Measured Attribute Weights Can Make a Difference

Richard A. Werbel, University of Illinois at Circle Campus
ABSTRACT - This study compares the correlation between stated attitudes and attitudes generated by the linear compensatory model using measured attribute weights to the same correlation using uniform weights. Unlike previous studies, attempts were made to minimize both an implicit weighting effect and a positive correlation between or among beliefs. In addition, a new approach of measuring attribute importance was used to minimize any systematic response bias. The correlations were substantially greater with measured weights than uniform weights.
[ to cite ]:
Richard A. Werbel (1978) ,"Measured Attribute Weights Can Make a Difference", in NA - Advances in Consumer Research Volume 05, eds. Kent Hunt, Ann Abor, MI : Association for Consumer Research, Pages: 180-185.

Advances in Consumer Research Volume 5, 1978      Pages 180-185

MEASURED ATTRIBUTE WEIGHTS CAN MAKE A DIFFERENCE

Richard A. Werbel, University of Illinois at Circle Campus

ABSTRACT -

This study compares the correlation between stated attitudes and attitudes generated by the linear compensatory model using measured attribute weights to the same correlation using uniform weights. Unlike previous studies, attempts were made to minimize both an implicit weighting effect and a positive correlation between or among beliefs. In addition, a new approach of measuring attribute importance was used to minimize any systematic response bias. The correlations were substantially greater with measured weights than uniform weights.

INTRODUCTION

A large number of studies have been conducted which compare a compensatory multi-attribute model with uniform importance weights to one with measured weights. [It has been argued that there is little reason to be concerned with attribute importance because the "value" component of Fishbein's model incorporates both attribute importance and the degree of deviation from an ideal point (Cohen, Fishbein, and Ahtola, 1972). Although it is likely that attribute importance is incorporated into this component, it seems desirable from a diagnostic standpoint to attempt to isolate all attitude components. For example, it might be relevant to know the distance between the ideal point and a cognitive belief to determine the likelihood of changing the cognitive belief.] Bass and Wilkie (1973) summarized the results of 15 earlier studies and other studies have been published since this review (for example, Dubois, 1974; Holbrook and Hulbert, 1974; Houston and Gillespie, 1974; Pekelman and Sen, 1974; Wildt and Bruno, 1974; and Mazis, Ahtola, and Klippel, 1975). This author was able to find only one study in which the correlation between stated and generated attitudes was dramatically higher with measured weights (Pekelman and Sen, 1974). Thus, the evidence to date indicates that uniform weights can predict attitudes about as well as measured weights.

Yet, it might be premature to conclude that uniform weights actually are used by consumers in forming attitudes. First, and probably most important, attitudes generated by a uniform weights model may be quite similar to those generated by measured weights, even when there is a large difference between measured and uniform weights. Second, methods used to measure weights may suppress true differences between measured and uniform weights. Both of these conditions are discussed in the following section.

In this study, attempts were made to increase the probability that attitudes generated by uniform weights differed from those generated by measured weights when a large difference between uniform and measured weights existed. In addition, a new procedure for measuring attribute importance was used. It was expected that this method might generate more accurate weights than methods used previously.

EXPLANATIONS FOR THE INABILITY OF MEASURED WEIGHTS TO OUTPERFORM UNIFORM WEIGHTS

If a belief toward a brand on one attribute is reasonably similar in an affective and relative sense to beliefs toward the same brand on other salient attributes, a model with weights substantially different from uniformity will tend to generate the same attitudes as a model with uniform weights (Beckwith and Lehmann, 1973). Although it is difficult to identify the number of studies in which this problem has existed because the correlation usually has not been reported, only Holbrook and Hulbert (1974), and Pekelman and Sen (1974) seem to have in large eliminated it.

Sheth and Talarzyk (1972) argued that there may be a greater spread of beliefs toward various brands on an attribute that is important than on one that is unimportant. In this situation, since attitudes would tend to be consistent with affective beliefs on the attribute or attributes with the greatest spread when uniform weights are used, attitudes generated by uniform weights would tend to be similar to those generated by measured weights. This "implicit weighting" effect has been reported in previous studies (Sheth and Talarzyk, 1972; Beckwith and Lehmann, 1973; Wilkie and Weinrich, 1973; Holbrook and Hulbert, 1974). Perhaps it is most significant that Wilkie and Weinrich discovered an implicit weighting effect because cognitive beliefs were used rather than affective ones and because some of the attributes included were reasonably objective. Based upon these results, the implicit weighting effect might have existed in other studies even though it was not reported.

There is a second explanation for implicit weighting that has not been advanced previously. The use of a number of reasonably specific attributes underlying the basic attribute of quality along with a single price attribute results in greater weight being attached to quality when uniform weights are used. If some consumers combine perceptions on reasonably specific attributes into a single "quality" perception and if quality has greater weight than price, an implicit weighting effect will exist.

Beckwith and Lehmann (1973) indicated that measures of attribute weights might no coincide with true weights. Using regression estimated weights to generate attitudes, they examined the correlation between generated attitudes and the group of stated attitudes which were used to determine the regression weights. Since the difference between the average correlation coefficient using regression estimated weights and that using stated weights was not that large (.095) it can be assumed that stated weights were similar to regression estimated weights and/or the existence of such factors as a positive correlation among beliefs resulted in suppressing the influence of weights upon generated attitudes. Although Beckwith and Lehmann did not indicate the association between regression estimated weights and stated weights, the existence of both a positive correlation among beliefs and an implicit weighting effect indicates that there may have been a reasonably substantial measurement error.

Scott and Wright (1976) and Hughes and Guerrero (1971) compared regression estimated weights with stated weights. In both of these studies, the difference between the two sets of weights was rather large. For example, Hughes and Guerrero found that the computed weight for the performance of automobiles was 57.3 compared with a stated weight of 43.6 using a base of 100. Furthermore, regression estimated weights were more extreme than stated weights in both studies. Thus, there is some evidence that the use of direct questions to measure attribute importance results in a systematic response error which reduces the difference between attitudes generated by uniform weights and those generated by true weights.

METHODOLOGY

Undergraduate students in two sections of Principles of Marketing at a large Midwestern university were questioned about their attitudes, beliefs, and the importance attached to various evaluative criteria. The product category examined was automobiles. The specific cars included were the 1) Chevrolet Chevette, 2) Ford Pinto, 3) Chevrolet Monza, 4) Ford LTD, and 5) Chevrolet Malibu. Due primarily to one of the methods used to measure attribute importance described later in the paper, an interactive computer program was used for the questioning process.

The two attributes used in the study were quality and price. The selection of quality and price as attributes should be explained, as quality has not been used in any previous studies, and because usually more than two attributes have been included in previous studies.

Before selecting quality and price, the decision was made to only include two attributes. This was done for three reasons. First, the use of two attributes lessens the likelihood of a positive correlation among beliefs existing, as it is difficult to select negatively correlated attributes when more than two attributes are used. [It was thought that the positive correlation could be minimized by selecting attributes that were likely of being negatively related. An overestimation of the degree of negative correlation would have likely resulted in uncorrelated beliefs, while the attempt to select un-correlated beliefs might have resulted in positively correlated beliefs. Furthermore, although the use of negatively correlated beliefs tended to result in similar attitudes being generated by two sets of weights when the rank orders of the attribute weights were equivalent, their use tended to result in attitudes generated by uniform weights different than those generated by nonuniform weights.] Second, any increase in the number of attributes might reduce the differences in the weights between attributes, particularly when a constant sum approach is used to measure weights. This argument is based on the assumption that it is reasonably unlikely that a weight of zero will be assigned to an attribute by a respondent Third, for the reason mentioned in the previous section, the use of two attributes lessens the likelihood of an implicit weighting effect.

Once the decision was made to use two attributes, quality and prices were selected because it was expected that they would be negatively correlated. Furthermore, because only two attributes were used, it was important to use a rather broad attribute, such as quality, which would incorporate more specific attributes.

Prior to answering any questions, respondents were given information dealing with the price, seating capacity, gas mileage, safety upon collision, and seating comfort of each car. A photograph of each car also was presented. This was done to lessen the likelihood of the existence of a positive correlation among beliefs because the low-priced objects were rated "low" on the nonprice information. Furthermore, the presentation of the price information made it possible to use objective price beliefs.

With one exception, an attempt was made to present accurate information. The exception was that all cars were depicted as equal in terms of gas mileage. If the correct information regarding gas mileage had been presented and if respondents had integrated this information into the quality dimension, the positive correlation between beliefs might have increased. The possibility of this information being integrated into a price dimension would have made it difficult to use objective price beliefs. It was thought that a positive correlation might be less likely of existing with objective price beliefs than with normalized or nonnormalized price beliefs.

Respondents were instructed to assume that all the information presented was accurate, including that pertaining to gas mileage. They were also told that they did not have to use this information if they did not feel it was relevant, and that they could use information dealing with attributes not included if they felt it to be relevant.

After the above instructions were presented, respondents were questioned about their attitude toward the act of purchasing five different cars. First, they were asked to rank the objects. Using a four-point scale, they then were asked to indicate the extent that they were less likely to purchase the brand ranked second than the brand ranked first. This question was repeated for the third and second, fourth and third, and fifth and fourth brands. Answers to these questions were used to construct an interval-type attitude scale.

Ten-point scales were used to measure beliefs. This particular scale was selected to lessen the probability of an implicit weighting effect by restricting respondent choice to some extent. At the same time, it was thought that this scale provided sufficient choice to allow the perceived relative differences between objects to be reflected. The scale endpoints were labeled "medium to higher quality," "lower quality," "lower priced" and "medium to higher priced." The term "medium'' was used to encourage use of extreme scale values.

In addition to perceived or nonnormalized beliefs, two other types of beliefs were used in the analysis. Normalized beliefs with both price and quality were used along with objective beliefs with price.

Both the reason and method of normalization used in this study differ from previous studies. In this study, normalized beliefs were calculated to equalize the quality spread between the lowest and highest ranked objects with the price spread for each respondent. This was done to lessen the possibility of an implicit weighting effect. Although this type of normalization might alter the perceptions of respondents, its use might be justified when an implicit weighting effect exists because of the differential weighting of attributes. In addition, the sensitivity of generated attitudes to changes in the relative spread of beliefs across attributes could be examined with this type of normalization.

This normalization was accomplished by giving the object that was perceived as highest in quality, (lowest in price), a value of 1 and the object that was perceived as lowest in quality, (highest in price), a value of 10. The criterion used in altering the beliefs of the other objects was the preservation of the relative differences in nonnormalized beliefs between objects.

Objective beliefs were used with price to lessen the possibility of the existence of a positive correlation between beliefs. Objective price beliefs were determined by converting actual prices into a ten-point scale in which the object with the lowest price was given a value of 1 and the object with the highest price a value of 10. The actual prices presented to respondents were $2900 for the Chevette, $3100 for the Pinto, $3900 for the Monza, $4700 for the LTD, and $4900 for the Malibu. Objective price beliefs were 1.0, 1.9, 5.5, 9.1 and 10.0. Another method that might have been used would have involved equating the spread of objective price beliefs with the spread with either nonnormalized quality or price beliefs, while preserving the relative price differences indicated by the actual prices. After examining the initial results, the decision was made to use the procedure indicated primarily because it allowed one to examine the impact that a price spread greater than a quality spread had upon the correlation between stated and generated attitudes with automobiles.

Two measures were used to measure attribute importance. One approach involved asking respondents directly to provide a numeric weight for both quality and price which indicated the relative importance of these two attributes. Respondents also were instructed with this approach that the sum of the weights for quality and price had to be equal to 1.0. With the exception of using a constant-sum scale, this approach is virtually identical to those used in previous studies. A new approach was used to measure attribute importance because, as indicated previously, the above approach may not be valid. This new approach involved asking either question (1) or (2).

(1) How much less would (Y) have to cost than (X) for you to be just as likely to purchase (Y) as (X)?

(2) How much more would (X) have to cost than (Y) for you to be just as likely to purchase (X) as (Y)?

X and Y were two of the five brands included in the study. Although the specific brands included could change from respondent to respondent and/or question (2) to question (1), X always was perceived as higher in quality than Y. Respondents were given nine specific prices to choose among in answering these questions. Answers were scaled for further analysis. The lowest price had a scale value equal to 2 and the largest price had a scale value equal to 10. Question (1) or (2) was repeated for each respondent with a different pair of brands. Mean weights were then calculated. These mean weights were used in generating attitudes using "trade-off" weights.

Equations (1) and (2) were used to algebraically deter- mine the weights for quality and price.

(Bqxk - Bqxk + 1) Wqk  + BpxkWpk =  ( Bqyk -Bqxk  + 1) Wqk  + BpykWpk    (1)

Wqk  + Wpk  =  1.0   (2)

Such that:

Wqk = weight of quality (q) for consumer k;

Wpk = weight of price (p) for consumer k;

Bqxk = consumer k's nonnormalized quality belief toward the higher quality brand included in question (1) or (2);

Bqyk = consumer k's nonnormalized quality belief toward the lower quality brand included in question (1) or (2);

Bpxk = scale value for price given by consumer k in response to question (1) or (2); and

Bpyk = scale value for price of base brand in question (1) or (2). This value was equal to 1.0 for all respondents.

It should be noted that the difference between Bqxk and Bqyk influences the possible range of values that Wqk and Wpk can assume. For example, if the difference between Bqxk and Bqyk is equal to 1, Wqk cannot assume a value less than .5 or greater than .9. This potential problem was solved by asking questions (3) and (4).

3. If you had to buy either (brand perceived as highest in quality) or (brand perceived as second highest in quality) and (latter brand) costs less than (former brand), which brand would you purchase?

4. If you had to buy either (brand perceived as lowest in quality ) or (brand perceived as highest in quality) and (former brand) costs -- less than (latter brand), which brand would you purchase?

Answers to these two questions were used to determine whether question (1) or (2) would be asked, and to determine the proper difference between X and Y in question (1)or(2) in terms of nonnormalized quality beliefs.

With both questions, the price changed from respondent to respondent as the specific quality difference between the two brands in the questions changed. This was done to establish a consistent range for Wqk and Wpk.

With question (3), the price was selected to determine whether Wqk was greater or less than approximately .67.

With question (4), the price was selected to determine whether Wqk was greater or less than approximately .30.

Respondents who selected the higher quality brand in both question (3) and (4) were asked question (1) if a pair of brands existed with which Bqyk - Bqxk was between .5 and 2.49. Respondents who selected the lower quality brand in question (3) and the higher quality brand in question (4) were asked question (1) if a pair of brands existed with which Bqyk - Bqxk was between 2.5 and 5.49. Although these two groups of respondents both were asked question (1), the allowable range of the difference between the quality beliefs of the two brands included in the question was different. This was done because the first group indicated in their answers to question (3) and (4) that the weight for quality was greater than .67, while the second group indicated that the weight for quality was between .30 and .67. Respondents who selected the lower quality brand in both question (3) and (4) were asked question (2) if a pair of brands existed with which Bqyk - Bqxk was greater than 5.49. Respondents in all of the above groups were not asked either question (1) or (2) if two brands did not exist with which Bqyk - Bqxk was in the proper range. Respondents who selected the higher quality brand in question (3) and the lower quality brand in question (4) were eliminated from the final analysis because this answer pattern indicated that the respondent's weights were quite unstable.

It was thought that this approach, which is termed the "tradeoff approach," might lessen or eliminate the response error with the "direct approach" primarily because the tradeoff approach does not directly ask respondents to evaluate the importance of an attribute. To clarify this reason, it is thought that when making a purchase decision, consumers do not need to think about the importance of an attribute unless a tradeoff exists. If a tradeoff exists, consumers might attempt to resolve the specific tradeoff, rather than directly evaluating the importance of an attribute. For example, if Brand "A" costs 10C more than Brand "B" and is perceived as somewhat higher in quality, a consumer will try to determine whether the perceived quality difference in favor of Brand "A" is large enough to compensate for its higher price.

The tradeoff approach was used rather than regression estimated weights primarily because a unique set of weights cannot be calculated using multiple regression when beliefs are positively or negatively correlated. A unique set of weights will exist with the tradeoff approach when beliefs are correlated. In addition, weights can be calculated using only two objects with the tradeoff approach and it is not necessary to use a holdout group of objects for model testing. This last factor is an advantage because of the practical problems involved in using a holdout group of objects (Pekelman and Sen, 1974).

RESULTS OF THE ANALYSIS

The analysis primarily consisted of using equation (3) to generate attitudes for each object used in the study.

EQUATION  (3)

such that:

"jk =consumer k's attitude toward object j,

Wik =importance weight given attribute i by consumer k,

Bijk = consumer k's cognitive belief toward object j on attribute i, and

Iik = consumer k's ideal point on attribute i. [In defining and determining the ideal points for quality and price, the attempt was made to isolate the use of price by consumers to determine quality beliefs through such factors as status or workmanship, from its use as a primary economic criterion. Thus, the ideal point was defined as the most preferred level of an attribute, all other things being equal. With this definition, the ideal point with both quality and price was equal to 0.]

Four different combinations of beliefs were used: 1) nonnormalized quality and price beliefs; 2) normalized quality and objective price beliefs; 3) nonnormalized quality and objective price beliefs; and 4) normalized quality and price beliefs. With each of these four combinations, three sets of weights were used; 1) direct weights; 2) tradeoff weights; and 3) uniform weights. In each of these 12 instances, Pearson product-moment correlation coefficients were calculated for each individual respondent. Mean coefficients were calculated and selective comparisons were made.

Although affective beliefs could have been used rather than cognitive beliefs and ideal points, the use of cognitive beliefs allowed the use of objective price beliefs. Furthermore, it is more consistent to use cognitive beliefs with the method of normalization used than affective beliefs. As mentioned earlier, this method should be used if the difference in the relative spread of beliefs across attributes exists because of the relative importance of the two attributes. This condition is more likely of existing when cognitive beliefs are used.

The decision to use the city block version of the model rather than the Euclidean distance version, or some other distance formulation, was a rather arbitrary one. Only one distance formulation was used because it was thought that the difference between the average correlation of generated and stated attitudes using one version of the model and the same correlation using another version of the model would not be affected by the particular distance formulation used.

88 students completed the questioning process. 19 of the 88 students were eliminated from the analysis because attribute weights could not be determined using the tradeoff approach. More specifically, they were eliminated either because their answers to questions (3) and (4) indicated that they had highly unstable weights, or because they did not meet the criterion used to select the brands to be included in questions (1), (2), (3), or (4). These students had an average Pearson product-moment correlation coefficient with uniform weights quite similar to that for the 69 respondents included in the analysis, but had a coefficient with direct weights about .18 less than that for the 69 respondents.

The means of Pearson product-moment correlation coefficients for the twelve versions of the model are presented in Table 1. In summarizing the correlations, when other factors are held constant the correlations were substantially greater with direct and tradeoff weights than with uniform weights. The differences ranged from .2841, which was the difference between uniform and direct weights using nonnormalized beliefs for both quality and price, to .7488, which was the difference between uniform and tradeoff weights using nonnormalized quality beliefs and objective price beliefs.

TABLE 1

MEAN OF INDIVIDUAL CORRELATIONS BETWEEN STATED AND GENERATED ATTITUDES

The use of various combinations of beliefs to lessen an implicit weighting effect had a rather substantial impact on the difference between uniform and measured weights (i.e., the combination of direct and tradeoff weights). The implicit weighting effect was greatest when nonnormalized beliefs were used with both quality and price. Here the average difference between uniform and measured weights was .2958. The implicit weighting effect was least when nonnormalized quality beliefs and objective price beliefs were used. [Although the use of normalized beliefs might minimize the implicit weighting effect in some instances, the use of nonnormalized quality beliefs and objective price beliefs minimized it here because the vast majority of respondents seemed to attach greater weight to quality than price.] Here the difference between uniform and measured weights was .6703. The use of either normalized quality and price beliefs, or normalized quality and objective price beliefs resulted in an implicit weighting effect between the two extremes above. Here the difference between uniform and measured weights was .4491.

In evaluating these differences dealing with the implicit weighting effect, it should be noted that the average difference between the spread with quality and the spread with price was 1.4 when nonnormalized quality and price beliefs were used, and 2.1 when nonnormalized quality and objective price beliefs were used. The Pearson product-moment correlation coefficient between 1) the difference between a) the spread of nonnormalized quality beliefs measured by the difference between the brand rated lowest in quality and the brand rated highest in quality, and b) the spread of nonnormalized price beliefs measured in the same manner, and 2) tradeoff weights was .33.

If all other factors are held constant, the difference in the average correlation between measured and uniform weights was only somewhat larger when tradeoff weights were used than when direct weights were used (.0617). However, the average correlation with tradeoff weights was a good deal greater than the correlation with direct weights when nonnormalized quality beliefs and objective price beliefs were used (.1571). Since the mean difference between direct and tradeoff weights was reasonably large (.158), it appears that the average correlation with the other three versions of the model was not particularly sensitive to the differences between direct and tradeoff weights. In explaining the reasons for the lack of sensitivity, it is again necessary to mention that the vast majority of respondents stated that they were more likely of purchasing the higher quality automobiles. Although the tradeoff weight for quality was greater than the direct weight for quality with 68 percent of the respondents, the direct weight for quality was greater than or equal to .6 70 percent of the time that tradeoff weights were greater than direct weights. In this situation, direct weights would predict that the higher quality cars would be most likely of being purchased unless the price spread was greater than the quality spread. The price spread was greater only when nonnormalized quality beliefs and objective price beliefs were used.

Finally, since the mean correlation coefficient between nonnormalized quality and nonnormalized price beliefs was - .8442, differences in the average correlation between various versions of the model were not suppressed by a positive correlation between beliefs.

SUMMARY AND CONCLUSIONS

The results of this study indicate that when the correlation between stated and generated attitudes is used as a criterion of validity, it is more appropriate to use measured attribute weights than uniform weights. Although this difference between measured and uniform weights might have been great than differences in previous studies partly because of situational differences, it is doubtful that these completely explain the differences among studies. The differences also may be due to 1) a reduction in the positive correlation between beliefs 2) a reduction in the implicit weighting effect, and 3) the use of a new approach for measuring attribute importance. Although it is likely that the positive correlation and the implicit weighting effect were substantially greater in many of the previous studies, the results of this study suggest that even moderate differences among studies in terms of the correlation between beliefs and the implicit weighting effect can substantially alter the results.

Although the procedures used to reduce the positive correlation between beliefs and the implicit weighting effect were successful in this study, there are instances in which these procedures should not be used, or in which they will not be successful.

Consumers may perceive a positive correlation between beliefs based upon an objective analysis. Although this author made the attempt to select brands, evaluative criteria, and a product in which this situation would not exist, there may be good reason to investigate attitude formation when the correlation exists. It is recommended that an approach such as examining the extent that an attitude model correctly predicts attitude change be used in this situation (Bettman, Capon and Lutz, 1975).

With respect to an implicit weighting effect, the use of various measures of beliefs to alter the relative spread of beliefs across attributes might not be successful. One approach used was equalizing the spread across attributes. Yet, as mentioned previously this approach might have suppressed the difference in the average correlation between tradeoff and direct weights. The use of nonnormalized quality beliefs and objective price beliefs reduced the implicit weighting effect only because there was a high degree of respondent homogeneity in terms of the relative importance of quality and price.

The issue of whether the difference between measured and uniform weights found in this study is atypical is worthy of discussion as it relates to the external validity of these results. The difference between trade-off and uniform weights was .236 and .163 between direct and tradeoff weights. Since the majority of the respondents attached more importance to quality than price, these differences might have been reduced substantially if respondents actually had to spend their own money. Yet, price might have become substantially more important than quality in this situation rather than the weights approaching uniformity. In addition, it is possible that respondents may have utilized rather extreme weights to allow them to differentiate clearly among objects. More specifically, since the price differences between objects tended to be similar to the quality differences, the use of uniform weights would have resulted in all objects being virtually equivalent in terms of the probability of purchase. On the other hand, one might argue that there will tend to be a difference between measured and uniform weights when respondents are allowed to select the brands used for the evaluation after being told that they should select those brands that they actually consider in making a purchase. If respondents make a selection among brands that tend to differ on one or two attributes (e.g., evaluate only subcompact automobiles or steel belted radials), one might expect that the weight of this attribute or attributes would be a good deal higher than the weight of other attributes.

Finally, since the results of this study indicate that there is a possibility that measured weights may be quite superior to uniform weights, it is relevant to ask whether there are any disadvantages in using measured weights rather than uniform weights. Other than eliminating the need to ask a single question or a limited number of questions to ascertain measured weights, which does not seem to be a very significant disadvantage, there appear to be no disadvantages in using measured weights rather than uniform weights.

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