The Effects of Range-Frequency Manipulations on Conjoint Importance Weight Stability

ABSTRACT - The effect of range-frequency manipulations on the attribute levels of a conjoint stimulus set was tested experimentally by manipulating 1) the number of levels of a given attribute and, 2) the range of values for those levels and testing 1) the relative (conjoint derived) importance of that attribute, 2) the relationship between the part-worths of that attribute, and 3) the subjects' subjective (self-explicated) importance rating for that attribute. Analysis of the results indicated that both the relative (conjoint derived) and the subjective (self-explicated) importances of the attribute were affected by the range manipulation. However, the frequency manipulation affected only the relative importance, not the subjective-importance. Finally, the relationship between the part-worths of the attribute was not affected by either of the manipulations.

Citation:

Elizabeth Creyer and William T. Ross (1988) ,"The Effects of Range-Frequency Manipulations on Conjoint Importance Weight Stability", in NA - Advances in Consumer Research Volume 15, eds. Micheal J. Houston, Provo, UT : Association for Consumer Research, Pages: 505-509.

Advances in Consumer Research Volume 15, 1988      Pages 505-509

THE EFFECTS OF RANGE-FREQUENCY MANIPULATIONS ON CONJOINT IMPORTANCE WEIGHT STABILITY

Elizabeth Creyer, New York University

William T. Ross, The Wharton School, University of Pennsylvania

ABSTRACT -

The effect of range-frequency manipulations on the attribute levels of a conjoint stimulus set was tested experimentally by manipulating 1) the number of levels of a given attribute and, 2) the range of values for those levels and testing 1) the relative (conjoint derived) importance of that attribute, 2) the relationship between the part-worths of that attribute, and 3) the subjects' subjective (self-explicated) importance rating for that attribute. Analysis of the results indicated that both the relative (conjoint derived) and the subjective (self-explicated) importances of the attribute were affected by the range manipulation. However, the frequency manipulation affected only the relative importance, not the subjective-importance. Finally, the relationship between the part-worths of the attribute was not affected by either of the manipulations.

INTRODUCTION

Since its introduction in the early 1970s, conjoint analysis has become one of the primary techniques used by marketing researchers to ascertain consumers' reactions to both existing products and new product concepts (Cattin and Wittink 1982). Commercial and academic research projects employing some form of conjoint analysis have been quite numerous during the last ten years (Green 1984, Cattin and Wittink 1982). As conjoint analysis has become an increasingly popular research tool, reliability estimation and stimulus set design for conjoint analyses have received a corresponding increase in attention.

Bateson, Reibstein, and Boulding (1985) review a number of studies that address the issue of conjoint analysis reliability, including the reliability of conjoint analysis over time (e.g., Acito 1977, McCullough and Best 1979, Segal 1982), stimulus set (e g., Green 1974), data collection method (e.g., Cattin and Wittink 1982), and attribute set (e.g., Johnson 1974, Malhotra 1982). The effect of various estimation techniques on the stability of results has been the focus of another research stream (e.g., Jain et al 1979, Acito and Jain 1980). However, the least amount of attention in this area has been paid to stimulus set design. Issues of reliability and estimation are of secondary concern if relatively small differences in the chosen stimulus set strongly influence the study's results.

Although some research has examined the effects of stimulus set design (Chakravarti and Lynch 1983, Wittink et al 1982), it has received relatively little attention. In addition, much of the research which has been done lacks theoretical structure, with the exception, though limited to range effects, of Chakravarti and Lynch (1983). The current study uses Parducci's (1966, 1974) range frequency theory of context effects as a framework from which to develop manipulations of the stimulus set. The effects of these manipulations on subjects' perceptions of the importance of attributes and levels of attributes are examined.

Thus, the present research investigates whether the part-worths for the levels of a given attribute and the relative importance level of that attribute remain stable as 1) the range of the levels of that attribute is manipulated and, 2) the number of levels used to define that attribute (e.g., two versus four levels) is manipulated. However, because of the use of Parducci's framework, this study goes beyond studying effects on relative (derived) importance stability to investigate the effects of these manipulations on subjects' subjective (directly elicited) importance ratings of the attribute involved.

The section which follows is a review of Parducci's range-frequency theory and those studies which have considered manipulation of the basic stimulus set in conjoint analysis, combined with a set of hypotheses which are derived from this review. Next, two sections which describe the method and results of an experiment which tested these hypotheses are presented. Finally, a discussion of the implications of the research findings for marketing practitioners and theoreticians is presented.

RANGE-FREQUENCY CONTEXT EFFECTS IN JUDGMENT

Individuals make a number of judgments each day, ranging from judging the similarity of two competing brands in a supermarket to estimating the speed of an oncoming vehicle which has moved into one's lane to pass a slower vehicle. Extensive research conducted in the social sciences has shown that an individual's judgment does not depend solely on the attributes of the stimulus object, but also on the context within which the stimulus is presented. The nature of the effect of context on an individual's judgment will be discussed below.

Much of the early work (e.g., Helson 1964, Parducci 1966) which investigated the effects of context on judgments dealt exclusively with unidimensional stimuli. For example, a typical experimental task would be to apply naturalistic verbal categories (e.g., very light) to a sequence of weights. Research indicated, not surprisingly, that whether a weight was judged very heavy or very light depended on the context within which it was presented. For example, if a subject was asked to assign verbal categories to weights ranging from 100 to 600 grams, the 100 gram weight would be considered very light. However, when the task was to assign verbal categories to weights from 10 to 100 grams, the 100 gram weight was judged very heavy.

Parducci (1966) developed a range-frequency model to account for this phenomenon. According to his theory, there are two fundamental features of the stimulus context that influence an individual's judgment process. First, the individual uses categories to divide the psychological range. A category refers to a subrange and the number of subranges depends only on the number of categories, not on stimulus conditions. For example, a subject asked to judge weights may decide to use three categories--light, moderate, and heavy. Thus, each category corresponds to one-third of the range. According to the range principle, that subject's judgment is not affected by the frequency of items--one-third of the items are always in each category.

Second, an individual uses each category for a specific proportion of his or her judgments. This is the frequency principle. Unlike the range principle, the frequency principle assumes that an individual's judgments are affected by the frequency of the stimuli. For example, if the subject was asked to place a series of weights into three categories, and there were a greater number of light weights than moderate and heavy weights, then the light category would contain a greater percentage of weights than the other two categories.

A linear combination of the range and frequency principles can be used to predict the category to which a stimulus will be assigned. That is,

J_i = (R_i + F_i) / 2       (1)

where

J_i = judgment for ith stimulus

R_i = range value of ith stimulus

F_i = frequency value of ith stimulus

The range value of the ith stimulus is the hypothetical rating of that stimulus if there were no frequency effects and depends solely on the relationship between the stimulus and the two end points. The frequency value is the hypothetical mean rating of the ith stimulus if each of the categories had been assigned a fixed proportion of the stimulus presentations (Parducci 1974). Parducci and his colleagues found the range-frequency model to account for over 80% of the variance of the context effects associated with differences in item spacing and frequency.

Context effects are more complicated to understand when the stimuli are multidimensional (e.g., a conjoint stimuli). A study by Chakravarti and Lynch (1983b) investigated range effects within the context of conjoint analysis by extending the range of an attribute to see if that reduced the derived differences in utility between the two levels of that attribute in the control condition. They found that, while ratings of the control stimuli were affected by the range manipulations, there were no significant changes in the overall rank order of the profiles. However, Mellers ( 1982) found that rank order of the profiles did change as a function of context. She presented scattergrams to subjects that contained a numerical rating of faculty members and their salaries. The subjects' tasks were to determine how over-benefitted or under-benefitted each of the faculty members were. She found that subjects' judgments of under-benefitted versus over-benefitted changed systematically as a function of context.

Frequency effects have received less attention than range effects, perhaps due to the fact that "range" is both a more obvious and a more effective feature of a stimulus context. That is, perhaps range effects are easier to empirically demonstrate than frequency effects. Still, Currim, Weinberg and Wittink (1981) found that attribute importance weights from a conjoint analysis are influenced by the number of levels used to define that attribute. In a study of rank order preferences for subscription plans to a performing arts series, they found that attributes defined on three levels were judged more important than attributes defined on two levels. They presented a mathematical explanation for this finding based on work by Krishnamurthi and Wittink (1983). These findings were replicated by Wittink, Krishnamurthi, and Nutter (1982).

We argue from Parducci's theory that both range and frequency effects can be specified for conjoint stimulus sets. While the precise effects of range remain unclear, there have been such effects in all research to date. Wittink et al's (1982) findings of number of level effects on attribute importance also suggest that frequency effects are at work in a conjoint task. Hence, we develop the following hypotheses with respect to derived attribute importance.

H1a: An increase in the overall range of the values of the levels of a given attribute will increase the relative importance of that attribute.

H1b: An increase in the number of levels used to define a given attribute will increase the relative importance weight of that attribute.

Based on Parducci's hypothesis with respect to weights, it can be hypothesized that two levels of an attribute will be valued differently depending on where they occur in the range of stimuli (Chakravarti and Lynch 1983). For example, in conjoint analysis, the levels 20 and 30 MPG for the attribute "miles per gallon" may have S lower relative importance difference when the level values range from 10 to 40 "miles per gallon" than when the level values range from 20 to 30 "miles per gallon". An opposite argument can be made for frequency effects. That is, if 20 and 30 MPG are the extreme points of a range which contains four rather than two levels, they should be further apart in relative importance. This notion, if true, has serious implications for conjoint based research. As a result, we hypothesize

H2a: An increase in the range of the level values of a given attribute will increase the relative importance weight of the extreme values of that attribute.

H2b: An increase in the number of levels used to define a given attribute will increase the relative importance weight of the extreme values of that attribute.

If Parducci's (1966) theory holds for conjoint stimuli, we are able to posit that subjects' actual perceptions of an attribute's importance are affected by both the range of level values assigned to the attribute and by the number of levels assigned to that attribute. Specifically, subjects' subjective (directly elicited) ratings of the importance of the manipulated attributes will be consistent with the derived attribute importance weights from the conjoint analysis. Thus,

H3a: Subjects' subjective importance ratings for an attribute will be higher when the range of values for that attribute are greater.

H3b: Subjects' subjective importance ratings for an attribute will be higher when that attribute has four levels than when that attribute has two levels.

METHOD

Design overview. To test the above hypotheses we employed a 3 cell design manipulating the levels of a single attribute of a seven attribute conjoint task. The three cells included a control cell, a frequency manipulated cell, and a range manipulated cell. The conjoint task was followed by a thirty minute distractor task and, finally, a task in which the subjects reported the subjective importance to their purchase of an automobile of each of the attributes from the conjoint task. In the conjoint task, subjects rated (on a scale from 1 to 7) 32 profiles, each with seven attributes. Automobiles were chosen as the product class to ensure that the subjects would be reasonably interested in and knowledgeable of the product.

Subjects. The subjects were two groups: 1) 89 undergraduate students at a private Southeastern University who participated in partial fulfillment of the requirements for an introductory Psychology course, and 2) 47 undergraduate students at the same university who participated as a classroom exercise in an introductory marketing course.

Stimuli. Stimuli for the first task were 32 conjoint profiles developed from an orthogonal, main effects, fractional factorial design (Addelman, 1962, Basic Plan 7, p. 39). As noted above, automobiles were used as the product class in the conjoint task. Each profile was described by seven attributes: country of origin, miles per gallon (MPG), body style, transmission type, top speed, price, and wheel size. Body style, transmission type, and top speed were four level attributes. Price and country of origin were defined on three levels and wheel size was defined on two levels. Finally, MPG was the attribute involved in the manipulation described in the following subsection. The seven attributes are detailed in Figure A.

FIGURE A

ATTRIBUTES AND LEVELS

The conjoint task was presented as a paper and pencil task with instructions on the first page, followed by the profiles listed one per line with the seven attributes listed across the page followed by a space for evaluating the profile. Evaluation of the profile was on a scale from 1 to 7 with 1 indicating high preference and 7 indicating low preference.

The stimulus for the final task consisted of a single sheet of paper with instructions at the top on which subjects rated the importance of each of the seven attributes from the conjoint task when purchasing an automobile. Rating was on a scale from 0 to 100 where the most important attribute had to be valued at 100, ties were allowed, and the least important attribute did not have to be valued at zero. This scale was chosen to ensure a ratio scaled response.

Design. The attribute MPG was varied with respect to the 1) range of the levels of the attribute and 2) number of levels used to define an attribute. Subjects in the extended range cell responded to a conjoint task in which MPG was defined on four levels (10, 25, 40, and 55). Subjects in the increased frequency cell responded to a conjoint task in which the MPG attribute was also a four level attribute, but with levels of 25, 30, 35, and 40. Finally, subjects in the control cell responded to a conjoint task in which the MPG attribute was a two level attribute with levels of 25 and 40. Other than differences in the attribute MPG, all other facets (instructions, attributes, profile order, and profile wording) of the task were held constant. Thus, comparison of cell 1 with cell 2 directly tests the range hypotheses (H1a, H2a, and H3a); comparison of cell 2 with cell 3 tests the frequency hypotheses (H1b, H2b, and H3b).

Procedure. Subjects from the psychology pool attended one of two sessions, each consisting of approximately 45 students. On entry to the auditorium, each subject of the first group was randomly given one of the three versions of the stimuli in a packet containing the stimuli for all of the experimental tasks. After receiving the packets, subjects sat anywhere in the auditorium, and worked through the packet at their own pace. On completion of the tasks, they returned the packet to the experimenters, received a debriefing sheet, and left the auditorium. Students from the second group took part during a class session. They performed the first task, carried on with class, and then completed the final task at the end of class.

Dependent Variables. The dependent variable for the conjoint tests was Green's index of relative importance (Green and Wind, 1975). This index is calculated from an Ordinary Least Squares regression of each subject's ratings of the stimulus profiles on a dummy variable design representing the various levels of the attributes involved. The index is calculated as the coefficient of the highest rated level for an attribute minus the lesser of zero or the lowest rated level for that attribute normalized such that the importances of all of the attributes sum to one. This index is based on the assumption that a large coefficient indicates attribute salience to the subject.

Green's relative importance index is used without modification for our tests of hypotheses H1a and H1b (the relative (derived) importance hypotheses). A modification, used to test H2a and H2b, involves calculating the index for the two constant levels, 25 and 40, exactly as if they are the extremes of an attribute, a modification which is intuitively appealing and identical to the original index when utilities are monotonic. The dependent variables for our tests of hypotheses H3a and H3b are the subjects' subjective (self-explicated) evaluations of the importance of the attributes involved.

RESULTS

Table 1 presents the results of our analyses. The following two sub-sections describe these results in some detail.

TABLE 1

CELL MEANS

Range Effects Analyses Tests of the range effects hypotheses involved planned comparisons between cell 1, the range manipulated cell, and cell 2, the frequency manipulated cell. The two cells were significantly different for two of the three dependent variables at the .05 level. The mean for relative importance (Hypothesis la) for the MPG attribute was .287 and significant at the p < .0001 level. The means for subjective importance (Hypothesis 3a) were 87.17 and 78.71, a difference of over 10% and significant at the p < .025 level. However, the means for the levels 25 and 40 (Hypothesis 2a) were .100 and .114, a difference of 14% in the right direction, but not significant. In summary, Hypotheses 1a and 3a, that both the relative and subjective importances of the attribute are affected by the range manipulation, were supported. Hypothesis 2a, that the importance between two internal levels would be affected by the range manipulation, was not supported.

Frequency Effects Analyses. Tests of the frequency effects hypotheses involved planned comparisons between cell 2, the frequency manipulated cell, and cell 3, the control cell. The two cells were significantly different for one of the three dependent variables at the p < .05 level. The means for relative importance (Hypothesis lb) for the MPG attribute were .147 and .107 for cells 2 and 3 respectively, a difference of 35% and significant at the p < .03 level. The means for subjective importance (Hypothesis 3b) were 78.71 and 75.54, a difference of 4% in the correct direction, but not significant. Also, the means for the levels 25 and 40 (Hypothesis 2b) were .114 and .108, a difference of 5% in the correct direction but not significant. In summary, 1) Hypothesis lb, that frequency manipulation affects relative importance weights, is supported, and 2) Hypothesis 3b, that frequency manipulation affects subjective importance weights, and Hypothesis 2b, that frequency manipulation affects the importance difference between MPG levels 25 and 40, are not supported.

DISCUSSION

General Discussion: The results of the analyses have demonstrated that conjoint estimates of the relationship between two specific levels of an attribute appear to remain stable as 1) the number of levels used to define that attribute and 2) the range of values for those levels are manipulated. In making this conclusion, however, it must be noted that the means for the relative importance measure for the two levels were, in both cases, in the hypothesized direction. More significantly, estimates of the importance of an attribute are affected by the number of levels and the range chosen for the attribute. In addition, our results show that a subject's perceptions of an attribute are affected by the range of values of the levels of that attribute. That is, confirmation of Hypothesis 3a suggests that subjects believe that an attribute is, in fact, more important when the range of values of the levels of that attribute increases which, in turn, suggests a perceptual basis for the phenomenon.

Implications There are several implications of these findings for research practitioners who employ conjoint analysis. These findings re-emphasize that it is inappropriate to refer to an attribute's importance in absolute terms. That is, an attribute's importance weight is influenced by the context within which it is presented. Instead, one would refer to the importance of a difference between the two extreme levels of a given attribute in the context of a specific conjoint task. If we consider price, we can only speak of the importance of the difference between a price of $2,000 and one of $12,000, not of some global importance of price itself. Clearly, if a different range were employed, for example, $4,000 to $4,500, then price might be perceived as an unimportant attribute. These results suggest specific, practical options for conjoint stimulus design. The first of these is the need to carefully consider the range over which the levels of an attribute are spread. Green and Srinivasan (1978) argue for end points of the range slightly more extreme than those "found in nature." This research suggests a real need to correspond with the range found in nature to avoid over or under evaluation of an attribute. With respect to frequency effects on attribute importance, two options are to 1) use equal numbers of levels for each attribute or 2) use different versions of the instrument with different numbers of levels for each attribute to test the effects of frequency differences.

This study has theoretical implications since it suggests that at least the effects of range manipulations are perceptual in nature rather than artifacts of the estimation process itself. As a result of this finding, one can argue that conjoint analyses not only capture a subject's utility for various attributes, but, in fact, can to some extent, modify or even create that utility. Nevertheless, these findings require further research.

Future Research. There are several opportunities for further research which arise out of this study. The first group of research opportunities are those which explore the characteristics of the effects. For example, one project of interest is to study changes in the effects of range or frequency manipulations given different starting points with respect to number of levels and attribute ranges. Does addition of one level to an attribute have a different effect with a starting point of four versus six levels? Another study would include systematic exploration of the effects of these manipulations on the unmanipulated attributes. That is, if a range increase also increases the importance of the manipulated attribute, is there another unmanipulated attribute which decreases in importance? This would require use of a different scale in the subjective importance task. Another study might be concerned with the effect of number of attributes on the strength of these effects. One might guess that the fewer attributes the more effective range and frequency manipulations are. A final study in this area would be to attempt to replicate the findings using a rank order task rather than a rating task.

The second group of studies of interest would deal with the nature of the effects of the manipulation. For example, how long would subjects' subjective importances stay different after the manipulation of range and/or frequency? Another interesting study would explore how the effects work, in terms of recall and recognition differences between manipulated and nonmanipulated groups. In short, demonstration of the existence of these range-frequency effects and, most particularly, their perceptual basis, offers scope for several new research projects.

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