Event frequency and comparative optimism: Another look at the indirect elicitation method of self-others risks q

Transcription

1 Journal of Experimental Social Psychology 40 (2004) Journal of Experimental Social Psychology Event frequency and comparative optimism: Another look at the indirect elicitation method of self-others risks q Yechiel Klar * and Shahar Ayal Department of Psychology, Tel-Aviv University, Ramat Aviv, 69978, Israel Received 10 April 2003; revised 4 April 2004 Available online 9 June 2004 Abstract Price, Pentecost, and Voth (2002) argue that common rather than rare negative future life events elicit greater indirect self-others comparative optimism. We argue that this finding may reflect a measurement effect: Rare events generate small differences (but large ratios), whereas common events produce larger differences (but smaller ratios). In Study 1, we show that the greater is event s perceived frequency, the greater is the numerical value assigned to express a given degree of risk discrepancy. In Study 2, we found weak negative rather than positive relations between perceived event frequency and the sense of risk discrepancy. Thus, it is crucial to understand how participants relate the two risk probabilities to each other to estimate their indirect comparative optimism. Ó 2004 Elsevier Inc. All rights reserved. Introduction Imagine two judges, A and B, who assess their own risk and the risk of the average peer to experience a particular negative event. Judge A is assigned to a common negative life event, whose rate of incidence in the general population is 80%. This judge concludes that the risk probability of the average peer to experience this negative event is 80% and that her own corresponding risk is 70%. Judge B is assigned to a rare negative life event, whose rate of incidence in the general population is 2%. This judge assesses the risk of the average peer as 2% and her own risk as 1%. Which judge, A or B, exhibits greater comparative optimism? Self-others comparative optimism, in which people systematically judge their own vulnerability to negative future life events as lower than that of their peers, is one of the most robust findings in social psychology (for reviews, Armor & Taylor, 1998; Helweg-Larsen & Shepperd, 2001; Klein & Weinstein, 1997). Two different methodologies are generally employed to study selfothers comparative optimism. In the direct elicitation q Research on this paper was supported by Grant 883/01 from the Israel Science Foundation to the first author. We are grateful to Paul Price, Heather Pentecost, and an anonymous reviewer for their helpful comments on a previous version of this paper. We also thank Chen Magal and Maher Mashour for their help in collecting the data. * Corresponding author. address: yklar@freud.tau.ac.il (Y. Klar). method, participants rate their own risk relative to that of the average peer on a single item (e.g., compared to the average classmate of your age and gender what are your chances of experiencing divorce in your lifetime ). In the indirect elicitation method (as is our two judge example), participants are asked to make two separate absolute risk estimates: one regarding the self and one regarding the average peer (e.g., my/the average member of my group s/probability of experiencing divorce during my/his/her lifetime is %) and the researcher later computes a score which is considered to reflect the participant s perceived discrepancy between personal risk and the risk of the average peer. Although these two methods have traditionally been regarded as basically interchangeable (e.g., Armor & Taylor, 1998; Klein & Weinstein, 1997), several authors have recently argued that they may mirror different judgmental processes (Giladi & Klar, 2002; Helweg-Larsen & Shepperd, 2001; Klar, 2002; Klar & Giladi, 1997, 2001; Otten & Van der Plicht, 1996; Price, Pentecost & Voth, 2002). In the most recent reassessment, Price et al. (2002) proposed a comparative optimism reversal, which states that people, when approached with the comparative method, exhibit a greater sense of self-others comparative optimism regarding rare events (e.g., committing suicide) as compared to common events (e.g., making a bad career choice), but when approached with the indirect /$ - see front matter Ó 2004 Elsevier Inc. All rights reserved. doi: /j.jesp

2 806 Y. Klar, S. Ayal / Journal of Experimental Social Psychology 40 (2004) comparative method, they demonstrate a greater sense of comparative optimism regarding common (e.g., making a bad career choice) than rare (e.g., committing suicide) events. The fact that the direct method elicits greater comparative self-others optimism for rare negative life events than more common negative life events is consistent with the bulk of the comparative optimism literature. This finding was first reported by Weinstein (1980) and has since been repeatedly replicated (e.g., Chambers, Windschitl, & Suls, 2003; Klar, Medding, & Sarel, 1996; Weinstein, 1987). Several authors (e.g., Diener & Fujita, 1997; Eiser, Pahl, & Prins, 2001; Epley & Dunning, 2000; Klar & Giladi, 1999; Kruger, 1999) have argued that in making comparative risk judgments with the direct method, participants rely primarily on their own perceived risk rather than on the corresponding others risk. As a result, rare negative life events, in which the perceived risk to both self and others is small, generate a greater sense of comparative optimism than common life events, in which both the risk to the self and to others is high. Kruger and Burrus (2004) have even showed most recently (as predicted by Klar et al., 1996) that when the negative life events are highly common, a comparative pessimism bias to the disfavor of the self emerges in the direct comparative method. However, the Price et al. paper s second contention that common rather than rare negative life events provoke greater self-others comparative optimism with the indirect method is a novel proposal, and one which raises a number of problems. First, it is inconsistent with the existing (admittedly, scant) literature on this issue. For example, Klar et al. (1996) found indirect self-others optimism for relatively rare life events (e.g., breaking a bone; injury in a car accident) but no indirect (or direct) self-others optimism whatsoever, for highly common life events (e.g., buying a faulty product; receiving poor service in restaurant). Chambers et al. (2003), using a large set of common (e.g., the store closed just when you arrived ) and rare (e.g., receiving a dog bite ) undesirable life events failed to find any positive event frequency/indirect comparative optimism correlation. Second, and most important in the context of the current paper, this proposal raises several methodological and substantial issues that relate to the very nature of the indirect method. The difference in epistemic status of the direct and indirect comparative methods Despite the fact that both the direct and indirect methods are intended to capture participants sense of self-others comparative risk, their epistemic status is strikingly different. The direct method is a straightforward self-report measure in which participants themselves directly relay to the researchers their sense of the self-others risk discrepancy. 1 In the indirect method, on the other hand, the participants do not present the researchers with their perceptions of the self-others risk discrepancy but rather provide them with the raw data to assess this discrepancy. In other words, in the indirect method, participants assess separately: (1) their own absolute risk and (2) the absolute risk of the average peer. In fact, it is not even necessary for the same participants to make the own and others risk judgments: although many indirect method studies have used a within-participants design, in which the same participants provide the two risk probabilities (e.g., Perloff & Fetzer, 1986), other studies (e.g., Harris and Middleton, 1994; Heine & Lehman, 1995; Voth and Price, 1999 cited in Price et al., 2002) have employed a betweenparticipants design, in which one group of participants provides the own risk judgment and the other group provides the others risk judgment. In both cases the researcher rather than the participants later calculates a discrepancy score from these two separate risk judgments. This may be done in more than one way. Difference or ratio scores? To estimate the magnitude of the discrepancy between two risk probabilities one may use a difference or a ratio framework. This choice determines the direction (e.g., sign) of the correlation between event frequency and comparative optimism. To demonstrate this point, the reader is invited to revisit the Judge A and Judge B example at the beginning of this paper. Clearly, which of the two judges exhibits greater comparative optimism depends on how the comparative score is analyzed. In a difference framework, Judge A, who perceives herself as 10% safer than the others in the group, is the more optimistic of the two (compared to Judge B, who perceives herself to be only 1% less at risk than the others in the group). However, in a ratio framework, Judge B, who perceives the others to be twice as much at risk than herself, is the more optimistic of the two (compared to Judge A, who perceives the others to be only 1.14 times more at risk than herself). Obviously, common (high probability) events are most likely to create greater difference scores and smaller ratios, whereas rare (low probability) events are most likely to create smaller difference scores and larger ratios. Consequently, a difference framework is likely to lead to a positive correlation between event frequency and the score for indirect comparative optimism, whereas a ratio framework for the same behavioral responses is likely to 1 This is not to claim that the direct method truly reflects the difference between own and others perceived risk. As just stated the direct measure relies mostly on own rather than others perceived risk. However, this imbalance can be regarded as a bona fide statement regarding participants sense of direct self-others risk discrepancy.

3 Y. Klar, S. Ayal / Journal of Experimental Social Psychology 40 (2004) lead to a negative correlation between event frequency and the score for indirect comparative optimism. To illustrate this point further, we analyzed the same dataset (reported in Price et al. Study 2) as either difference (other s risk minus self s risk) or ratio (other s risks divided by self s risk) scores. As can be seen in Figs. 1A and 1B, the same self-others discrepancy led to a positive correlation (r ¼ :39) between event commonness and comparative optimism when computed as difference scores, and to a negative correlation (r ¼ :35) when computed as a ratio scores. The comparative optimism literature is generally silent on whether self-others risk discrepancies are better represented as a difference or a ratio. In fact, the classical Weinstein (1980) study using the direct method adopted a ratio approach in which participants were asked to estimate their comparative risk vis-a-vis the average peer with response categories such as 80% less, 20% less, average, 100% more, 3 times average, and 5 times average (see also Price et al. Study 2 for a similar ratio scale in the direct method condition). However, most direct method studies have used ambiguous terms such as much below average to much above average, which can be construed in either ratio or difference terms. In the indirect method literature, the two separate risk probabilities are commonly analyzed as difference scores. Comparative optimism with rare and common events Clearly, the key psychological issue is how participants themselves perceive the discrepancy between the risk to self and the average peer regarding rare and common life events. As just mentioned, this issue has rarely been touched upon in the comparative optimism literature, but several insights from the perception and decision-making literatures are worth consideration. These involve possible size and unit effects. The size effect A classic psychophysical finding reflected in Weber and Fechner s laws is that the perceived magnitudes of differences change as a function of the absolute size of the stimuli creating this difference. To cite a famous illustration, the transition from the perceived light of one candle to the perceived light of two candles (i.e., small size stimuli) is much greater than the transition from 100 to 101 candles (i.e., stimuli of greater size). This perceptual truth has been noted in the decisionmaking literature, which has acknowledged the nonlinearity of probability (see Lopes, 1983, 1996 for a review). A well known example in this area is the decision weights concept in Kahneman and Tversky (1979) prospect theory which states that decision weights tend to overweight small probabilities and underweight moderate and high probabilities (the latter effect is predicted to be greater than the former). Thus, it is highly probable that the same numerical difference between own and others risk would be experienced differently in the context of rare and common life events. For example, 1.5% less at risk than the others might be perceived as a highly significant discrepancy in the context of a rare (e.g., 2%) life event, but rather insignificant in the context of a highly common (e.g., 62%) life event. Similarly, participants may assign a greater difference score to common rather than rare events to express the same felt magnitude of comparative optimism. 2 Fig. 1. (A) Relationship between mean judged frequency and mean difference scores for 20 negative life events as computed from the Price et al. (Study 2, 2002) means. (B) Relationship between mean judged frequency and mean ratio scores for 20 negative life events as computed from the Price et al. (Study 2, 2002) means. 2 The size effect is not the only problem that complicates the interpretation of the difference scores as a measure of comparative optimism. A related problem is the scale latitude effect: With a 2% life event the most optimistic participants can judge their risk as only 2% less than the others but with a 62% event the same participants can judge their risk up to 62% less at than the others. This has to do with the fact that the probabilistic scale is bounded by the absolute zero at its lower end. This allows for only small differences in the context of low probability events but much larger differences in the context of high probability events.

4 808 Y. Klar, S. Ayal / Journal of Experimental Social Psychology 40 (2004) To estimate the possible size effect, participants can be asked to provide a numerical analogue to the verbal statement X is at lower risk than the others in X s group in the context of various life events which differ in their objective frequency (i.e., size). Such a method may help to determine whether the psychological meaning of a given numerical discrepancy (e.g., being 1% less at risk) is variable or invariable across life events of different frequencies. The unit effect The numerical analogues assigned to a particular verbal statement ( X is at lower risk than the others in the group ) may further depend on the level of precision of the numerical units employed. To appreciate this problem, imagine one judge being told that others probability for a particular negative life event is 82% and a second judge being told that the same probability is 80%. Both judges are then asked to provide a numerical estimate for the statement X is at lower risk than the others in X s group. As judgmental graininess research (e.g., Yaniv & Foster, 1997) suggests, probabilistic estimates presented in more refined measurement units (e.g., 82 % rather than 80%) elicit smaller discrepancy estimates. That is, in the 82% case, participants may use single digit numbers to express the downward deviation (e.g., X risk s is 74%), whereas in the 80% case, they may use a two digit number to express the same deviation (e.g., X risk s is 70%). Several indirect method studies (e.g., Price et al., 2002, Study 2; Rothman, Klein, & Weinstein, 1996) have used response scales with varying intervals for different frequency events. Such scales may encourage participants to use more refined units for rare events and less refined units for more common events. 3 It is possible that the unit effect may emerge in conjunction with the size effect. Study 1: What is lower risk in rare and common life events: A psychophysical approach 3 For example, the indirect method participants in the Price et al. Study 2 were presented with the following visual analogue: This was a horizontal line with probabilities from 0 to 1% labeled at intervals of 0.1%, probabilities of 1 10% labeled at intervals of 1%, and probabilities from 10 to 100% labeled at 10%. This was done to encourage participants to use small probabilities including probabilities less than 1% when they thought it appropriate (p. 248). To estimate size and unit effects, we conducted a study in which participants were asked to estimate the numerical equivalent of lower risk than the others in the group for different hypothetical diseases which vary only in their objective frequency which ranges in the general population from 2 to 92% in the size only condition, and from 2 to 90% in the size with rounded units condition. Method Participants The participants were 34 students enrolled in the Israeli Open University (17 female, 17 male) who volunteered to participate in this study (mean age ¼ 29, SD ¼ 7:7). They were randomly assigned to the two experimental conditions. Design and procedure A mixed design was used. In the size only condition, participants were presented with a series of eight hypothetical scenarios of the following type: According to a survey conducted by the Israeli Health Ministry the probability that an adult will contract disease CC in the next 2 years is 72%. Dan is aware of this statistic but he believes his own probability of having the CC disease is lower than the reported probability (i.e., lower than 72%). In your opinion, what odds would Dan assign to himself? (0 100%). All participants in this condition responded to eight versions of the task, which differed only in the reported objective risk (2, 12, 22, 32, 52, 72, 82, and 92%). Order of presentation was counterbalanced and different protagonists first names were used in different versions. The disease was only identified by two letters (e.g., RR, CC, JJ, YY, EE, and MM) to avoid the possible influence of world knowledge on the true frequency of diseases. In the size with rounded units condition, the tasks and procedure were identical, with the exception that all probabilities higher than 10% were rounded off to the nearest 10. The probabilities were 2, 10, 20, 30, 50, 70, 80, and 90%. Results and discussion As can be seen in Fig. 2A, the correlations between the mean difference scores and objective event frequencies were nearly perfect in both the size only (r ¼ :97) and the size with rounded units (r ¼ :98) conditions; the joint correlation for all 16 event frequencies in Fig. 2A is.97. That is, the numerical equivalences of lower risk than the others were almost perfectly predictable by the frequency of the judged event, with a rare event (i.e., 2%), being 1.3% less at risk than the others (in the size only condition) and 1.5% less at risk (in the size with rounded units condition). However the numerical values expressing lower risk increased steadily with event frequency. In the size only condition they were 5.2, 8.4, 12.2, 17.8, 18.7, 24.4, and 22.3%, respectively, and in the size with rounded units condition, they were 4.4, 8.9, 12.3, 16.3, 19.2, 26.8, and 24.9%. We also computed individual correlations between difference scores and

5 Y. Klar, S. Ayal / Journal of Experimental Social Psychology 40 (2004) the joint correlation for all 16 events was ).68. Averaging these correlations for each participant yielded somewhat lower negative correlations in the size only (r ¼ :50; SD ¼ :27) and size with rounded units condition (r ¼ :49; SD ¼ :26). A paired samples t test revealed that the ratio scores were less impacted by the size effect than the difference scores (t ¼ 3:1, df ¼ 33, p <:005). To test whether the rounded units manipulation had an effect over and above the size effect, we conducted a series of independent sample t tests for each of the pairing probabilities (e.g., 70 vs. 72%) in the two conditions but failed to find any added unit effect. However, given the robustness of the size effect, the main withinparticipants variable in this study, it is possible that there was little room for the unit influence to have an effect over and above the size effect. Further research on this issue is needed to conclude whether unit graininess does or does not have an effect on judgments of selfothers risk discrepancies. To conclude, the robust size effect found in Study 1 strongly suggests that people are aware of the fact that the same magnitude of risk discrepancy should be expressed with greater numerical values, the more common the life event is. These results do not support the Price et al. (2002) claim that with the indirect method people experience a greater sense of comparative selfothers optimism regarding common as compared to rare negative life events. Thus, the raw difference score may indeed increase with event frequency but not the sense of risk discrepancy. Study 2: A meta-cognitive measure for further assessing the sense of self-others risk discrepancy Fig. 2. (A) Relationship between objective event frequencies and mean difference scores for 16 fictional diseases in the two experimental conditions in Study 1. (B) Relationship between objective event frequencies and mean ratio scores for sixteen fictional diseases in the two experimental conditions in Study 1. event frequency for each participant (because correlations involving averaged responses are likely to be inflated). The average of these individual correlations was.67 (SD ¼ :35) in the size only condition and.78 (SD ¼ :17) in the size with rounded unit condition. 4 In addition to the difference scores, we also computed ratio scores. The correlations between the mean ratio and event frequency across all participants (presented in Fig. 2B) were negative both in the size only (r ¼ :67) and in the size with rounded units condition (r ¼ :72); 4 We replicated the size effect with a sample of 33 high school teachers. The correlation between the mean difference scores and objective event frequencies was again nearly perfect (r ¼ :996). There are, however, several notable differences between Study 1 and the typical studies involving the indirect method. In addition, there are several limitations to the psychophysical measure employed in this study as discussed below. First, in typical indirect method studies, participants generate both risk probabilities (i.e., own and others) whereas in Study 1, the others probability was provided by the researchers, and participants were only asked to generate a corresponding numerical value for the protagonist s perceived risk. Second, in typical indirect method studies participants can choose any degree of self-others comparative optimism or pessimism, whereas in Study 1, they were explicitly instructed to generate a risk probability that represented lower risk than the others. Third, in typical indirect method studies, participants are required to provide risk estimates regarding concrete life events (e.g., heart attack) for which they most likely have rich real-life information and attitudes, whereas in Study 1 they were asked to generate risk probabilities

6 810 Y. Klar, S. Ayal / Journal of Experimental Social Psychology 40 (2004) for hypothetical diseases, with no information about the nature of these diseases, their severity, outbreak conditions, vulnerability, and consequences. Fourth, as was already alluded to, the results of Study 1 could be affected by a scale latitude effect in addition to the size effect. In other words, when others risk is small (e.g., 2%) the maximum possible downward deviation could not be larger than 2% lower than the others. However, when others risk is large (e.g., 60%), the maximum optimism could range to 60% lower than the others. Thus, expression of optimism for small probability events was constrained by the absolute zero at the lower end of the probability scale, and consequently, the scale latitude effect could have contributed to the Study 1 results. Fifth, although the Study 1 results seriously challenge the notion of a true positive correlation between event frequency and the sense of self-others indirect optimism, these results fall considerably short of portraying the relations between perceived frequency of events and the sense of indirect comparative optimism. Sixth, although Study 1 demonstrated that the ratio score is somewhat less confounded with size effect relative to the difference score, it still unclear how these two measures fare with each other in accounting for selfothers risk discrepancies for concrete, real life negative events. Furthermore, the relative efficiency of the ratio and difference scores in capturing the sense of self-others risk frequency might vary across life events which differ in their absolute frequency. It is possible that the ratio score better captures people s sense of self-others discrepancy than the difference score in small frequency events, but the superiority of the ratio may diminish or even reverse in high frequency events. For example, when thinking about a rare event our Judge B could possibly conceive her own risk (1 vs. 2%) as half the risk of the others, whereas our Judge A, thinking about a common event, might be more inclined to judge her risk (70 vs. 80%) as 10% less than the risk of the others. The meta-cognitive measure To address all these issues and further explore the Study 1 results with a converging operation, Study 2 uses a novel meta-cognitive measure for assessing the sense of self-others risk discrepancy (or pessimism), regarding own and others risk probabilities, constructed by the participants themselves. The first two steps required by the meta-cognitive measure are, in fact, identical to the standard, indirect method procedure (in within-participants studies). That is, for each life event, participants are first asked to provide two risk probabilities, own and others. In the third step, however, participants are immediately asked to review their two separate risk probabilities, and estimate how far apart from each other these risk probabilities are. For example, if they estimated others risk as 2% and own risk as 1%, they were asked to state how much lower the 1% probability is from the 2% probability. Similarly, if they estimated others risk as 60% and own risk as 50%, they were asked to estimate how much lower the 50% probability is from the 60%. The meta-cognitive approach thus addresses all the six aforementioned limitations of Study 1. In the meta-cognitive approach, participants are required (1) to generate two separate risk probabilities ( own and others ) rather than one, (2) in which they can report any degree of comparative optimism/pessimism, and (3) this is done in the context of concrete negative life events. In fact, Study 2 tests the same 20 life events used by Price et al. (2002). In addition, (4) the meta-cognitive measure is unbiased by the scale latitude constraints, because it is unbounded by a fixed 0% probability at its lower end, and does not have a fixed 100% probability at its higher end. Thus, it enables the participants to report how large or small the discrepancy between the two risk probabilities is felt to be regardless of the absolute size of the event. Furthermore, (5) the meta-cognitive measure can be used to estimate the relations between the perceived frequency of events (as indicated by others perceived risk) and the sense of selfothers discrepancies (as indicated by the meta-cognitive measure). Finally, (6) estimates of the correlations between both ratio and difference scores with the sense of self-others risk discrepancy and these correlations can be calculated for each one of the 20 events, (which differ from each other in perceived frequency). Assessing the relative efficiency of the difference and ratio frameworks within each of the events can test the notion that the advantage of the ratio over the difference is greater in low rather than high frequency life events. Method Participants Sixty nine (41 males; 28 females) paid participants, all students of the Israeli Open University (mean age ¼ 28.4; SD ¼ 7:5) took part in the study. Procedure Participants were presented with the 20 negative life events from the Price et al. (2002) study and they were asked to assess others risk, self risk, and immediately afterwards they were asked to evaluate the magnitude of risk discrepancy between these two risk judgments. Others risk. What, in your view, is the probability that the average person in the Israeli population (above 18) would experience the event (e.g., limb amputated) in the next 2 years on a scale from 0 to 100%? Participants were asked to write a percentage from 0 to 100%. Owns risk. What, in your view, is the probability that you would experience the event (e.g., limb amputated) in the next 2 years on a scale from 0 to 100%?

7 Y. Klar, S. Ayal / Journal of Experimental Social Psychology 40 (2004) Once again, the participants were asked to write a percentage from 0 to 100%. The sense of self-others risk discrepancy (SORD; the meta-cognitive measure). Immediately after completing the two separate risk judgments, participants were instructed as follows Please look at the two risk probabilities you have just made (1) the risk probability regarding the average person in the population (above 18) % and (2) the risk probability regarding yourself %. Relative to the risk probability you assigned to the average person in the entire population how did you judge your own risk probability? Participants made the SORD judgment on 11-point scale ranging from )5 (I judged my risk probability as much lower than that of the average person in the population) through 0 (I judged my risk probability as equal to that of the average person) to +5 (I judged my risk probability as much higher than that of the average person). Results and discussion The data collected in Study 2 were analyzed in a number of complementary ways. First, to obtain a preliminary picture, we examined how the event means were related to the other variables. Second, because each participant completed all experimental conditions (in a full within-participant design), we created a matrix of correlations for each participant between the main variables (e.g., others risk, own risk, and the sense of discrepancy) across life events. With these 69 (our N) independent replications, we could test for the average relations between the variables. Finally, we looked at the relations between the variables within each of the 20 life events. The events as unit of analysis Table 1 presents the means of self and others perceived risk probabilities for each of the 20 life events. In addition, this table presents the means of the difference and ratio scores, computed for the 20 life events, and the means of the sense of self-others risk discrepancies (SORD) measure for the same life events, as generated by the participants themselves. As can be seen from the table, significant indirect biases were found with the difference, ratio, and SORD measure on 19 out of the 20 life events. The exception was experiencing gum disease that generated no comparative optimism. Of major interest in the current study was whether the higher the frequency of events (as indicated by perceived others risk) was accompanied by a greater sense of selfothers risk discrepancy. The present analysis provides a preliminary assessment of these relations. We correlated the mean others risk judgments with the SORD means Table 1 Means of perceived risk for self and others, difference and ratio scores and the sense of self-others risk discrepancy (SORD) for each of the 20 life events examined in Study 2 1. Perceived others risk 2. Perceived self risk 3. Diff. (others-self) 4. Ratio (others/self) 5. SORD (sense of risk discrepancy) 6. Others- SORD correlation 7. Self-SORD correlation Limb amputated ).03 ).39 Suicide ).02 ).54 House fire ).35 AIDS ).21 ).41 Gum disease ).07 ).50 Hearing loss ).01 ).50 Death by car crash ).18 Sued ).13 ).57 Cancer ).36 Alcoholism ).72 Heart attack ).09 ).65 Car stolen ).49 Death before ).43 years of age Drops out of school ).20 ).718 college Depression ).17 ).60 Burglarized ).01 ).36 Fired from job ).23 ).70 Bad career choice ).01 ).69 Broken bone ).05 ).42 Divorce ).11 ).63 * Correlation is significant at the.05 level (two tailed). ** Correlation is significant at the.01 level (two tailed). *** Correlation is significant at the.001 level (two tailed).

8 812 Y. Klar, S. Ayal / Journal of Experimental Social Psychology 40 (2004) for the various life events. As can be seen in Fig. 3A, inconsistent with the Price et al. prediction, the direction of the correlation was negative rather than positive (r ¼ :33; p ¼ :16). In addition, the corresponding correlation with self risk judgments (portrayed in Fig. 3B) was highly negative (r ¼ :78; p <:001). A related question is whether a difference or ratio framework better captures the sense of self-others risk discrepancy. According to the rudimentary calculation that is feasible at this level of analysis, the better fit was with the ratio (r ¼ :90; p <:001) rather than the difference (r ¼ :72; p <:001) score. The participants as the unit of analysis To obtain a more refined level of analysis, we constructed a correlations matrix between the experimental events for each of the participants. The findings replicate the results obtained for the cross-event measure. We found a weak but statistically significant negative correlation (average r ¼ :12; p <:005) between the sense of self-others risk discrepancy and others risk. That is, Fig. 3. (A) Relationship between the means of perceived others risk and the SORD (sense of self-others risk discrepancy) for the 20 negative life events in Study 2. (B) Relationship between the means of perceived self risk and SORD (sense of self-others risk discrepancy) for the 20 negative events in Study 2. the SORD was somewhat lower (rather than higher) when others risk was perceived as high. The correlation of the SORD with own risk was high and negative (average r ¼ :64; p <:001). That is, the lower the self perceived risk, the higher the SORD. We also tested the cross-event correlations between the SORD and the ratio and difference scores. The average correlation was (r ¼ :88; SD ¼ :14) with the ratio and (r ¼ :68; SD ¼ :21) with the difference score. Here too, the ratio rather than the difference score showed better fit with the SORD (t ¼ 7:5; df ¼ 68; p <:001). The participants within events as the unit of analysis Finally, we calculated within-event correlations where the participants served as the unit of analysis (see also Price et al., 2002). These correlations are presented in Table 1, column 6 presents the SORD/others risk correlations for each of the events. As can be seen, 14 of the 20 correlations were negatively rather than positively signed; the average correlation with the others risk (Average r ¼ :05, SD ¼ :1) was significant (t ¼ 2:19, df ¼ 19, p <:05). These within-events results are consistent with the between-events and between-participants results. In addition, and also consistent with previous results, all 20 SORD/self risk correlations were negative and 19 out of the 20 were significantly so. The average within-event correlation with the self risk (average r ¼ :51, SD ¼ :15) was significant (t ¼ 15:33, df ¼ 19, p <:001). Difference or ratio? We analyzed the correlations between the ratio and difference measures and the SORD for each of the 20 life events. As in the previous analyses, the average correlation with the ratio (average r ¼ :81) was significantly higher than the corresponding correlation with the difference (average r ¼ :61) (t ¼ 5:3, df ¼ 19, p <:001). To explore whether the relative advantage of the ratio over the difference framework diminishes in the move from rare to more common life events, we created a ratio over difference relative efficiency measure, in which we subtracted the absolute SORD/difference correlation coefficient from the corresponding absolute SORD/ratio coefficient for each of the life events. The higher the resultant value, the greater the relative advantage of the ratio. As can be seen in Fig. 4, there is a negative slope (b ¼ :44, p <:05), where the advantage of the ratio over the difference decreases with event frequency. It should be noted that this tendency was found despite the fact that our sample of events (taken from the Price et al. study) did not include either very rare life events (the frequency of hearing loss, our lowest frequency event, was about 14%) or very common events (the frequency of bad career choice, our highest frequency event, was about 52%). Yet, despite this restricted range, a tendency for diminishing ratio advantage emerged.

9 Y. Klar, S. Ayal / Journal of Experimental Social Psychology 40 (2004) Fig. 4. The relative efficiency of the ratio over the difference score in predicting the SORD score in the 20 negative life events in Study 2 (the SORD/RATIO correlation the SORD/DIFFERENCE correlation). Note. The higher the number, the greater is the relative efficiency of the ratio relative to the difference score. All in all, the Study 2 results showed that the sense of self-others risk discrepancy (SORD) did not increase with the perceived frequency of events. If anything, it decreased mildly. In addition, these results show that the ratio framework is generally advantageous over the difference framework for capturing the SORD. However, there are also preliminary indications that the relative advantage of the ratio over the difference framework is greater for low rather than high frequency events. Conclusions The nature of the indirect measure of self-others optimism regarding future personal risks is that participants provide the researchers with two separate, own and others, risk probabilities. To derive participants sense of self-others risk discrepancy from these two risk probabilities, it is crucial to understand how they actually relate the two risk probabilities to each other. We approached this issue with psychophysical and metacognitive approaches. One question was whether the sense of self-others risk discrepancy is greater for common rather than for rare life events, as suggested by Price et al. (2002). Our results did not support this contention: the results of Study 1, employing the psychophysical approach, showed that participants expressed the same degree of risk discrepancy with greater numerical values, with greater absolute probability. Thus, a greater difference score in the context of common rather than rare events does not necessarily imply greater self-others optimism. The results of Study 2, employing a meta-cognitive approach, suggested that there are weak negative rather than positive relations between the perceived frequency of an event and the sense of perceived risk discrepancy. Thus, we failed to find any evidence for a positive frequency/optimism correlation in the indirect measure, or any evidence for comparative optimism reversal, in the move from the direct to the indirect method. Although it is likely that the two elicitation methods are not the same, there is no reason to assume that they lead to a risk reversal. We also tested whether a ratio or difference framework better fits the sense of self-others risk discrepancy. Overall, we found evidence in both studies for the relative superiority of the ratio over the difference framework. However, we also found some suggestive evidence for the possibility that this relative superiority of the ratio is moderated by event frequency. In other words, the ratio format may better capture self-others optimism in the context of rare events (e.g., others risk is double that of mine rather than others risk is 1% greater than mine ) but this advantage may wane for more common events. It is possible that with highly common life events, difference rather than ratio scores may better capture self-others optimism (e.g., others risk is 10% greater than mine rather than others risk is 1.14 greater than mine ). This, however, is a matter for further research. References Armor, D. A., & Taylor, S. E. (1998). Situated optimism: Specific outcome expectations and self-regulation. In M. P. Zanna (Ed.), Advances in experimental social psychology (Vol. 30, pp ). New York: Academic Press. Chambers, J. R., Windschitl, P. D., & Suls, J. (2003). Egocentrism, event frequency, and comparative optimism: When what happens frequently is more likely to happen to me. Personality and Social Psychology Bulletin, 29, Diener, E., & Fujita, F. (1997). Social comparisons and subjective wellbeing. In P. B. Buunk & F. X. Gibbons (Eds.), Health, coping and well-being: Perspectives from social comparison theory (pp ). Mahwah, NJ: Earlbaum. Eiser, R. J., Pahl, S., & Prins, Y. (2001). Optimism, pessimism, and the direction of self-other comparisons. Journal of Experimental Social Psychology, 37, Epley, N., & Dunning, D. (2000). Feeling holier than thou : Are selfserving assessments produced by errors in self- or social prediction? Journal of Personality and Social Psychology, 79, Giladi, E. E., & Klar, Y. (2002). When standards are wide of the mark: Nonselective superiority and inferiority biases in comparative judgments of objects and concepts. Journal of Experimental Psychology: General, 131, Heine, S., & Lehman, D. (1995). Cultural variation in unrealistic optimism: Does the west feel more invulnerable than the east? Journal of Personality and Social Psychology, 68, Helweg-Larsen, M., & Shepperd, J. A. (2001). Do moderators of the optimistic bias affect personal or target risk estimates? A review of the literature. Personality and Social Psychology Review, 5,

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