The Effects of Psychological Distance on the Diagnosticity of Digits to the Left Versus Right of a Separator

Many important product attributes—such as price, weight, quantity, battery life, and calories—are expressed quantitatively; therefore, consumer decisions often involve numerical comparisons. For example, how much better is a hotel with an average rating of 4.59 than another one with a rating of 4.09? How much cheaper is $2,690 than $2,990? Similarly, people often use numbers to set goals (e.g., save $5,000 per year, achieve a 3.5 grade point average). Therefore, people's perceived goal progress and whether they will successfully achieve their goals is a function of the numerical comparison. For instance, how much progress has been made if a person's time to swim five laps has dropped from 2.39 minutes to 1.98 minutes?

The growing literature on numerical cognition has discovered that under many circumstances, individuals’ numerical judgment may not exactly follow, or may even violate, arithmetic principles in predictable ways (Chen and Rao 2007; Pandelaere, Briers, and Lembregts 2011; Raghubir 2008; Raghubir and Srivastava 2009; Thomas and Morwitz 2005; Thomas, Simon, and Kadiyali 2010). For example, studies have shown that individuals’ perceptions of numerical differences can be affected by factors such as fluency (Thomas and Morwitz 2009), unit (Pandelaere, Briers, and Lembregts 2011), presentation sequence (Biswas et al. 2013), visual characteristics (Coulter and Coulter 2007; Coulter and Norberg 2009), and pronunciation (Coulter and Coulter 2010), among others.

While previous studies have often focused on the influence of how numerical information is framed or communicated, the present work enriches this line of research by examining the possible impact of a situational factor, namely, psychological distance, on numerical comparisons. Understanding how psychological distance influences numerical comparisons is also important from a practical perspective. For example, if psychological distance could influence comparative judgment, then the same discount might be perceived differently if the purchase is made by oneself (vs. others).

The current research explores how psychological distance as a situational factor affects numerical information processing by focusing on numbers containing a separator such as a comma or decimal point that divides the number into left and right parts. This type of number is ubiquitous in the marketplace. Integrating insights from several streams of research, we hypothesize and find that psychological distancing decreases individuals’ reliance on the digits to the right of the separator and consequently changes their perception of numerical difference. By operationalizing psychological distance in different ways and using various numerical stimuli, five studies offered triangulating support for the core effect, demonstrated the underlying psychological mechanism, and identified a few theoretically derived and practically relevant boundary conditions for this effect.

The current investigation enriches the numerical cognition literature by examining how psychological distance as a situational factor influences people's processing of a particular type of number—that is, numbers containing a separator. In addition, the present work not only draws from but also adds to the psychological distance literature in several different ways. First, we demonstrate that previous findings regarding the effects of psychological distance on how people mentally construe verbal information (Bar-Anan, Liberman, and Trope 2006; Liberman, Sagristano, and Trope 2002; Trope and Liberman 2010) and visual information (Alter and Oppenheimer 2008; Amit, Algom, and Trope 2009) cannot be directly generalized to numerical comparisons, which are more nuanced and bear unique characteristics. Specifically, while previous research has robustly demonstrated that the perceived difference between two targets often decreases as psychological distance increases, we found that this is not always the case for the judgment of numerical difference.

Second, this work contributes to the literature on psychological distance by demonstrating that psychological distance affects numerical comparison differently than other types of comparisons. Previous research has shown that psychological distancing often increases perceived similarity between targets (e.g., Henderson, Trope, and Carnevale 2006; Hong and Lee 2010). By showing that psychological distance shifts the relative weight placed on left versus right digits, we shed light on the nuanced influence of how psychological distance can shape comparison judgments.

Finally, although considerable research has provided evidence for this proposition by documenting the effects of various types of psychological distance (e.g., physical, spatial, social) on construal level and related downstream consequences (Aggarwal and Zhao 2015; Irmak, Wakslak, and Trope 2013), the mechanisms underlying the effect of psychological distance on construal level remain largely unclear (see Yan, Sengupta, and Hong [2016] for an exception). By manipulating and directly measuring digit diagnosticity, we provide evidence that diagnosticity is one factor that underlies the effects of psychological distance.

Theoretical Development

The present conceptualization is built on the notion of diagnosticity. The literature on diagnosticity suggests that, all else being equal, individuals are more likely to rely on information they perceive to be diagnostic to aid their judgment and decision-making (Feldman and Lynch 1988; Lynch 2006; Menon, Raghubir, and Schwarz 1995). Following the prior literature, perceived diagnosticity here is defined as the extent to which consumers believe that a certain focal information helps them come up with a successful solution (Dick, Chakravarti, and Biehal 1990). The solution could be forming a preference, judgment, categorization, and so on. For instance, in the context of online shopping, perceived diagnosticity reflects the perceived ability of the interface to convey to customers relevant product information that helps them understand and evaluate the quality and performance of products and eventually making more informed purchase decisions (Jiang and Benbasat 2004). Taking categorization as another example, when people sort sets of objects into clusters, these clusters are usually created such that they maximize the similarity of objects within the cluster and the dissimilarity of objects between the clusters. In this process, a feature will be perceived as more diagnostic if it can help people cluster stimuli into subgroups more effectively and efficiently. Compared with a feature that is shared by all the stimuli, a feature that is only shared by some stimuli but not others will be perceived as more diagnostic (Tversky 1977).

Next, we turn to the question of how psychological distance may influence the perceived diagnosticity of digits to the left versus right of a separator. We argue that as psychological distance increases, the relative perceived diagnosticity of right digits decreases. There are several lines of reasoning for our conjecture: First, quantitative information about a psychologically distant target is more likely to change than that of a close distance, and these changes are more reflected in right digits (than left digits), thereby lowering their diagnosticity in numerical comparison. For instance, if a consumer is planning to book a restaurant for an event that is several months later, the food or service quality is likely to change during this period. However, such change is less likely to happen within a short temporal distance (e.g., in a few days). Moreover, this change is much more likely to occur for the right digits (precise decimal ratings) whereas the left digits (ballpark ratings) will be relatively stable. Therefore, the right digits of the current review score of a restaurant might be less diagnostic of future service quality. It should be acknowledged that although the relationship between temporal distance and digits diagnosticity might be objectively true in many situations, such a relationship is less intuitive for other dimensions of psychological distance. Take probabilistic distance as an example. Bagchi and Ince (2016) found that the information about a prospect will be perceived as more accurate and trustworthy (i.e., less likely to change) if that prospect will happen with a high likelihood than when the likelihood is low. For instance, when an analyst predicts that the Dow Jones will increase by 1.23% with 90% likelihood (i.e., shorter probabilistic distance), people will assume that the actual amount of increase will be very close. However, if the likelihood is only 10% (i.e., longer probabilistic distance), then people may assume a larger discrepancy between the prediction and reality. In summary, this analysis from an instability of numeric information perspective supports our notion that psychological distancing will lower the diagnosticity of the right digits.

Second, psychological distance decreases people's confidence in precise numerical processing, leads them to perceive right digits as less diagnostic. Prior research suggests that the same information is considered more diagnostic if the individual has the ability and confidence to use it (Jiang and Benbasat 2007). In the context of psychological distance, individuals often have more knowledge about psychologically close events (e.g., things that occur next week or in their local community) than distant events (e.g., things that occur next year or in a different country) and should thus have higher confidence about outcomes of close events relative to distant ones (Trope, Liberman, and Wakslak 2007). The level of confidence has been shown to affect individuals’ use of numbers such that people who are more confident about their judgments tend to use more precise numbers that contain more nonzero right digits, whereas individuals who are less confident tend to use round numbers that end with one or more zeros (Welsh, Navaro, and Begg 2011).

Even if we hold information (in)stability and confidence constant, our prediction could still be derived from a mental construal perspective. The literature has shown that psychologically close events are represented at a lower level, which is characterized by subordinate goals, secondary features, less abstraction, and context dependence. Conversely, psychologically distant stimuli are represented at a higher level, which is characterized by superordinate goals, primary features, more abstraction, and context independence (Liberman and Trope 1998; Trope and Liberman 2003; Trope, Liberman, and Wakslak 2007). Drawing on this framework, we suggest that construing targets at a higher (vs. lower) level decreases the usefulness of right digits because relying on the left digits will often be sufficient to cluster numerical information into fewer and broader subsets. Take the number 5,199 for example. If individuals only need to categorize at the broad level of thousands, then the left digit 5 will be diagnostic, whereas the right digits 199 are of little diagnostic value. However, if the classification involves a narrower category of hundreds or tens, then the diagnostic value of the right digits increases while the left digit remains diagnostic.

Finally, psychological distance may decrease people's motivation in precise numerical processing, thereby decreasing the perceived diagnosticity of right digits. Even if the information could help individuals reliably achieve desirable outcomes, they may not consider it very useful if the marginal benefit is outweighed by the cost of using it. While an extremely sensitive laboratory scale can deliver very accurate results (thus objectively very diagnostic), most people may still consider a common kitchen scale as more helpful than this high-end one if they simply want to make a bread. In the present context, while the right digits may provide additional useful information, they are usually much more difficult to process (Dehaene 1997; King and Janiszewski 2011). Therefore, the perceived diagnosticity of these digits should be lower if individuals’ need for accuracy is relatively low. In line with this reasoning, Pena-Marin and Yan (2021) found that consumers’ reliance on more or less precise numbers is contingent on their accuracy versus efficiency goals. When creating a consideration set, individuals rely more on product attributes described with less (vs. more) precise numbers because consumers’ efficiency (vs. accuracy) motivation is higher. However, at the final choice stage, when accuracy motivation increases, they weigh more a product attribute when it is more (vs. less) precise. The same logic applies for psychological distancing. For example, consumers who need to buy a house now (temporally close) are more likely to process the listing price in a more precise way ($22,380). However, those who don’t have an urgent need may simply process the first one or two digits (e.g., $20,000-ish) to have a rough idea about the housing market. Similarly, people living in the United States are sensitive to small changes in many economic indices (e.g., when the unemployment rate decreased from 6.7% to 6.3%) because a small change may make a huge difference and is relevant to many individuals.

We summarize the preceding discussion in the following hypotheses:

H₁: Psychological distancing decreases the perceived diagnosticity of digits to the right (vs. left) of a separator.

H₂: Individuals rely less on the digits to the right of a separator when making numerical judgment involving a longer (vs. shorter) psychological distance.

Moderating Role of a Separator

While our theorizing implicitly assumes that people can separate a multidigit number into two parts (i.e., left and right), this is not always the case. Thus, we suggest that our proposed effect is more likely to be observed when the number contains a separator (such as a comma or a decimal point) versus not. First, when developing our theory, one of the arguments is that psychological distance influences categorization breadth. We argue that the presence of a separator may amplify this effect. Consider the number 4,985 as an example. When psychological distance is long, the salient separator might encourage individuals to cluster at the most superordinate thousands level, making all the digits right to the separator (i.e., 985) less diagnostic. However, when the separator is absent, the categorization level will be more varied, with more categorizations being at the hundreds or tens level. As a result, the diagnosticity of the right digits (e.g., 9 or 98) will be higher. In addition to diagnosticity, individuals’ reliance on information also depends on how easy it is to use. In the current context, a separator may help people easily differentiate between more and less diagnostic information. Relatedly, a separator may also function as a psychological marker, which has been found to amplify the difference between parts separated by the marker (Dai, Milkman, and Riis 2014; Zhao, Lee, and Soman 2012). In summary, it is postulated that our effect will be less pronounced or attenuated when a separator is absent. Formally,

H₃: The proposed effect is less pronounced or attenuated when a separator is absent (vs. present).

Integrating into Construal Level Theory

Finally, it is also important to discuss how the present research relates to and further contributes to extant research on construal level theory (CLT; Trope and Liberman 2010). CLT posits that people tend to construe information at low levels and use subordinate categories when it is physically closer (spatial distance), is happening in the near future (temporal distance), is related closely to the self (social distance), or is real rather than imaginary (probabilistic distance). In contrast, when the targets are psychologically distant, people tend to construe them at a high level and use superordinate categories. Under this framework, previous research has examined a conceptually similar question, that is, how psychological distance may influence the judgment of similarity. According to this theory, two targets are more likely to be classified into the same, broader, more superordinate, and inclusive categories when individuals are psychologically far from (rather than close to) the targets, leading them to perceive the targets as more similar to each other.

For example, in a negotiation context, Henderson, Trope, and Carnevale (2006) found that agreements were more likely to be reached in the temporally distant (vs. close) condition, implying that participants saw more common interests or similarities between themselves and another player when using high- (vs. low-) level construals. Similarly, Hong and Lee (2010) found that, compared with low-level construals, high-level construals facilitate a tolerance for mixed emotions by enabling people to process opposite emotions (e.g., happiness and sadness) more inclusively, which renders them more coherent and less conflicting. However, despite these findings suggesting a main effect of psychological distance on perceived numerical difference, our theorizing suggest these findings cannot be readily generalized to numerical comparisons because of the unique properties of numerical processing.

Numerical information processing often involves a digit-by-digit approach (Coulter and Coulter 2007; Thomas and Morwitz 2005; Verguts and De Moor 2005), and this processing characteristic leads to a unique manifestation of construal level when it comes to numbers. In other verbal or visual contexts, construing an object (e.g., soda) at a higher or lower level would require moving upward to a more inclusive, superordinate category (e.g., beverage) or downward to a more specific subordinate category (e.g., Coke). However, in numerical processing, superordinate versus subordinate categories are manifested in terms of the position of the digits. The rightmost digit represents the units place, the next digit to the left represents the tens place, and so on. Therefore, digits on the left represent more superordinate categories, whereas digits on the right represent more subordinate categories. For example, in the number 1,538, the digit 1 in the thousandth place represents a high-level, superordinate category, whereas the digits 538 represent a low-level, subordinate category.

In summary, when considered within the broader framework of CLT, the resulting predictions align consistently with our prior theorizing. By highlighting the nuanced difference in terms of how construal level is manifested in verbal versus numerical contexts, the present work enriches our understanding of the CLT literature.

Overview of Studies

This research reports four studies that examine these hypotheses. Study 1 provides initial evidence for our premise that psychological distancing decreases the relative perceived diagnosticity of right (vs. left) digits (H₁). Building on this initial finding, the remaining studies examine H₂ while also evaluating H₁ through a mediation or moderation approach. Specifically, Study 2 demonstrates the downstream effects on consumer choice using an incentive-compatible task and obtains supportive evidence for the proposed underlying mechanism via mediation. Study 3 shows that our effect is attenuated among participants who believe that numerical ratings tend to be stable over time. Finally, Study 4 demonstrates that our finding is attenuated when the distinction between left and right digits is made less obvious (by removing the digit separator).

Study 1: Effects of Psychological Distance on the Diagnosticity of Left Versus Right Digits

We conducted Study 1 (https://osf.io/6yf2p) to evaluate the foundational premise underlying our theorizing that increasing psychological distance would decrease the perceived diagnosticity of the right digits to a greater extent than that of the left digits.

Method

Design

This study employed a 2 (psychological distance: close vs. far) × 2 (digit position: left vs. right) × 4 (distance dimension replicates: temporal, spatial, social, and probabilistic distances) mixed design in which the first factor was varied between subjects while the other two variables were all manipulated within subjects. In other words, each participant responded to eight items, all of which featured either a close or distal psychological distance. In addition, among the four replicates, three (temporal, spatial, and probabilistic) used a decimal point as a separator and one (social) operationalized the separator using a comma.

Participants and procedure

Recruited from Amazon's Mechanical Turk (MTurk) via CloudResearch, 210 participants (81 women, 129 men; average age = 39.33 years) were told that the study was conducted to understand how people process numeric information and estimate numeric values. On this pretense, each participant read and responded to a series of four scenarios (see Web Appendix A). For example, one of the items stated, “The monthly salary of Billy is $2,905. If you are asked to estimate the monthly salary of Sam, who is Billy's best friend and socially very close to him (who is Billy's acquaintance and socially distant from him) …” Following prior literature (Aaker and Sengupta 2000; Ahluwalia, Rao Unnava, and Burnkrant 2001), we measured participants’ perceived diagnosticity of left and right digits by asking them to indicate the extent to which they agree or disagree with two statements (1 = “strongly disagree,” and 7 = “strongly agree”): (1) “The digit ‘2’ in $2,905 is relevant and important for my estimate,” and (2) “The digits ‘905’ in $2,905 are relevant and important for my estimate.”

Results

The perceived diagnosticity measures were submitted to a repeated-measures ANOVA in which digit position and distance dimension served as within-subject variables and psychological distance served as a between-subjects factor (see the Appendix for all the means). This analysis yielded several significant effects. Specifically, the main effect of digit position shows that participants perceived the left digits (M = 6.18, SD = .75) to be more diagnostic than right digits (M = 3.85, SD = 1.06; F(1, 208) = 844.39, p < .001, d = 4.03). In addition, participants also perceived all digits to be more diagnostic when psychological distance was near (M = 5.25, SD = .58) than far (M = 4.78, SD = .74; F(1, 208) = 25.35, p < .001, d = .70), which implies that psychological distancing decreases the perceived usefulness of numeric information. More importantly, the significant interaction effect (F(1, 208) = 6.36, p = .012, d = .35) implies that psychological distance influences the perceived diagnosticity of left versus right digits unequally. In line with our hypothesis, as psychological distance increased, the perceived diagnosticity of right digits (M_near = 4.18, SD = .99 vs. M_far = 3.52, SD = 1.03; F(1, 208) = 22.93, p < .001, d = .66) decreased to a greater degree than that of the left digit (M_near = 6.31, SD = .65 vs. M_far = 6.05, SD = .83; F(1, 208) = 6.51, p = .01, d = .35). In addition, the effect of psychological distance replicate (F(1, 208) = 4.21, p = .04) and its interaction with digit position (F(1, 208) = 7.95, p = .005) are also significant.

Study 2: Testing the Downstream Consequence and Underlying Process

Study 2 (https://osf.io/bhs48) had two objectives. First, it sought to provide an initial test of the downstream consequences of Study 1's findings. To this end, we investigated the effect of temporal distance on numerical comparison and consumer choice. Temporal distance is the first dimension of psychological distance that was examined in CLT (Liberman and Trope 1998) and has been the most widely studied in the literature. In addition, understanding the temporal dynamics of consumer preference is important in its own right because consumers often need to make judgments or choices not only pertaining to the present moment in time but also with regard to the future. In addition, this experiment also employed an incentive-compatible task to assess the external validity of our findings.

Second, this study aimed to evaluate our proposed mechanism by measuring perceived digit diagnosticity and testing whether the effect of temporal distance on consumer choice could be attributable to the relative diagnosticity of the right digits. At the same time, we also assess one possible alternative account based on task involvement. According to this explanation, individuals might be more engaged in tasks related to a shorter (vs. longer) psychological distance. As a result, they would pay more attention to details such as the right digits. In this and subsequent studies, we included these measures and evaluated this possibility.

Method

Participants and design

An online panel of 200 people (130 women, 70 men; average age = 30.03 years) recruited from Credamo (an online panel in China) participated in this experiment in exchange for a small monetary award. We randomly assigned them to either the temporally close or distant condition.

Procedure

After completing a few unrelated studies, all participants were told that as a reward for their participation, they had a chance to win a 100 RMB (approximately 15 USD) voucher for a local restaurant. Participants were also informed that there were two different vouchers for two restaurants and were asked to indicate their choice. We told participants that if they eventually win the lottery, they will get the voucher for the restaurant that they have selected. To manipulate temporal distance, we told participants that the voucher could only be redeemed during the coming week or after six months. Participants in both conditions were presented with rating information for two restaurants. Restaurant A has a food rating of 4.1 and service rating of 4.3, whereas Restaurant B has a higher food rating of 4.5 but lower service score of 3.9 (see Web Appendix B).

After reviewing the information and indicating their choice, participants rated how far it was from redeeming the voucher using a seven-point scale (1 = “very close,” and 7 = “very far”). They also responded to two items measuring the perceived diagnosticity of left versus right digits. Specifically, they were asked to indicate the extent to which they agree or disagree with two statements using a seven-point scale (1 = “strongly disagree,” and 7 = “strongly agree”): (1) “The integers of the review scores were very useful/important when I made the choice,” and (2) “The decimals of the review scores were very useful/important when I made the choice.” Finally, as a measure of task involvement, they reported how engaged and careful they were when choosing the restaurant voucher (1 = “not at all,” and 7 = “very much”), for which we did not find any significant difference (p = .38 and p = .39, respectively).

Results and Discussion

Manipulation check

Participants in the temporally close condition (M = 2.05, SD = .92) felt closer to redeeming the voucher than those in the temporally distant condition (M = 5.64, SD = 1.00; F(1, 199) = 698.77, p < .001, d = 3.75), indicating that our manipulation of temporal distance worked as intended.

Restaurant choice

We predicted that in the temporally distant condition, the increased psychological distance would lead people to place less attention on right digits. As a result, Restaurant B's advantage over Restaurant A (i.e., the difference between food rating scores 4.5 vs. 4.1) would be perceived as insignificant. Furthermore, Restaurant B's disadvantage compared with Restaurant A (i.e., the difference between service rating scores 4.3 vs. 3.9) would be magnified. Therefore, participants in the temporally distant condition would be more likely to choose Restaurant A than those in the close condition. Consistent with our reasoning, the choice share of Restaurant A was higher in the temporally distant condition (61/95 or 64.2%) than in the close condition (51/105 or 48.6%), and the difference was significant (χ²(1) = 4.95, p = .026).

Diagnosticity of left versus right digits

We used two items to measure perceived diagnosticity of the integers and decimals, respectively. These two items were submitted an ANOVA with repeated measure. This analysis yielded two significant results. First, the significant within-subject effect (F(1, 198) = 30.33, p < .001, d = .78) suggests that left digits (i.e., integers; M = 5.86, SD = 1.15) are perceived as more diagnostic than right digits (i.e., decimals; M = 5.16, SD = 1.26). More importantly, a significant interaction effect (F(1, 198) = 5.08, p = .025, d = .32) shows that temporal distancing decreased the perceived diagnosticity of the right digits (M_near = 5.32, SD = 1.34 vs. M_far = 4.99, SD = 1.14; F(1, 198) = 3.58, p = .06, d = .27) but not the diagnosticity of the left digits (M_near = 5.74, SD = 1.37 vs. M_far = 5.99, SD = .83; p > .10).

Mediation analysis

We computed the difference score between the second item and the first item, with a higher score indicating greater perceived left digit diagnosticity. Then, we conducted a mediation analysis using the PROCESS macro (Hayes 2017) to examine our hypothesis that the effect of temporal distance on restaurant choice is in part driven by the change in perceived left digit diagnosticity. First, as mentioned previously, the direct effect of temporal distance on choice was significant. In addition, the effect of temporal distance on the left versus right digit diagnosticity was significant (B = .58, SE = .25; t(198) = 2.25, p = .025, d = .32). However, when both temporal distance and digit diagnosticity were included in the model, the direct path from temporal distance to restaurant choice was suppressed (B = −.47, SE = .31; Z = −1.51, p = .13), while the effect of digit diagnosticity was significant (B = −.46, SE = .10; Z = −4.45, p < .001). Bootstrapping results involving generating 5,000 resamples suggest that the indirect effect is significant, with a 95% confidence interval excluding zero [−.58, −.04]. Thus, as hypothesized, the effect of temporal distance on participants’ restaurant choice was mediated by the relative diagnosticity of the left versus right digits.

Discussion

In summary, using temporal distance, Study 2 demonstrates that the shift in the relative diagnosticity of left versus right digits caused by different psychological distance can have a downstream effect on consumer preference. It also lends support to our theorizing by demonstrating the intervening role of perceived digit diagnosticity between psychological distance and consumer choice and ruling out task involvement as an alternative explanation.

Study 3: Moderating Role of Individual Belief in Diagnosticity

In Study 3 (https://osf.io/r8hsk), we sought to further evaluate the underlying role of digit diagnosticity by examining people's lay belief (Dweck 1996) of how stable numerical ratings are over time. We argue that one reason for the decreased diagnosticity of right digits for psychological distant judgments is because numerical ratings tend to change over time. However, while people might generally believe that the right digits in numeric ratings are less diagnostic when making judgments about psychologically distant targets (as we demonstrated in Study 1), not everyone subscribes to this belief equally. To the extent that our theorizing rests on the assumption that people perceive numerical ratings to change over time, our effect should be less pronounced among people who only weakly or do not hold such a belief. For example, in the context of temporal distance, if consumers believe that a restaurant's review scores are relatively stable over time, then right digits should be perceived as being more diagnostic of future ratings or future quality, and consumers’ reliance on right digits in judgments should increase. In other words, the effect we observed previously should be attenuated or even suppressed.

In summary, we propose that our effect should be more attenuated among people who perceive that numerical ratings are relatively stable over time, thereby increasing the perceived diagnosticity of right digits. Study 3 was designed to test these predictions by means of operating psychological distance on the dimensions of spatial distance and testing the lay belief on stability of information depending on temporal distance.

Method

Design and participants

This experiment employed a two-cell (spatial distance: close vs. far) between-subjects design. We randomly assigned 210 participants recruited from MTurk (98 women, 112 men; average age = 38.97 years) to one of the conditions.

Procedure

All participants were asked to imagine booking a hotel for their upcoming trip to a city that was either close to or far away from the place they lived (Web Appendix C). After searching on the apps for a while, they find Hotels A and B, with review scores of 4.4 and 4.6, respectively. Participants were asked to indicate their willingness to pay (WTP) for Hotel B if the price of Hotel A was $100 per night (the dependent variable). To avoid extreme values, we asked participants to indicate their WTP using an 11-point scale (1 = “$100,” and 11 = “$150”). Then, participants responded to a manipulation check item (1 = “very close,” and 7 = “very far”) and two items measuring task difficulty and effort (how difficult the task was and the amount of effort they spent on it; 1 = “not at all,” and 7 = “very much”). Finally, to measure participants’ belief about whether restaurant numerical ratings are stable over time, we asked all participants to indicate the extent to which they agreed or disagreed (1 = “strongly disagree,” and 7 = “strongly agree”) with the following two statements: (1) “Hotel review scores are variational, going up and down wildly from time to time,” and (2) “Hotel review scores are generally quite stable, even though they may go up and down a little from time to time.” We then created a stability belief index by subtracting the first item from the second item, with a higher score indicating a stronger belief that review scores are stable over time. This measure was not affected by the spatial distance manipulation (p = .57).

Results and Discussion

Manipulation check

Participants in the psychologically close condition judged the trip to be closer (M = 1.57, SD = 1.20) than those in the distant condition (M = 5.99, SD = 1.83; F(208) = 440.35, p < .001, d = 2.91), indicating that our spatial distance manipulation was effective.

Willingness to pay

Since shorter psychological distance enhances attention to the right digits, we expected participants in the close condition to perceive the difference between 4.4 and 4.6 to be greater than those in the distant condition. As a result, those in close condition should be willing to pay more for the superior hotel. More importantly, we expected this effect to be attenuated among those who believe that review scores are relatively stable.

To test these predictions, we regressed participants’ WTP on spatial distance, stability belief, and their interactions. This analysis revealed three significant effects. While the main effects of spatial distance (B = −.85, SE = .27; t(206) = −3.09, p = .002, d = .43) and stability belief (B = −.56, SE = .16; t(206) = −3.56, p = .005, d = .50) are both significant, they are qualified by the interaction effect (B = .29, SE = .10; t(206) = 2.78, p = .006, d = .39).

To explore the meaning of this interaction effect, we conducted spotlight analyses at one standard deviation above and below the mean stability belief. We predicted that the effect of spatial distance on WTP would be attenuated when participants perceive review scores as more stable. In line with our predictions, when participants’ stability belief was one standard deviation below the mean (M = −2.19; i.e., participants believe that review scores will change over time), we replicated previous results such that participants in the psychologically close condition indicated a higher WTP than their counterparts in the distant condition (t(206) = −3.85, p < .001, d = .54). However, when participants’ stability belief was one standard deviation above the mean (i.e., participants believed that review scores are stable over time; M = 3.11), we did not find the previously observed effect (t(206) < 1, p > .90).

Task involvement

Finally, we found that participants in the far condition rated the task as more difficult (M_near = 1.57, SD = 1.06 vs. M_far = 1.83, SD = 1.18; F(1, 207) = 2.85, p = .09) and effortful (M_near = 4.50, SD = 1.96 vs. M_far = 4.93, SD = 1.93; F(1, 208) = 2.45, p = .12) than those in the near condition. These differences are marginally significant or very close. If these two measures were included as covariates in the previous regression analysis, the results would not change any conclusions.

Discussion

In addition to testifying the robustness of our findings by using a different dimension of psychological distance, Study 3 supports our proposed mechanism by showing that the effect of psychological distance observed in previous studies is contingent on the extent to which individuals expect the target numerical information to be fluid. Consistent with our reasoning, while we replicate previous findings among participants who believe in fluidity (therefore allowing psychological distance to change digit diagnosticity), the effect was mitigated when participants believed that the target information was relatively stable (thus, digit diagnosticity remained at a high level). Collectively, the results of this study support our proposed underlying mechanism.

Study 4: The Moderating Role of a Separator

While numbers used in prior studies all contained separators, we conducted Study 4 (https://osf.io/9hezu) to examine H₃, which predicts that our effect will be less pronounced or attenuated when a separator is absent. Investigating this question also has the potential to enrich the practical implications of the findings.

Method

Participants and design

Four hundred participants recruited from MTurk through CloudResearch were randomly assigned to one of the four conditions using a 2 (social distance: close vs. far) × 2 (comma: present vs. absent) between-subjects design.

We operationalized social distance by varying interpersonal similarities. The target person described in the decision scenario was either a 30-year-old woman named Jessica or a 60-year-old man named Michael. When recruiting participants from MTurk, we added two criteria: (1) gender was female, and (2) age was between 25 and 35 years old. Therefore, participants should perceive the 30-year-old Jessica as socially closer than the 60-year-old Michael.

Procedure

All participants read the following scenario: “To celebrate her 30^th (his 60^th) birthday, Jessica (Michael) recently wanted to buy a new car. At the locally used car dealership, she (he) finally narrowed the choice to two options. These two cars are of the same brand and make but differ in terms of miles and prices.”

The two cars differ in terms of miles and price. Relative to Car A, Car B has a high odometer reading (Car A: 36,631 miles vs. Car B: 43,256 miles) but a lower price (Car A: $22,134 vs. Car B: $19,563). Both the miles and price are five-digit numbers. In the comma present condition, both values contain a comma that separates the first two digits from the remaining three digits, whereas the comma was removed in the comma absent condition (Web Appendix D).

After reviewing the information about the two cars, all participants indicated which car they thought Jessica (Michael) would choose, which served as the main dependent variable. Then, participants responded to two manipulation check items (Liviatan, Trope, and Liberman 2008), rating how similar the target was to themselves and how close they felt to the target, using seven-point scales (1 = “not at all,” and 7 = “very much”). Finally, to test whether the social distance manipulation affected participants’ information processing motivation, they indicated how difficult the task was and the amount of effort they spent on it on a seven-point scale ranging from 1 (“not at all”) to 7 (“very much”) (Liviatan, Trope, and Liberman 2008). These two measures were not significantly influenced by the social distance manipulation (difficult: M = 1.89 vs. M = 1.77; p = .345; effort: M = 4.81 vs. M = 4.66; p = .377).

Results and Discussion

Manipulation checks

The results of two 2 (social distance: close vs. far) × 2 (comma: present vs. absent) ANOVAs show that participants rated the similar target (Jessica) as more similar to themselves (M = 4.37, SD = 1.45) and closer to themselves (M = 3.37, SD = 1.73) than the dissimilar target (Michael; similarity: M = 3.74, SD = 1.50; F(1, 396) = 18.22, p < .001; closeness: M = 2.87, SD = 1.50; F(1, 396) = 9.79, p = .002). In addition, these measures were not influenced by the presence of a comma (p = .639 and p = .410, respectively). Taken together, these results indicate that the social distance manipulation worked as intended. It is also worth mentioning that there are 38 observations in which participants’ indicated age and gender were inconsistent with our specifications (for the full dataset with 400 respondents: 396 women, 4 men; average age = 28.49 years, range = 23 to 34 years). All the conclusions remain mostly unchanged if these 38 observations were excluded (see Web Appendix E).

Car choice

We conducted a logistic regression analysis in which the manipulation of social distance, the presence of a comma, and their interaction were included to predict participants’ car choice. The main effect of comma presence is significant (B = −1.47, SE = .65, Z = −2.27, p = .023) and that of social distance is not (B = −.44, SE = .29, Z = −1.51, p = .13). Most importantly, the interaction effect is significant (B = 1.00, SE = .41, Z = 2.43, p = .0149).

To explore the meaning of this interaction, we examined the effect of social distance separately when the comma was present versus absent. When the comma is present, we expect more participants to choose Car A when social distance is proximal than distant because more attention to the right digits would strengthen Car A's advantage (miles) while mitigating its weakness (price). In line with this reasoning and replicating our previous findings, when commas were present, participants were more likely to choose Car A when social distance was close (47/99 = 47.5%) than distant (34/100 = 34%; B = .56, SE = .29, Z = 1.93, p = .0539). However, when the commas were absent, the choice share of Car A in the close condition (36/100 = 36%) did not significantly differ from that in the distant condition (47/101 = 46.5%; B = −.44, SE = .29, Z = −1.51, p = .13).

General Discussion

In this research, we investigated how psychological distance influences the perceived difference between two numbers containing a separator. Integrating insights from prior research on diagnosticity, numerical cognition, and psychological construal, we hypothesize and find that increasing psychological distancing decreases the relative diagnosticity of the right (vs. left) digits and consequently changes people’s perception of numerical difference. The four experiments provide triangulating support for this theorizing, showing that the basic effect is robust across a variety of psychological distance dimensions (e.g., temporal distance, social distance, spatial distance), numerical stimuli (different numbers, different magnitude), and dependent measures (e.g., WTP, choice). While some of these operationalizations might have introduced an alternative account, this convergence enhances our confidence in the posited conceptualization. In addition, we observed supportive evidence for our proposed underlying mechanism by measuring diagnosticity and evaluating the mediation model (Study 2) and testing two theoretically derived boundary conditions, namely, an individual's belief in numerical rating stability (Study 3) and the presence of a separator (Study 4).

However, it is worth noting that the likelihood of the present effects being observed might also be a calibration issue, depending on the numerical stimuli and how psychological distance is operationalized. Take the difference between 2,059 and 1,899, for example. While the objective difference between these two numbers is not big, their left digits differ, which would amplify the effect caused by paying more attention to the left digits. However, if these two numbers are 2,059 and 2,219, the effect of psychological distancing on comparative judgment would be less likely to be observed, since the left digits are the same. Moreover, under circumstances where individuals perceive the right digits to be highly diagnostic, the proposed effect of psychological distance is also less likely to emerge.

Theoretical Contributions

The current investigation advances theoretical knowledge on multiple fronts. First, we extend research on numerical cognition. The numerical cognition literature has shown that the perception of numerical differences is not fixed; rather, it is subject to various contextual factors such as fluency (Thomas and Morwitz 2009), units (Pandelaere, Briers, and Lembregts 2011), presentation sequence (Biswas et al. 2013), visual characteristics (Coulter and Coulter 2007; Coulter and Norberg 2009), and sound (Coulter and Coulter 2010). For example, the ease-of-computation effect (Thomas and Morwitz 2009) shows that the difference between two numbers is judged to be smaller if it is difficult to calculate the difference (e.g., 4.97 and 3.96) than when it is easy (e.g., 5.00 and 4.00), even though the objective difference is slightly higher in the former scenario. Furthermore, consumers’ perception of numerical difference can also be influenced by how these two numbers are visually presented. For instance, Coulter and Coulter (2005) found that participants judged the same discount to be more attractive when regular prices were displayed in a larger font than sale prices. Our findings not only reinforce the notion that numerical judgment is malleable but also introduce a novel situational factor by showing that the perception of numerical difference can also be shaped by situational factors such as psychological distance.

Second, our work also adds to the literature on psychological distance and construal level. Previous research on psychological distance has primarily focused on verbal (Bar-Anan, Liberman, and Trope 2006; Liberman, Sagristano, and Trope 2002; Trope and Liberman 2010) and visual (Alter and Oppenheimer 2008; Amit, Algom, and Trope 2009) information. Furthermore, most of the prior research has demonstrated a main effect of psychological distance on perceived difference such that the perceived difference between two objects is smaller when the psychological distance is greater (e.g., Henderson, Trope, and Carnevale 2006; Hong and Lee 2010; Levy, Freitas, and Salovey 2002). Our research extends prior research by focusing on numerical judgment. We provide novel insights, under certain conditions, that the traditional effect of greater distance leading to smaller perceived differences can be reversed. More generally, the present work suggests that it is important to consider the unique characteristics of how people process focal information when analyzing the effect of psychological distance.

Finally, our research contributes to literature on information diagnosticity. Previous research has demonstrated that information diagnosticity is a subjective perception influenced by various factors. Information becomes more diagnostic if it is compatible with the nature of the task (Fischer and Hawkins 1993; Lichtenstein and Slovic 1971; Tversky, Sattath, and Slovic 1988). For example, positive attributes are weighted more heavily if participants are asked to choose (vs. eliminate) one of the options (Shafir 1993). Information diagnosticity could also be affected by how information is communicated (e.g., simultaneous vs. separate presentation; Hsee 1996). More related to the present context, Nowlis and Simonson (1997) have shown that numerical information (e.g., price) is more diagnostic than nonnumerical information (e.g., brand names) in a choice task, which involves comparisons. The current work adds additional nuances to this literature by showing that even within numerical information, the relative diagnosticity of different digits may be influenced by situational factors such as psychological distance.

Practical Implications

This research also offers practical implications for marketers, especially on designing numerical marketing stimuli. First, by demonstrating that the same discount might be perceived differently depending on psychological distance, our findings suggest that marketers may need to take contextual and consumer factors into consideration. One common antecedent to psychological distance in the marketing context is the consumer–brand relationship (Connors et al. 2021). Consumers who are more connected to a brand often feel psychologically closer to it than those who are not. Thus, the same numerical difference might be perceived differently when it is expressed in different currencies or for consumers with different levels relationship with the brand. Furthermore, prior research has shown that culture and age are associated with chronic construal levels (Hong and Lee 2010). Given the conceptual overlap between psychological distance and construal level, it is possible that numerical comparative judgment may vary across people from different cultures and age groups. Thus, in designing numerical marketing stimuli, marketers may want to pay extra attention to such individual and cultural factors that may be related to psychological distance.

In addition, our research also suggests some tactics that marketers could use to influence numerical judgment. For example, by identifying the mediating role of digit diagnosticity, the present findings also suggest that marketers could influence numerical comparison by temporarily manipulating the perceived diagnosticity of different digits. For another example, the results of Study 4 show that the effect is more pronounced when a separator is present (vs. absent). Thus, depending on the situation, marketers could consider adding or removing a separator. This could be done in different ways such as switching to a different unit (e.g., 1.5 lbs vs. 24 oz) or using visual design (e.g., using different colors, adding an extra space).

Future Research

Future research could extend the current work in several ways. First, while this work highlights the distinctive features of numerical information processing, we also want to note that such distinctive characteristics of numerical cognition should not be overemphasized while ignoring commonalities. In many situations, psychological distance may influence the processing of numerical information in very similar ways, as it affects verbal and visual information processing. For example, the present findings appear to be compatible with previous findings that psychological distance influences people's reliance on primary versus secondary features (Trope and Liberman 2000), if we treat digits to the left (right) of a separator as primary (secondary) feature of a number. Therefore, a higher-level theory that specifies the conditions under which numerical information processing and other types of information processing will converge versus diverge will have the potential to make a significant contribution to the information processing literature.

In addition, it is unclear how our findings may interact with other established effects on numerical judgments. One of the most well-documented phenomena in numerical judgments is the nine-ending effect, where consumers perceive prices ending in nine (e.g., $2.99) as cheaper than prices that are just one cent higher (e.g., $3.00; Thomas and Morwitz 2005). Previous research has identified conditions under which this effect is mitigated. Hodges and Chen (2022), for example, found that the nine-ending effect is less pronounced among consumers who are more (vs. less) able to understand and work with numbers. An interesting question is whether our findings will moderate the nine-ending effect. One possibility is that consumers process nine-ending prices in a qualitatively different way, with the nine-ending digits immediately capturing consumers’ attention, in which case we would expect the nine-ending effect to hold regardless of psychological distance. Another possibility is that consumers process nine-ending prices in the same way as processing non-nine-ending prices, in which case we would expect psychological distance to moderate the nine-ending effect. Therefore, future empirical investigations addressing this question could contribute to the extensive body of research on nine endings (e.g., Schindler and Wiman 1989) by potentially uncovering another set of boundary conditions.

Lastly, in Study 4 when the commas were absent, the reversed (though not significant) pattern we observed might also be worth further investigation. In particular, the pattern suggests that the presence versus absence of a separator may lead individuals to process multidigit numbers differently. For instance, when a separator is absent, individuals may use a more holistic processing strategy, which could increase the tendency to round. Such a tendency would be stronger when the judgment is psychologically distant (vs. close). If both prices were rounded as $20,000, the price difference between Car A and Car B would be mitigated. As a result, the choice share of Car A would increase from 35.6% in the close condition to 48.3% in the distant condition. While such interpretation is in line with the data, this is purely post hoc and speculative. Future research is needed to systematically investigate the potential impact of a separator on consumer processing of numeric information (e.g., attention, memory, comprehension). Because the numeric feature of separator has not been widely examined in extant research, we believe that this would be a fruitful direction for future research.

Supplemental Material

sj-pdf-1-mrj-10.1177_00222437241262799 - Supplemental material for The Effects of Psychological Distance on the Diagnosticity of Digits to the Left Versus Right of a Separator

Supplemental material, sj-pdf-1-mrj-10.1177_00222437241262799 for The Effects of Psychological Distance on the Diagnosticity of Digits to the Left Versus Right of a Separator by Dengfeng Yan, Suhas Vijayakumar and Jiewen Hong in Journal of Marketing Research