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A belief-updating process for minimizing waiting time in multiple waiting-time events: Application in website design
A BELIEF-UPDATING PROCESS FOR MINIMIZING WAITING TIME IN MULTIPLE WAITING-TIME EVENTS: APPLICATION IN WEBSITE DESIGN BRUCE D. WEINBERG is associate professor of marketing and ecommerce, McCallum Graduate School of Business, Bentley College, Waltham, MA; e-mail: [email protected]
Bruce D. Weinberg Paul D. Berger Richard C. Hanna f
PAUL D. BERGER is a professor of marketing, School of Management, Boston University; e-mail: [email protected] RICHARD C. HANNA is assistant professor of marketing, Carroll School of Management, Boston College; e-mail: [email protected]
ABSTRACT Tim Berners-Lee, the inventor of the World Wide Web, has identified the waiting time problem, commonly referred to as the World Wide Wait, as a major problem that must be resolved in order for people to have rich robust Internet experiences. For the foreseeable future, slow download speeds may cost Web sites billions of dollars in opportunity loss. Using consumer behavior theory, we formulate a method for minimizing perceived waiting time in phenomena which involve multiple waits or time delays, here applied to Web site design and the Internet waiting problem. Solutions for two types of design situations are provided: (1) the © 2003 Wiley Periodicals, Inc. and Direct Marketing Educational Foundation, Inc. f JOURNAL OF INTERACTIVE MARKETING VOLUME 17 / NUMBER 4 / AUTUMN 2003 Published online in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/dir.10065
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MINIMIZING WAITING TIME IN MULTIPLE WAITING-TIME EVENTS
optimal ordering of a predefined number of Web pages, and (2) an optimal number of Web pages and the amount of information on each page, for a set of information in a predefined order. We provide a solution for the general case, and a simplified solution for specific beliefupdating patterns suggested by previous literature as frequently occurring in practice. This research contributes to the extant waiting time literature as well as provides solutions to, enhances understanding of, and encourages future research for, a persistent and important Internet and ecommerce problem that has received relatively little attention in the marketing literature.
mation that reduces uncertainty about the wait helps Web users evaluate the Web site material independently from their frustration with waiting time. Weinberg (2000) establishes that consumers process waiting time in accordance with an anchoring and adjustment process, and that this can influence perceptions of waiting time, which, in turn, can impact Web site utilization. The Internet industry has made some progress in resolving the waiting time problem. The approaches to reducing waiting time on the Internet have been primarily technical or operational in nature. However, perceptions are often more important than reality for consumers’ subjective evaluations of, for example, quality and customer satisfaction (Iacobucci, 1998).
Current Research Focus The focus of this research is to devise and describe a methodology for minimizing total perceived waiting time as part of the web design process. We provide solutions for two types of Web site design situations: (1) the optimal ordering of a predefined number of Web pages (with no predefined order) and their associated amount of information; and (2) an optimal number of Web pages and the amount of information on each Web page, for a set of information in a predefined order (with no predefined number of Web pages). This research is important because it (1) provides solutions to, enhances understanding of, and encourages future research for a persistent and important Internet and e-commerce problem that has received very little attention in the marketing literature; (2) contributes to the extant waiting time literature; and (3) offers a methodology that has promise for addressing similarly structured allied problems in different application areas.
INTRODUCTION Tim Berners-Lee, the inventor of the World Wide Web (Web), has identified the waiting time problem, commonly referred to as the World Wide Wait, as a major problem that must be resolved in order for people to have rich robust Internet experiences (Howe, 2001; Rubenstein, 2001). The speed at which information downloads from a Web site server to a Web user is central to her or him having a satisfying experience. Slow downloads are resulting in lost e-commerce sales estimated to be on the order of billions of dollars (Rebello, 1999). The persistence of the waiting time problem is limiting the advancement of true interactivity through the Internet (Banks, 1997).
WAITING TIME ON THE INTERNET Waiting time is a well-established area of importance in the marketing literature, with implications for service quality (e.g., Hui and Tse, 1996; Iacobucci, 1998; Maister, 1985; Taylor, 1994, 1995; Taylor and Claxton, 1994; Katz, Larson, & Larson, 1991). An important finding is that a reduction in perceived waiting time can influence service evaluations positively. Research by marketers on Internet waiting time, however, is sparse. Dalleart and Kahn (1999) suggest inforJOURNAL OF INTERACTIVE MARKETING
HOGARTH AND EINHORN’S BELIEFADJUSTMENT MODEL Hogarth and Einhorn (1992), in a paper discussing order effects in belief updating after new information is provided, suggest that re●
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S m⫺1 ⫽ anchor or prior opinion after evaluating (m ⫺ 1) pieces of information (the initial strength of belief is denoted S 0 ) s( x m ) ⫽ subjective evaluation of the mth piece of evidence R ⫽ the reference point or background against which the impact of the mth piece of evidence is evaluated W m ⫽ the adjustment weight for the mth piece of evidence (0 ⱕ W m ⱕ 1)
search studying the effect of temporal delays (among other variables) on this process would be “illuminating.” This paper discusses research pertaining to the effects of temporal delays in systems with multiple waiting-time events on consumer information search behavior—specifically, when consumers search for information on the World Wide Web. We now discuss the belief-adjustment model proposed by Hogarth and Einhorn (1992). Then, we adapt their model to situations where a sequence of ordered temporal delays (i.e., waiting times) are estimated by consumers and are the basis for continuing or ceasing information search. Specifically, we apply the model to Web site design and consider the implications for other types of systems that contain multiple waiting-time events. The Belief-Adjustment model, which is based on anchoring and adjustment, may not have explicitly stated the applicability of the anchoring and adjustment process to perceptions of waiting time. However, Weinberg (2000) showed explicitly that the anchoring and adjustment process does apply to perceptions of waiting time; therefore, we believe that it is reasonable to model waiting time perceptions under this assumption. It should be noted that there are several processes that can be consistent with our adapted model. However, we retain the anchoring and adjustment phrasing since it is consistent with the stated philosophy of Hogarth and Einhorn’s (1992) belief-updating model, which we rely upon heavily.
In essence, the adjustment weight measures the degree to which an update influences the current data (i.e., the ”evidence”) vs. the previously held opinion.
MODIFYING THE BELIEF-ADJUSTMENT MODEL FOR WAITING-TIME ON THE WORLD WIDE WEB It is assumed that after “clicking” on a linking icon (i.e., selecting a link to another Web page), a consumer experiences a wait of some duration for the Web page information (to which one is linking) to fully load and appear (on a monitor). In addition, it is assumed that a consumer has a waiting tolerance for each Web page; i.e., there is a maximum length of a time that a consumer is willing to wait for Web page information to fully load and appear. A consumer ceases to wait for the Web page information, and, hence, does not view the Web page information if the waiting duration exceeds a consumer’s waiting tolerance; otherwise, a consumer waits for the Web page information to fully load and appear. Given this process, a consumer is using a step-by-step process1 when waiting for information on the Web. Using R ⫽ Sm (for estimation tasks2), (1) becomes
The Model Hogarth and Einhorn (1992) describe a model of belief updating with a focus on order effects. Their Belief-Adjustment Model is S m ⫽ S m⫺1 ⫹ W m关s共 x m兲 ⫺ R兴
S m ⫽ S m⫺1 ⫹ ␣ 䡠 S m⫺1 䡠 共s共 x m兲 ⫺ S m⫺1兲
(1)
when s共xm 兲 ⱕ Sm⫺1
(2a)
where 1
S m ⫽ degree of belief in some hypothesis, impression or attitude after evaluating m pieces of evidence (0 ⱕ S m ⱕ 1) JOURNAL OF INTERACTIVE MARKETING
For a discussion of step-by-step processes vs. end-of-sequence processes, see Hogarth and Einhorn (1992). 2 For discussion of Estimation tasks vs. Evaluation tasks, again see Hogarth and Einhorn (1992).
●
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proportional) to the anchor. These weights may be constant or take on any pattern. A model of perceived waiting time, independent of the direction of (atm ⫺ ptm⫺1) is
and S m ⫽ S m⫺1 ⫹  䡠 共1 ⫺ S m⫺1兲 䡠 共s共 x m兲 ⫺ S m⫺1兲 when s共xm 兲 ⬎ Sm⫺1
(2b)
t ⫽ pt m⫺1 ⫹ W m 䡠 共 at m ⫺ pt m⫺1兲.
The general formulations of Eqs. (2a) and (2b), fully derived in Hogarth and Einhorn (1992), were for negative and positive information, respectively. Waiting time, of course, is not one of the more frequently-encountered “higher the better” criterion variables, but a “lower the better” criterion variable; thus, we take the view that a waiting time greater than Sm ⫺ 1 is analogous to negative information and a waiting time less than Sm⫺1 is analogous to positive information. Retaining the orientation of ␣ and , and modifying the notation to specifically reflect actual waiting time and perceived waiting time, Eqs. (2a) and (2b) become
p m
And to, perhaps, more directly emphasize the anchoring and adjustment bias, (4) may be rewritten as t ⫽ pt m⫺1 ⫹ 共1 ⫺ m兲 䡠 共 at m ⫺ pt m⫺1兲
p m
t ⫽ pt m⫺1 ⫹ ␣ m 䡠 共 at m ⫺ pt m⫺1兲 t ⬎ p tm⫺1
a m
(3a)
and
Minimizing Waiting Time One important criterion/objective in optimal Web site design is to minimize total perceived waiting time. In this paper, we consider two different specific situations that a Web site designer could face. “In What Order?”: In this situation, two conditions exist. First, a Web site is already designed—specifically, the number of Web pages and the content/size of each page have been determined (by management opinion or by the nature of the circumstances of the message [e.g., a certain total set of products or features must be illustrated, and for practical reasons, one per page]); and second, the marketer maintains control over (download) waiting times. There are two general types of Web sites where marketers maintain this control: In one type, the user has no control over the order in which Web pages may be viewed, and in the other type, the user has control over the order in which Web pages may be viewed. The former type is not encountered with great
t ⫽ pt m⫺1 ⫹  m 䡠 共 at m ⫺ pt m⫺1兲
p m
when
t ⱕ p tm⫺1
a m
(3b)
where ⫽ the perceived waiting time for webpage m (to fully load and appear) a t m ⫽ the actual waiting time for webpage m p t m⫺1 ⫽ the anchor or perceived waiting time for webpage m ⫺ 1 ␣ m ⫽ negative-information adjustment weight for the mth waiting time (associated with the mth webpage), when its actual waiting time exceeds its perceived waiting time  m ⫽ positive-information adjustment weight for the mth waiting time (associated with the mth webpage), when its actual waiting time is less than its perceived waiting time. ptm
Note that the adjustment weights, ␣ and , are not assumed to be proportional (or inversely JOURNAL OF INTERACTIVE MARKETING
(5)
where (1 ⫺ m) ⫽ Wm and 0 ⱕ m ⱕ 1. Equation (5) is key - in this form, it can be seen more clearly how m represents the degree to which the anchor “retards” the perceived waiting time. When m ⫽ 0, there is “zero” retardation, and ptm ⫽ atm. As m increases toward 1, the larger the degree to which ptm ⫽ atm, and the larger the degree to which the anchor, ptm⫺1, plays a more prominent role.
p m
when
(4)
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t ⫽ pt 0 ⫹ 共1 ⫺ 1兲 䡠 共 at 1 ⫺ pt 0兲 pt 2 ⫽ pt 1 ⫹ 共1 ⫺ 2兲 䡠 共 at 2 ⫺ pt 1兲
frequency; for example, see the photo galleries at Boston.com where each photo may be viewed only in the order pre-determined by Boston.com. The latter type is observed reasonably often and, given Web site developer preferences and trends, will become increasingly common; an example of this type of Web site (or coherent set of Web pages) is (Macromedia) Flash-based. Flash provides Web site developers with control over when waiting times will occur (through control over when content is to be downloaded), irrespective of the order in which users view Web pages (for example, see Rolls-RoyceMotorCars.com, Sony’s S2 Sports “Experience” Web pages, or Versace.com). What is to be determined (i.e., the decision variable) is, technically, the order in which waiting times are to occur; however, without too much loss of generality, we can also consider the decision variable as the order of the Web pages or the order in which Web pages are downloaded. “Where to Slice?”: A Web site is already designed in terms of the content and length, and the order of the information is fixed. What is to be optimized is where to slice the content into pages (Situation 2).
p 1
(6) (7)
and then plug (6) into (7) to produce t ⫽ 兵 pt 0 ⫹ 共1 ⫺ 1兲 䡠 共 at 1 ⫺ pt 0兲其 ⫹ 共1 ⫺ 2兲
p 2
䡠 共 at 2 ⫺ 兵 pt 0 ⫹ 共1 ⫺ 1兲 䡠 共 at 1 ⫺ pt 0兲其兲
(8)
Note that in (8) the perceived waiting time of Web page 2 is now expressed in terms of actual waiting times (assuming that pt0 ⫽ at0—which is reasonable given that pt0 is unaffected by the anchoring and adjustment process). The expression in (8) for the perceived waiting time of Web page 2 can be simplified further: t ⫽ at 0 䡠 1 䡠 2 ⫹ at 1 䡠 共1 ⫺ 1兲
p 2
䡠 2 ⫹ at 2 䡠 共1 ⫺ 2兲 In general, the perceived waiting time of Web page m, ptm, can be expressed in terms of actual waiting times (again, assuming that pt0 ⫽ at0), which is shown in (9): t ⫽ at 0 䡠 1 ⫹ at 1 䡠 共1 ⫺ 1兲
p m
t ⫽ at 0 䡠 共 1 䡠 2 䡠 · · · 䡠 m兲 ⫹
p m
IN WHAT ORDER?
for m ⫽ 1
冘
i⫽1,. . .,关m⫺1兴
In this section, we first derive the general solution to the “In what order?” situation, for any pattern of adjustment weights, [i.e., (l – m) values]. Hogarth and Einhorn (1992) suggest that the pattern of adjustment weights are likely to be either constant or increasing, while agreeing that no pattern can be completely ruled out. We wish to minimize the sum of the perceived waiting times,
t 䡠 共1 ⫺ i兲 䡠 共 i⫹1 䡠 i⫹2 䡠 · · · 䡠 m兲
a i
⫹ at m 䡠 共1 ⫺ m兲
T ⫽ 共 pt 1
t
p 2
···
(9)
t
p J⫺1
t 兲,
p J
a 1 ⫻ J dimensional vector,
共 pt m兲
m⫽1,. . .,J
A
T ⫽ 共 at 0
t
a 1
···
t
a J⫺1
t 兲,
a J
a 1 ⫻ 关 J ⫹ 1兴 dimensional vector
We can use (5) m consecutive times to obtain an iterative expression for any ptm for all m ⬎ 0. For example, for pt2 we can write JOURNAL OF INTERACTIVE MARKETING
1⬍mⱕJ
where J ⫽ number of Web pages. We may represent the above in matrix form by P T ⫽ A T 䡠 K, where P
冘
for
and K ⫽ a [J ⫹ 1] ⫻ J matrix, as follows: ●
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0 1 2 3 䡠 䡠 J⫺1 J
冤
Matrix K 共inside brackets兲 1 2··· J⫺1 1 1 2 1 2 · · ·J⫺1 共1 ⫺ 1 兲 共1 ⫺ 1 兲2 共1 ⫺ 1 兲2 · · ·J⫺1 0 共1 ⫺ 2 兲 共1 ⫺ 2 兲3 · · ·J⫺1 0 0 共1 ⫺ 3 兲4 · · ·J⫺1 䡠 䡠 䡠 䡠 䡠 䡠 0 0 共1 ⫺ J⫺1 兲 0 0 0
J 1 2 · · ·J⫺1 J 共1 ⫺ 1 兲2 · · ·J⫺1 J 共1 ⫺ 2 兲3 · · ·J⫺1 J 共1 ⫺ 3 兲4 · · ·J⫺1 J 䡠 䡠 共1 ⫺ J⫺1 兲J 共1 ⫺ J 兲
冥
total perceived waiting time, ¥m ⫽ 1, . . ., J (ptm), can be written
Let kij ⫽ the (i, j)th element of matrix K, for 0 ⱕ i ⱕ J, 1 ⱕ j ⱕ J, and note that kij ⫽ 0 for i ⬎ j. Since ptm may be written as the inner product of the AT vector and the mth column vector of K, and since the total perceived waiting time, TPWT, is ¥m ⫽ 1, . . ., J (ptm), then, if we let the sum of row i of K be denoted by Si, with Si forming the (column) vector S, the total perceived waiting time can also be viewed as the inner product of AT and S. Thus,
TPWT ⫽
冘
m⫽1,. . .,J
共p tm 兲 ⫽
冘
共a tm 䡠 Sm 兲
(10)
m⫽1,. . .,J
and, as indicated in (10), TPWT is equal to a linear combination of the actual waiting times. The weights, Sm, are
S0 ⫽ 1 ⫹ 1 䡠 2 ⫹ 1 䡠 2 䡠 3 ⫹ · · · ⫹ 1 䡠 2 䡠 · · · 䡠 J S 1 ⫽ 共1 ⫺ 1 兲 ⫹ 共1 ⫺ 1 兲 䡠 2 ⫹ 共1 ⫺ 1 兲 䡠 2 䡠 3 ⫹ · · · ⫹ 共1 ⫺ 1 兲 䡠 2 䡠 · · · 䡠 J S 2 ⫽ 0 ⫹ 共1 ⫺ 2 兲 ⫹ 共1 ⫺ 2 兲 䡠 3 ⫹ · · · ⫹ 共1 ⫺ 2 兲 䡠 3 䡠 · · · 䡠 J · · · 关z兴 S m ⫽ 共1 ⫺ m 兲 䡠 1 ⫹
再
冘
冉
冊冎
写
l⫽m⫹1,. . .,J z⫽m⫹1,. . .,l
· · · S J ⫽ 0 ⫹ 0 ⫹ 0 ⫹ · · · ⫹ 共1 ⫺ J 兲
General Case
page, indeed, is chosen to be the second page, etc.). We introduce “x” to index the order of the Web pages (since their order is to be determined— up until now we have used “m” also to index the Web pages, without ambiguity, because up to now, when presenting the above, the Web pages were assumed to be in a particular order—now the order is precisely what is at stake!). It is clear that TPWT is minimized when the largest Sm is multiplied by the smallest atx the next largest Sm is multiplied by the second smallest atx, . . ., and the smallest Sm is multiplied by the largest of the atx. This “rule” deter-
Consider the minimizing of TPWT, noting that the “decision variables” are how to order the different (set number of) Web pages, when each Web page has a specific actual time, and that the Sm values are fixed (i.e., S1, S2, etc., are fixed and are a function of the values, but are independent of our choice of the order of the pages). Then, in examining (10), we use “m” to index the S values (which are in a fixed, known order—i.e., S1 corresponds with the first page, whichever page, indeed, is chosen to be first, S2 corresponds with the second page, whichever JOURNAL OF INTERACTIVE MARKETING
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loading of Web pages in general, based on the user’s past experience4):
mines the optimal choice of ordering the Web pages.3 For example, suppose that there are five Web pages, A, B, C, D, and E, and the actual loading times, atx, are 1, 2, 3, 4, and 5, respectively (i.e., atA ⫽ 1, atB ⫽ 2, atC ⫽ 3, etc.). Suppose further that the values of the Sm are .88, 1.76, .38, .60, and .50, respectively; the source of the S values is discussed below. Then: ●
●
●
●
●
Webpage Optimal Order 1
3
4
5
Total
Page order: B A E C D Actual waiting time: 2 1 5 3 4 15 Perceived waiting time: 1.5 1.15 1.92 2.352 3.176 10.098 (1 ⫺ m ): .5 .7 .2 .4 .5
Since S1 is the second largest of the five S values, .88, then the Web page with the second smallest actual time, B in this case, with time ⫽ 2, should go first. Since S2 is the (first) largest of the five S values, 1.76, then the Web page with the (first) smallest actual time, A in this case, with time ⫽ 1, should go second. Since S3 is the fifth largest (i.e., smallest) of the S values, .38, then the Web page with the fifth smallest (i.e., largest) actual time, E in this case, with time ⫽ 5, should go third. Since S4 is the third largest of the five S values, .60, then the Web page with the third smallest actual time, C in this case, with time ⫽ 3, should go fourth. Since S5 is the fourth largest (i.e., second smallest) of the five S values, .50, then the Web page with the fourth smallest (i.e., second largest) actual time, D in this case, with time ⫽ 4, should go fifth.
The optimal order is B, A, E, C, D. The values of the Perceived waiting time row in the above table are based directly on equation (10). We have 1.5 ⫽ 1 ⫹ .5 䡠 共2 ⫺ 1兲 1.15 ⫽ 1.5 ⫹ .7 䡠 共1 ⫺ 1.5兲 1.92 ⫽ 1.15 ⫹ .2 䡠 共5 ⫺ 1.15兲 2.352 ⫽ 1.92 ⫹ .4 䡠 共3 ⫺ 1.92兲 3.176 ⫽ 2.352 ⫹ .5 䡠 共4 ⫺ 2.352兲
We illustrate how two other orders sum to a LARGER total perceived waiting time. Consider ascending order of actual waiting time: A, B, C, D, E: Webpage Optimal Order
It should be noted that, of course, the S values need to be computed from the (presumed given) values; however, this is an easy, albeit potentially tedious, task that is easily programmed, using Excel or other software. The S values above of (.88, 1.76, .38, .60, .50) were generated from values of (.5, .3, .8, .6, .5), or (1 ⫺ ) values of (.5, .7, .2, .4, .5). To summarize (assuming, arbitrarily, that pt0 ⫽ 1, reflecting, say, expectations of the time of
1
2
3
4
5
Total
Page order: A B C D E Actual waiting time: 1 2 3 4 5 15 Perceived waiting time: 1 1.7 1.96 2.776 3.888 11.324 (1 ⫺ m ): .5 .7 .2 .4 .5
Now consider descending order of actual waiting time, E, D, C, B, A:
3 For example, if we were choosing the order of 1, 2, 3, 4, 5 to form an inner product with the fixed order, 5, 4, 3, 2, 1, we would achieve a minimum by having {1 ● 5 ⫹ 2 ● 4 ⫹ 3 ● 3 ⫹ 4 ● 2 ⫹ 5 ● 1} ⫽35, and, indeed, achieve a maximum by having {1 ● 1 ⫹ 2 ● 2 ⫹ 3 ● 3 ⫹ 4 ● 4 ⫹ 5 ● 5} ⫽55.
JOURNAL OF INTERACTIVE MARKETING
2
4 The optimal order is independent of pt0. However, the total perceived waiting time at the optimal order does, of course, change with pt0.
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noted earlier, the optimal order is independent of pt0); and, we have (1 ⫺ m) ⫽ .5. We illustrate all of the (six) possible orders:
Webpage Optimal Order 1
2
3
4
5
Total
Possible solution 1:
Page order: E D C B A Actual waiting time: 5 4 3 2 1 15 Perceived waiting time: 3 3.7 3.56 2.936 1.968 15.164 (1 ⫺ m ): .5 .7 .2 .4 .5
Webpage Order
Actual waiting time: Perceived waiting time: (1 ⫺ m ):
Note how in each of the three tables, the actual waiting times (and their total), and the values of the (1 ⫺ m) position-by-position, are the same. The differences are only in the perceived waiting time row, especially the total perceived waiting time at the end of the row, based on Eq. (5), and the concept of anchoring and adjustment, as adopted from Hogarth and Einhorn’s (1992) belief adjustment model.
Possible solution 2:
1
2
3
Total
3 3.5 .5
4 3.75 .5
5 4.38 .5
12 11.63
(3, 5, 4) Webpage Order
Actual waiting time: Perceived waiting time: (1 ⫺ m ):
(1 ⴚ m) Constant A frequent situation is when the (1 ⫺ m) are constant. Indeed, as we noted above, Hogarth and Einhorn (1992) suggest that in the vast majority of cases, the (1 ⫺ m) are either constant, or, if, as information accumulates and people become more firmly committed to their beliefs, increasing. The increasing case is covered by the general case above, and cannot be further simplified, since examples can be constructed in which the (1 ⫺ m) are increasing, but different patterns of the Sm are generated. However, for the case of (1 ⫺ m) constant, we can simplify the general solution. An examination of the Sm for (1 ⫺ m) constant quickly reveals that the Sm values will be in decreasing order. That is S1 ⬎ S2 ⬎ S3 ⬎ . . . ⬎ SJ. This, in turn, leads to the simple rule:
Possible solution 3:
1
2
3
Total
3 3.5 .5
5 4.25 .5
4 4.13 .5
12 11.88
(4, 3, 5) Webpage Order
Actual waiting time: Perceived waiting time: (1 ⫺ m ):
Possible solution 4:
1
2
3
Total
4 4 .5
3 3.5 .5
5 4.25 .5
12 11.75
(4, 5, 3) Webpage Order
Actual waiting time: Perceived waiting time: (1 ⫺ m ):
To minimize total perceived waiting time when (1 ⫺ m) is constant for each position, just order the pages in ascending order of actual waiting time.
Possible solution 5:
1
2
3
Total
4 4 .5
5 4.5 .5
3 3.75 .5
12 12.25
(5, 3, 4) Webpage Order
Here is an example. Suppose there are three Web pages to be ordered, with actual times of 3, 4, and 5. Further, assume, based on past experience of this user group, that pt0 ⫽ 4 (as we JOURNAL OF INTERACTIVE MARKETING
(3, 4, 5)
Actual waiting time: Perceived waiting time: (1 ⫺ m ):
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31
1
2
3
Total
5 4.5 .5
3 3.75 .5
4 3.88 .5
12 12.13
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Possible solution 6:
Web page, 6 seconds for the 3rd Web page, and 3 seconds for the 4th Web page). Web users were asked for their assessments of the total waiting time. Based on the theory derived for optimal ordering, we predicted that the total perceived waiting time for the ascending treatment condition would be less than the total perceived waiting time for the descending treatment condition.
(5, 4, 3) Webpage Order
Actual waiting time: Perceived waiting time: (1 ⫺ m ):
1
2
3
Total
5 4.5 .5
4 4.25 .5
3 3.63 .5
12 12.38
As can be seen, the minimum total perceived time is when the order is 3, 4, 5, ascending order, the order in “Possible solution 1” above.
Results. Total perceived waiting time was the dependent variable, and the order was the independent variable in a between-subjects analysis of variance (ANOVA). Total perceived waiting time was significantly related to the order [F(1, 45) ⫽ 4.682, p ⫽ .036]. On average, the total perceived waiting time for all four Web pages was less for those exposed to the waiting times in ascending order than for those exposed to the waiting times in descending order. The mean total perceived waiting time, in seconds, for those in the ascending and descending treatment conditions were 25.48 and 30.50, respectively. This was consistent with our prediction.
EXPERIMENTS To assess the predictive validity of the model, we performed two experiments. The first experiment tested whether the order of the waiting times affected perceptions of total waiting time. The second experiment tested whether the order of the waiting times affected two variables of importance to Web site designers and marketers, specifically, the design quality of the Web site, and the likelihood of recommending the Web site to others.
Experiment #1 Forty-seven (47) Web users from a northeastern United States university community sat before a computer monitor and viewed a Web site consisting of four Web pages about the 2003 Nissan 350Z automobile. For experimental purposes, each subject viewed Web pages in the same order. A time delay, controlled by the experimenter, preceded the appearance of each Web page on the monitor; the sum of the four time delays was 30 seconds. During each time delay (i.e., while a user waited for a Web page to load), the message “Page Loading, Please Wait. . .” appeared on the monitor. Web users were assigned to one of two treatments: the length of the time delays occurred in ascending order (3 seconds while waiting for the 1st Web page to load and appear on the monitor, 6 seconds for the 2nd Web page, 9 seconds for the 3rd Web page, and 12 seconds for the 4th Web page) or in descending order (12 seconds while waiting for the 1st Web page to load and appear on the monitor, 9 seconds for the 2nd JOURNAL OF INTERACTIVE MARKETING
Experiment #2 Sixty-one (61) Web users from a northeastern United States university community (who did not participate in experiment 1) participated in experiment 2. The procedures were identical to those in experiment 1 except that Web users were asked to evaluate the design quality of the Web site (a three-item scale), and to indicate the likelihood of recommending the Web site to others. We predicted that the Web site design quality would be rated as better by those in the ascending order treatment condition than by those in the descending order treatment condition. Similarly, we predicted that the likelihood of recommending the Web site to others would be greater for those in the ascending order treatment condition than for those in the descending order treatment condition. Results. The Cronbach’s alpha for the Web site design quality scale was .8156. Design qual●
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“actual time,” in essence, equating I to a fixed total actual time. In essence, the “anchoring and adjustment bias” is beneficial when the perceived waiting time is lower than the actual waiting time, and is harmful when the perceived waiting time exceeds the actual waiting time. The optimal solution is when Total Anchoring and Adjustment Bias, “TAAB” ⫽ ¥m ⫽ 1, . . ., J (atm – ptm), is maximized; of course, J is not “preordained,” but is to be determined. (It is easily seen that maximizing TAAB is equivalent to minimizing ¥m ⫽ 1, . . ., J (ptm), since the sum of the actual waiting time, essentially, I, is fixed.) Without any constraints, the optimal solution (which maximizes TAAB) is to create one Web page with all I on it.
ity was the dependent variable, and waiting time order was the independent variable in a between-subjects analysis of variance (ANOVA). The design quality was significantly related to order [F(1, 59) ⫽ 6.324, p ⫽ .015]. On average, users who experienced waiting times in ascending order rated the design quality as being better than did those who experienced the waiting times in descending order (with means of 4.22 and 3.41, respectively, on a scale of 1[poor] to 7[excellent]). This was consistent with our prediction. In addition, the likelihood of recommending the site to others was the dependent variable, and waiting time order was the independent variable in another between-subjects analysis of variance (ANOVA). For likelihood of recommending the site to others, the result was marginally significant [F(1, 59) ⫽ 3.742, p ⫽ .058]. On average, the likelihood of recommending the Web site to others was greater for users who were exposed to the waiting times in ascending order than for those who were exposed to the waiting times in descending order (with means of 3.40 and 2.53, respectively, on a scale of 1[very unlikely] to 7[very likely]). This was consistent with our prediction.
Waiting Time Tolerance Having one “massive” page with all I units of information on it may not be very satisfactory to consumers even though total perceived waiting time is minimized. Indeed, consumers may have a waiting time tolerance for a single Web page. Let ⫽ a consumer’s maximum waiting time tolerance for a Web page to fully load and appear (before, let’s say, the consumer gives up and abandons the Web site—a most undesirable result!). Then, we wish, by choice of the locations for slice (and, thus, implicitly, J, the number of pages), to
WHERE TO SLICE?
Minimize 共Total Perceived Waiting Time兲
Now we consider the situation in which the content of the Web site is predetermined, and the order is fixed, but the locations of “slicing” into distinct pages are flexible and able to be set by the web designer. Our goal is to determine the optimal locations to slice. Since the number of pages is NOT fixed, and, indeed, is part of what is to be determined, we formulate the problem by beginning with I “units of Information” in total (as opposed to a predetermined number of pages), and desire to allocate the I units of information optimally (which determines precisely how many pages and how much of I is on each page). However, we assume that each part of I has a fixed actual time to load and appear, and, since time is what is relevant to the user, as well as being consistent with our previous exposition, we can think of I in terms of JOURNAL OF INTERACTIVE MARKETING
冘
共p tm 兲
m⫽1,. . .,J
or, equivalently, Maximize
共TAAB兲
冘
AABm ,
m⫽1,. . .,J
subject to
t ⱕ
p m
for all m
We consider here only the case in which (1 ⫺ m) is constant. In this case, and with the addition of the constraint, the optimal solution changes. In fact, in general, there is no unique solution. Indeed, an optimal solution is any solution satisfying the following conditions: The last page of the sequence of pages should have a perceived waiting time of . Nothing else mat●
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ters, except, as noted above, satisfying the constraint! (Proof discussed later.) However, as we shall see, this simple-sounding statement does not indicate that it is trivial to find a set of alternative optimal solutions.5
Consider the following illustration: Suppose that the total of the actual times (essentially, “I”) is 20, and that ⫽ 5, (1 ⫺ m) ⫽ .5, and pt0 ⫽ 1. We illustrate three optimal solutions:
Webpages Solution 1:
1
2
3
4
Actual time:
1
9
5
5
20
Perceived time:
1
5
5
5
16
Solution 2:
1
2
3
4
5
6
7
8
9
10
11
12
Sum
Actual time:
1
1
1
1
1
1
1
1
1
1
1
9
20
Perceived time:
1
1
1
1
1
1
1
1
1
1
1
5
16
Solution 3:
1
2
3
4
5
6
7
8
9
10
11
12
Sum
Actual time:
1
7
2
3
7
20
Perceived time:
1
4
3
3
5
16
5
6
8
9
10
11
12
Sum
limiting the actual “times” [amounts of I] to being an integer), it is not as flexible as it might, at first, appear. For example, as a variant of solution 1, you could not simply slice into four pages of the same lengths as in the example, but reorder the pages to be in an order of 1, 5, 5, 9. The perceived waiting times would be, respectively, 1, 3, 4, 6.5, the latter violating the constraint (making it irrelevant that the total perceived waiting time happens to be less than 16). In a variant of solution 3, pages ordered as 1, 2, 3, 7, 7, for example, would also violate the constraint (as would another variant: 7, 7, 3, 2, 1). Indeed, finding a solution to “match” the requirement that the last page have a perceived waiting time of without violating the constraint, may require an algorithm, albeit, easily constructed using Excel. Of course, some insights to an optimal solution are readily available. For example, the actual time of the last page must be greater than or equal to ; this is because the perceived waiting time of the next-to-last page has to be less than or equal to (as is the case for every page), and the perceived waiting time of the last
Note how in each solution the last perceived waiting time is 5 (boldface, inside an octagon). Recall that the perceived waiting times are determined in accordance with our key equation (5). The three solutions above have a different number of pages. However, in general, we can have multiple optimal solutions with the same number of pages (i.e., two or more optimal solutions with the same number of pages and the same total perceived waiting time). It is, perhaps, useful that there is so much flexibility in the optimal design. In fact, this flexibility provides the opportunity to choose among optimal solutions in accordance with a secondary criterion, such as a preference for ascending order, or descending order. However, even though there are potentially an infinite number of optimal solutions (not
5 It is possible that no solution exists where the perceived time of the last page equals t. For example, if I ⬍ , or I not much above , there may be no solution where ptJ ⫽ (depending, in part, on pt0). In these cases, the optimal solution is simply to have one page of I. If I can be viewed as being infinitely divisible, no generality is lost by assuming that there otherwise exists a solution.
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7
●
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constraint (i.e., perceived waiting times for each page ⱕ 5), but, while the solutions are thus feasible, the total perceived waiting time is higher than 16 (the minimum), keeping total actual time constant at 20.
page is a weighted average of the actual time of the last page and the aforementioned perceived waiting time of the next-to-last page, and must average out to a value of . Here are two examples in which the perceived waiting times for all pages do satisfy the Solution 4:
1
2
3
4
5
Actual time: Perceived time:
4 2.5
4 3.75
4 3.875
4 3.938
4 3.969
Solution 5:
1
2
3
4
5
Actual time: Perceived time:
7 4
2 3
3 3
7 5
1 3
7
8
9
10
11
Sum 20 18.03
6
7
8
9
10
11
Sum 20 18
and consider a feasible solution with (J ⫹ 1) pages, with the same condition that that last page has a perceived waiting time of , the TAAB (and thus the total perceived waiting time!) remains the same (and thus, the [J ⫹ 1] solution is an alternative optimal solution).
In both of these cases (solutions 4 and 5), the last perceived time is not ⫽ 5, but is under 5, and, thus, the total perceived waiting time exceeded the minimum (optimal) value of 16. The proof that all that matters for optimality is that the last page have a perceived waiting time of (and, of course that the constraints be satisfied that each individual page have a perceived waiting time of at most ) is somewhat tedious. Thus, we simply outline the steps it takes. Step 1 is to show that for an individual page, the “AAB” (the anchoring and adjustment benefit for an individual page— earlier we defined the total AAB, TAAB) will be larger if that page has a higher actual waiting time, everything else equal. A second step is to recognize that whenever an actual waiting time for an individual page is larger, the same page’s perceived waiting time is also larger, again, everything else equal. The next, and key step, that can be shown using the previous steps’ findings is that, for any number of pages, and the constraint that no page can have a perceived waiting time that exceeds , the TAAB is maximized (which, as we mentioned earlier, is equivalent to minimization of total perceived waiting time, our objective) when the last page has perceived waiting time of . Finally, we can show iteratively that if we have an optimal solution with J pages (i.e., one with a last page having perceived waiting time of ), JOURNAL OF INTERACTIVE MARKETING
6
SUMMARY Using consumer behavior theory (e.g., Hogarth & Einhorn, 1992; Tversky & Kahneman, 1974; Weinberg, 2000), a method was formulated for minimizing perceived waiting time in phenomena which may involve multiple waits or time delays, such as interacting with a Web site. This approach was applied to Web site design and the Internet waiting time problem, also known as the World Wide Wait. Solutions for two types of web design situations were provided: (1) The optimal ordering of a predefined number of Web pages and their associated amount of information, and (2) an optimal number of Web pages and the amount of information on each page, for a set of information in a predefined order. We provide a solution for the general case, and a simplified solution for specific patterns of belief updating behavior suggested by Hogarth and Einhorn (1992) as frequently occurring in practice. ●
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LIMITATIONS AND FUTURE RESEARCH
greater (smaller) difference between actual and perceived total waiting time (TAAB). Second, issues involving the probability distribution of individuals’ waiting time tolerance for a page, in this paper, can be explored and exploited. This issue is partially addressed for tele-queues, though not specifically for the Internet, in Mandelbaum and Shimkin (2002). Third, other types of multiple waiting-time phenomena can be investigated, such as waiting for a series of rides at an amusement park or, to order, obtain, and pay for ski equipment at different stations at a mountain ski shop (or, for that matter, in any similar retail store analogous situation). Fourth, the derived analytics can be applied to many other situations where information processing follows an anchoring and adjustment process. For example, the aggregate adjustment weights (i.e., the S’s) that obtained in the “In what order?” problem can be used to estimate precisely how far a first, last, or any ordered impression goes, and the impact of any impression relative to another. It is very likely that other extensions not noted here also exist. Finally, in modeling to minimize total perceived waiting time, it was assumed that a waiting time perception for a current Web page was based on the anchor and the actual wait for the current Web page. Other factors impact perceptions of online waiting time, such as presenting information about the wait (e.g., see Weinberg, 2000) or the color of a Web page (e.g., see Gorn et al., in press). It would be interesting to assess whether other factors interact with the anchoring and adjustment process in influencing waiting time perceptions
Certain assumptions were made for purposes of tractability. It is assumed that consumers would continue to search a Web site as long as more information was available. Situations exist, however, where this is not the case, of course. Nevertheless, the derived method for minimizing total perceived waiting time still holds in principal when applied with respect to different conditions that are known. For example, in the “slice problem” situation, if it were known that a segment of consumers would view only part of a Web site’s information, say 33% of it, then only this information should be used as the “total” in decisions about forming Web pages, and the perceived waiting time for the last Web page, among those made from this 33% subset of information, should be equal to . It is also assumed in the “slice problem” that all information is divisible without loss in meaning or impact. This, of course, will not always be true. For example, an optimal solution based on our methodology may require the information bits associated with an image to be divided across two or more Web pages (e.g., a photograph of the Red Sox’ Pedro Martinez throwing the 2003 World Series victory-clinching pitch). In some cases, however, this situation could be finessed, depending on a decision-maker’s flexibility in presenting information. For example, after seeing the “current solution,” the number of bits for the image might be begrudgingly reduced slightly, by modifying its dimensions or resolution, so that it could be placed entirely on one page, without materially affecting the total perceived waiting time. Opportunities exist to extend this research along several lines. First, issues pertaining to the area of the Internet waiting time problem can be explored further. For example, the impact of segmentation by waiting time tolerance, and a total waiting time constraint on Web site usage can be explored. Tradeoffs in designing Web pages to satisfy lower (higher) waiting time tolerances would include: more (fewer) people who would wait for a Web page’s information to load and appear, more (fewer) Web pages for displaying a fixed amount of information, and a JOURNAL OF INTERACTIVE MARKETING
REFERENCES Banks, D. (1997, March 20). What clicks? Wall Street Journal, 230 R1–R4. Dellaert, B.G.C., & Kahn, B.E. (1999). How Tolerable Is Delay?: Consumers’ Evaluations of Internet Web Sites After Waiting. Journal of Interactive Marketing, 13 (Winter), 41–54. Gorn, G., Chattopadhyay, A., Sengupta, J., & Tripathi, S. (in press). Download Times on the Internet; Does Relaxation Make the Time Go Faster? Journal of Marketing Research. ●
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ory and Empirical Support. Management Science, 48 (4), 566 –583.
Hogarth, R.M., & Einhorn, H.J. (1992). Order Effects in Belief Updating: The Belief-Adjustment Model. Cognitive Psychology, 24 (January), 1–55. Howe, P.I. (2001, June 11). Berners-Lee Aims To Fix Web Wait. The Boston Globe, C3. Hui, M.K., & Tse, D.K. (1996). What To Tell Consumers in Waits of Different Lengths: An Integrative Model of Service Evaluation. Journal of Marketing, 60 (April), 81–90. Iacobucci, D. (1998). Services: What Do We Know And Where Shall We Go? A View From Marketing. In T.E. Swartz, D.E. Bowen, & D. Iacobucci (Eds.), Advances in Services Marketing and Management (Volume 7, pp. 1–96). Greenwich, CT: JAI Press. Katz, K.L., Larson, B.M., & Larson, R.C. (1991). Prescription for the Waiting-in-Line Blues: Entertain, Enlighten, and Engage. Sloan Management Review, 32 (Winter), 44 –53. Maister, D.H. (1985). The Psychology of Waiting Lines. In J.A. Czepiel, M.R. Solomon, & C. Surprenant (Eds.), The Service Encounter (pp. 113–123). Lexington, MA: Lexington Books. Mandelbaum, A., & Shimkin, N. (2002). Adaptive Behavior of Impatient Customers in Tele-queues: The-
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Rebello, K. (1999, July 26). The Road to Webville. Businessweek, p. EB11. Rubenstein, D. (2001, May 1). Curl Adds Muscle to the Web. Software Development Times, 1. Taylor, S. (1994). Waiting for Service: The Relationship Between Delays and Evaluations of Service. Journal of Marketing, 58 (April), 56 – 69. Taylor, S. (1995). The Effects of Filled Waiting Time and Service Provider Control over the Delay on Evaluations of Service. Journal of the Academy of Marketing Science, 23 (Winter), 38 – 48. Taylor, S., & Claxton, J.D. (1994). Delays and the Dynamics of Service Evaluations. Journal of the Academy of Marketing Science, 22 (Summer), 254 –264. Tversky, A. & Kahneman, D. (1974). Judgment Under Uncertainty: Heuristics and Biases. Science, 185 (September), 1124 –1131. Weinberg, B.D. (2000). Don’t Keep Your Internet Customers Waiting Too Long at the (Virtual) Front Door. Journal of Interactive Marketing, 14 (1), 30 – 39.
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Bruce D. Weinberg Paul D. Berger Richard C. Hanna f
PAUL D. BERGER is a professor of marketing, School of Management, Boston University; e-mail: [email protected] RICHARD C. HANNA is assistant professor of marketing, Carroll School of Management, Boston College; e-mail: [email protected]
ABSTRACT Tim Berners-Lee, the inventor of the World Wide Web, has identified the waiting time problem, commonly referred to as the World Wide Wait, as a major problem that must be resolved in order for people to have rich robust Internet experiences. For the foreseeable future, slow download speeds may cost Web sites billions of dollars in opportunity loss. Using consumer behavior theory, we formulate a method for minimizing perceived waiting time in phenomena which involve multiple waits or time delays, here applied to Web site design and the Internet waiting problem. Solutions for two types of design situations are provided: (1) the © 2003 Wiley Periodicals, Inc. and Direct Marketing Educational Foundation, Inc. f JOURNAL OF INTERACTIVE MARKETING VOLUME 17 / NUMBER 4 / AUTUMN 2003 Published online in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/dir.10065
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MINIMIZING WAITING TIME IN MULTIPLE WAITING-TIME EVENTS
optimal ordering of a predefined number of Web pages, and (2) an optimal number of Web pages and the amount of information on each page, for a set of information in a predefined order. We provide a solution for the general case, and a simplified solution for specific beliefupdating patterns suggested by previous literature as frequently occurring in practice. This research contributes to the extant waiting time literature as well as provides solutions to, enhances understanding of, and encourages future research for, a persistent and important Internet and ecommerce problem that has received relatively little attention in the marketing literature.
mation that reduces uncertainty about the wait helps Web users evaluate the Web site material independently from their frustration with waiting time. Weinberg (2000) establishes that consumers process waiting time in accordance with an anchoring and adjustment process, and that this can influence perceptions of waiting time, which, in turn, can impact Web site utilization. The Internet industry has made some progress in resolving the waiting time problem. The approaches to reducing waiting time on the Internet have been primarily technical or operational in nature. However, perceptions are often more important than reality for consumers’ subjective evaluations of, for example, quality and customer satisfaction (Iacobucci, 1998).
Current Research Focus The focus of this research is to devise and describe a methodology for minimizing total perceived waiting time as part of the web design process. We provide solutions for two types of Web site design situations: (1) the optimal ordering of a predefined number of Web pages (with no predefined order) and their associated amount of information; and (2) an optimal number of Web pages and the amount of information on each Web page, for a set of information in a predefined order (with no predefined number of Web pages). This research is important because it (1) provides solutions to, enhances understanding of, and encourages future research for a persistent and important Internet and e-commerce problem that has received very little attention in the marketing literature; (2) contributes to the extant waiting time literature; and (3) offers a methodology that has promise for addressing similarly structured allied problems in different application areas.
INTRODUCTION Tim Berners-Lee, the inventor of the World Wide Web (Web), has identified the waiting time problem, commonly referred to as the World Wide Wait, as a major problem that must be resolved in order for people to have rich robust Internet experiences (Howe, 2001; Rubenstein, 2001). The speed at which information downloads from a Web site server to a Web user is central to her or him having a satisfying experience. Slow downloads are resulting in lost e-commerce sales estimated to be on the order of billions of dollars (Rebello, 1999). The persistence of the waiting time problem is limiting the advancement of true interactivity through the Internet (Banks, 1997).
WAITING TIME ON THE INTERNET Waiting time is a well-established area of importance in the marketing literature, with implications for service quality (e.g., Hui and Tse, 1996; Iacobucci, 1998; Maister, 1985; Taylor, 1994, 1995; Taylor and Claxton, 1994; Katz, Larson, & Larson, 1991). An important finding is that a reduction in perceived waiting time can influence service evaluations positively. Research by marketers on Internet waiting time, however, is sparse. Dalleart and Kahn (1999) suggest inforJOURNAL OF INTERACTIVE MARKETING
HOGARTH AND EINHORN’S BELIEFADJUSTMENT MODEL Hogarth and Einhorn (1992), in a paper discussing order effects in belief updating after new information is provided, suggest that re●
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S m⫺1 ⫽ anchor or prior opinion after evaluating (m ⫺ 1) pieces of information (the initial strength of belief is denoted S 0 ) s( x m ) ⫽ subjective evaluation of the mth piece of evidence R ⫽ the reference point or background against which the impact of the mth piece of evidence is evaluated W m ⫽ the adjustment weight for the mth piece of evidence (0 ⱕ W m ⱕ 1)
search studying the effect of temporal delays (among other variables) on this process would be “illuminating.” This paper discusses research pertaining to the effects of temporal delays in systems with multiple waiting-time events on consumer information search behavior—specifically, when consumers search for information on the World Wide Web. We now discuss the belief-adjustment model proposed by Hogarth and Einhorn (1992). Then, we adapt their model to situations where a sequence of ordered temporal delays (i.e., waiting times) are estimated by consumers and are the basis for continuing or ceasing information search. Specifically, we apply the model to Web site design and consider the implications for other types of systems that contain multiple waiting-time events. The Belief-Adjustment model, which is based on anchoring and adjustment, may not have explicitly stated the applicability of the anchoring and adjustment process to perceptions of waiting time. However, Weinberg (2000) showed explicitly that the anchoring and adjustment process does apply to perceptions of waiting time; therefore, we believe that it is reasonable to model waiting time perceptions under this assumption. It should be noted that there are several processes that can be consistent with our adapted model. However, we retain the anchoring and adjustment phrasing since it is consistent with the stated philosophy of Hogarth and Einhorn’s (1992) belief-updating model, which we rely upon heavily.
In essence, the adjustment weight measures the degree to which an update influences the current data (i.e., the ”evidence”) vs. the previously held opinion.
MODIFYING THE BELIEF-ADJUSTMENT MODEL FOR WAITING-TIME ON THE WORLD WIDE WEB It is assumed that after “clicking” on a linking icon (i.e., selecting a link to another Web page), a consumer experiences a wait of some duration for the Web page information (to which one is linking) to fully load and appear (on a monitor). In addition, it is assumed that a consumer has a waiting tolerance for each Web page; i.e., there is a maximum length of a time that a consumer is willing to wait for Web page information to fully load and appear. A consumer ceases to wait for the Web page information, and, hence, does not view the Web page information if the waiting duration exceeds a consumer’s waiting tolerance; otherwise, a consumer waits for the Web page information to fully load and appear. Given this process, a consumer is using a step-by-step process1 when waiting for information on the Web. Using R ⫽ Sm (for estimation tasks2), (1) becomes
The Model Hogarth and Einhorn (1992) describe a model of belief updating with a focus on order effects. Their Belief-Adjustment Model is S m ⫽ S m⫺1 ⫹ W m关s共 x m兲 ⫺ R兴
S m ⫽ S m⫺1 ⫹ ␣ 䡠 S m⫺1 䡠 共s共 x m兲 ⫺ S m⫺1兲
(1)
when s共xm 兲 ⱕ Sm⫺1
(2a)
where 1
S m ⫽ degree of belief in some hypothesis, impression or attitude after evaluating m pieces of evidence (0 ⱕ S m ⱕ 1) JOURNAL OF INTERACTIVE MARKETING
For a discussion of step-by-step processes vs. end-of-sequence processes, see Hogarth and Einhorn (1992). 2 For discussion of Estimation tasks vs. Evaluation tasks, again see Hogarth and Einhorn (1992).
●
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proportional) to the anchor. These weights may be constant or take on any pattern. A model of perceived waiting time, independent of the direction of (atm ⫺ ptm⫺1) is
and S m ⫽ S m⫺1 ⫹  䡠 共1 ⫺ S m⫺1兲 䡠 共s共 x m兲 ⫺ S m⫺1兲 when s共xm 兲 ⬎ Sm⫺1
(2b)
t ⫽ pt m⫺1 ⫹ W m 䡠 共 at m ⫺ pt m⫺1兲.
The general formulations of Eqs. (2a) and (2b), fully derived in Hogarth and Einhorn (1992), were for negative and positive information, respectively. Waiting time, of course, is not one of the more frequently-encountered “higher the better” criterion variables, but a “lower the better” criterion variable; thus, we take the view that a waiting time greater than Sm ⫺ 1 is analogous to negative information and a waiting time less than Sm⫺1 is analogous to positive information. Retaining the orientation of ␣ and , and modifying the notation to specifically reflect actual waiting time and perceived waiting time, Eqs. (2a) and (2b) become
p m
And to, perhaps, more directly emphasize the anchoring and adjustment bias, (4) may be rewritten as t ⫽ pt m⫺1 ⫹ 共1 ⫺ m兲 䡠 共 at m ⫺ pt m⫺1兲
p m
t ⫽ pt m⫺1 ⫹ ␣ m 䡠 共 at m ⫺ pt m⫺1兲 t ⬎ p tm⫺1
a m
(3a)
and
Minimizing Waiting Time One important criterion/objective in optimal Web site design is to minimize total perceived waiting time. In this paper, we consider two different specific situations that a Web site designer could face. “In What Order?”: In this situation, two conditions exist. First, a Web site is already designed—specifically, the number of Web pages and the content/size of each page have been determined (by management opinion or by the nature of the circumstances of the message [e.g., a certain total set of products or features must be illustrated, and for practical reasons, one per page]); and second, the marketer maintains control over (download) waiting times. There are two general types of Web sites where marketers maintain this control: In one type, the user has no control over the order in which Web pages may be viewed, and in the other type, the user has control over the order in which Web pages may be viewed. The former type is not encountered with great
t ⫽ pt m⫺1 ⫹  m 䡠 共 at m ⫺ pt m⫺1兲
p m
when
t ⱕ p tm⫺1
a m
(3b)
where ⫽ the perceived waiting time for webpage m (to fully load and appear) a t m ⫽ the actual waiting time for webpage m p t m⫺1 ⫽ the anchor or perceived waiting time for webpage m ⫺ 1 ␣ m ⫽ negative-information adjustment weight for the mth waiting time (associated with the mth webpage), when its actual waiting time exceeds its perceived waiting time  m ⫽ positive-information adjustment weight for the mth waiting time (associated with the mth webpage), when its actual waiting time is less than its perceived waiting time. ptm
Note that the adjustment weights, ␣ and , are not assumed to be proportional (or inversely JOURNAL OF INTERACTIVE MARKETING
(5)
where (1 ⫺ m) ⫽ Wm and 0 ⱕ m ⱕ 1. Equation (5) is key - in this form, it can be seen more clearly how m represents the degree to which the anchor “retards” the perceived waiting time. When m ⫽ 0, there is “zero” retardation, and ptm ⫽ atm. As m increases toward 1, the larger the degree to which ptm ⫽ atm, and the larger the degree to which the anchor, ptm⫺1, plays a more prominent role.
p m
when
(4)
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t ⫽ pt 0 ⫹ 共1 ⫺ 1兲 䡠 共 at 1 ⫺ pt 0兲 pt 2 ⫽ pt 1 ⫹ 共1 ⫺ 2兲 䡠 共 at 2 ⫺ pt 1兲
frequency; for example, see the photo galleries at Boston.com where each photo may be viewed only in the order pre-determined by Boston.com. The latter type is observed reasonably often and, given Web site developer preferences and trends, will become increasingly common; an example of this type of Web site (or coherent set of Web pages) is (Macromedia) Flash-based. Flash provides Web site developers with control over when waiting times will occur (through control over when content is to be downloaded), irrespective of the order in which users view Web pages (for example, see Rolls-RoyceMotorCars.com, Sony’s S2 Sports “Experience” Web pages, or Versace.com). What is to be determined (i.e., the decision variable) is, technically, the order in which waiting times are to occur; however, without too much loss of generality, we can also consider the decision variable as the order of the Web pages or the order in which Web pages are downloaded. “Where to Slice?”: A Web site is already designed in terms of the content and length, and the order of the information is fixed. What is to be optimized is where to slice the content into pages (Situation 2).
p 1
(6) (7)
and then plug (6) into (7) to produce t ⫽ 兵 pt 0 ⫹ 共1 ⫺ 1兲 䡠 共 at 1 ⫺ pt 0兲其 ⫹ 共1 ⫺ 2兲
p 2
䡠 共 at 2 ⫺ 兵 pt 0 ⫹ 共1 ⫺ 1兲 䡠 共 at 1 ⫺ pt 0兲其兲
(8)
Note that in (8) the perceived waiting time of Web page 2 is now expressed in terms of actual waiting times (assuming that pt0 ⫽ at0—which is reasonable given that pt0 is unaffected by the anchoring and adjustment process). The expression in (8) for the perceived waiting time of Web page 2 can be simplified further: t ⫽ at 0 䡠 1 䡠 2 ⫹ at 1 䡠 共1 ⫺ 1兲
p 2
䡠 2 ⫹ at 2 䡠 共1 ⫺ 2兲 In general, the perceived waiting time of Web page m, ptm, can be expressed in terms of actual waiting times (again, assuming that pt0 ⫽ at0), which is shown in (9): t ⫽ at 0 䡠 1 ⫹ at 1 䡠 共1 ⫺ 1兲
p m
t ⫽ at 0 䡠 共 1 䡠 2 䡠 · · · 䡠 m兲 ⫹
p m
IN WHAT ORDER?
for m ⫽ 1
冘
i⫽1,. . .,关m⫺1兴
In this section, we first derive the general solution to the “In what order?” situation, for any pattern of adjustment weights, [i.e., (l – m) values]. Hogarth and Einhorn (1992) suggest that the pattern of adjustment weights are likely to be either constant or increasing, while agreeing that no pattern can be completely ruled out. We wish to minimize the sum of the perceived waiting times,
t 䡠 共1 ⫺ i兲 䡠 共 i⫹1 䡠 i⫹2 䡠 · · · 䡠 m兲
a i
⫹ at m 䡠 共1 ⫺ m兲
T ⫽ 共 pt 1
t
p 2
···
(9)
t
p J⫺1
t 兲,
p J
a 1 ⫻ J dimensional vector,
共 pt m兲
m⫽1,. . .,J
A
T ⫽ 共 at 0
t
a 1
···
t
a J⫺1
t 兲,
a J
a 1 ⫻ 关 J ⫹ 1兴 dimensional vector
We can use (5) m consecutive times to obtain an iterative expression for any ptm for all m ⬎ 0. For example, for pt2 we can write JOURNAL OF INTERACTIVE MARKETING
1⬍mⱕJ
where J ⫽ number of Web pages. We may represent the above in matrix form by P T ⫽ A T 䡠 K, where P
冘
for
and K ⫽ a [J ⫹ 1] ⫻ J matrix, as follows: ●
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0 1 2 3 䡠 䡠 J⫺1 J
冤
Matrix K 共inside brackets兲 1 2··· J⫺1 1 1 2 1 2 · · ·J⫺1 共1 ⫺ 1 兲 共1 ⫺ 1 兲2 共1 ⫺ 1 兲2 · · ·J⫺1 0 共1 ⫺ 2 兲 共1 ⫺ 2 兲3 · · ·J⫺1 0 0 共1 ⫺ 3 兲4 · · ·J⫺1 䡠 䡠 䡠 䡠 䡠 䡠 0 0 共1 ⫺ J⫺1 兲 0 0 0
J 1 2 · · ·J⫺1 J 共1 ⫺ 1 兲2 · · ·J⫺1 J 共1 ⫺ 2 兲3 · · ·J⫺1 J 共1 ⫺ 3 兲4 · · ·J⫺1 J 䡠 䡠 共1 ⫺ J⫺1 兲J 共1 ⫺ J 兲
冥
total perceived waiting time, ¥m ⫽ 1, . . ., J (ptm), can be written
Let kij ⫽ the (i, j)th element of matrix K, for 0 ⱕ i ⱕ J, 1 ⱕ j ⱕ J, and note that kij ⫽ 0 for i ⬎ j. Since ptm may be written as the inner product of the AT vector and the mth column vector of K, and since the total perceived waiting time, TPWT, is ¥m ⫽ 1, . . ., J (ptm), then, if we let the sum of row i of K be denoted by Si, with Si forming the (column) vector S, the total perceived waiting time can also be viewed as the inner product of AT and S. Thus,
TPWT ⫽
冘
m⫽1,. . .,J
共p tm 兲 ⫽
冘
共a tm 䡠 Sm 兲
(10)
m⫽1,. . .,J
and, as indicated in (10), TPWT is equal to a linear combination of the actual waiting times. The weights, Sm, are
S0 ⫽ 1 ⫹ 1 䡠 2 ⫹ 1 䡠 2 䡠 3 ⫹ · · · ⫹ 1 䡠 2 䡠 · · · 䡠 J S 1 ⫽ 共1 ⫺ 1 兲 ⫹ 共1 ⫺ 1 兲 䡠 2 ⫹ 共1 ⫺ 1 兲 䡠 2 䡠 3 ⫹ · · · ⫹ 共1 ⫺ 1 兲 䡠 2 䡠 · · · 䡠 J S 2 ⫽ 0 ⫹ 共1 ⫺ 2 兲 ⫹ 共1 ⫺ 2 兲 䡠 3 ⫹ · · · ⫹ 共1 ⫺ 2 兲 䡠 3 䡠 · · · 䡠 J · · · 关z兴 S m ⫽ 共1 ⫺ m 兲 䡠 1 ⫹
再
冘
冉
冊冎
写
l⫽m⫹1,. . .,J z⫽m⫹1,. . .,l
· · · S J ⫽ 0 ⫹ 0 ⫹ 0 ⫹ · · · ⫹ 共1 ⫺ J 兲
General Case
page, indeed, is chosen to be the second page, etc.). We introduce “x” to index the order of the Web pages (since their order is to be determined— up until now we have used “m” also to index the Web pages, without ambiguity, because up to now, when presenting the above, the Web pages were assumed to be in a particular order—now the order is precisely what is at stake!). It is clear that TPWT is minimized when the largest Sm is multiplied by the smallest atx the next largest Sm is multiplied by the second smallest atx, . . ., and the smallest Sm is multiplied by the largest of the atx. This “rule” deter-
Consider the minimizing of TPWT, noting that the “decision variables” are how to order the different (set number of) Web pages, when each Web page has a specific actual time, and that the Sm values are fixed (i.e., S1, S2, etc., are fixed and are a function of the values, but are independent of our choice of the order of the pages). Then, in examining (10), we use “m” to index the S values (which are in a fixed, known order—i.e., S1 corresponds with the first page, whichever page, indeed, is chosen to be first, S2 corresponds with the second page, whichever JOURNAL OF INTERACTIVE MARKETING
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loading of Web pages in general, based on the user’s past experience4):
mines the optimal choice of ordering the Web pages.3 For example, suppose that there are five Web pages, A, B, C, D, and E, and the actual loading times, atx, are 1, 2, 3, 4, and 5, respectively (i.e., atA ⫽ 1, atB ⫽ 2, atC ⫽ 3, etc.). Suppose further that the values of the Sm are .88, 1.76, .38, .60, and .50, respectively; the source of the S values is discussed below. Then: ●
●
●
●
●
Webpage Optimal Order 1
3
4
5
Total
Page order: B A E C D Actual waiting time: 2 1 5 3 4 15 Perceived waiting time: 1.5 1.15 1.92 2.352 3.176 10.098 (1 ⫺ m ): .5 .7 .2 .4 .5
Since S1 is the second largest of the five S values, .88, then the Web page with the second smallest actual time, B in this case, with time ⫽ 2, should go first. Since S2 is the (first) largest of the five S values, 1.76, then the Web page with the (first) smallest actual time, A in this case, with time ⫽ 1, should go second. Since S3 is the fifth largest (i.e., smallest) of the S values, .38, then the Web page with the fifth smallest (i.e., largest) actual time, E in this case, with time ⫽ 5, should go third. Since S4 is the third largest of the five S values, .60, then the Web page with the third smallest actual time, C in this case, with time ⫽ 3, should go fourth. Since S5 is the fourth largest (i.e., second smallest) of the five S values, .50, then the Web page with the fourth smallest (i.e., second largest) actual time, D in this case, with time ⫽ 4, should go fifth.
The optimal order is B, A, E, C, D. The values of the Perceived waiting time row in the above table are based directly on equation (10). We have 1.5 ⫽ 1 ⫹ .5 䡠 共2 ⫺ 1兲 1.15 ⫽ 1.5 ⫹ .7 䡠 共1 ⫺ 1.5兲 1.92 ⫽ 1.15 ⫹ .2 䡠 共5 ⫺ 1.15兲 2.352 ⫽ 1.92 ⫹ .4 䡠 共3 ⫺ 1.92兲 3.176 ⫽ 2.352 ⫹ .5 䡠 共4 ⫺ 2.352兲
We illustrate how two other orders sum to a LARGER total perceived waiting time. Consider ascending order of actual waiting time: A, B, C, D, E: Webpage Optimal Order
It should be noted that, of course, the S values need to be computed from the (presumed given) values; however, this is an easy, albeit potentially tedious, task that is easily programmed, using Excel or other software. The S values above of (.88, 1.76, .38, .60, .50) were generated from values of (.5, .3, .8, .6, .5), or (1 ⫺ ) values of (.5, .7, .2, .4, .5). To summarize (assuming, arbitrarily, that pt0 ⫽ 1, reflecting, say, expectations of the time of
1
2
3
4
5
Total
Page order: A B C D E Actual waiting time: 1 2 3 4 5 15 Perceived waiting time: 1 1.7 1.96 2.776 3.888 11.324 (1 ⫺ m ): .5 .7 .2 .4 .5
Now consider descending order of actual waiting time, E, D, C, B, A:
3 For example, if we were choosing the order of 1, 2, 3, 4, 5 to form an inner product with the fixed order, 5, 4, 3, 2, 1, we would achieve a minimum by having {1 ● 5 ⫹ 2 ● 4 ⫹ 3 ● 3 ⫹ 4 ● 2 ⫹ 5 ● 1} ⫽35, and, indeed, achieve a maximum by having {1 ● 1 ⫹ 2 ● 2 ⫹ 3 ● 3 ⫹ 4 ● 4 ⫹ 5 ● 5} ⫽55.
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2
4 The optimal order is independent of pt0. However, the total perceived waiting time at the optimal order does, of course, change with pt0.
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noted earlier, the optimal order is independent of pt0); and, we have (1 ⫺ m) ⫽ .5. We illustrate all of the (six) possible orders:
Webpage Optimal Order 1
2
3
4
5
Total
Possible solution 1:
Page order: E D C B A Actual waiting time: 5 4 3 2 1 15 Perceived waiting time: 3 3.7 3.56 2.936 1.968 15.164 (1 ⫺ m ): .5 .7 .2 .4 .5
Webpage Order
Actual waiting time: Perceived waiting time: (1 ⫺ m ):
Note how in each of the three tables, the actual waiting times (and their total), and the values of the (1 ⫺ m) position-by-position, are the same. The differences are only in the perceived waiting time row, especially the total perceived waiting time at the end of the row, based on Eq. (5), and the concept of anchoring and adjustment, as adopted from Hogarth and Einhorn’s (1992) belief adjustment model.
Possible solution 2:
1
2
3
Total
3 3.5 .5
4 3.75 .5
5 4.38 .5
12 11.63
(3, 5, 4) Webpage Order
Actual waiting time: Perceived waiting time: (1 ⫺ m ):
(1 ⴚ m) Constant A frequent situation is when the (1 ⫺ m) are constant. Indeed, as we noted above, Hogarth and Einhorn (1992) suggest that in the vast majority of cases, the (1 ⫺ m) are either constant, or, if, as information accumulates and people become more firmly committed to their beliefs, increasing. The increasing case is covered by the general case above, and cannot be further simplified, since examples can be constructed in which the (1 ⫺ m) are increasing, but different patterns of the Sm are generated. However, for the case of (1 ⫺ m) constant, we can simplify the general solution. An examination of the Sm for (1 ⫺ m) constant quickly reveals that the Sm values will be in decreasing order. That is S1 ⬎ S2 ⬎ S3 ⬎ . . . ⬎ SJ. This, in turn, leads to the simple rule:
Possible solution 3:
1
2
3
Total
3 3.5 .5
5 4.25 .5
4 4.13 .5
12 11.88
(4, 3, 5) Webpage Order
Actual waiting time: Perceived waiting time: (1 ⫺ m ):
Possible solution 4:
1
2
3
Total
4 4 .5
3 3.5 .5
5 4.25 .5
12 11.75
(4, 5, 3) Webpage Order
Actual waiting time: Perceived waiting time: (1 ⫺ m ):
To minimize total perceived waiting time when (1 ⫺ m) is constant for each position, just order the pages in ascending order of actual waiting time.
Possible solution 5:
1
2
3
Total
4 4 .5
5 4.5 .5
3 3.75 .5
12 12.25
(5, 3, 4) Webpage Order
Here is an example. Suppose there are three Web pages to be ordered, with actual times of 3, 4, and 5. Further, assume, based on past experience of this user group, that pt0 ⫽ 4 (as we JOURNAL OF INTERACTIVE MARKETING
(3, 4, 5)
Actual waiting time: Perceived waiting time: (1 ⫺ m ):
●
31
1
2
3
Total
5 4.5 .5
3 3.75 .5
4 3.88 .5
12 12.13
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Possible solution 6:
Web page, 6 seconds for the 3rd Web page, and 3 seconds for the 4th Web page). Web users were asked for their assessments of the total waiting time. Based on the theory derived for optimal ordering, we predicted that the total perceived waiting time for the ascending treatment condition would be less than the total perceived waiting time for the descending treatment condition.
(5, 4, 3) Webpage Order
Actual waiting time: Perceived waiting time: (1 ⫺ m ):
1
2
3
Total
5 4.5 .5
4 4.25 .5
3 3.63 .5
12 12.38
As can be seen, the minimum total perceived time is when the order is 3, 4, 5, ascending order, the order in “Possible solution 1” above.
Results. Total perceived waiting time was the dependent variable, and the order was the independent variable in a between-subjects analysis of variance (ANOVA). Total perceived waiting time was significantly related to the order [F(1, 45) ⫽ 4.682, p ⫽ .036]. On average, the total perceived waiting time for all four Web pages was less for those exposed to the waiting times in ascending order than for those exposed to the waiting times in descending order. The mean total perceived waiting time, in seconds, for those in the ascending and descending treatment conditions were 25.48 and 30.50, respectively. This was consistent with our prediction.
EXPERIMENTS To assess the predictive validity of the model, we performed two experiments. The first experiment tested whether the order of the waiting times affected perceptions of total waiting time. The second experiment tested whether the order of the waiting times affected two variables of importance to Web site designers and marketers, specifically, the design quality of the Web site, and the likelihood of recommending the Web site to others.
Experiment #1 Forty-seven (47) Web users from a northeastern United States university community sat before a computer monitor and viewed a Web site consisting of four Web pages about the 2003 Nissan 350Z automobile. For experimental purposes, each subject viewed Web pages in the same order. A time delay, controlled by the experimenter, preceded the appearance of each Web page on the monitor; the sum of the four time delays was 30 seconds. During each time delay (i.e., while a user waited for a Web page to load), the message “Page Loading, Please Wait. . .” appeared on the monitor. Web users were assigned to one of two treatments: the length of the time delays occurred in ascending order (3 seconds while waiting for the 1st Web page to load and appear on the monitor, 6 seconds for the 2nd Web page, 9 seconds for the 3rd Web page, and 12 seconds for the 4th Web page) or in descending order (12 seconds while waiting for the 1st Web page to load and appear on the monitor, 9 seconds for the 2nd JOURNAL OF INTERACTIVE MARKETING
Experiment #2 Sixty-one (61) Web users from a northeastern United States university community (who did not participate in experiment 1) participated in experiment 2. The procedures were identical to those in experiment 1 except that Web users were asked to evaluate the design quality of the Web site (a three-item scale), and to indicate the likelihood of recommending the Web site to others. We predicted that the Web site design quality would be rated as better by those in the ascending order treatment condition than by those in the descending order treatment condition. Similarly, we predicted that the likelihood of recommending the Web site to others would be greater for those in the ascending order treatment condition than for those in the descending order treatment condition. Results. The Cronbach’s alpha for the Web site design quality scale was .8156. Design qual●
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“actual time,” in essence, equating I to a fixed total actual time. In essence, the “anchoring and adjustment bias” is beneficial when the perceived waiting time is lower than the actual waiting time, and is harmful when the perceived waiting time exceeds the actual waiting time. The optimal solution is when Total Anchoring and Adjustment Bias, “TAAB” ⫽ ¥m ⫽ 1, . . ., J (atm – ptm), is maximized; of course, J is not “preordained,” but is to be determined. (It is easily seen that maximizing TAAB is equivalent to minimizing ¥m ⫽ 1, . . ., J (ptm), since the sum of the actual waiting time, essentially, I, is fixed.) Without any constraints, the optimal solution (which maximizes TAAB) is to create one Web page with all I on it.
ity was the dependent variable, and waiting time order was the independent variable in a between-subjects analysis of variance (ANOVA). The design quality was significantly related to order [F(1, 59) ⫽ 6.324, p ⫽ .015]. On average, users who experienced waiting times in ascending order rated the design quality as being better than did those who experienced the waiting times in descending order (with means of 4.22 and 3.41, respectively, on a scale of 1[poor] to 7[excellent]). This was consistent with our prediction. In addition, the likelihood of recommending the site to others was the dependent variable, and waiting time order was the independent variable in another between-subjects analysis of variance (ANOVA). For likelihood of recommending the site to others, the result was marginally significant [F(1, 59) ⫽ 3.742, p ⫽ .058]. On average, the likelihood of recommending the Web site to others was greater for users who were exposed to the waiting times in ascending order than for those who were exposed to the waiting times in descending order (with means of 3.40 and 2.53, respectively, on a scale of 1[very unlikely] to 7[very likely]). This was consistent with our prediction.
Waiting Time Tolerance Having one “massive” page with all I units of information on it may not be very satisfactory to consumers even though total perceived waiting time is minimized. Indeed, consumers may have a waiting time tolerance for a single Web page. Let ⫽ a consumer’s maximum waiting time tolerance for a Web page to fully load and appear (before, let’s say, the consumer gives up and abandons the Web site—a most undesirable result!). Then, we wish, by choice of the locations for slice (and, thus, implicitly, J, the number of pages), to
WHERE TO SLICE?
Minimize 共Total Perceived Waiting Time兲
Now we consider the situation in which the content of the Web site is predetermined, and the order is fixed, but the locations of “slicing” into distinct pages are flexible and able to be set by the web designer. Our goal is to determine the optimal locations to slice. Since the number of pages is NOT fixed, and, indeed, is part of what is to be determined, we formulate the problem by beginning with I “units of Information” in total (as opposed to a predetermined number of pages), and desire to allocate the I units of information optimally (which determines precisely how many pages and how much of I is on each page). However, we assume that each part of I has a fixed actual time to load and appear, and, since time is what is relevant to the user, as well as being consistent with our previous exposition, we can think of I in terms of JOURNAL OF INTERACTIVE MARKETING
冘
共p tm 兲
m⫽1,. . .,J
or, equivalently, Maximize
共TAAB兲
冘
AABm ,
m⫽1,. . .,J
subject to
t ⱕ
p m
for all m
We consider here only the case in which (1 ⫺ m) is constant. In this case, and with the addition of the constraint, the optimal solution changes. In fact, in general, there is no unique solution. Indeed, an optimal solution is any solution satisfying the following conditions: The last page of the sequence of pages should have a perceived waiting time of . Nothing else mat●
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ters, except, as noted above, satisfying the constraint! (Proof discussed later.) However, as we shall see, this simple-sounding statement does not indicate that it is trivial to find a set of alternative optimal solutions.5
Consider the following illustration: Suppose that the total of the actual times (essentially, “I”) is 20, and that ⫽ 5, (1 ⫺ m) ⫽ .5, and pt0 ⫽ 1. We illustrate three optimal solutions:
Webpages Solution 1:
1
2
3
4
Actual time:
1
9
5
5
20
Perceived time:
1
5
5
5
16
Solution 2:
1
2
3
4
5
6
7
8
9
10
11
12
Sum
Actual time:
1
1
1
1
1
1
1
1
1
1
1
9
20
Perceived time:
1
1
1
1
1
1
1
1
1
1
1
5
16
Solution 3:
1
2
3
4
5
6
7
8
9
10
11
12
Sum
Actual time:
1
7
2
3
7
20
Perceived time:
1
4
3
3
5
16
5
6
8
9
10
11
12
Sum
limiting the actual “times” [amounts of I] to being an integer), it is not as flexible as it might, at first, appear. For example, as a variant of solution 1, you could not simply slice into four pages of the same lengths as in the example, but reorder the pages to be in an order of 1, 5, 5, 9. The perceived waiting times would be, respectively, 1, 3, 4, 6.5, the latter violating the constraint (making it irrelevant that the total perceived waiting time happens to be less than 16). In a variant of solution 3, pages ordered as 1, 2, 3, 7, 7, for example, would also violate the constraint (as would another variant: 7, 7, 3, 2, 1). Indeed, finding a solution to “match” the requirement that the last page have a perceived waiting time of without violating the constraint, may require an algorithm, albeit, easily constructed using Excel. Of course, some insights to an optimal solution are readily available. For example, the actual time of the last page must be greater than or equal to ; this is because the perceived waiting time of the next-to-last page has to be less than or equal to (as is the case for every page), and the perceived waiting time of the last
Note how in each solution the last perceived waiting time is 5 (boldface, inside an octagon). Recall that the perceived waiting times are determined in accordance with our key equation (5). The three solutions above have a different number of pages. However, in general, we can have multiple optimal solutions with the same number of pages (i.e., two or more optimal solutions with the same number of pages and the same total perceived waiting time). It is, perhaps, useful that there is so much flexibility in the optimal design. In fact, this flexibility provides the opportunity to choose among optimal solutions in accordance with a secondary criterion, such as a preference for ascending order, or descending order. However, even though there are potentially an infinite number of optimal solutions (not
5 It is possible that no solution exists where the perceived time of the last page equals t. For example, if I ⬍ , or I not much above , there may be no solution where ptJ ⫽ (depending, in part, on pt0). In these cases, the optimal solution is simply to have one page of I. If I can be viewed as being infinitely divisible, no generality is lost by assuming that there otherwise exists a solution.
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7
●
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constraint (i.e., perceived waiting times for each page ⱕ 5), but, while the solutions are thus feasible, the total perceived waiting time is higher than 16 (the minimum), keeping total actual time constant at 20.
page is a weighted average of the actual time of the last page and the aforementioned perceived waiting time of the next-to-last page, and must average out to a value of . Here are two examples in which the perceived waiting times for all pages do satisfy the Solution 4:
1
2
3
4
5
Actual time: Perceived time:
4 2.5
4 3.75
4 3.875
4 3.938
4 3.969
Solution 5:
1
2
3
4
5
Actual time: Perceived time:
7 4
2 3
3 3
7 5
1 3
7
8
9
10
11
Sum 20 18.03
6
7
8
9
10
11
Sum 20 18
and consider a feasible solution with (J ⫹ 1) pages, with the same condition that that last page has a perceived waiting time of , the TAAB (and thus the total perceived waiting time!) remains the same (and thus, the [J ⫹ 1] solution is an alternative optimal solution).
In both of these cases (solutions 4 and 5), the last perceived time is not ⫽ 5, but is under 5, and, thus, the total perceived waiting time exceeded the minimum (optimal) value of 16. The proof that all that matters for optimality is that the last page have a perceived waiting time of (and, of course that the constraints be satisfied that each individual page have a perceived waiting time of at most ) is somewhat tedious. Thus, we simply outline the steps it takes. Step 1 is to show that for an individual page, the “AAB” (the anchoring and adjustment benefit for an individual page— earlier we defined the total AAB, TAAB) will be larger if that page has a higher actual waiting time, everything else equal. A second step is to recognize that whenever an actual waiting time for an individual page is larger, the same page’s perceived waiting time is also larger, again, everything else equal. The next, and key step, that can be shown using the previous steps’ findings is that, for any number of pages, and the constraint that no page can have a perceived waiting time that exceeds , the TAAB is maximized (which, as we mentioned earlier, is equivalent to minimization of total perceived waiting time, our objective) when the last page has perceived waiting time of . Finally, we can show iteratively that if we have an optimal solution with J pages (i.e., one with a last page having perceived waiting time of ), JOURNAL OF INTERACTIVE MARKETING
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SUMMARY Using consumer behavior theory (e.g., Hogarth & Einhorn, 1992; Tversky & Kahneman, 1974; Weinberg, 2000), a method was formulated for minimizing perceived waiting time in phenomena which may involve multiple waits or time delays, such as interacting with a Web site. This approach was applied to Web site design and the Internet waiting time problem, also known as the World Wide Wait. Solutions for two types of web design situations were provided: (1) The optimal ordering of a predefined number of Web pages and their associated amount of information, and (2) an optimal number of Web pages and the amount of information on each page, for a set of information in a predefined order. We provide a solution for the general case, and a simplified solution for specific patterns of belief updating behavior suggested by Hogarth and Einhorn (1992) as frequently occurring in practice. ●
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greater (smaller) difference between actual and perceived total waiting time (TAAB). Second, issues involving the probability distribution of individuals’ waiting time tolerance for a page, in this paper, can be explored and exploited. This issue is partially addressed for tele-queues, though not specifically for the Internet, in Mandelbaum and Shimkin (2002). Third, other types of multiple waiting-time phenomena can be investigated, such as waiting for a series of rides at an amusement park or, to order, obtain, and pay for ski equipment at different stations at a mountain ski shop (or, for that matter, in any similar retail store analogous situation). Fourth, the derived analytics can be applied to many other situations where information processing follows an anchoring and adjustment process. For example, the aggregate adjustment weights (i.e., the S’s) that obtained in the “In what order?” problem can be used to estimate precisely how far a first, last, or any ordered impression goes, and the impact of any impression relative to another. It is very likely that other extensions not noted here also exist. Finally, in modeling to minimize total perceived waiting time, it was assumed that a waiting time perception for a current Web page was based on the anchor and the actual wait for the current Web page. Other factors impact perceptions of online waiting time, such as presenting information about the wait (e.g., see Weinberg, 2000) or the color of a Web page (e.g., see Gorn et al., in press). It would be interesting to assess whether other factors interact with the anchoring and adjustment process in influencing waiting time perceptions
Certain assumptions were made for purposes of tractability. It is assumed that consumers would continue to search a Web site as long as more information was available. Situations exist, however, where this is not the case, of course. Nevertheless, the derived method for minimizing total perceived waiting time still holds in principal when applied with respect to different conditions that are known. For example, in the “slice problem” situation, if it were known that a segment of consumers would view only part of a Web site’s information, say 33% of it, then only this information should be used as the “total” in decisions about forming Web pages, and the perceived waiting time for the last Web page, among those made from this 33% subset of information, should be equal to . It is also assumed in the “slice problem” that all information is divisible without loss in meaning or impact. This, of course, will not always be true. For example, an optimal solution based on our methodology may require the information bits associated with an image to be divided across two or more Web pages (e.g., a photograph of the Red Sox’ Pedro Martinez throwing the 2003 World Series victory-clinching pitch). In some cases, however, this situation could be finessed, depending on a decision-maker’s flexibility in presenting information. For example, after seeing the “current solution,” the number of bits for the image might be begrudgingly reduced slightly, by modifying its dimensions or resolution, so that it could be placed entirely on one page, without materially affecting the total perceived waiting time. Opportunities exist to extend this research along several lines. First, issues pertaining to the area of the Internet waiting time problem can be explored further. For example, the impact of segmentation by waiting time tolerance, and a total waiting time constraint on Web site usage can be explored. Tradeoffs in designing Web pages to satisfy lower (higher) waiting time tolerances would include: more (fewer) people who would wait for a Web page’s information to load and appear, more (fewer) Web pages for displaying a fixed amount of information, and a JOURNAL OF INTERACTIVE MARKETING
REFERENCES Banks, D. (1997, March 20). What clicks? Wall Street Journal, 230 R1–R4. Dellaert, B.G.C., & Kahn, B.E. (1999). How Tolerable Is Delay?: Consumers’ Evaluations of Internet Web Sites After Waiting. Journal of Interactive Marketing, 13 (Winter), 41–54. Gorn, G., Chattopadhyay, A., Sengupta, J., & Tripathi, S. (in press). Download Times on the Internet; Does Relaxation Make the Time Go Faster? Journal of Marketing Research. ●
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ory and Empirical Support. Management Science, 48 (4), 566 –583.
Hogarth, R.M., & Einhorn, H.J. (1992). Order Effects in Belief Updating: The Belief-Adjustment Model. Cognitive Psychology, 24 (January), 1–55. Howe, P.I. (2001, June 11). Berners-Lee Aims To Fix Web Wait. The Boston Globe, C3. Hui, M.K., & Tse, D.K. (1996). What To Tell Consumers in Waits of Different Lengths: An Integrative Model of Service Evaluation. Journal of Marketing, 60 (April), 81–90. Iacobucci, D. (1998). Services: What Do We Know And Where Shall We Go? A View From Marketing. In T.E. Swartz, D.E. Bowen, & D. Iacobucci (Eds.), Advances in Services Marketing and Management (Volume 7, pp. 1–96). Greenwich, CT: JAI Press. Katz, K.L., Larson, B.M., & Larson, R.C. (1991). Prescription for the Waiting-in-Line Blues: Entertain, Enlighten, and Engage. Sloan Management Review, 32 (Winter), 44 –53. Maister, D.H. (1985). The Psychology of Waiting Lines. In J.A. Czepiel, M.R. Solomon, & C. Surprenant (Eds.), The Service Encounter (pp. 113–123). Lexington, MA: Lexington Books. Mandelbaum, A., & Shimkin, N. (2002). Adaptive Behavior of Impatient Customers in Tele-queues: The-
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Rebello, K. (1999, July 26). The Road to Webville. Businessweek, p. EB11. Rubenstein, D. (2001, May 1). Curl Adds Muscle to the Web. Software Development Times, 1. Taylor, S. (1994). Waiting for Service: The Relationship Between Delays and Evaluations of Service. Journal of Marketing, 58 (April), 56 – 69. Taylor, S. (1995). The Effects of Filled Waiting Time and Service Provider Control over the Delay on Evaluations of Service. Journal of the Academy of Marketing Science, 23 (Winter), 38 – 48. Taylor, S., & Claxton, J.D. (1994). Delays and the Dynamics of Service Evaluations. Journal of the Academy of Marketing Science, 22 (Summer), 254 –264. Tversky, A. & Kahneman, D. (1974). Judgment Under Uncertainty: Heuristics and Biases. Science, 185 (September), 1124 –1131. Weinberg, B.D. (2000). Don’t Keep Your Internet Customers Waiting Too Long at the (Virtual) Front Door. Journal of Interactive Marketing, 14 (1), 30 – 39.
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