Equivalence Range in Categorization

ABSTRACT - To test equivalence range preference in categorization, several sorting, band-width tasks were given to respondents. Analysis of these sorting and band-width tasks demonstrated large individual differences in the number of categories used and width of categories preferred. Correlations within categorization task type and, to a lesser extent, between task types lends support to the hypothesis of preferred equivalence ranges.


Jonathan Gutman (1980) ,"Equivalence Range in Categorization", in NA - Advances in Consumer Research Volume 07, eds. Jerry C. Olson, Ann Abor, MI : Association for Consumer Research, Pages: 411-416.

Advances in Consumer Research Volume 7, 1980     Pages 411-416


Jonathan Gutman, University of Southern California


To test equivalence range preference in categorization, several sorting, band-width tasks were given to respondents. Analysis of these sorting and band-width tasks demonstrated large individual differences in the number of categories used and width of categories preferred. Correlations within categorization task type and, to a lesser extent, between task types lends support to the hypothesis of preferred equivalence ranges.


"To categorize is to render discriminably different things equivalent, to group the objects and events and people around us into classes, and to respond to them in terms of their class membership rather than their uniqueness" (Bruner, Goodnow, and Austin, 1956, p- 1). Categorizing is inherently a cognitive task as opposed to being perceptual. "When two things are classified together perceptually, it is because differences between them are not taken into account; when things are classified together conceptually, it is because differences between them are actively disregarded" (Anderson, 1975, p. 226).

The act of categorizing creates equivalence categories which are essential to the maintenance of an orderly flow of behavior in a changing environment. If consumers did not deliberately ignore some of the diversity in their environment, they would be overwhelmed by it. One important way this reduction in complexity manifests itself in consumer behavior is through the concept of product class. Howard (1977, p. 8) suggests that the concept of product class is fundamental to understanding consumer behavior. He goes on to define a product class as a group of brands consumers view as close substitutes. In effect, a product class is an equivalence category--a group of objects which are cognitively equivalent insofar as some aspects of their consumption is concerned. The narrowness or breadth of the product class is a function of the individual consumer's perception of potential brands and his or her predisposition toward broad or narrow cognitive categorization.

Equivalence as a concept has been amply demonstrated by the work of Bruner and his colleagues (Bruner et al., 1966). That equivalence ranges vary across people comes to us from studies which seek to demonstrate that equivalence range is a generalized trait within people (Pettigrew, 1958; Sloane, Gorlow, and Jackson, 1963). Equivalence has also been shown to be a function of attitude (Sherif and Sherif, 1967), culture (Bruner et al., 1966, pp. 68-85; pp. 257-318), personality (Pettigrew, 1958; Zajonc, 1960), cognitive style (Sloane, Gorlow, Jackson, 1963) or experience with the objects to be categorized (Luborsky, 1945).

Sloane, Gorlow, and Jackson (1963) studied cognitive style in equivalence range through a number of cognitive tasks devised to measure different styles of cognizing behavior. Three general factors were extracted from the correlations among the cognitive tasks. The first factor was Sorting Equivalence Range, which pertained to all the sorting tasks. The second factor was Conceptual Bandwidth, which appeared to measured subject's willingness to assign conceptually remote stimuli to a given category. The third factor was a Verbal Factor in terms of strength of association between comparison stimuli and verbal referents. This research, while encouraging, suggests that there is more than one factor at work in determining response to different tasks all purporting to measure equivalence range.

If equivalence range is shown to have some independence from the objects used to demonstrate its existence and can be shown to be a matter of personality or cognitive style, it becomes subject to individual differences-These individual differences, in turn, become bases for understanding why people differ with respect to the behaviors they exhibit as consumers.

When faced with a set of stimuli, people often organize them into clusters to reduce information load and facilitate further processing (Tversky & Gati, 1978). These groupings represent a basis for establishing an initial similarity among objects grouped together and are mutually determined by object properties and value-determined criteria for goal instrumentality. It seems reasonable to assume that consumers who create many smaller object clusters do so on different bases than do consumers who create a few larger clusters.

Rosch's discussion of basic level categories (Rosch, 1978) is appropriate here. A basic level category is one which is at the appropriate level of abstraction for that individual. This means that one strikes a balance between creating highly homogeneous categories and more heterogeneous ones. If one creates homogeneous groupings, then objects in some categories will bear a high resemblance to objects in some other categories. If one creates heterogeneous groupings, then objects within categories will be dissimilar in some respects.

If equivalence range is a generalized orientation, some consumers would have broad-gauge categories into which they would group products, and others would have tightly-defined categories. Such tendencies would transcend product class involvement and would be an independent variable for study. Knowledge of such a variable could assist in fine-tuning marketing programs by providing a clearer understanding of how product classes are perceived by consumers. Such a perspective would also seem useful in developing advertising copy that would address itself to appropriate levels of abstraction by factoring the ways consumers go about creating equivalences.


The purpose of this research is to demonstrate the extent to which individual differences exist in equivalence ranges. The degree of consistency in equivalence range will also be assessed by having respondents engage in a variety of equivalence range tasks.



Four phases comprised the research sequence to which each subject was exposed. First, subjects were given 18 breakfast cereals to sort (each one on a slip of paper) into as many categories as they felt they needed (see Table 1). The sorting task was presented first so as to avoid any bias that the subsequent tasks might have. Secondly, subjects were asked to array these cereals with respect to how "crunchy" the cereals were on a 0 to 100 scale, and, subsequently, how "nutritious" they were. Each respondent was asked to indicate respectively how many cereals he or she would classify as "crunchy" or "nutritious," by specifying a minimum level on the 0 to 100 scale.

The third phase of research entailed sortings of two sets of words (see Table 1) into categories such that words with similar meanings were put into the same categories. One set of words described the textures of various foods; the other set of words involved some of the effects food has on us (e.g., nutritious, fattening, etc.). The measure here, as in Phase I, involved the number of categories used by the respondents in creating equivalence groupings. In the last phase of the research, respondents rated the importance of nutrition to good health and the importance of choice of breakfast cereal.




Respondents were students in introductory psychology classes at the University of Southern California. All respondents spoke English as their native language, thus reducing language as a source of bias and increasing the likelihood of familiarity with all the cereals. They participated in the experiment as part of their course requirements. Two hundred respondents were administered the questionnaire in five groups. Respondents were asked to omit from the sorting and rating any cereal they did not know well enough to rate. Thirty respondents were eliminated for having incomplete data, leaving 170 cases for analysis.


Numbers of Categories Used in Sorting Tasks

Table 2 shows the means and distributions of the number of categories used in the three sorting tasks. The average number of categories used in the three tasks varies between 4.5 and 6. The number of categories used in sorting the words was greater than that used for the cereals (probably because of greater diversity of stimuli). There is considerable variability in the number of categories used across respondents. Some respondents were satisfied in using only two groups; others felt the need to make finer distinctions (the maximum number of categories used was 11).

Table 3 shows the distribution of numbers of cereals per category for persons using two to eight or more categories for their cereal sorts. Obviously, as the number of categories gets larger, the number of cereals per category gets smaller. It should also be noted that persons using a larger number of categories (up to 6 categories) show a predominance of using similar sized groupings rather than one large group and several small ones. There is a sizable percentage of single cereal groups for those persons using 7 and 8 or more categories. As people become less willing to treat different objects as equivalent, the objects under consideration tend to be treated as "one of a kind."

More objects are placed in single categories for the texture word sort (Table 4) and food-effect word sort (Table 5) than for the cereal sort. Inspection of the words use (see Table 1) shouldn't make this a surprising finding. Nevertheless, for respondents using less than 7 categories for the texture words and less than 5 categories for the food effect words there is only a small percentage using categories containing only one word.

Band-Width Tasks

Table 6 shows the lower limits of the "crunchy" and "nutritious" categories. Both limit estimates are about identical at just over 50. Respondents evidently used the mid-point of the 100-point scale in ascribing crunchiness and nutritiousness to cereals. There is, however, considerable variability. Along with this variation in limits is the number of cereals ascribed to the crunchy and nutritious categories. The average number of cereals is about the same in each case (10.4 and 11.0 respectively), but, again, there is considerable variability about these means from a minimum of two cereals to a maximum of 17 cereals described as "crunchy" and "nutritious." In effect, some people would say that, other than oatmeal and cream of wheat, every cereal is "crunchy." Others would say that, other than Cap'n Crunch and Grape Nuts, no cereals are "crunchy."

Intercorrelations Among Tasks

Table 7 shows the correlations between the various tasks respondents performed. The three groups of tasks are sorting tasks (the cereal sort and the two word-sorting tasks), band-width tasks (for limits of crunchy and nutritious dimensions), and importance ratings of nutrition and cereal choice. The results show that correlations which significantly differ from zero are within types of tasks, and, for the most part, not between tasks. The highest set of correlations occur within the band-width tasks, where high correlations occur between lower-limit estimates of crunchiness and nutrition and the number of cereals included in the category (-.66 and -.63). The wider the category (the lower the boundary), the more cereals were included within it. There are also significant correlations between the lower limits of the crunchy and nutritious boundaries used by respondents as well as the number of cereals included in the categories (.42 and .35 respectively).





The correlations among the three sorting tasks are lower than the band-width correlations, but still significantly different from zero. The number of categories used in the two-word sorting tasks have a Pearson correlation of .52, whereas the correlations of the number of categories used in cereal sort has a lower correlation with the number of categories used in the two word sorting tasks (.22 and .33).

The correlations of importance of nutrition with the number of categories used in the cereal sort is statistically significant from zero but lower still (-.19) than the other correlations within tasks. There is a low, but statistically significant from zero (p < .05), correlation of .14 between importance of crunchiness and number of cereals placed in the "crunchy" category. Other correlations between task types are essentially zero. Thus, there seems to be some support for equivalence range within task types but not between them.

Relation of Importance of Nutrition to Number of Categories Used In Sorting Cereals and Food Effect Words

There isn't much variation in the ratings for importance of nutrition to general health. Only eleven people of 170 rated importance of nutrition below the top two scale values on a 5-point scale. However, this group did use significantly fewer categories in sorting the cereals than those in the high-rating group (4.72 categories vs. 3.27 categories used on average).






The correlations within task type but not between task types offer support for Sloane, Gorlow, and Jackson's (1963) finding of factor-types relating to sorting equivalence and conceptual band-width. Results also lend support to the notion that people who are more involved with a subject area have more highly developed cognitive structures (Scott, 1962) and, hence, use more categories in classifying objects.

This research has offered limited support for a preference for the number of categories used in creating equivalence groupings. Since no two objects categorized in the tasks used in this study are identical, respondents had to make their own decisions as to the cut-off limits of what was alike and different. This is obviously a cognitive choice, not a perceptual threshold phenomenon. People seek a level of abstraction at which they feel comfortable--at which intracategory homogeneity is balanced by intercategory heterogeneity. It is hard to maximize both, simultaneously.





These findings can be viewed relative to an alternative sorting task. Respondents could have been asked to perform a phenomenological hierarchical clustering exercise. The first step would be to put the two most similar objects together from the 18 objects; then of the 17 remaining nodes, the two most similar would then be grouped, and so forth, until the subject could or would go no further. (This experimenter doubts that many respondents would reduce the 18 objects to two groups.) For each respondent the question is where in this hierarchy would his or her sort in the present study match up most closely. The continuum stretches from distinctions that are perhaps too fine to those that are perhaps too broad. Somewhere along that continuum is the preferred level.

In this context, equivalence range preference is conceptualized as a response set phenomenon. Response set or bias has been viewed as a response to a test item that tends to be altered so as to indicate something other than that which the item was intended to measure (Guildford, 1954, P. 451). Some response sets represent enduring qualities that represent consistent behavior over time. It is important to remember that we are not measuring consumers' abilities to make distinctions, but rather their preferences for making distinctions. And, their preferred level of discrimination depends on the instructions they are operating under or their reason for making these discriminations.

The hierarchical clustering example itself can be viewed as a special case of multiple sorting. In multiple sorting tasks, the respondent is given more than one opportunity to sort the objects so that any single sort doesn't have to represent all that the respondent wants to express about the objects. A better model is to compare the single sorting opportunity such as in the present experiment with multiple sorting task instructions to respondents that they may have as many opportunities to sort the objects as they desire (see Rosenberg and Kim, 1975, for an example). A single sort should encourage the respondent "to make his or her personal statement" in his or her sort.

The ultimate goal is to determine how decision-making needs and style relate to the preferred level of categorization or equivalence range. If consumers group objects to simplify and reduce information processing, then these groupings should be tied to the objectives they are pursuing and how they are pursuing them. Further research in this area will deal more closely with the issue of product class definition. This is an area that brings all these issues together in the context of substitutability of means for desired ends.


Anderson, B. F. (1975), Cognitive Psychology, New York: Academic Press.

Bruner, J. S., Goodnow, J., and Austin, G. A. (]956), A Study of Thinking, New York: John Wiley & Sons, Inc.

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Pettigrew, T. F. (1948), "The Measurement and Correlates of Category Width as a Cognitive Variable," Journal of Personality, 26, 532-544.

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Sherif, M., and Sherif, C. W. (1967), "The Own Categories Procedure in Attitude Research" in Fishbein, M. ed., Readings in Attitude Theory and Measurement, New York: John Wiley & Sons, Inc.

Sloane, H. N., Gorlow, L., and Jackson, D. N. (1963), "Cognitive Styles in Equivalence Range," Perceptual and Motor Skills, 16: 389-404.

Tversky, A. and Gati, I. (1978), "Studies of Similarity,'' in Cognition and Categorization, E. Rosch and B. Lloyd, eds., Hillsdale, New Jersey: John Wiley and Sons, 81-98.

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Jonathan Gutman, University of Southern California


NA - Advances in Consumer Research Volume 07 | 1980

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