Using Taguchi methods in a marketing study to determine features for a Smartphone.
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.
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).
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.
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
[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
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.
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%
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|Author:||Sutterfield, J.S.; McKinley-Floyd, Lydia A.|
|Publication:||Academy of Marketing Studies Journal|
|Date:||Jan 1, 2012|
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