Physical Distribution, Ultimate Consumers and Weber's Law

ABSTRACT - This study examines perceptions of three physical distribution systems commonly used by ultimate consumers. For each physical distribution system, these perceptions are compared with objective measures of cost, distance and delivery time. In addition, unexpected delivery events, early and late arrivals, are examined within the context of Weber's Law. Finally, differences among physical distribution systems are assessed from the standpoint of economic equilibrium, and the implications for public policy and corporate decision-making are discussed.


Arthur V. Highland and Anthony F. McGann (1977) ,"Physical Distribution, Ultimate Consumers and Weber's Law", in NA - Advances in Consumer Research Volume 04, eds. William D. Perreault, Jr., Atlanta, GA : Association for Consumer Research, Pages: 133-137.

Advances in Consumer Research Volume 4, 1977   Pages 133-137


Arthur V. Highland (student), University of Wyoming

Anthony F. McGann, University of Wyoming


This study examines perceptions of three physical distribution systems commonly used by ultimate consumers. For each physical distribution system, these perceptions are compared with objective measures of cost, distance and delivery time. In addition, unexpected delivery events, early and late arrivals, are examined within the context of Weber's Law. Finally, differences among physical distribution systems are assessed from the standpoint of economic equilibrium, and the implications for public policy and corporate decision-making are discussed.

Physical distribution is a topic which has been extensively treated within the context of industrial marketing and industrial buying behavior. Unfortunately, physical distribution as it relates to the behavior of ultimate consumers has been largely overlooked. This neglect is surprising for two reasons. First, there exists a lively controversy over one mode of physical distribution used by ultimate consumers, the United States Postal Service (Business Week, 1976). Second, almost all of us, as ultimate consumers, purchase physical distribution services from time to time.

In order to reverse some of the current financial difficulties of the USFS, proposals which include less frequent delivery of parcels are being considered. "Mail that is considered less important--including... fourth-class parcels--may be delivered only three times a week" (Business Week, 1976). From the standpoint of investigations of consumer behavior, these proposals are interesting for several reasons:

1. The USPS does not enjoy monopoly status in the sale of physical distribution services to ultimate consumers as it does in the sale of "First Class" postal service. Rather, it operates in a competitive environment where there are several other sellers of this service.

2. Public records do not reveal any extensive testing, by USPS, of consumer reactions to the current levels of physical distribution services nor to proposed modifications to these services. In the absence of these data, both public debate and legislative oversight of USPS are impaired.

3. The spirit of the proposals to modify the physical distribution services offered by USPS implies that a substantial number of customers, both industrial and ultimate, will find reduced delivery frequencies tolerable and will purchase physical distribution services from USPS.

This study is devoted to a measurement of consumer impressions of three competing physical distribution services. In addition to USPS, impressions of the service provided by United Parcel Service (UPS) and by Greyhound Bus Lines (GBL) were examined. Thus, representation is obtained from a publicly-owned service, a privately-owned service devoted primarily to physical distribution, and a privately-owned service which performs physical distribution as an ancillary service. Perceptions of delivery time, cost and distance were obtained for combinations of the three physical distribution services and six cities. In addition, actual costs, distances and employee estimates of delivery times were obtained for the same combinations.

It was the authors' suspicion that consumer impressions of delivery times within each of the three physical distribution services would be roughly proportional to the perceptions of intercity distances. Further, a small but remarkably consistent body of literature (Mittelstaedt, et al., 1974; Lundberg, 1973; Lowrey, 1973; Briggs, 1973; Bratfisch, 1969) suggests that perceptions of physical distance follow a "Power Law" of the form:

y = axb   (1)

where: y - perceived distance,

x - actual, or functional distance, and

a and b are empirically fitted constants.

This literature also finds that "errors" in the perception of physical distances tend toward overestimates, i.e., perceived distance is typically greater than actual distance. Secondly, it was hypothesized that each physical distribution service would have a characteristic "just noticeable difference," which is the difference in the number of days a parcel would have to arrive (either early or late) compared with the "normal" delivery interval. While the application of a form of Weber's Law to issues in consumer behavior is subject to a fair amount of controversy (see Monroe, 1971; Gabor, et al., 1971; and Stapel, 1972), reasonably successful attempts may be found in the literature. Nwokoye's (1975) work is illustrative of such attempts, and the design of this research parallels his work. Finally the authors were interested in examining any interservice differences which were detected from the standpoint of perceived economic equilibrium. Here, if the three services were economically equivalent, each would have an approximately equal value for k, where:


Thus, if consumers perceive economic equivalency among the three services, and further, perceive differences in delivery times among services for a given intercity distance, these differences must be offset by proportional differences in costs. This study, then attempts to test three substantive hypotheses:

Hr1: Within each physical distribution system, perceptions of expected delivery time for a parcel vary directly with perceptions of intercity distance.

Hr2: Within each physical distribution system, there is a "just noticeable difference" for early or late arrivals which is directly proportional to perceptions of intercity distance.

Hr3: Among physical distribution services, and for a given intercity distance, differences in perceived delivery times are inversely proportional to differences in perceived cost.


The data used for analysis were collected by means of a two-page questionnaire which was constructed in scenario form. Alternative forms of the questionnaires were randomly distributed to 180 University of Wyoming undergraduate and graduate students. Each student responded to only one scenario.

The first page of the questionnaire was designed to obtain measurements of the respondents' perceptions of price, road distance, and delivery time for one of the three transportation services. The second page was designed to obtain values for the testing of directional deviations from anticipated delivery times. Deviations from anticipated delivery times were measured directionally, and in this paper labeled and defined as:

Delay tolerance, or the number of days, beyond the anticipated delivery time, when a consumer considers an expected package "late."

Pleasant surprise, or the number of days before the anticipated delivery time, a package must arrive for a consumer to consciously notice the "earliness" of its arrival.

Ninety of the respondents received questionnaires with a delay tolerance ending, while the other ninety students responded to a pleasant surprise ending. The actual scenarios are presented in Appendix I.


Regarding the relationship between expected delivery time and perceptions of intercity distances, a preliminary check on the accuracy of perceived distances was deemed useful. Therefore, a comparison of group means for this perception and actual road distances is presented in Table 1.



rank order. Subjects typically overestimated actual distance, by slightly under 20 percent. Table 2 shows the relationship between perceived delivery time and perceived intercity distance expressed as common variation. These correlations suggest a significant positive relationship between perceptions of distance and delivery time, although the levels of common variance (12-22 percent) indicate a considerably less-than-perfect relationship. It may also be inferred that the perceptual relationship between these two variables is strongest in the case of Greyhound, and weakest for the U.S. Postal Service. As an aside, it is interesting to note that the actual delivery times, averaged across the six intercity distances, are 7.4 days; 4.8 days; and 3.7 days for USPS, UPS and GBL respectively. The authors conclude, on the basis of the analysis summarized in Tables 1 and 2, that moderate support has been detected for Hr1.



The second research hypothesis, that "noticeable" deviations from expected delivery intervals are directly proportional to perceptions of intercity distances, was scrutinized in two ways. First, linear regressions of both types of deviations (both early and late arrivals), on perceived distance were calculated for each distribution service. Then, similar regressions for each type of deviation were performed. Summaries of these analyses are presented in Table 3. Based on these analyses,



From these data, it can be seen that the subjects provided reasonably accurate estimates of actual intercity distances. With the exception of the intercity distance from Chicago to Laramie, where the greatest error occurred, the perceived distances are in the correct it seems that there is, again, modest support for the hypothesis that a service-specific constant expresses the perception of the ratio between deviations from expected arrival and intercity distance. This support is strongest when the parcel arrives later than expected and less evident when the parcel arrives early enough to provide the recipient with a pleasant surprise. When both types of deviations are combined, only 10 percent of the variation in delivery deviations and perceived distances is common.

Although not explicitly hypothesized at the out, et, the authors became curious over the possible existence of a "Weber's Law" type of relationship between delivery deviations and expected delivery times. Using regressions similar to those described above, this curiosity was pursued. Summaries of these regressions are contained in Table 4. These attempts to express a "just noticeable difference" in delivery deviations as a function of expected delivery intervals met with modest success when both types of deviations were combined, and there is an increase of about three percentage points in common variation over the parallel analysis using perceived distances. However, when separate analyses for each type of deviation are performed, the results are considerably more dramatic. For parcels arriving noticeably earlier-than-expected, only responses for the USPS exhibit significant levels of common variance, about 22%. For parcels arriving later-than-expected, all three distribution services elicit significant levels of common variance. This relationship is particularly strong in responses to both USPS and UPS. Overall, the second research hypothesis is most strongly supported in the instances where parcels arrive late and when the Weber fraction is calculated using expected delivery intervals in the denominator.



The third portion of this study relates to differences which exist in consumer impressions among the three physical distribution services. A preliminary assessment of interservice differences was obtained by a one-way ANOVA. These results are summarized in Table 5.



The only perceptual variable on which significant between-service differences were detected was delivery time. Using Tukey's method of simultaneous comparison, it was found that the mean delivery time for USPS is significantly greater than that for either UPS or GBL, but that mean delivery times are not significantly different between UPS and GBL at the .05 level. The means for actual delivery times are in the same rank order as were consumer perceptions; values are 5 days, 4 days, and 2.9 days for USPS, UPS and GBL, respectively. Thus, respondents believe all three of the services to be slower in delivering parcels than they actually are, based on employee supplied information.

The next step in making interservice comparisons is to calculate perceived and actual costs per mile for each service. These values are shown in Table 6. The information in Table 6 supports the inference that consumers of physical distribution services have a precise impression of the cost per mile when shipping via GBL. For the other two services, erroneous impressions are characteristic. USPS is thought to be about 25 percent less expensive than it actually is, while UPS is perceived to be almost 85 percent more expensive than it actually is. Inspection of actual costs per mile also reveals substantial interservice differences. UPS costs less than half of the tariff charged by either USPS or GBL on a cost per mile basis.



Of course, an investigation of possible economic equilibrium among physical distribution services must include not only a cost per distance measure but also a velocity measure. The presumption suggested by equilibrium is that a service which provides very rapid delivery would charge a higher price while slower delivery would be associated with a lower price. Substitution of mean values in equation (2) permits an assessment of this presumption. Results of these calculations are contained in Table 7.' Here K values may be interpreted as indices of relative shipping efficiency and equilibrium would be indicated by K values being equal or approximately equal across services.

Concerning perceptions of interservice equivalence, it seems that consumers do mot judge the three services to he in equilibrium. Again, using the Tukey method of comparison, respondents perceive UPS to be significantly more efficient than either USPS or GBL at the .05 level; they do not report significant differences between USPS and GBL. Inspection of the efficiency indices obtained from actual data reveals interservice differences which are dramatic. Compared with USPS, GBL is more efficient by an approximate factor of 2; UPS is almost three times more efficient. Thus, the third research hypothesis cannot be supported for objective data, nor for perceptual comparisons between UPS and the other two services.




This study suggests the ultimate consumers of physical distribution services, at least to the extent that the subjects used here are representative of that consumer group, have a reasonably accurate understanding of selected intercity distances. While the complete external validity of a design such as this one cannot be asserted, two important findings in this study tend to support a claim of such validity beyond that possible in the "usual college student" sample. First, the perceptions of intercity distance are similar to the "Power Law" phenomena demonstrated in a number of other studies which have measured per-captions of physical distance. Second, the "Weber's Law" findings reported here and elsewhere, substantiate the proposition that certain phenomena are judged in a common way by most persons in a large variety of situations. These findings, when combined with the actual and potential consumption of physical distribution services by the subjects in this study, provides the basis for a reasonably strong claim to external validity. Further, they report significant associations between their perceptions of distance and delivery interval for each of the services examined. It has also been suggested that a Weber's Law effect cam be detected for perceptions of physical distribution service when a parcel arrives at other-than-expected times. This effect seems to be most noticeable when the parcel arrives late and most noticeable when the Weber fraction is constructed from delivery deviations and expected delivery intervals. Finally, this study suggests that general economic equilibrium does not characterize the inter-service differences which were considered. Consumers do perceive significant differences in efficiency between UPS and the other two services. 'And, the objectively derived differences in efficiency among all tares services are substantial.

From the standpoint of managerial decision making, this study indicates that UPS is in an attractive position to improve its image among consumers as well as its market share. While consumers recognize it to be the most efficient of the three systems considered here, these perceptions do not fully capture the actual advantage it provides. This discrepancy between actual and perceived UPS efficiency seems to be caused by massive consumer overestimation of the actual cost per mile for this service. Comparative, substantiated advertising copy which describes actual UPS efficiency would be one promising strategy available to the organization.

It would also seem that GBL might use a research design parallel to the one reported here to develop a basis for increasing patronage of its physical distribution service among ultimate consumers. By all measures considered here, GBL provides the shortest delivery intervals among the three services. Further, while consumers do not report a significant efficiency difference between GBL and USPS, a substantial actual difference exists. Again, comparative advertising copy is one promising method by which this organization might increase consumer acceptance of the physical distribution service it provides.

Regarding the USPS, it would seem that the situation is considerably less favorable. Consumers characterize the physical distribution service offered by this organization to be the slowest of the three services, significantly slower than either UPS or GBL. Further, they underestimate the actual cost per mile of this service by 25%. It might be hypothesized from the data that consumers will be unpleasantly surprised by Fourth-Class postage rates when they actually purchase this service. Such an hypothesis would not indicate improvements in public support for USPS. Then, USPS is only about half as efficient as GBL and about one-third as efficient as UPS when objective measures of cost and speed are considered. And, although consumers do not appear to fully recognize the magnitude of this relative inefficiency they do report impressions of USPS which are significantly lower than those of UPS. Finally, some of the proposals to correct financial difficulties at USPS would seem counterproductive when considered in light of the findings in this study. It is hard to imagine how USPS might improve either its image among consumers or its market share of physical distribution services by increasing delivery intervals and thus exacerbating already unfavorable consumer sentiment.




D. Bratfisch, "A Further Study of the Relation Between Subjective Distance and Emotional Involvement," Acta Psychologica, 29, 1969, 244-255.

R. Briggs, "Urban Cognitive Distance," in R. M. Downs and D. Shea (eds.) Image and Environment. Chicago: Aldine Publishing Company, 1973, 361-388.

A. Gabor, C. Granger, and A. Sowter, "Comments on 'Psychophysics of Prices. '" Journal of Marketing Research, May 1971, 8, 251-252.

R. Lowrey, "A Method for Analyzing Distance Concepts of Urban Residents," in R. M. Downs and D. Shea (eds.) Image and Environment. Chicago: Aldine Publishing Company, 1973, 338-360.

U. Lundberg, "Emotional and Geographical Phenomena in Psychophysical Research," in R. M. Downs and D. Shea (eds.) Image and Environment. Chicago: Aldine Publishing Company, 1973, 322-337.

R. Mittelstaedt, ,W. Curtis, S. Grossbart, and R. Rogers, "Psychophysical and Evaluative Dimensions of Cognized Distance in an Urban Shopping Environment," Combined Proceedings, American Marketing Association, 1974, 190-193.

K. B. Monroe, "Psychophysics of Prices: A Reprisal." Journal of Marketing Research, May 1971, 8, 248-250.

N. Nwokoye, "An Experimental Study of the Relationship Between Responses to Price Changes and the Price Level for Shoes." Advances in Consumer Research, Vol. #2, 1975, 693-703.

J. Stapel, "'Pair' or 'Psychological' Pricing?" Journal of Marketing Research, February 1972, 9, 109-110.

"Why the Post Office Can't Break Even," Business Week, March 29, 1976, 2425, 63+.



Arthur V. Highland, (student), University of Wyoming
Anthony F. McGann, University of Wyoming


NA - Advances in Consumer Research Volume 04 | 1977

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