Abstract
The weaker the data available upon which to base one’s conclusion, the greater the precision which should be quoted in order to give the data authenticity.
Perceptions of other people’s confidence have serious implications. For example, although the link between eyewitness confidence and accuracy is tenuous, jurors rely on the perceived confidence of witnesses to determine a testimony’s factuality (e.g., Fox & Walters, 1986). This has led researchers to examine which cues reliably signal confidence and whether observers are sensitive to these cues. Observers use cues such as speech rate (Street, Brady, & Lee, 1984) and eye gaze (Ridgeway, Berger, & Smith, 1985), as well as posture and use of nervous gestures (Wells, Ferguson, & Lindsay, 1981), to determine the confidence of speakers.
One signal of confidence recently identified by Welsh, Navarro, and Begg (2011) is the use of precision. Participants were tested on almanac-style facts and indicated their confidence in their answers. On average, confident participants used more significant digits (i.e., numbers with final digits other than 0) than nonconfident participants did (e.g., 3,962 vs. 4,000, respectively).
Precision is potentially a highly useful confidence cue because, unlike many other cues that require the observer to be in the judge’s presence (e.g., posture, eye contact, or prosody; Ridgeway et al., 1985), precision can be observed merely by knowing the judge’s estimate. Recent research demonstrates that precise opening bids in negotiations can signal informed offers (Mason, Lee, Wiley, & Ames, 2013), thus reducing the likelihood and magnitude of counteroffers. Other studies show that precise anchors lead to precise judgments and are particularly influential when the anchor is construed as relevant to the judgment at hand and when it comes from an intentional agent (i.e., a human as opposed to a computer; Zhang & Schwarz, 2013). Although those studies show that precision affects the extent to which advice is adopted into judgment, they did not examine whether observers interpret precision as confidence signals, nor how precision affects from whom estimators seek advice. In the two studies reported here, we investigated both of these previously unexplored questions.
Study 1
Method
One hundred eighty-seven undergraduates volunteered for this study. Participants read 10 questions about the lengths of rivers and heights of mountains—each ostensibly already answered by another participant (see Table 1). However, the observed answers were actually predetermined by the experimenter to be either imprecise (rounded to the 100th place; e.g., 2,600) or precise (rounded to the 1st place; e.g., 2,611), depending on condition. Participants were asked to estimate the confidence level of the person who had provided those answers using an 8-point rating scale, with 1 indicating complete lack of confidence and 8 indicating complete confidence.
Questions and Answers Shown to Participants in Study 1
Note: Participants in the low-precision condition were shown only imprecise answers, and participants in the high-precision condition were shown only precise answers.
Results
Participants judged the person who had generated the answers to be more confident when those answers were more precise (M = 6.26) than when those answers were less precise (M = 5.76). An independent samples t test confirmed that this difference was statistically significant, t(185) = −2.37, p < .05, d = 0.34.
Study 2
Method
Study 1 revealed that participants believed precision to be an indication of confidence. Study 2 examined whether this belief has downstream implications for how people weight advice from others and, more important, which others they seek advice from.
One hundred sixty-three participants were recruited using Amazon’s Mechanical Turk and given monetary compensation for their participation. 1 For Round 1, participants completed a survey modeled after the game show “The Price Is Right” (Goodson & Todman, 1972). First, participants viewed three products (Coffee Joulies, Robostirs, and color-matching pens) and provided a range in which they thought the true price of the item fell. To help them, we provided participants with audience suggestions. These suggestions were all two-digit numbers; precision was manipulated by whether or not the last digit was a 0; amounts ending in 0 were coded as imprecise, and amounts ending in 1 through 9 were coded as precise. Half of the subjects received suggestions above the true value (overestimates), and half heard suggestions below the true values (underestimates).
After providing upper and lower bounds, participants started Round 2, in which they chose which of two audience members would advise them in subsequent price estimations. Each participant made three choices—one audience member for each of the three products. To inform this decision, we displayed past suggestions (precise vs. imprecise) of each audience member (see the Supplemental Material available online for more details).
Results
Ranges were computed for the interval given by each participant in Round 1. Narrower ranges indicated more confidence. Ranges were standardized by product to allow comparability across items. Participants who had been provided with precise suggestions provided narrower ranges (mean z = −0.098) than those provided with imprecise suggestions (mean z = 0.096). An independent samples t test confirmed this to be significant, t(483) = −2.15, p = .031, d = 0.196.
Scores for participants’ choice of adviser in Round 2 ranged from 0 to 3, with higher numbers representing a preference for advisers who gave more precise estimates. Participants’ average score was 1.86, which was significantly different from chance—one-sample t(165) = 4.43, p < .0001, d = 0.69.
Discussion
Welsh et al. (2011) found that confident people make more precise estimates than nonconfident people. The present studies showed that observers infer others’ confidence on the basis of this precision. Moreover, we confirmed previous findings that participants more heavily incorporate precise advice than imprecise advice into their own judgments (cf. Mason et al., 2013; Zhang & Schwarz, 2013), and more important, we demonstrated that participants prefer advice from people who provide more precise estimates. This latter finding speaks to the social-cognitive consequences of numerical precision beyond a single interaction and has real-world implications, including which politician to vote for, which stockbroker to take on as financial advisor, and which doctor to trust with a diagnosis.
Most cues toward confidence require direct observation of the person making the estimate (e.g., posture, prosody). However, with so much numerical information being provided online and in written documentation, it is important to identify confidence cues that can be gleaned from the estimates themselves. The precision of stock analysts’ profit forecasts, political pundits’ budget forecasts, and medical professionals’ disclosures of side-effect risks (cf. Young & Oppenheimer, 2009) may be interpreted as signals of confidence, which have important implications for judgments and behaviors (e.g., jury decision making; Fox & Walters, 1986).
Researchers have found that people have a strong preference for making estimates ending in 0 (e.g., Baird, Lewis, & Romer, 1970). However some media analysts use false precision, which may lend an air of confidence and expertise. For example, sports pundits often discuss National Football League draft prospects to hundredths of milliseconds—more precision than measurement error allows for (Easterbrook, 2010). Our studies show that people prefer sources that provide precise estimates, which creates incentives for such overprecise and misleading reporting.
Welsh et al. (2011) showed that people are more precise when they are more confident. The present studies extended those findings by confirming that observers can detect others’ confidence based on that precision, which influences their judgments and preferences for advisors. Given the importance of confidence judgments, more research on the cues that inform these judgments is precisely what is needed.
Footnotes
References
Supplementary Material
Please find the following supplemental material available below.
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