Comparison of Methods For Analyzing Sources of Perceived Differences in Products

Citation:

Alan B. Flaschner and Lyndon E. Dawson, Jr. (1972) ,"Comparison of Methods For Analyzing Sources of Perceived Differences in Products", in SV - Proceedings of the Third Annual Conference of the Association for Consumer Research, eds. M. Venkatesan, Chicago, IL : Association for Consumer Research, Pages: 536-545.

Proceedings of the Third Annual Conference of the Association for Consumer Research, 1972      Pages 536-545

COMPARISON OF METHODS FOR ANALYZING SOURCES OF PERCEIVED DIFFERENCES IN PRODUCTS

Alan B. Flaschner, University of Georgia

Lyndon E. Dawson, Jr., Northeast Louisiana University

[Alan B. Flaschner is an Assistant Professor of Marketing at the University of Georgia and Lyndon E. Dawson, Jr. is a Professor of Marketing and Management and Coordinator of Graduate Studies in Business Administration at Northeast Louisiana University.]

An attitude is the organization of concepts, beliefs, habits, and motives associated with a particular object or phenomenon (McKeachie and Doyle, 1966, p. 560). Consumer attitudes toward a product or service (an object or phenomenon) are viewed on the basis of several attributes which usually vary in terms of their relative "importance". ["Importance" is the desire or need for the presence of a particular attribute in a product (Schendel, Wilkie, and McCann, 1971, p.415).]

In order to develop appropriate marketing strategies, a marketing manager may wish to know the relative importance of the factors that contribute to the overall perceived differences between his product and those of competitors. An understanding of the relative importance of the evaluative criteria used by consumers, then, is the core of a consumer-oriented approach to marketing (Engel, Kollat and Blackwell, 1968, p. 439). For maximum effectiveness, the marketing manager must design and market products in a manner consistent with the evaluative criteria consumers use (Engel, Kollat and Blackwell, 1968, p. 439).

The purpose of this research is to compare and evaluate alternative techniques which may be useful in judging the importance of product attributes.

Typical methods for obtaining measures of attribute importance include a dichotomous scale (Important-Not Important) for each attribute, rank ordering of the attributes, gradient scales, (e.g., 1-6) for each attribute, and point assignments from a common sum for each attribute (Schendel, Wilkie, McCann, 1971, p. 404).

The work reported in this paper is based on the assumption that the variation between stimuli, evaluated on a particular attribute, indicates the relative importance of that attribute. For example, in the tradition of multidimensional scaling it is assumed that the more important a criterion, the greater will be the respondent's ability to discriminate between stimuli on that criterion (Green and Carmone, 1970, p. 63).

METHOD

The problem, then, is to measure the "importance" of various attributes of a product without asking the direct question, "How important is that attribute?" The technique chosen to accomplish the task is magnitude estimation. Magnitude estimation is a procedure of free or unconstrained number matching. As was .done in the present experiment the subject is given a reference point, or standard (a five percent alcoholic solution) which is assigned an arbitrary value such as 100. The subject indicates for each stimulus how it compares to the standard. For example, if, on a particular characteristic, the subject gives the stimulus a rating of 50, he is saying that it is half the standard on that characteristic; if, on a particular characteristic, he gives the stimulus a rating of 300 he is saying that it is 3 times the standard on that characteristic.

The assumptions underlying magnitude estimation are (1) that the range of numbers that can be assigned to a stimulus is unconstrained and (2) that estimation error will be random. That is, even though there may be wide variation between subjects, a subject's sense of the magnitude of a particular stimulus is valid. Given a random sample, it is assumed that if one subject overestimates another will underestimate; thereby, making the mean of the distribution the best estimate of the value of the stimulus.

STIMULI

The stimuli toward which the attitudes were measured were five (5) solutions of beer containing 5 percent, 7 percent, 9 percent, 11 percent, and 13 percent alcohol. To make sure that a relatively complete and unambiguous set of product characteristics were presented to the respondent (Schendel, Wilkie and McCann, 1971, p. 404) only attributes which fall within the cognitive-potency dimension (Engle, Kollat and Blackwell, 1968, p. 166) were used. "Strength, body, lightness, and sweetness" appear to be four mutually exclusive and all-inclusive "facts or beliefs" about beer.

SUBJECTS AND PROCEDURE

The nineteen volunteer subjects, whose attitudes were measured, varied between the ages of 18 and 26. The subjects who received the solution in random-order were asked to compare the solution to the standard on one randomly selected attribute. The subjects rated all five solutions (concentrations) on the randomly selected attribute before they rated the solutions on another randomly selected attribute.

RESULTS

Table 1 is a summation of the subjects' perceptions of the five (5) concentrations of beer on four (4) attributes.

As indicated in Table 2 parts A, B, C, and D, using .05 level of significance as the criterion, the subjects were able to perceive differences among the five concentrations on the basis of strength and body, but were not able to do so on the basis of lightness and sweetness. Table 2 parts A, B, C, and D, using the .05 level of significance as the criterion, indicates that the variation among subjects was significant when they estimated the strength, body and lightness of the concentrations but was not significant when they estimated the sweetness of the concentrations. While it is acknowledged that the authors could have increased the sample size, without an increase in the variation among subjects, the increase in sample size would cause the variation among subjects to be significant.

Using the .05 level of significance as the criterion, Table 3, in which the experiment is treated as a complete factorial design (4 attributes x 5 concentrations x 19 subjects) with no replications and the three-way interaction term (attributes x concentrations x subjects) is used as the error term, indicates that there was a significant difference among attributes.

DETERMINING ATTRIBUTE IMPORTANCE

The authors have shown that there was a significant difference among attributes. The relative importance of the attributes can be determined in several ways.

TABLE 1

PERCEPTION OF MAGNITUDE (AVERAGE ACROSS SUBJECTS, VARIATION AMONG SUBJECTS)

TABLE 2

RANDOMIZED BLOCK DESIGN

TABLE 3

INCOMPLETE FACTORIAL DESIGN (SUBJECTS X CONCENTRATIONS X ATTRIBUTES)

One method of determining attribute importance is to examine the range of magnitude estimates. Discrimination theory leads one to believe that the perception of the difference between stimuli is a function of the relevance of that perception to the perceiver. Magnitude estimates, being ratio data, suggest that if the perceived difference between stimuli on one attribute is greater than the perceived difference between stimuli on another attribute and if this greater perceived difference between differences is caused by a greater importance of that attribute to the perceiver; then, by reverse logic, the attribute on which the concentrations are perceived to be most different is the most important to the respondent and the other attributes are correspondingly less important.

Welch (1971, pp. 76-87) suggests that the arithmetic mean consistently overestimates the central tendency of pooled ratio information. Using the geometrically averaged magnitude estimates to correct for this bias, Table 1 indicates that on the basis of: strength, the highest estimate is 5.82 times the lowest estimate; on the basis of body, the highest estimate is 1.68 times the lowest estimate; on the basis of lightness, the highest estimate is 2.16 times the lowest estimate; and on the basis of sweetness, the highest estimate is 7.1 times the lowest estimate.

This method of estimating attribute importance allows one to state the degree to which one attribute is more important than another. For example, based on Table 1, one can say that sweetness in beer is 1.22 (7.1/5.82) times as important to the respondents as is strength, that sweetness is 4.22 (7.1/1.68) times as important to the respondents as is body, that strength is 3.46 (5.82/1.68) times as important to the respondents as is body, etc.

The problem with this method of estimating attribute importance is that it fails to consider the expected monotonic relationship between the alcohol concentrations and the corresponding magnitude estimates.

A second method of determining attribute importance is to examine the degree to which the magnitude estimates for the various concentrations of alcohol fit the equation:

R = kSⁿ

"where R is the subjective, or response, magnitude in arbitrary units; S is the stimulus magnitude in physical units (alcohol concentrations of 5 percent, 7 percent, 9 percent, 11 percent and 13 percent); n is an empirical but non-arbitrary exponent; and k is an empirical constant dependent on the value assigned to the standard (100)" (Welch, 1971, p. 76). Because this simple power function has been found to hold for more than three dozen sensory continua (Stevens and Galanter, 1957), Welch (1971), Stevens (1957) and Shinn (1969) propose that the observed psychophysical relationship in which equal stimulus ratios produce equal perceptual ratios has achieved the status of a natural law (Stevens and Galanter, 1957, pp. 377-411; Welch, 1971, pp. 76-87; Stevens, 1957, pp. 153181: Shinn. 1969).

By reverse logic, the attribute on which the concentrations are perceived to be most in accord with the power function is the most important to the respondents and the other attributes are correspondingly less important.

Table 4, in which is presented the amount of variation in the geometrically averaged magnitude estimates that can be explained by knowledge of the alcohol concentrations, shows that the most important attribute is "strength, the next most important attribute is "sweetness" etc.

By using the degree to which the data fits the power function as a test of attribute relevance, we are able to show which attribute is more important but are unable to show the degree to which it is more important.

A third method for unobtrusively estimating attribute importance consists of running estimates of the "overall" perceived differences between the stimuli through a multistage nometric multidimensional scaling program. Since the first dimension that is derived from a multidimensional scaling program explains the majority of the variance between the products and the second dimension explains a little less of the variance, etc., the order in which the dimensions are listed indicates their degree of contribution to the "overall" perceived differences between the stimuli. A high degree of correlation between these calculated dimensions and the original attributes should indicate possible labels for the dimensions.

The influence of which solution was chosen as the standard was removed by using a normalization procedure based on the median (Thorndike, 1922, pp. 116121) to rescale the data on each attribute.

Based on the assumption that a stimulus compared to a standard must bear a ratio relationship to another stimulus compared to the same standard in the present experiment the magnitude scalings were converted to paired comparison information (data that is appropriate for input to a multidimensional scaling program). The "overall" perceived difference between stimuli for an individual was calculated by using an expansion of the Pythagorean theorem for a 4 dimensional space. For an individual, the overall perceived difference between the two stimuli D. (say the .05 percent and .07 percent alcohol concentrations) was the square root of the squares of the perceived difference between the stimuli summed over the four attributes.

EQUATION

where:

D = overall perceived difference between concentrations, given:

j = alcohol concentration

k = alcohol concentration other than j

X = magnitude estimate, given:

i = particular attribute on which the magnitude estimate was made

j = alcohol concentration

k = alcohol concentration other than j

n = 4, the number of attributes on which the magnitude estimates were made.

The geometric average of the 19 Djk, the "overall" estimates of the perceived difference between the stimuli, were used as input to TORSCA, a nometric multidimensional scaling program (Young, 1968, pp. 319-321). For the one dimensional solution (see Table 5), satisfactory stress of 0.0 was achieved. This means that one dimension explains the overall perceived difference between the concentrations and it makes little sense to discuss the two, three or four dimensional solutions.

To fit the power function, R = kSⁿ all R values must be positive and greater than 0.0. Retaining the distance between stimuli (retaining the interval between them), the configuration was revised by adding 1.0 to each value. As is indicated in Table 6, when the revised configuration is fit by the power function R = kSⁿ, 98 percent of the variation in R (the revised configuration) can be explained by knowledge of S (the alcohol concentrations).

Correlation between the TORSCA created values and the Thorndike (1922) rescaled perceptions, indicates that the configuration is "strength" (see Table 7). The coefficient of stress in this configuration (0.0) indicates that strength and only strength was the attribute the respondents were considering when asked to evaluate concentrations on the basis of strength, body, lightness, and sweetness.

CONCLUSION

In an experiment in which the respondents estimated the magnitude of five alcohol concentrations of beer on four attributes the authors attempted to unobtrusively estimate attribute importance.

Based on the assumption that the perception of greater differences reflects greater importance, the ratio data revealed that the attributes could be ranked in terms of importance as follows: (1) sweetness, (2) strength, (3) lightness, (4) body. This method considered the degree to which one attribute was more relevant than another but ignored the expected monotonic nature of the data.

Based on the assumption that the better the magnitude estimates on a particular attribute fit the power function R - kS the more relevant is that attribute, the ratio data revealed that the attributes could be ranked in terms of their importance as follows: (1) strength, (2) sweetness, (3) lightness, and (4) body. This method considered the monotonic nature of the data but ignored the degree to which one attribute was more relevant than another.

Rescaling the data, then collapsing the attributes into an "overall" estimate of the perceived difference between stimuli, multidimensional scaling revealed that the only attribute that was important to the subjects was "strength, the other attributes being unimportant. Because it considers both the degree of importance of the attributes as well as the monotonic nature of the data, multidimensional scaling seems to hold the most promise for unobtrusive attribute importance estimation.

REFERENCES

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Green, P. E. & Carmone, F. J. Multidimensional Scaling and Related Techniques in Marketing Analysis. Boston: Allyn and Bacon, Inc., 1970.

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Shinn, A. M., Jr. The Application of Psychophysical Scaling Techniques to Measurement of Political Variables, Working papers in Methodology No. 3. Chapel Hill: University of North Carolina, Institute for Research in Social Science. 1969.

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Stevens, S. S. & Galanter, E. Ratio Scales and Category Scales for a Dozen Perceptual Continua. Journal of Experimental Psychology, 1957, 54, 377-411.

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Welch, R. E., Jr. The Use of Magnitude Estimation in Attitude Scaling: Constructing a Measure of Political Dissatisfaction. Social Science Quarterly, 1971, 52, 76-87.

Young, F. W. TORSCA, an IBM Program for Nometric Multidimensional Scaling. Journal of Marketing Research, 1968, 5, 319-321.

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