# Male Apparel Innovativeness and Social Context: an Application of Multivariate Analysis of Variance

##### Citation:

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William R. Darden and Fred D. Reynolds (1974) ,"Male Apparel Innovativeness and Social Context: an Application of Multivariate Analysis of Variance", in NA - Advances in Consumer Research Volume 01, eds. Scott Ward and Peter Wright, Ann Abor, MI : Association for Consumer Research, Pages: 473-483.
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In this study three such subcultures of a university city were examined for possible differential rates of diffusion for four men's apparel innovations. The method of analysis was multivariate analysis of variance since (1) the independent variable (subculture) is nominally scaled, (2) there is more than one criterion variable (four men's apparel innovations) and (3) the criteria measurements are assumed metric. While this statistical model is later explained in greater detail, it is worth mentioning at this juncture that the approach is relatively unused in marketing; and yet, it shows promise in the statistical analysis of many problems in promotion, distribution and consumer segmentation.

In summary, this paper considers the possibility of differential rates of product diffusion in different subcultures. In the process, it also describes and demonstrates a relatively unused statistical model, multivariate analysis of variance. The rest of this paper proceeds through three stages. In the first stage, the approach to the problem is delineated, including sampling plan, measurement of innovativeness, subcultures, and a summary of the nature and assumptions of multivariate analysis of variance. In the second stage, the results are presented and interpreted. Finally, the findings are summarized and some conclusions are tentatively offered as to (1) the possibility of differential rates of diffusion in marketing and how marketers may use this information and, (2) the potential of multivariate analysis of variance in analyzing data from other marketing problems.

APPROACH

In order to test the hypothesis of differential diffusion rates among the more subtle social contexts within a given social structure, samples were selected from three subcultures. The overall social structure was that of a medium-sized university city. Subcultures chosen included (1) medium to upper middle class suburban male heads of households (N=104), (2) fraternity undergraduate students (N=76), and undergraduate male independents (N=102). The subcultures were chosen on the basis of (1) the degree of in-group social integration (strong for the fraternity and suburban subcultures) [5,9]; (2) the need for groups to provide matched but different social contexts; and (3) the convenience and economic feasibility with which the groups could be sampled and surveyed.

The four male apparel innovations chosen for study were (1) flares (bell-bottomed trousers), (2) vest suits, (3) velour shirts and (4) dress boots. At the-time of the study these products were considered at least partially diffused in each group.

Sampling and Measurement

The data were gathered through personal interviews with the respondents in each of the three groups. Students were randomly chosen from the student-faculty directory of the University. Seventy-six fraternity and one hundred and two independent questionnaires were completed out of original samples of one hundred and fifteen. The suburban sample was collected in the following fashion: first, nine middle to upper middle class suburban areas were randomly chosen from a list supplied by local realtors; second, streets were randomly selected within each of the chosen areas; and third, the male household head in every other house was interviewed. Not-at-homes were recalled on two separate occasions. The survey resulted in one hundred and four usable questionnaires with the balance not-at-homes, refusals and incomplete and/or unusable questionnaires.

The four innovative behavior scores for each respondent were obtained through recall procedures. Respondents were asked to recall the number of months from the survey date backwards to first use of the product. Thus time from introduction to first use of a given innovation is the measure of innovativeness employed in this study. This measure, while not generally regarded as being as accurate as an objective time-of-adoption measure, is a widely employed operation of the construct innovativeness and is preferred over an adoption scale (summation of the total kinds of products purchased in a product class) because it incorporates the notion of firstness--a notion more isomorphic to the constitutive definition of innovativeness. [For more complete discussion of alternative measures of innovativeness, see Rogers [13], King and Ryan [10], and Robertsen [12].]

Thus innovativeness was viewed as a vector variable, with four recall innovations scores (one for each apparel innovation) for each respondent. After inspecting their frequency distributions, each innovation score was subjected to a square root transformation recommended by Banks [1], to compensate for some skewness.

The Multivariate Analysis of Variance Technique

A useful way to view multivariate analysis of variance is as an analogy to the more familiar univariate analysis of variance. While extensions are discussed later, we are presently content to consider only the one-way design. [If the independent variable was subject to experimental control and test units were randomly assigned to treatment levels we would have a completely randomized experimental design. In this case statements as to the direction of causation are possible. When using Ex Post Facto data, however, only inferences as to relationship are possible.] The data below represent adoption scores for organic food products measured from samples of three nominally scaled categories (professional, white collar and blue collar). Each sample (n1, n2 and n3) is

assumed randomly selected from its respective subpopulation. Thus Xij is the measure of organic plant innovativeness of the ith individual in the sth group (i = 1, n and j = 1, 3). [The one-way ANOVA Model is considered "fixed effects" or "random effects" depending upon whether the levels of the independent variable (occupation) are chosen because of their interest or randomly selected from a population of occupations. The results of the latter are generalizable to all occupations, while results of the former are only germane to the levels selected.] The hypothesis to be tested is the degree of independence between organic plant food innovativeness and occupation. In other words are X.1, X.2 and X.3 computed from samples drawn randomly from the same overall population? Or do they represent means drawn from different sampling distributions? The symbolic statement of the null hypothesis is then:

U1 = U2 = U3.

The above discussion is intended solely to remind the reader of the basis of the Fisherian univariate ANOVA approach. The multivariate extension is demonstrated with the example below; in this case there are multiple dependent measures on each respondent and the independent variate is

nominally scaled with three categories (economic, ethical and apathetic shoppers). For purposes of exposition we have assumed that Xj1, Xj2, and Xj3 represent interval scaled measurements on different aspects of each respondent's consumption pattern. In fact, Vij can be viewed as a vector variable, whose elements (Xij1, Xij2, Xij3) are usage rates for three product categories for a consumer in the jti group. The major assumptions of the multivariate analysis of variance statistical model include:

1. The null hypothesis of interest is u1 = u2 = ... = uj = ... = ug where uj is a vector whose elements are the p criteria means for the jth group. We are testing, then whether the group centroids are estimates of a centroid from an overall multivariate population.

2. The criterion variables in each group are assumed to be multinormally distributed. This is analogous to the univariate case where the criterion variable in each group is assumed normally distributed.

3. The dispersion matrices computed among the criterion variables for each population are assumed equal. The equivalent analogy for univariate analysis stipulates that populations have equal variances. This assumption is not as exacting, however, if roughly the same number of sampling units are present in each sample [1]. a e test used in the multivariate application is also considered robust [3 and 4].

4. The criterion variables are interval scaled. In a sense we are considering a statistical model very close to that of the more familiar discriminant analysis; however, in discriminant analysis the nominally scaled variable may be the criterion and the interval scaled variables would be the predictors (the reverse of the multivariate analysis of variance problem).

Basically, the overall test of equal group centroids is carried out by use of Rao's approximate F [11], which is derived from Wilk's Lambda [16]. Appendix A contains the more technical aspects of multivariate analysis of variance, as well as the derivation of Lambda and the approximate F test statistic.

ANALYSIS

Table 1 contains the four mean innovation scores for each subculture. Given the assumptions of our statistical model, the first hypothesis tested was that group centroids are equal; i.e., innovative behavior for the select men's apparel products are independent of subculture. Rao's approximate F is 6.60 indicating a highly significant relationship between the nominal variable (social context) and the innovative behavior among the groups.

Now that significant differences have been reasonably demonstrated between nominal categories, univariate analysis of variance for each innovation category is possible. This procedure demonstrates which of the men's apparel fashions have diffused at differential rates among different subcultures. Table 2 contains the four univariate F ratios, one for each new apparel fashion. Diffusion rates for flares, velour shirts, vest suits and dress boots are significantly different among the selected subcultures. The group centroids in Table 1 suggest that the greater differential between group diffusion rates exists for the suburban and fraternity groups (slowest for suburban and fastest for fraternity). The diffusion rates of independents, while slower than that of fraternity groups, is faster than that of the suburbanites. > us there is support for the view that male college students are key change agents in the diffusion of many men's apparel fashions. The criteria products would appear to be representative of a cross-section of men's apparel products (footwear, trouser, suits and shirts), giving some evidence for generalization to the entire product category.

MULTIVARIATE ANALYSIS OF VARIANCE OF APPAREL INNOVATIVENESS

UNIVARIATE ANOVA OF APPAREL FASHIONS

The product showing the greatest differential diffusion is flare trousers with dress boots running a close second (see Table 1). This leads to the speculation that undergraduate students are more innovative toward trouser and footwear fashions; it is also suggestive that they may be the key influentials for the diffusion of these products. If further research supports this view, marketing strategists should strongly consider these aspects:

1. Media, and copy themes be initially oriented toward student innovators and their influentials for new ideas in male footwear and trouser products.

2. Test marketing those subcultures with the highest differential rates of diffusion for similar products may be faster, less expensive, and more indicative of product success.

3. If these ideas are approximately correct, the probability of successful diffusion would be enhanced with intelligent pacing of emphasis on strategic segments through time to accomplish predetermined objectives based on the characteristics of those subcultures with differential rates of diffusion.

Assumptions of MANOVA for the Study

The validity of statistical analysis is no better than the degree to which the assumptions of the statistical models have been met. Earlier, the assumptions of MANOVA were given, including interval level measurement for the criteria and equal variation-covariation matrices for each population being sampled. The work of Box provides a statistical test of the latter hypothesis [2]. When applied to the dispersion matrices of these subcultures, the following was determined:

1. Hypothesis A1 A2 = A3

Where A1 is the population dispersion matrix for the ith group.

2. F = 2.60 with V1 = 20, V2 = 236, 235

Checking the tabled values for the F distribution with the appropriate degrees of freedom leads us to reject the above hypothesis at the .01 level. m is result is consistent with the observed differences in the dispersion determinants computed for each group and shown in part II of Table 1. While the MANOVA test is considered robust with regard to this assumption [3] some question is still raised as to its appropriateness. Nevertheless, the levels of significance attained leads us to the conclusion that the results are still useful [1].

MANOVA Post-Mortem

If its assumption can be approximately met, multivariate analysis of variance offers marketing a most promising tool. Some areas for possible applications are listed and discussed below:

1. Media readership and/or viewing scores--through appropriate transformations--can be analyzed for differences among market segment groups, thereby generating a more coordinated approach to media selection and timing.

2. Brand loyalty scores for a set of products can be treated as a vector variable, with each respondent's brand loyalties as its elements. Viewed from this perspective, brand loyalty can be generalized and tested for independence with respect to nominally scaled variables that have been hypothesized to be related.

3. Multiple criterion variable marketing experiments can use MANOVA as a model for statistical analysis. Adjustments for uncontrolled variables can be made through covariance analysis. In this case the vector variable would be partitioned into two vector variables taken over the sample; first, the usual criterion set: and second. the covariant set [7, pp. 45-53; 3].

4. Product usage and purchase rates can be meaningfully investigated across nominally scaled market segments. This approach complements the repertoire of multivariate tools assembled by Wells, Banks, and Tigert in their analysis of housewife usage and purchase data [15].

5. Brand or product images as measured on semantic differential bipolar adjectives can be treated as a dependent vector variable with nominally scaled independent variables being samples from groups exposed to different kinds of copy--or simply different market segments or other categorizations. This is equivalent to using Hotelling's T2 test in the special case of measuring the same image in two groups [8].

The above examples are given only to emphasize the nature and scope of MANOVA applications in marketing, obviously, there are many others than can be cited.

SUMMARY AND CONCLUSIONS

This paper is designed to demonstrate (1) that subcultures within a given social structure have differential rates of diffusion, (2) that multivariate analysis of variance--while virtually unused by marketers--has a great number of potential applications in promotion and distribution and (3) that the nature of MANOVA is easy to grasp and utilize by marketers. While the objectives seem unrelated, in fact, the former needed a method of analysis and the latter required a concrete marketing example for purposes of exposition. It is felt that a synergistic integration has been achieved. Some conclusions include:

1. Differential rates of diffusion exist among the subcultures that comprise the categories of the nominally scaled variable. The generalized association as measured by Wilk's generalization of eta-square is .166, indicating significant relation between the nominal categories and innovative behavior.

2. Subsequent univariate analyses demonstrated that fraternity respondents were the most innovative with suburbanites the least innovative (see Tables 1 and 2).

3. The data suggest that footwear and trouser fashions are diffused at differential rates among groups.

4. Analysis and exposition suggests that multivariate analysis of variance is useful in analyzing a wide array of marketing problems.

REFERENCES

Banks, Seymour. Experimentation in Marketing. New York: McGraw-Hill Book Company, 1965.

Box, G. E. P. "A General Distribution Theory for a Class of Likelihood Criteria," Biometrika, 36 (1949), 317-46.

Cooley, William W. and Paul R. Lohnes. Multivariate Data Analysis. New York: John Wiley and Sons, Inc., 1971.

Cooley, William W. Multivariate Procedures for the Behavioral Science. John Wiley and Sons, Inc., 1962.

Darden, William R. and Fred D. Reynolds. "Predicting Opinion Leadership for Male Apparel Fashions," Journal of Marketing Research, 9 (August 19 72), 324-8.

Frank, Ronald A., William A. Massy and Yoram Wend. Market Segmentation. Englewood Cliffs, New Jersey: Prentice-Hall, Inc., 1972.

Green, Paul E. and Donald S. Tull. "Covariance Analysis in Marketing Experimentation," Journal of Advertising Research, 6 (June 1966), 45-53.

Hotelling, Harold. "The Generalization of Student's Ratio," Analysis of Mathematical Statistics, 2 (1931), 360-78.

Katz, Elihu and Paul F. Lazarsfeld. Personal Influence. Glencoe, Illinois: Free Press. 1955.

King, Charles W. and George E. Ryan. "Identifying the Innovator as a Consumer Change Agent," Proceedings, 2nd Annual Conference, Association for Consumer Research, 1971.

Rao, C. R. Advanced Statistical Methods in Biometric Research. New York: Wiley, 1952.

Robertson, Thomas S. Innovative Behavior and Communication. New York: Holt, Rinehart and Winston, 1971.

Rogers, Everett. Diffusion of Innovations. New York: Free Press, 1962.

Stone, Gregory P. "Appearance and Self," in Arnold M. Rose, ed., Human Behavior and Social Processes, Boston: Houghton Mifflin Company, 1962, 86-118.

Wells, William D., Seymour Banks and Douglas J. Tigert. "Order in the Data," in David T. Kollat, Roger D. Blackwell and James F. Engel, eds., Research in Consumer Behavior, New York: Holt, Rinehart 1970.

Wilks, S. S. "Certain Generalizations in the Analysis of Variance," Biometrika, 24 (1932), 471-94.

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##### Authors

William R. Darden, University of Georgia [Associate Professor of Marketing.]

Fred D. Reynolds, University of Georgia [Associate Professorsof Marketing.]

##### Volume

NA - Advances in Consumer Research Volume 01 | 1974

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