2 (Best choice)
EV (A3) = [(-$40) x (0.405)] + [($0) x (0.486)] + [($70) x (0.108)] = -$8.7
Z3: Highly Successful Test Market
Revise Probabilities: P(S1) = 0.179; P(S2) = 0.321; P(S3) = 0.50
EV(A1) = [($100) x (0.179)] + [($55) x (0.321)] + [(-$55) x (0.50)] = $8.0
EV(A2) = [($60) x (0.179)] + [($95) x (0.321)] + [(-$30) x (0.50)] = $26.2
EV(A3) = [(-$40) x (0.179)] + [($0) x (0.321)] + [($70) x (0.50)] = $27.8 (Best choice)
Example 2
AJ Incorporated is the world’s leader in roadrunner statues. Mr. Harry Byrd, the CEO, is
considering a promotion that would cost $200,000; he hasn’t had any meaningful experience
running such promotions and has no idea whether or not that $200,000 will be wasted or spent
successfully. Ms. Pinky Stork, the head of marketing, is unsure about the likely consumer
response to this promotion; nonetheless, her best guesses about the consumer response
probabilities are as follows:
P (S1): More than 15% increase in revenue (Fantastic reaction) = 0.2
P (S2): From 5-15% increase in revenue (Favorable reaction) = 0.5
P (S3): 0% increase in revenue (Unfavorable reaction) = 0.3
As uncertainty about the efficacy of this $200,000 promotional campaign is high, Pinky is faced
with a dilemma; she could either (1) spend the $200,000 on the promotion, which has a 30%
chance of gaining no customers, or (2) first spend $30,000 on copy testing research—the amount
charged by research firm MRH Research Inc.—to gain a better sense about the likelihood of a
Page | 5
$200,000 loss. As a first step in deciding whether (2) is the best approach, Pinky should
determine the historical accuracy of MRH Research Inc.’s copy tests in forecasting consumer
responses to such promotions. Table 1 below relates the different consumer reactions (states of
nature) to the likelihood of different research outcomes.
Table 5
Conditional Probability of Consumer Reaction Given Each State of Nature
MRH Research
Inc.’s Experience
Strongly Positive
Moderately Positive
Slightly Positive
Fantastic
0.6
0.4
0.0
Σ = 1.0
Consumer Reaction
Favorable
Unfavorable
0.1
0.0
0.6
0.2
0.3
0.8
Σ = 1.0
Σ =1.0
As with Table 2 in Example 1, Table 5 shows the predictive accuracy of MRH Research Inc.’s
copy test results. Notice in Table 5 that the numbers in each column sum to 1.0, but the numbers
across rows do not. For example, a fantastic consumer reaction to MRH Research Inc.’s copy
tests means there’s a 60% chance that revenue will increase by more than 15%, a 40% chance
that revenue will increase by 5-15%, and a 0% chance that revenue won’t increase. In contrast,
the last column shows that if MRH Research Inc. runs its copy test and the result is unfavorable,
then there’s a 0% chance that revenue will increase by more than 15% (so that big $500,000
revenue increase won’t occur), a 20% chance that revenue will increase by 5-15% (thus
increasing revenue by $200,000), and an 80% chance that revenue won’t increase (thus costing
the $200,000 associated with the promotion).
The first step in helping Pinky solve this problem is setting up a payoff table like the one shown
in Table 6. One trick in setting up this table is setting up a don’t run the promotion row. In other
words, you must recognize that the expected value of doing nothing is nothing ($0), hence the
three $0 entries in that row. In contrast, if Pinky decides to run the promotion, there’s a 20%
chance—based on intuition and/or minimal prior experiences—that AJ Incorporated will net
$500,000 additional profit, a 50% chance it’ll net $200,000 additional profit, and a 30% chance
it’ll lose $200,000 by running a promotion that fails to increase revenues.
Table 6
Payoff Table for Promotional Decision without Research
Promotion Decision
A1: Don’t run
A2: Run
Prior probability (of response
without research)
Consumer Response to Promotion
S1: Fantastic
S2: Favorable
S3: Unfavorable
$0
$0
$0
$500,000
$200,000
-$200,000
0.2
0.5
0.3
Table 7 shows the calculations for the revised probabilities if AJ Incorporated receives certain
copy testing results from MRH Research, Inc. The prior probabilities in Column #3 indicate
Page | 6
Pinky believes there’s a 20% chance revenue will increase more than 15%, a 50% chance
revenue will increase 5-15%, and a 30% chance revenue won’t increase at all. If AJ Incorporated
receives a strongly positive copy testing result from MRH Research Inc., that 20%—50%—30%
(0.2—0.5—0.3) distribution is replaced by a 70.5% chance revenue will increase by more than
15%, a 29.4% chance revenue will increase between 5-15%, and a 0% chance revenue will not
increase, which means there’s a 0% chance that AJ Incorporated would lose its $200,000
promotion investment.
Table 7
Revision of Prior Probabilities in Light of a MRH Research Inc. Copy Test
Research
Result
ZK
(1)
Consumer
Response
SJ
(2)
Prior
Probability
P(SJ)
(3)
Conditional
Probability
P(ZK|SJ)
(4)
Joint
Probability
P(ZKSJ)
(5)=3x4
Posterior
Probability
P(SJ|ZK)
(6)=5/Σ of 5
Z1: Strongly
Positive
Fantastic
Favorable
Unfavorable
.2
.5
.3
.6
.1
.0
.12
.05
.00
Σ=.17
.705
.294
.000
Σ=1.000
Z2: Moderately
Positive
Fantastic
Favorable
Unfavorable
.2
.5
.3
.4
.6
.2
.08
.30
.06
Σ=.44
.181
.681
.136
Σ=1.000
Z3: Slightly
Positive
Fantastic
Favorable
Unfavorable
.2
.5
.3
.0
.3
.8
.00
.15
.24
Σ=.39
Σ=1.00
.000
.384
.615
Σ=1.000
In further analyzing Table 7, consider the range of probabilities for the moderately positive and
slightly positive copy testing results. Start with the slightly positive ones. If MRH Research
Inc.’s results are only slightly positive, then there’s a 0% chance revenue will increase by more
than 15%, a 38.4% chance revenue will increase 5-15%, and a 61.5% chance revenue will not
increase.
Now consider the general accuracy of MRH Research Inc.’s copy testing studies for predicting
changes of demand. Column #4 shows that there’s a 0% chance a strongly positive copy test will
precede 0% revenue growth and a 0% chance a slightly positive copy test will precede a greater
than 15% revenue growth. In essence, there’s a 0% chance of an extremely inaccurate forecast
based on MRH Research Inc.’s copy testing results. Even the likelihood of a moderately
inaccurate result is minimal; for example, there’s only a 30% chance of either a strongly or
slightly positive test result and a subsequent market share increase of 5-15%.
Page | 7
So, MRH Research Inc.’s research seems highly predictive and costs only $30,000. Furthermore,
Table 7 suggests that when the copy test results are either highly positive or slightly positive,
Pinky goes from moderate uncertainty to relatively high certainty. For example, when the test
result is only slightly positive, the probabilities shift from 20%—50%—30% (0.2—0.5—0.3) to
0%—38.4%—61.5% (0.000—0.384—0,615) for the three levels of revenue increases. This
greater certainty strongly suggests that the MRH Research Inc. research is worth purchasing.
However, the remaining analysis suggests otherwise.
Value of Optimal Act without Research
The optimal decision for Pinky, in the absence of conducting any research, is to run the
promotion. The expected value (EV) of doing nothing is nothing ($0), but the EV of running the
promotion is [$500,000 x 0.2] + [$200,000 x 0.5] + [-$200,000) x 0.3]. These numbers are taken
from the payoff table (Table 6). As the sum of these three sets of numbers is $140,000, the
expected value of running the promotion is positive, which suggests that Pinky should run it.


EV(A1) = $0
EV(A2) = [$500,000 x (0.2)] + [$200,000 x (0.5)] + [-$200,000 x (0.3)] = $140,000
Value of Optimal Act with Absolute Certainty
What should Pinky do if she knew, with absolute certainty, the result of running the promotion?
Knowing what will happen doesn’t mean a specific outcome is guaranteed to happen; it merely
means that she’s certain about what the future will bear. The expected value under certainty
indicates a 20% chance that revenue will increase more than 15% ($500,000), a 50% chance that
revenue will increase between 5-15% ($200,000), and a 30% chance revenue won’t increase
($0). If Pinky knew in advance that the promotion wouldn’t boost revenue, then she wouldn’t run
it. The expected value of the optimal decision for Pinky, knowing with certainty about an
increase or lack of increase in revenue, is $200,000.

EV(Certainty) = [$500,000 x (0.2)] + [$200,000 x (0.5)] + [$0 x (0.3)] = $200,000
Value of Optimal Act with Perfect Information
The value of perfect information is the difference between the expected value under certainty—
knowing the future without doubt—and the expected value with additional information. The
difference between $200,000 and $140,000 is the maximum value of MRH Research Inc.’s
research. Because MRH Research Inc. is charging $30,000 for research that could be worth as
much as $60,000, it’s possible that Pinky should buy it; but, that possibility depends on how
close MRH Research Inc.’s findings are to perfect information.

EV(Perfect Information) = EV(Certainty) – EV(A2)
= $200,000 – $140,000 = $60,000
Page | 8
Determine Value of Research Information
To determine whether or not the value of MRH Research Inc.’s copy test exceeds $30,000, the
following calculation is needed. If the test result is extremely positive, then the expected value of
doing nothing is nothing ($0) and the expected value of doing the promotion is $411,300; as
$411,300 far exceeds $0, running the promotion is the optimal action. If the test result is only
moderately positive, then the expected value of running the promotion is $199,500; again, far
more than $0, so the optimal decision is to run the promotion. Finally, if the test result is only
slightly positive, then the expected value of running the promotion is -$46,200, which is far less
than $0. In this case, the optimal decision is to avoid the promotion.

Z1 – Extremely positive
o EV (A1) = $0
o EV (A2) = [0.705 x $500,000] + [0.294 x $200,000] + [0.000 x -$200,000] = $411,300

Z2 – Moderately positive
o EV (A1) = $0
o EV (A2) = [0.181 x $500,000] + [0.681 x $200,000] + [0.136 x -$200,000] = $199,500

Z3 – Slightly positive
o EV (A1) = $0
o EV (A2) = [0.000 x ($500,000] + [0.384 x $200,000] + [0.615 x -$200,000] = -$46,200
The Expected Value of the Copy Test Research
The final question is, “What is the expected value of the copy test research? To answer this
question, it’s imperative to know the expected value of the optimal act with and without
research. Table 7 shows that there’s a 17% chance that MRH Research Inc. will get a highly
positive result, a 44% chance it will get a moderately positive result, and a 39% chance that it
will get a slightly positive result. The expected value for the optimal act in each of those cases is
$411,300, $199,500, and $0, respectively. If Pinky calculates this weighted sum, she’ll get
$157,701. As noted earlier, the expected value of the optimal act without research is $140,000,
leaving a difference of only $17,701. At most, MRH Research Inc.’s research is worth $17,701
to AJ Incorporated, yet MRH Research Inc. is charging $30,000. Therefore, Pinky shouldn’t
retain MRH Research Inc. to conduct a copy test.

EV(Research) =
[Probability(Z1) x EV(Optimal Act / Z1)] +
[Probability(Z2) x EV(Optimal Act / Z2)] +
[Probability(Z3) x EV(Optimal Act / Z3)] =
[0.17 x $411,300] + [0.44 x $199,500] + [0.39 x $0] = $157,701

EV(No Research) = $140,000
Maximum Value of Research = $157,701 - $140,000 = $17,701
Cost of Research = $30,000
Page | 9