Using Taguchi methods in a marketing study to determine features for a Smartphone.
Sutterfield, J.S. ; McKinley-Floyd, Lydia A.
INTRODUCTION
Statistical experimental methods have emerged as a powerful method
for analyzing cause and effect relationships among factors over the past
75 years. Design of Experiments (DoE) methods are used in industry for
process improvement and optimization purposes (Singh et al. 2006; Huang
and Lin 2004. Taguchi (1986) introduced a simplified and modified DoE
approach, which has been widely adopted in industry. More recently, the
power of Taguchi's approach is that it is quite generally
applicable to a broad range of experimental situations in which the
components of variation, including those of interaction, are desired.
It has been used for such diverse applications as bearing
deflections, diesel engine nozzle design, cloth quality evaluation, the
design of clothing, bank and insurance contracting and electrical power
consumption (Taguchi, 1988b) as well as engineering and science in
general (Wright 2002). One limitation of the method is the actual
process tends to cause disruption in the plant, and may be uneconomical
(Sukthomya and Tannock 2005). In recent years, researchers have
developed approaches in Neural Networks (Guh and Tannock 1999); and
Evolutionary Operations (Box 1978)) to test process parameters, without
production interruptions. However, in this study, classical experimental
analysis and Taguchi Methods, without actual experimentation, are used
to investigate process parameter effects.
While Taguchi methods have been used widely in all sorts of
applications, their use in marketing is relatively limited. Their most
common applications have been in advertising and sales, and direct
marketing campaigns where success factors, thought to have major
influence on sales, are tested to create optimal ads for increasing
response rates. The techniques have been used to increase response to
email, website and more recently pay per click advertising. In these
cases orthogonal arrays were created to test which combination of
features or success factors such as pricing, subject line, monthly fee,
message text, sender, image, etc. generate optimum response. The methods
have been touted as producing response increases of hundreds sometimes
thousands of percent (Kowalick 2004; Roy and Bullock 2004).
More relevant to the current study, Taguchi methods have also been
used in marketing in later stage product design where optimal values are
determined for product features. For example, the size or weight of a
SmartPhone, or its data transfer rate, or its storage capacity might be
optimized as to cost of manufacture versus the market share to be
garnered by the new product. As a matter of fact, as will be seen below
in the Literature Review, the literature on the use of experimental
method in Marketing, particularly Taguchi's method, is relatively
sparse. This is perhaps due to marketing's growth out of and
reliance on social rather than hard sciences. As will be demonstrated,
the adoption of this method, more commonly used in engineering design
and process management, can prove quite useful in marketing research.
Rather than traditional one-factor-at-a-time experiments Taguchi
technique "can be used to study effects of change of many factors
at a time. Because the behavior of all kinds of things may usually be
dependent on more than one factor, the areas of use of the technique are
unlimited" (Roy and Bullock, p. 3), including testing many factors
in combination in order to optimize market share. Thus, this paper
provides a novel addition to the relatively sparse literature.
The SmartPhone was chosen for analysis as an extension of a
research project originally given to an advanced marketing class taught
by one of the authors. This project simply provided a convenient
opportunity to demonstrate the use of Taguchi methods in marketing
analysis.
LITERATURE REVIEW
The work of Sir Ronald A. Fisher of England (Fisher 1942) is
credited with the immense contribution to experimentation over several
decades ago (Kempthorne 1967). Up to the time that Fisher began his
important work, estimation of population parameters and tests of
hypotheses were performed by making assumptions as to the distribution
of the unknown population parameters. Fisher argued that this approach
was completely wrongheaded, and that the population parameters should be
estimated from samples taken from the population (Fisher 1942). This
insight revolutionized the entire field of experimental analysis As a
matter of fact, it was Fisher who originated most of the ideas used in
modern experimental method (Box, Hunter and Hunter 1978).
In the late 1940s and early 1950s experimentation received another
very large benefit when it began to merge with the quality movement that
began taking root in Japan. During this period the ideas of Deming had
been largely rejected by American industrialists. However, Deming found
that his ideas concerning quality were readily accepted by the Japanese,
who were attempting to rebuild their industrial base after WW II and
were interested in reducing costs to the greatest extent possible.
Moreover, Japan did not have extensive natural resources, and was
solicitous of eliminating as much waste as possible. With this situation
prevailing, Deming's ideas readily took hold. At the time Deming
began work with the Japanese, he had been using statistical methods to
improve quality (Sutterfield and Kelly, 2005), and soon began teaching
them Statistical Quality Control. The Japanese had already discovered
that statistical methods could be employed for much more than monitoring
and improving quality (Montgomery, 1991). At about the same time, such
pioneers as Ishikawa (1952), Masuyama (1955, 1956) and Taguchi (1956a,
1956b) had begun to use such methods to facilitate scientific
experimentation.
In a third 1956 work, Taguchi published the original version of his
monumental work on experimental method. Although many other Japanese
scientists have made many substantial contributions to the field of
experimental method, it is Taguchi, more than any other, who has
advanced this area of science, and after whom the field has been named
as "Taguchi Methods." Considering the immense success achieved
by the Japanese using designed experiments, it is to be regretted that
they have not been more widely used in the West (Montgomery 1991).
METHODOLOGY
The philosophy and approach of experimental methodology are the
same no matter which approach is used for the analysis of experimental
results. Thus, the experimental methodology is identical whether
classical analysis or Taguchi analysis is used. The experimental method
has been discussed in detail by its trailblazers (Kempthorne 1967; Box
et al. 1978), as well as a previous work by (Sutterfield, Drake and
Kelly 2005). This latter work may be consulted for a concise statement
of the philosophy and approach of the experimental method.
What the Taguchi method attempts to do is to estimate the strength
of some response variable, in our case consumer preference, using
variance as a measure of that preference. The control variables, in our
case product features, are what cause the consumer response. Other
approaches that might have been used to determine desirable features are
Quality Function Deployment (QFD), and Analytical Hierarchy Process
(AHP). These, however, do not seek to measure the strength of the
consumer response, and certainly are not aimed at measuring feature
interactions. So far as the authors are aware, no other method, not even
conjoint analysis, seeks to measure the response of a large group of
respondents to product features, nor the interaction among those
features. In the present case, the approach was conceived after one of
the writers, and engineer with a background in Taguchi methods, and the
other writer, with a background in marketing, began to discuss how they
might collaborate in a project.
In using Taguchi's experimental method, the experimenter first
determines those factors (called control variables) thought to be
responsible for causing a given effect (the response variable). The
number of those factors, along with their possible interactions,
determines the size of the experiment and, consequently, the orthogonal
array to be employed. Orthogonal arrays have been developed for
extremely large experiments. Software is available for Taguchi
experimental analysis from Nutek, Inc., called Qualitek-4. The authors
chose to perform such analysis manually, because manual analysis
sometimes discloses information that is concealed when software is used
to perform calculations.
In applying this methodology to marketing analysis, it was first
necessary to decide which product features for a SmartPhone would be
selected to be sampled with the respondents. Product features were
determined through exploratory research including review of secondary
data, a focus group and interviews with self described early
adopters/heavy users. Along with those features to be tested, it was
also necessary to determine the number to be included in the analysis at
one time. In an actual product development application, more features
might have been chosen for consumer testing. However, this would have
meant that more feature interactions would have to have been
investigated. Since the purpose of the authors was to demonstrate a
methodology, the more limited set of factors, shown below in Table 1,
was selected for analysis.
APPLICATION OF METHODOLOGY
The control factors (product features) to be investigated were
identified, and an orthogonal array selected to accommodate the factors
and their interactions. The survey instrument was then designed to
conform to the selected orthogonal array, and an extensive focus group
conducted. The survey instrument was then administered. The experimental
data used for this analysis were obtained from a survey performed with
177 students in a university class. The survey instrument was designed
for several purposes, among which was to obtain a set of responses for
this experiment. The relevant portion of the survey instrument for this
experiment is shown below in Table 1.
Although this instrument has four categories of responses, and
could have been analyzed using a slightly different type of factorial
analysis, the resulting analysis would have been considerably more
complex. Thus, it was decided for the purposes of this experiment to
combine the two categories involving agreement and the two involving
disagreement, so that two final categories resulted: The categories of
disagreement becoming "No," and the categories of agreement
becoming "Yes." Also, the features were rearranged to
facilitate assignment to the orthogonal array. The result of these
operations is shown in Table 2.
Further, in order to facilitate assignment of the above features to
the orthogonal array, a factor identification, along with column
identifications for each factor and factor interactions, was made for
each of the above features as shown in Table 3.
It is important at this point to discuss several of the finer
points of Taguchi experimental analysis. First, once the factors to be
examined have been selected, it is necessary to determine the possible
interactions among these factors. Next, any interactions that are
logically impossible are eliminated. Once this is done, an orthogonal
array is chosen of a size that will accommodate all control factors
(product features) plus their interactions plus one additional column
for experimental error. Once selected, the orthogonal array becomes a
template, or alternatively specifies a protocol, for conducting an
experiment.
Factors may be assigned arbitrarily to columns, but are generally
assigned so as to facilitate calculating the interactions between
factors. In an orthogonal array, the sum of the column numbers for any
two factors yields the number of the column in which their interaction
is found. Take for example three factors: A, B and C. If factor A is
assigned to column 1 and factor B to column 2, then their interaction
AxB will be found in column 3 (1+2). Further, if factor C is then
assigned to column 4, the interaction AxC will be found in column 5
(1+4) and that for BxC in column 6 (2+4), etc. All of this will explain
the relationship between Tables 3 and 4. With regard to Tables 2 and 3,
the order of the factors in Table 2 is the order in which the factors
(product features) were originally arranged in the survey instrument.
The same identical factors appear in Table 3 rearranged to facilitate
calculating interactions.
For this type of experiment, the experimental method selected was
that of factorial analysis. In using factorial analysis, the orthogonal
array chosen becomes the format for executing the experiment. Further,
it is necessary to select an orthogonal array that will accommodate not
only the principal factors (in the instant case SmartPhone features),
but also the factor interactions that are thought to be significant.
Since one of the chief purposes of this experiment was that of
determining interactions among features, an orthogonal array of type L16
([2.sup.15]) was selected. What the preceding convention means in
factorial analysis is that the necessary orthogonal array has sixteen
rows and will accommodate fifteen factors, each with two levels. Since
it is necessary to dedicate one column to experimental error, only seven
feature interactions can be analyzed. However, there are twenty-one
possible feature interactions (seven things taken two at a time). Thus,
it was necessary to pare down the possibilities to seven before
performing the analysis. For example, although there exists the formal
possibility of an interaction between the Camera and Music Player 3
features, there is no logical reason as to why there should be one.
Consequently, this formal possibility was eliminated. Other possible
formal feature interactions were similarly eliminated. The final result,
along with column assignments for features and interactions, is shown in
Table 4.
The values in the Response Data column were obtained by adding
together the number of responses corresponding to the "1s" and
"2s" in the row corresponding to the levels of the features in
the columns. For example, the 378 for row 1 was obtained by adding
together the "No" responses for all of the features, etc. One
of the aspects of Taguchi methods is that of deducting an amount from
each of the response datum called the working mean. In the present
analysis, a working mean of 950 was deducted from each of the response
datum to obtain the values in the rightmost column labeled Working Data.
RESULTS
The total variation was obtained by summing the squares of the
coded values, and deducting the square of the sum of these divided by
16, the number of coded values. This is illustrated in the following
calculation:
[S.sub.T] = [X.sup.2.sub.1] + [X.sup.2.sub.2] + [X.sup.2.sub.3] +
... + [X.sup.2.sub.n] - [(CF).sup.2]/n
Then substituting the coded data for the response variable from
Table 2 ....
[S.sub.T] = [(-572).sup.2] + [(-171).sup.2] + ... + [(73).sup.2] +
[(22).sup.2] - [(-572 - 171 + ... + 73 + 22).sup.2]/16
[S.sub.T] = 1,210,114
The effect for a given control factor is obtained by summing the
values of the response factor for the "1s" in a given column,
summing the values of the response factor for the "2s" in the
column, taking the difference between the two sums, and squaring it. The
result of this calculation is the variation for the effect is known as
the variation. For a 2n orthogonal array, the variation for any factor
may be written as ...
S = [[([summation][RV.sub.2])-([summation][RV.sub.1])].sup.2]/n
where ...
[RV.sub.2]--the value of the response variable at the high level of
the control factor in question
[RV.sub.1]--the value of the response variable at the low level of
the control factor in question n--the number of experiments performed
This computation is illustrated for control factor "A" as
follows:
[summation](coded values corresponding with "1s" in
column for A) = 1,433
[summation](coded values corresponding with "2s" in
column for A) = -1,016
[S.sub.G] = [[(1,433-(-1,016)].sup.2]/16
The variations for the remaining control factors and their
interactions were calculated similarly. The error term was calculated in
the manner just outlined, and then independently checked using the
equation ...
[S.sub.e] = [S.sub.T] - [S.sub.A] - [S.sub.B] - .... - [S.sub.n]
In order to calculate the interactions between features, it was
necessary to employ an approach similar to that of calculating marginal
probabilities. A two-way table was laid out for the two features,
similar to that for marginal probabilities and the fractions answering
"No" and "Yes" for each of the features. This
resulted in four different possibilities. By performing the four
multiplications, it was possible to obtain the number of respondents
wanting neither feature, the numbers for two cases in which respondents
wanted one feature but not the other, and the number of respondents who
wanted both features. Tables 5 and 6 below show an example calculation
for obtaining these four possibilities.
The numbers in Table 6 were obtained by multiplying the four
marginal fractions in Table 5 by 177. The interpretation of the four
numbers in Table 6 is as follows: [B.sub.1] x [G.sub.1] means that 14
respondents did not desire either feature; [B.sub.1] x [G.sub.2] that 14
respondents desired feature G but not feature B; [B.sub.2] x [G.sub.1]
that 75 respondents desired feature B but not feature G; and [B.sub.2] x
[G.sub.2] that 74 respondents desired both features. The reader will
observe that the numbers in Table 6 sum to 177. The results for all of
these calculations are shown in Table 7, the analysis of variance.
For an F test significant at 95%, the significance value is 161.
Thus, in our application for any feature to be significant, it must have
an [F.sub.0] of 161 or greater. Thus, any features or feature
interactions having an [F.sub.0] less than 161 were deemed to be
insignificant at the 95% level, and were eliminated. Since neither these
features nor the feature interactions were significant at the 95% their
variation was attributed to experimental error and combined with the
variation of 284 for e, which yielded the value of 60,505, designated as
(e). Also, the degrees of freedom for these features and interactions
were combined with that for e to yield the value of 10 for the degrees
of freedom for (e).
In arriving at final estimates of the variation attributable to
each of the principal features, it is necessary to calculate the net
variation for each. This is done by subtracting one error variance, in
the instant case 6,050, for each degree of freedom in each of the
principal features. Thus, the values for net variation in column S ? of
Table 7 were obtained by deducting the amount of 6,050 from each of the
values for gross variation in column S, to obtain the net variations for
each of the significant features. In addition these five amounts of
6,050, totaling 30,250, were added to the (e) amount of 60,505 to obtain
90,755. The net variations resulting from these operations are shown
under column S in Table 8.
ANALYSIS OF RESULTS
As might have been expected at the onset of the analysis, Feature
A, Quick Internet Access, proved to receive the strongest response from
the participants. Also, Feature F, Music Player 3, did not receive a
strong participant response, and was not therefore significant at the
95% level of significance. Although it was anticipated initially that
the interaction between Features A and F would not be significant, it
was retained from the possible feature interactions for illustrative
purposes. As was anticipated, this feature interaction proved virtually
nonexistent, and so this interaction was eliminated from further
consideration. The conclusion at this stage is that Feature A should be
included in the SmartPhone, but that MusicPlayer3 would not necessarily
have to be included.
Of particular interest are Features B and C, the Qwerty Keyboard
and the Touch Screen. Both were found to have been significant at the
95% level, but Feature B was decidedly more so. Although these two
features tend to be mutually exclusive, they are not necessarily so.
Thus, it was desirable to examine their interaction. Again, it was found
that the interaction between the two was not significant at the 95%
level. All of this would indicate that the Qwerty Keyboard should be
offered as a design feature, without the necessity for offering either
the Touch Screen or the Swype Texting features. Other features that
should be offered in the final design are D and E, Global Positioning
System and Camera. Both of these features proved to be significant at
the 95% level, with the Camera being very strongly so.
In summary then, the features to be included in a final design for
the SmartPhone would be ...
Quick Internet Access
Qwerty Keyboard
Global Positioning System
Camera
CONCLUSIONS
The purpose of this paper was to demonstrate a method for using
Taguchi methods of experimental analysis to determine which of several
possible features might best be made available in a SmartPhone design in
order to maximize market share for the product. The method advanced in
this paper enables a firm contemplating a new product not only to
identify those features that should be included in the product design,
but also to measure the strength of the preference for those features.
Thus, this approach affords the very important advantage of including or
excluding features in the product design based upon computing the actual
strength of user preference for one or another of the possible features.
In addition, it enables a firm to assess the strength of
interactions between possible features. This is extremely important
because it is possible that with two features, one might prove
statistically significant, and other statistically insignificant.
However, the interaction between the two features might prove
statistically significant, in which case a decision would be necessary
as to whether the statistically insignificant feature should be offered
as part of the design because of the benefit to the product from the
interaction of the two features. In the final analysis, such a decision
as this would have to be made based upon the economics of the situation:
If the economic advantage of offering the statistically insignificant
feature, due to its interaction with the statistically significant
feature, were to exceed the economic disadvantage, then the
statistically insignificant feature would be offered. Also, it should be
noted that the Taguchi method might be used to investigate new features
to an existing design, or for that matter to investigate currently
offered features that might be discontinued. Supposing that the product
were available, one would design the test instrument so as to include
both existing features and those contemplated for addition. An
orthogonal array would then be selected to accommodate the existing and
contemplated features. Once the experiment was conducted, the ANOVA
would be performed as usual to obtain the strength of the control
group's preferences for each of existing features, the contemplated
features and their interactions. Again, application of the F-test would
disclose which product features should be included in the final design,
and which would be excluded.
At this point it is worth considering how Taguchi methods differ
from another well known experimental approach used in marketing,
Conjoint Analysis. Conjoint analysis is an approach that attempts to
quantify the complex psychological factors underlying individual product
choices. It would seek to draw general conclusions about consumer
choices for use in other product developments. The approach becomes
problematical when the individual must choose from among the large
number of combinations that can result from a relatively few features.
In contrast to conjoint analysis, the Taguchi approach seeks only to
draw conclusions about the preferences of large groups for a specific
suite of features for some contemplated product offering. As a matter of
experimental method applied to product design, it is important to
identify strong group feature preferences early, so that such features
can be optimized for inclusion in a product design. Taguchi's
experimental method permits this early feature identification with a
relatively simple experiment. In summary, it is suggested that
Taguchi's method be employed initially. Then, if more investigation
were desired as to the psychological basis for feature choice, conjoint
analysis might be employed.
Finally, it should be mentioned that in such product development as
a SmartPhone that Taguchi methods would play a very important role in
the next phase, viz, that of advanced design. In this phase, Taguchi
methods might be used to optimize the measure of each feature as a
function of market share. Through such an approach, it would be possible
to estimate profits as a function of feature measures. Thus, although
relatively new and little used, there is a very powerful and useful
synergism to be realized through the use of Taguchi Methods in
Marketing.
REFERENCES
Box, George E. P., William G. Hunter, J. Stuart Hunter (1978).
Statistics for Experimenters, John Wiley and Sons, New York, Chichester,
Brisbane, Toronto and Singapore, pg. 15
Cochran, W. G. and G. M. Cox. (1957). Experimental Design, John
Wiley and sons, New York
Fisher, R. A. (1966). The Design of Experiments, Hafner Publishing
Company, New York, 8th edition.
Fisher, Ronald A. (1942). The Design of Experiments, Oliver and
Boyd, Ltd.
Guh, R. and Tannock, J.(1999). "A Neural Network Approach to
Characterize Pattern Parameters in Process Control Charts", Journal
of Intelligent Manufacturing, Vol.10 (5), pp.449-462.
Huang, M.F. and T.R. Lin (2004). "Application of grey-Taguchi
method to optimize drilling of aluminum alloy 6061 with multiple
performance characteristics", Materials Science and Technology,
Vol. 20 (4), pp. 528-533.
John, P. W. M. (1971). Statistical Design and Analysis of
Experiments, The MacMillan Company, New York.
Kempthorne, Oscar (1967). Design and Analysis of Experiments, John
Wiley and Sons, Inc., New York, London and Sydney.
Kowalick, James F. (2004). Absolute Certainty in Media with the
Taguchi Method Maximizing Ad Response: Ad Optimization Breakthrough with
Emphasis on On-Line Advertising. AD TECH, San Francisco.
http://www.davidbullock.com/AD-Tech/Speaker_Notes_Ad_Tech.pdf Accessed
June 5 2020.
Margolin, B. H. (1967). "Systematic Methods of Analyzing 2n3m
Factorial Experiments with Applications," Technometrics, vol. 9,
pgs. 245-260
Margolin, B. H. (1969). "Results on factorial Designs of
Resolution IV for the 2n and 2n3m Series," Technometrics, vol. 11,
pgs. 431-444
Masuyama, Motosaburo, (1955). Design of Experiments Explained for
the Plant Technician, Japanese Standards Association, Tokyo, Japan.
Masuyama, Motosaburo, (1956) Design of Experiments, Iwanami
Zensho,.
Montgomery, Douglas C. (1991). Design and Analysis of Experiments,
John Wiley and Sons, New York, Chichester, Brisbane, Toronto and
Singapore, 3rd edition, pgs. 414-415
Plackett, R. L., and J. P. Burman (1946). "The design of
Multi-factorial Experiments," Biometrika, vol, 33, pgs. 305-325
Roy, Ranjit K., and David S. Bullock (2004). Taguchi for Marketers:
Plain-English Explanation of the Taguchi and Design of Experiments
Methodologies. How an Innovative Mathematical Formula Produces Explosive
Results for Direct Marketing Campaigns. White Bullock Group, Inc.
Murfreesboro, TN. http://www.results-squared.com/images/DrRoy_Article.pdf. Accessed June 3, 2010
Singh, Sehijpal, Pradeep Kumar and H.S. Shan (2006). "Quality
optimization of surface finishing by magnetic field assisted abrasive
flow machining through Taguchi technique", International Journal of
Computer Applications in Technology, Vol. 27(1), pp. 31-56.
Sukthomya, W. and Tannock, J. (2005). "Taguchi Experimental
Design for Manufacturing Process Optimisation Using Historical Data and
a Neural Network Process Model", International Journal of Quality
and Reliability Management, Vol.22 (5), pp.485-502.
Sutterfield, J. S., Dominique D. I. Drake and Conrod S. J. Kelly.
(2005). Investigation of animal survival times for poison antidotes
using standard factorial design methods as computed with Taguchi
Methods. Proceedings of the 2005IEMS Conference: Cocoa Beach, FL, pp.
470-478.
Sutterfield, J. S., Conrod S. J. Kelly. (2005). "Metrics for
Continuous Process Improvement," Proceedings of the 2005 IEMS
Conference: Cocoa Beach, FL, pp. 370-378.
Taguchi, Genichi. (1956). How to Determine Tolerances, Japanese
Standards Association, Tokyo, Japan,.
Taguchi, Genichi. (1956). A Text on Design of Experiments,
Electrical Communications Laboratory, Tokyo, Japan, 2nd revised edition,
Taguchi, Genichi. (1988). System of Experimental Design:
Engineering Methods to Optimize Quality and Minimize Cost, UNIPUB, Kraus
International Publications, White Plains, NY, vol. 1
J. S. Sutterfield, Florida A&M University
Lydia A. McKinley-Floyd, Clark Atlanta University
Table 1: Original Data from SmartPhone Experiment
My ideal smartphone absolutely must have the following features:
Top number is the count Strongly Agree Disagree Strongly
of respondents selecting Agree Disagree
the option. Bottom % is
percent of the total
respondents selecting the
option.
Quick Internet Access 118 42 3 14
67% 24% 2% 8%
Qwerty (standard) 104 45 8 20
Keyboard 59% 25% 5% 11%
Touch Screen 70 50 37 20
40% 28% 21% 11%
GPS 68 56 36 17
38% 32% 20% 10%
Camera 119 40 6 12
67% 23% 3% 7%
MP3 79 54 29 15
45% 31% 16% 8%
Swype Texting 32 57 61 27
18% 32% 34% 15%
Table 2: Adjusted Data from
SmartPhone Experiment
Responses
Factor Definition No Yes Totals % No % Yes
1 Qwerty Keyboard 28 149 177 0.158 0.842
2 Swype Texting 89 88 177 0.503 0.497
3 Touch screen 57 120 177 0.322 0.678
4 Quick Internet 17 160 177 0.096 0.904
Access
5 Global Positioning 53 124 177 0.299 0.701
System
6 Camera 18 159 177 0.102 0.898
7 MP3 44 133 177 0.249 0.751
Table 3: Factor Definition for Orthogonal Array
Column Factor Definition
1 B Querty Keyboard
2 G Swype Texting
3 BxG Interaction of BxG
4 C Touch Screen
5 BxC Interaction of BxC
6 CxG Interaction of CxG
7 A Quick Internet Access
8 D Global Positioning System
9 E Camera
10 AxF Interaction of AxF
11 ExG Interaction of ExG
12 e Error term
13 F Music Player 3
14 AxE Interaction of AxE
15 AxD Interaction of AxD
Table 4: Orthogonal array for SmartPhone Experiment
1 2 3 4 5 6 7 8 9
No. B G BxG C BxC GxC A D E
1 1 1 1 1 1 1 1 1 1
2 1 1 1 1 1 1 1 2 2
3 1 1 1 2 2 2 2 1 1
4 1 1 1 2 2 2 2 2 2
5 1 2 2 1 1 2 2 1 1
6 1 2 2 1 1 2 2 2 2
7 1 2 2 2 2 1 1 1 1
8 1 2 2 2 2 1 1 2 2
9 2 1 2 1 2 1 2 1 2
10 2 1 2 1 2 1 2 2 1
11 2 1 2 2 1 2 1 1 2
12 2 1 2 2 1 2 1 2 1
13 2 2 1 1 2 2 1 1 2
14 2 2 1 1 2 2 1 2 1
15 2 2 1 2 1 1 2 1 2
16 2 2 1 2 1 1 2 2 1
10 11 12 13 14 15 Response Working
No. AxF GxE e F AxE AxD Data Data
1 1 1 1 1 1 1 378 -572
2 2 2 2 2 2 2 779 -171
3 1 1 2 2 2 2 835 -115
4 2 2 1 1 1 1 1,193 243
5 2 2 1 1 2 2 612 -338
6 1 1 2 2 1 1 1,255 305
7 2 2 2 2 1 1 578 -372
8 1 1 1 1 2 2 929 -21
9 1 2 1 2 1 2 1,343 393
10 2 1 2 1 2 1 1,023 73
11 1 2 2 1 2 1 972 22
12 2 1 1 2 1 2 922 -28
13 2 1 1 2 2 1 919 -31
14 1 2 2 1 1 2 674 -276
15 2 1 2 1 1 2 1,318 368
16 1 2 1 2 2 1 1,206 256
Table 5: Calculation of marginal fractions
Feature G
No (%) Yes (%)
0.503 0.497
Feature B No (%) 0.158 0.080 0.079
Yes (%) 0.842 0.423 0.419
Table 6: Example marginal
interactions for features G and B
[G.sub.1] [G.sub.2]
[B.sub.1] 14 14
[B.sub.2] 75 74
Table 7: Initial ANOVA for SmartPhone
Source dof S V F0(95%) S' [rho]
B 1 206,464 206,464 725.82 200,413 0.17
G 1 141 141 -- -- --
BxG 1 6,942 6,942 -- -- --
C 1 58,741 58,741 206.50 52,691 0.04
BxC 1 171 171 -- -- --
GxC 1 1,851 1,851 -- -- --
A 1 434,127 434,127 1,526.16 428,077 0.35
D 1 65,732 65,732 231.08 59,682 0.05
E 1 384,545 384,545 1,351 86 378,496 0.31
AxF 1 3,878 3,878 -- -- --
GxE 1 3,062 3,062 -- -- --
F 1 33,991 33,991 -- -- --
AxE 1 9,415 9,415 -- -- --
AxD 1 770 770 -- -- --
e 1 284 284 -- -- --
(e) 10 60,505 6,050 -- 90,755 0.07
Table 8: Final ANOVA for SmartPhone
Source dof S V F0(95%) S' [rho]
B 1 206,464 206,464 725.82 200,413 0.17
C 1 58,741 58,741 206.50 52,691 0.04
A 1 434,127 434,127 1,526.16 428,077 0.35
D 1 65,732 65,732 231.08 59,682 0.05
E 1 384,545 384,545 1,351.86 378,496 0.32
(e) 10 60,505 6,050 -- 90,755 0.07
Total 15 1,210,114 1,210,114 100.00%
