Applying Bayesian Parameter Estimation to A/B Tests

in e-Business Applications

Examining the Impact of Green Marketing Signals

in Sponsored Search Advertising

Tobias Blask

Institute of Electronic Business Processes, Leuphana University of Lueneburg, Lueneburg, Germany

Keywords:

Bayesian Statistics, Bayesian Parameter Estimation, Sponsored Search, Paid Search Advertising, A/B Testing.

Abstract:

We develop and perform a non reactive A/B-test setting that enables us to evaluate the inﬂuence of green

marketing signals on the customer’s decision to take a speciﬁc online-shop into account in the process of

buying a speciﬁc product by clicking on an ad on a search engine results page (SERP). We analyze campaign

performance data generated by a European e-commerce retailer, apply a Bayesian parameter estimation to

compare speciﬁc advertisements and discuss the implications of the results.

1 INTRODUCTION

Internet search engines like Google, Yahoo! or Bing

play an undisputed key role in the modern informa-

tion society. On the one hand they serve the informa-

tion needs of their users, on the other hand they repre-

sent an important source of customer acquisition for

companies in a broad variety of industries and sizes

(Jansen and Mullen, 2008; Alby and Funk, 2011).

They also provide the search engine companies with

signiﬁcant amounts of their revenues through Spon-

sored Search Advertising. While still growing rapidly

Sponsored Search Advertising already dominates the

online media-spendings of companies that advertise

on the internet. In this form of advertising, devel-

oped in 1998 by Overture, advertisers provide search

engines with text-advertisements and a list of key-

words, which can consist of one or more terms, they

want these ads to be displayed. The advertiser usu-

ally also provides attributes to each of these key-

words, but at the very least the amount of money he

is willing to pay for a click on an ad for this spe-

ciﬁc keyword (CPC

max

)(Jansen et al., 2009). Every

time a user types in a query the search engine gener-

ates individual personalized result pages, depending

on the users’ location, his search history and other

factors. If ads are available that could probably sat-

isfy the need of the user, the search engine displays

these ads alongside the organic results. If more than

one advertiser is willing to pay for the display of an

ad the search engine auctions the position of these

ads among all interested players typically based on

a Generalized Second Price Auction (GSP) (Jansen,

2011; Varian, 2009). In each auction only the adver-

tiser that wins the auction by getting a click on an ad

is charged by the search engine. The effective Cost-

Per-Click (CPC

ef f

) is basically the maximum bid of

the advertiser with the subsequent highest bid plus a

small additional fee. In practice search engine com-

panies use a more robust mechanism to maximize

their proﬁts by rewarding keyword/ad combinations

that have a high relevance to users (often referred to

as the quality score). Although detailed calculations

are not disclosed, the key metric is claimed to be the

historic Click-Through-Rate (CTR) where available,

otherwise an expected click probability for the spe-

ciﬁc advertiser-ad-keyword combination is used.

Figure 1: Two variations of an ad, similar to the ones that

were used in the A/B test: Carbon Neutral delivery vs. Fast

and Reliable delivery.

In the present paper we concentrate on the advertisers’

perspective and the direct impact of green signals in

312

Blask T..

Applying Bayesian Parameter Estimation to A/B Tests in e-Business Applications - Examining the Impact of Green Marketing Signals in Sponsored

Search Advertising.

DOI: 10.5220/0004523603120319

In Proceedings of the 4th International Conference on Data Communication Networking, 10th International Conference on e-Business and 4th

International Conference on Optical Communication Systems (ICE-B-2013), pages 312-319

ISBN: 978-989-8565-72-3

 2013 SCITEPRESS (Science and Technology Publications, Lda.)

text advertisements. We evaluate the probability that

a user will click on a given Sponsored Search text ad-

vertisement containing the promise of Carbon Neutral

delivery vs. another one offering generic information

on reliable fast delivery and conduct a Bayesian pa-

rameter estimation approach to analyze the data.

2 LITERATURE REVIEW

There are two streams in literature which are impor-

tant for the present research. The ﬁrst is green mar-

keting. The second studies the various inﬂuences on

Sponsored Search advertising effectiveness.

2.1 Green Marketing

Green marketing has been a widely recognized trend

for international ﬁrms over the last years. One can

clearly identify strong efforts in the development of

sustainable brand images in a number of branches.

One trend Leonidou et al identify in their review of

developments in green advertising research and prac-

tice from 1988 to 2007 is a strategy shift from com-

municating environmental aspects within the produc-

tion process to the communication of sustainable con-

sumption by the customers themselves. An other im-

portant expansion of this ﬁeld is observed in the in-

tensiﬁcation of efforts by B2C businesses in com-

municating green messages in their advertising ac-

tivities. (Leonidou et al., 2011) The use of ecola-

bels is a well known tactic is to provide the poten-

tial consumer with independent conﬁrmation of the

green efforts of the respective advertiser. In fact Rex

and Baumann state that there is still lack of empiri-

cal knowledge about the consumers reception in this

area. (Rex and Baumann, 2007) Recent studies indi-

cate that a number of consumers may be willing to

pay higher prices for products they identify as en-

vironmental friendly. (Haytko and Matulich, 2008)

What is still unanswered is the whether these green

signals still have an impact direct buying decisions in

situations in E-Commerce situations. Recent research

indicates that this is not the case but lacks a sufﬁcient

amount of data to draw conclusions about the ﬁnal

size of the measured effect so that the authors rec-

ommend further research when more data is available

(Blask, 2013).

2.2 Sponsored Search Advertising

In published research, Online Marketing and Spon-

sored Search especially has become an established

topic with a variety of high quality publications in

Computer- and Information Science as well as in the

ﬁelds of Operations Research and Marketing. Since

2004, Sponsored Search has become a continuously

more and more important topic in the Online Market-

ing research area (Evans, 2008; Evans, 2009; Jansen

and Mullen, 2008). Yao and Mela (Yao and Mela,

2009) contribute a ﬁrst comprehensive literature re-

view of Sponsored Search Advertising from the per-

spective of three stakeholders: (a) search engine com-

panies, (b) advertisers, and (c) users.

The search engine auctions the positions of the ads

on the Search Engine Result Page (SERP) between all

advertisers that placed a bid (CPC

max

) for the given

keyword. The ad position is the result of the com-

binedCPC

max

and so called quality scores of the play-

ers. The CPC

ef f

depends on the advertisers bid and

the ones provided by the other advertisers in the auc-

tion and the quality score of the ad / query combina-

tion.

Many publications in this area have an empirical

basis. Basically quantitative research is conducted

with three types of datasets: (a) Search engine query

data (b) aggregated media and e-Commerce statistics

and (c) individual user journeys. Search engine query

data is the rarest form of available data for researchers

who are not directly afﬁliated to the search engines as

it can only be collected by the search engine compa-

nies themselves. Although every search engine com-

pany generates masses of this type of data, there are

only few datasets available for academic use. One

of those is the well known AOL dataset. It consists

of about 20 million completely non-censored web

queries collected from about 650,000 users over a

three month period, arranged by anonymous individ-

ual IDs. This dataset has been extensively examined

since 2006 (Pass et al., 2006; Adar, 2007; Strohmaier

et al., 2007; Strohmaier et al., 2008; Brenes and

Gayo-Avello, 2009).

Aggregated media and e-Commerce statistics are

generated by the advertisers themselves during their

ad campaigns. One way this kind of data is produced

is by the campaigning tool itself (e.g. Google Ad-

Words) or the advertiser’s respective software solu-

tion. The data is usually aggregated on campaign, ad-

group and keyword-level and contains variables like

the total number of clicks, impressions, CTR, CPC,

and CVR as can be seen in table 1.

The third sort of available data enables researchers

to understand individual user behavior. User jour-

ney conversion datasets include information about

all measured touch-points that an individual user has

with a speciﬁc advertiser. These datasets make the de-

velopment of attribution-models possible where every

conversion success can be allocated to the ad-contacts

ApplyingBayesianParameterEstimationtoA/BTestsine-BusinessApplications-ExaminingtheImpactofGreen

MarketingSignalsinSponsoredSearchAdvertising

313

Table 1: Typical dataset from Google AdWords (ad level).

Keyword Clicks Impr. CTR Avg.

CPC

Cost Avg.

Position

Conv. Cost /

conversion

Conv.

rate

ad 1 132 2,198 6% 1.32 174.08 2 16 11 12%

ad 2 421 2,893 15% 2.32 976.72 3 21 46.51 5%

... ... ... ... ... ... ... ... ... ...

Table 2: Estimated parameters of the A/B Test results.

Parameter mean median mode HDIlow HDIhigh pcgtZero

mu1 0.132138406 0.132018013 0.131569530 0.11165869 0.15294856 NA

mu2 0.125833478 0.125631688 0.126106871 0.10429358 0.14779868 NA

muDiff 0.006304928 0.006340036 0.006486033 -0.02312652 0.03597397 66.45467

sigma1 0.060327010 0.059410333 0.057196013 0.04050337 0.08129424 NA

sigma2 0.066338944 0.065606745 0.064239271 0.04496894 0.08889838 NA

sigmaDiff -0.006011934 -0.005907207 -0.005017510 -0.03192138 0.02088154 32.31035

nu 2.559232839 2.410642280 2.174679973 1.28929893 4.12144979 NA

nuLog10 0.389457520 0.382132769 0.375861907 0.15221850 0.63937996 NA

effSz 0.101884502 0.101000518 0.102799453 -0.37368096 0.56259172 66.45467

a user has had. Like the other types of data too, user

journey data is always subject to several types of bias,

such as caused by media discontinuities.

2.3 Click Probability

Click probabilities have been widely studied since

the early beginning of the advertising format Spon-

sored Search. However, due the lack of possibilities

to observe the user behaviour while using a search en-

gines, a complete coverage of all factors inﬂuencing

the CTR is no easy task.

Evidence suggests that one of the most inﬂuencing

factors is the ad position within the Sponsored Search

results, which depends among other facts on the ad-

vertisers CPC

max

and the so called quality score. The

quality score, used by search engines to determine the

quality of an advertisement, is based primarily on the

historical CTR. A large number of studies has shown

the correlation between decreasing position and a de-

creasing CTR and vice versa (Richardson et al., 2007;

Agarwal et al., ). It should be emphasized, that the

highest positions leads to high CTRs but not manda-

torily to the highest conversion rates. From an adver-

tiser’s perspective, a topic of interest is to predict the

future CTR of sponsored ads. As argued before, the

position has a major inﬂuence on the CTR, called the

position bias. In the course of research, several mod-

els have been developed to explain the inﬂuence of

the position bias on the CTR.

Crasswell, Zoeter and Taylor (Craswell et al.,

2008) present several models for predicting the CTR:

(a) baseline model, (b) mixture model, (c) examina-

tion model, and (d) cascade model . The ﬁndings were

originally based on organicsearch results but, they are

applicable to Sponsored Search results as well (Agar-

wal et al., ). The underlying assumption of the (a)

baseline model is that a user screens every search re-

sult and decides afterwards, which one ﬁts the best

to the query. As a consequence, the click probabil-

ities for each individual search result are identically,

independently of its position. The (b) mixture model

extends the baseline model and divides user behavior

into two groups. One group behaves as described in

the baseline model, the other group clicks randomly

on one of the ﬁrst search results. The (c) examina-

tion model refers to ﬁndings from eye tracking studies

which state that with declining position, the probabil-

ity of a click declines as well (Joachims et al., 2005;

Joachims et al., 2007). The (d) cascade model is, ow-

ing to the high degree of explanation by click data,

one of the most applied explanation approaches. The

basic assumption is that the user scans each search re-

sult, beginning from the top to the bottom, comparing

the relevance of each ad with the relevance of the ad

before. The user continuous scanning the results until

the perceived ad relevance reaches a certain level and

the user clicks.

As mentioned above one challenge is to predict

the CTR of keywords or keyword combinations for

potential future Sponsored Search ads. One solu-

tion that has been proposed is aggregating historical

data from similar keywords (Regelson and Fain, ).

Here, the CTR is represented as a function of po-

sition, independent of a bid. In doing so, the de-

veloped models do not focus on a certain advertiser.

The same clustering approach can be applied in op-

timizing the search engines’ proﬁt (Dave and Varma,

2010). There are also models taking the quality score

into account (Gluhovsky, 2010; Dembczynski et al.,

ICE-B2013-InternationalConferenceone-Business

314

0.0 0.2 0.4 0.6

0 4 8

Data Group 1 w. Post. Pred.

(

)

0.0 0.2 0.4 0.6

0 4 8

Data Group 2 w. Post. Pred.

(

)

Normality

log10(!)

0.0 0.2 0.4 0.6 0.8 1.0

mode 0.376

95% HDI

0.152 0.639

Group 1 Mean

0.08 0.10 0.12 0.14 0.16 0.18

mean 0.132

95% HDI

0.112 0.153

Group 2 Mean

0.08 0.10 0.12 0.14 0.16 0.18

mean 0.126

95% HDI

0.104 0.148

Difference of Means

# "

-0.06 -0.02 0.02 0.04 0.06 0.08

mean 0.0063

33.5% < 0 < 66.5%

100% in ROPE

95% HDI

-0.0231 0.036

Group 1 Std. Dev.

0.04 0.06 0.08 0.10 0.12

mode 0.0572

95% HDI

0.0405 0.0813

Group 2 Std. Dev.

0.04 0.06 0.08 0.10 0.12

mode 0.0642

95% HDI

0.045 0.0889

Difference of Std. Dev.s

# $

-0.08 -0.04 0.00 0.02 0.04 0.06

mode -0.00502

67.7% < 0 < 32.3%

100% in ROPE

95% HDI

-0.0319 0.0209

Effect Size

# "

' $

& 2

-0.5 0.0 0.5 1.0

mode 0.103

33.5% < 0 < 66.5%

30% in ROPE

95% HDI

-0.374 0.563

Figure 2: Group 1 = CTR for ads advertising Carbon Neutral delivery, group 2 = CTR for ads advertising Fast and Reliable

delivery.

ApplyingBayesianParameterEstimationtoA/BTestsine-BusinessApplications-ExaminingtheImpactofGreen

MarketingSignalsinSponsoredSearchAdvertising

315

0.10 0.14 0.04 0.08

0.10 0.13 0.16

0.10 0.14

0.075

0.093 0.12

0.04 0.08

0.058 0.18 0.27

0.10 0.13 0.16

0.10

0.20

0.04 0.08

0.52

0.53

0.2 0.6 1.0

log10"#$

Figure 3: Posteriors for Bayesian Parameter Estimation.

2008). A model developed by Zhu et al. (Zhu et al.,

2010) called General Click Model focuses on theCTR

prediction of long-tail queries, based on a Bayesian

network. Dealing with the position bias mentioned

before, Zhong et al. (Zhong et al., 2010) incorpo-

rate post-click user behaviour data from the respective

landing page of the clicked ad into the click model to

reﬁne the estimation of the perceived user relevance

after clicking on a speciﬁc ad. A similar approach,

using Dynamic Bayesian networks can be found in

Chappelle and Zhang (Chapelle and Zhang, 2009).

Several models based on historical click data suffer

from limitations in terms of lacking consideration of

a possible user learning effect. Taking Gauzente’s re-

sults as an example, it has been shown that past user

satisfaction with Sponsored Search results inﬂuences

the current click behaviour (Gauzente, 2009). Besides

the incorporation of position data and the perceived

relevance of presented ads, the CTR of an advertiser

is also affected by the relationship between organic

and Sponsored Search results. Listing the results of

one company at the same time in sponsored and or-

ganic search results leads to a higher CTR and vice

versa (Yang and Ghose, 2010; Blask et al., 2011).

3 CASE STUDY

This study covers a test period over several days in

which a single element in selected Sponsored Search

text advertisements hast been alternated for a num-

ber of queries that users type into the Google search

engine to eventually buy products in the advertiser’s

online shop as can be seen in ﬁg. 1. The advertis-

ers’ products can be classiﬁed as B2C Fast Moving

Consumer Goods. The selected keywords include (a)

variations of the retailer brand, (b) the brand names of

product manufacturers as well as (c) several clear-cut

descriptions of selected products in the online-shop.

The data was generated directly by Google Adwords

as part of the normal campaign evolution of the ad-

vertiser.

The test has been carried out in early 2013. The

resulting dataset contains a large number of Spon-

sored Search key performance indicators (KPI) for

the given period as exempliﬁed in table 1. The con-

tent of the unﬁltered dataset as well as the exact dates

of the test period cannot be revealed to ensure con-

ﬁdentiality for the advertiser and are of no impor-

tance for what follows from here. To ensure that

ICE-B2013-InternationalConferenceone-Business

316

only the impact of the speciﬁc text alternation is ana-

lyzed and to exclude other factors that would blur the

results, especially the strong position effects we de-

scribe above, we only analyze the advertisements that

were displayed above the organic search results and

that were part of the described A/B test. The updated

dataset, which is only a small fraction of the adver-

tisers’ regular Sponsored Search campaign, includes

a total of 109 advertisements of which 52 advertise

”Carbon Neutral delivery” while the other 57 adver-

tise ”Fast and Reliable delivery” in the third row of

the advertisement as illustrated in ﬁg 1. It contains

a total number of 4,370 clicks. What is used for the

analysis is the aggregated CTR for each ad over the

whole test period.

Analytic Approach. Traditionally one makes prob-

abilistic assumptions about the magnitude of the dif-

ference between two observed groups by using null

hypothesis signiﬁcance testing (NHST). We, how-

ever, apply a Bayesian approach to answer the ques-

tion whether there is a positive, negative or zero im-

pact of sustainability information in ad texts in Spon-

sored Search advertising by comparing two groups

of users that took part in an A/B test. Even though

the applied method possibly inﬂuences the behavior

of the involved users and could therefore be catego-

rized as reactive in terms of social sciences, it shares

common criteria with non-reactive methods since in-

dividual users have no knowledge of the investigation

of their behavior.

4 CONCLUSIONS

AND OUTLOOK

We describe the data using mean and standard devia-

tion parameters for t-distributions representing both

groups individually and add a normality parameter

that is common for both groups. The prior alloca-

tion of credibility across the parameters is vague, so

that the prior has minimal inﬂuence on the estima-

tion, to let the data dominate the inference. Taking the

data into account the Bayesian estimation reallocates

credibility to parameter values that represent the ob-

served data best. The resulting distribution is a joint

distribution across the ﬁve parameters, thereby reveal-

ing combinations of the ﬁve parameter values that are

credible, given the data (Kruschke, 2012). The two

histograms in the top right in ﬁg. 2 are representations

of empirical data and display the two observed groups

(group 1 = ”Carbon Neutral delivery”,group 2 = ”Fast

and Reliable delivery”), with curves of representative

examples of posterior predictive t-distributions. In the

left column you will ﬁnd marginals of the posterior

distributions of credible values of means of group 1

and 2 as well as the same for the respective standard

deviations and a distribution of credible values for

the the combined normality parameter. Lower right

shows posterior distribution of differences in means

and effect size. Fig. 3 displays pairwise plots of the

parameters for the given study.

Taking a ﬁrst look at the data we ﬁnd a slightly

higher empirical mean CTR over all ads on ads

that advertise ”Fast and Reliable delivery” (14.39%)

than on the ”Carbon Neutral delivery” ads (15.94%).

These values are not to be confused with those in the

top left histograms in ﬁg. 2 which represent the sim-

ulated mean parameters of t-distributions to ﬁt the

empirical distribution. So, in the data we observe

a 1.55% higher empirical mean CTR for ”green”

ads which would eventually make us accept the hy-

potheses that ads with green marketing signals have a

higher click probability than their counterparts in the

A/B test. What is the central question is whether this

result is signiﬁcant and if it enables us to derive infer-

ences about the ”real” long-term distribution.

To answer this question a large number of param-

eter combinations for t- distributions that are credible

given the data is generated by Markov Chain Monte

Carlo simulation (MCMC). One gets a good insight

by comparing the distribution of credible values for µ

which has a mean of 0.132 and a 95% Highest Density

Interval (HDI) from 0.112 to 0.153 with µ

which has

a mean of 0.126 with a 95% HDI from 0.104 to 0.148

as can be seen in tab. 2. The exact difference µ

− µ

is 0.0063 on average as can be found in the plot in

the middle of the right column of ﬁg. 2. One can see

that 66.5% of the 95% HDI for µ

− µ

is positive.

What is even more relevant for the analysis is that all

computed values within the 95% HDI fall into the Re-

gion of Practical Equivalence (ROPE) which spreads

from -0.1 to 0.1. So, these results imply that there

is a 66.5% chance that the ”real” mean of group 1 is

grater than the ”real” mean of group 2. Nevertheless

the difference of means is so small that there is a high

probability that the groups are not credibly different

from each other in this aspect. Comparing the distri-

bution of credible values for σ

and σ

one can see

that these groups do not credibly differ too. This can

be seen in the respective histogram in ﬁg. 2 where all

computed values for σ

− σ

are found in the ROPE

with 67.7% being negative and 32.3% being positive.

This suggests that there is a 67.7% probability that the

standard deviation for group 2 is grater than for group

The lower right panel of ﬁg. 2 shows the distri-

bution of credible effect sizes, given the data. For

each combination of means and standard deviations,

ApplyingBayesianParameterEstimationtoA/BTestsine-BusinessApplications-ExaminingtheImpactofGreen

MarketingSignalsinSponsoredSearchAdvertising

317

the effect size is computed. The histogram of 100,000

credible effect sizes has a mode of 0.103 and the zero

included in the 95% HDI. 66.5% of all computed out-

comes are positive while 27.8% are negative.

What can we derive from that? What is true is that

there is some probability that there is absolutely no

effect caused by the different signals in the advertise-

ments as we do not observe strongly signiﬁcant un-

ambiguous results. If any effect is presumed, it will

have a higher probability of being positive for ”green

signals” in Sponsored Search ads, given the observed

data. How can this outcome be explained? One argu-

ment could be that ad texts do not inﬂuence users on

SERPs at all. Although we know about various other

effects, like the strong position bias described above,

that do affect the user there are too many indications

that ad texts do have inﬂuence on click decisions to

let this be true.

In fact, these results need to be interpreted with

caution. One possible explanation for this is that

users might not be as green in their decisions as mar-

keters would like them to be. In this case the promise

of ”Fast and Reliable delivery” seams to lead to a

slightly lower motivation to click on an ad than the

green signals the advertiser sends out to his potential

customers. This A/B test should be repeated over a

number of various branches before one can derive im-

plications for the whole e-Commerce industry. What

is an even more interesting outcome of this paper is

that more future research should be conducted on the

general impact of texts in Sponsored Search ads con-

sidering a variety of branches and containing more di-

versity in texts to make sophisticated assumptions on

the impact of text-details on click probabilities.

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