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Several individual differences including age have been suggested to affect the perception of slant. A cross-sectional study of outdoor hill estimation (N¼ 106) was analyzed using individual difference measures of age, experiential knowledge, fitness, personality traits, and sex. Of particular note, it was found that for participants who reported any experiential knowledge about slant, estimates decreased (i.e., became more accurate) as conscientiousness increased, suggesting that more conscientious individuals were more deliberate about taking their experiential knowledge (rather than perception) into account. Effects of fitness were limited to those without experiential knowledge, suggesting that they, too, may be cognitive rather than perceptual. The observed effects of age, which tended to produce lower, more accurate estimates of hill slant, provide more evidence that older adults do not see hills as steeper. The main effect of age was to lower slant estimates; such effects may be due to implicit experiential knowledge acquired over a lifetime. The results indicate the impact of cognitive, rather than perceptual factors on individual differences in slant estimation. Keywords 3D perception, slant perception, spatial cognition, individual differences, aging The perception of the slants of hills has been the focus of a great deal of research in the past 20 years. Very large distortions are evident in the conscious perception of slant (Kammann, 1967; Li & Durgin, 2009; Proﬃtt, Bhalla, Gossweiler, & Midgett, 1995; Ross, 1974; Shaﬀer & Flint, 2011). A hill of 5 is typically perceived as being 20 ; conversely, a hill that looks to be 30 might actually be only 8 . Models of slant perception taking viewing distance into account have revealed that perceived slant is exaggerated at all viewing distances Corresponding author: Frank H. Durgin, Swarthmore College, 500 College Avenue, Swarthmore, PA 19081, USA. Email: email@example.com Creative Commons CC-BY: This article is distributed under the terms of the Creative Commons Attribution 3.0 License (http://www.creativecommons.org/licenses/by/3.0/) which permits any use, reproduction and distribution of the work without further permission provided the original work is attributed as specified on the SAGE and Open Access pages (https://us.sage- pub.com/en-us/nam/open-access-at-sage). 2 i-Perception (even near small surfaces appear more slanted from horizontal than they should; Durgin, Li, & Hajnal, 2010), but that perceived slant increases with the log of viewing distance (Bridgeman & Hoover, 2008; Li & Durgin, 2010). There has been controversy over whether there exists a separate accurate representation of slant that can be measured by motor actions (Creem & Proﬃtt, 1998, 2001; Durgin, Hajnal, Li, Tonge, & Stigliani, 2010, 2011). A preponderance of evidence now suggests that haptic perception of slant is just as exaggerated as visual perception (Durgin, Hajnal et al., 2010; Durgin & Li, 2012; Hajnal, Abdul-Malak, & Durgin, 2011). Systematic measurement biases such as anchoring (Feresin, Agostini, & Negrin-Salviolo, 1998; Shaﬀer, McManama, & Durgin, 2015; Shaﬀer, McManama, Swank, Williams & Durgin, 2014), postural eﬀects (Li & Durgin, 2011), and reference frame bias (Coleman & Durgin, 2014) may all contribute to the cognitive illusion that manual measures (e.g., palm boards) tap into an accurate representation of hill slant (Durgin, Hajnal et al., 2010). In general, it appears possible that because action is calibrated to perception, stable distortions in perception can eﬀectively support the control of action without requiring accuracy (e.g., Durgin, 2009, 2014). The exaggeration of perceived slant relative to horizontal may therefore be an adaptive coding strategy that is useful even in the control of action (Durgin, 2009; Durgin & Li, in press). Some of the most puzzling results concerning slant perception are the individual diﬀerences that have been reported based on sex (Proﬃtt et al., 1995) and age (Bhalla & Proﬃtt, 1999). In many studies, it has been found that slant estimates of hills are higher for female participants than for male participants, but it has not been clear whether this reﬂects a (perceptual) gender diﬀerence in how hills actually appear, or if it reﬂects a (cognitive) gender diﬀerence in the cognitive transformation of perceptual experience into a spatial or numeric response. Second, the claim has been advanced that hills appear steeper to older adults (Bhalla & Proﬃtt, 1999). However, the data originally reported in support of this claim appear to better support the idea that older adults give lower (i.e., more accurate) estimates of hill slant (perhaps because of greater life experience; see Durgin, Hajnal et al., 2010, for a review): Bhalla and Proﬃtt’s older participants only gave relatively high estimates for a couple of very steep hills for which no direct comparison data were available from younger participants, whereas for hills of 4 to 10 (which include fairly challenging, but walkable slopes), the data of Bhalla and Proﬃtt (1999; Table 2) consistently show that older adults gave lower, more accurate, estimates than did younger participants. Recent data for small, near surfaces have also suggested that slant estimates given by older participants are also lower and more accurate than the estimates given by younger participants (Norman, Crabtree, Bartholomew, & Ferrell, 2009). One of the concerns that has complicated the interpretation of individual diﬀerences in slant perception is that the results of estimation tasks can be biased by subtle or not-so-subtle instructional manipulations (see Durgin et al., 2009; Durgin, Hajnal et al., 2010). For example, the data from older adults reported by Bhalla and Proﬃtt (1999) were collected in a very diﬀerent experimental design than the ‘‘normative’’ data to which it was compared. Moreover, they were preceded by instructions that might be said to invoke stereotype threat (Steele & Aronson, 1995) or experimental demand (Durgin et al., 2009). That is, older participants were ﬁrst asked how hard the hill would be to climb for someone of their age and physical ability. This initial question might well have aﬀected older adults’ subsequent estimates (e.g., Woods, Philbeck, & Danoﬀ, 2009) for very steep hills. The younger participants in the normative study (Proﬃtt et al., 1995) to which Bhalla and Proﬃtt’s data from older adults were compared had not been asked any such (potentially biasing) question before making their estimates, so any comparison of the two sets of data ought to be done with caution. Dean et al. 3 Similarly, studies involving ﬁtness, fatigue, or burden manipulations (Bhalla & Proﬃtt, 1999) may also tap into individual diﬀerences in combination with biases introduced by experimental demand. Durgin et al. (2009) and Durgin, Klein, Spiegel, Strawser, and Williams (2012) found that most participants asked to wear a heavy backpack during a perception experiment assumed the backpack was intended to aﬀect the slant estimates they were asked to make while wearing the backpack. Participants asked to do strenuous exercise in advance of making slant estimates (e.g., Bhalla & Proﬃtt, 1999; Proﬃtt et al., 1995) probably draw similar inferences about the experimenter’s intent. Durgin et al. (2009) found that only a subset of participants indicated that they had cooperated with the experimental demand, and this subset showed reliably higher slant estimates (see also Shaﬀer, McManama, Swank & Durgin, 2013). Bhalla and Proﬃtt reported that individual diﬀerences in physical ﬁtness aﬀected estimates of hill slant. However, their study of this confounded physical ﬁtness with sex, which rendered the results hard to interpret (see Durgin et al., 2010, for discussion). To try to minimize experimental demands of direct manipulation of ﬁtness or age (Durgin et al., 2009; Firestone, 2013; Firestone & Scholl, in press), we conducted an exploratory cross- sectional study on slant perception. We sought to be able to model our data not only with respect to individual diﬀerences, such as age and gender, but also with respect to other forms of individual diﬀerence, such as personality variables that covary with sex (Schmitt, Realo, Voracek, & Allik, 2008), as well as cognitive diﬀerences, such as knowledge of slant bias (Durgin & Li, 2011; Stigliani, Li, & Durgin, 2013). A personality variable like agreeableness, for example, is sex-linked, such that females tend to be higher than males on this trait (Schmitt et al., 2008). If many participants guess that experimenters want them to give high estimates, but more agreeable participants are more likely to cooperate with this implicit demand, a sex diﬀerence in slant estimation (but not slant perception) could result from this personality trait. By testing for eﬀects of agreeableness in a variable population, it may be possible to test whether sex diﬀerences in slant estimation might arise from trait diﬀerences. Moreover, by sampling an oﬀ-campus population in a multidimensional study along with on-campus participants, we sought to minimize experimenter bias eﬀects associated with null hypothesis testing. To maximize sensitivity to population variables (individual diﬀerences), our study focused primarily on a single hill, which was assessed with manual, visual, and verbal measures. All participants were ﬁrst tested with this hill. In a classic study reporting sex diﬀerences, Proﬃtt et al. (1995) collected three measures similar to these at a single hill for each participant. We devoted our entire N to a single hill, though two further hills were tested with verbal measures. Our primary analysis is of the perceived slant of a paved path on a single steep (9 ) hill. Methods Participants One-hundred and six adults (46 males), naı¨ ve to the purpose of the study, were successfully recruited to participate in our study from the student body at Swarthmore College or from the surrounding community. Forty-eight of the participants were nonstudent community members, ranging in age from 18 to 72 years old (15 males); 58 of the participants were Swarthmore College students, ranging in age from 18 to 22 (31 males). Recruitment materials indicated that participants were to wear corrective lenses if they needed them, that participants must be able to speak and read English, and that they must be able to stand while making their judgments. Visual acuity was measured using a Snellen chart for all but one participant (with whatever corrective lenses they wore during the experiment); only two 4 i-Perception participants had (corrected) vision worse than 20/40 (one was 20/50; one 20/70). The study methods were approved by the local institutional review board. Hills Three hills were tested in the same order for each participant. The primary hill, shown in Figure 1, left panel, is a steep campus path with a slant of 9 as measured by an inclinometer at the location marked by the orange cone oﬀ to one side. The second hill was a very steep grassy embankment at the side of a nearby path, with a slant of 22.5 . The third hill was a broad campus path with a slant of 4.5 . The to-be-judged portion of each hill was marked with either a small orange cone (hills 1 and 2) or by an existing landmark to the side of the path (hill 3). Participants stood at a ﬁxed location when making their estimates from the base of each hill, and the portion of the path or embankment to be judged was roughly at eye level. Measures of Perceived Slant Three measures were used for the primary (9 ) hill. The measures were collected in a ﬁxed order designed to minimize the risk of measure-to-measure bias. Participants were ﬁrst asked to indicate the slant of the hill by holding their hand parallel to the hill (they held their hand up behind a vertical screen so that they could not see their hand). They wore a lightweight inclinometer on their hand so that we could measure the orientation of the back of their hand. We also measured the angular thickness of their hand when they placed it on a horizontal level surface after holding it up. The calculated orientation of the midline axis of their hand relative to horizontal was used as measure of their intended orientation (see Li & Durgin, 2011). We call this the manual matching response (MMR). The second measure used was based on the visual measure developed by Proﬃtt et al. (1995). In this case, the participant had to adjust a 2D depiction of a hill (see Figure 1, right panel). An estimate in degrees (relative to horizontal) was then read oﬀ a digital protractor mounted on the measure. This will be called the visual matching response (VMR). It was always started from a slant of 0 . Figure 1. The primary, 9 , hill (left) and the two nonverbal measures depicted in use. Dean et al. 5 Finally, a verbal estimate was requested in degrees relative to horizontal. This measure was collected last so that it would be less likely to inﬂuence the nonverbal measures. The reasoning for this was that if a participant ﬁrst gave a verbal response, they might be likely to try to match their visual and manual responses to the verbal response, which would be easier to remember than would be the manual and visual matches. We call this the numeric estimation response (NER). Note that for the 22.5 and 4.5 hills only an NER was collected. Measures of Individual Differences To avoid inﬂuencing slant judgments, all demographic information and other measures of individual diﬀerences were collected after the slant judgments were completed. An assessment of visual acuity was ﬁrst performed using a Snellen eye chart viewed from 6.1 m. After this, all of the individual diﬀerence information was collected on computer by a custom program implemented in E-Prime. The personality variables were tested ﬁrst. These were three scales of the Big Five Inventory that are known to be sex-linked (Schmitt et al., 2008): Female participants tend to score higher than male participants on agreeableness (AG) and conscientiousness (CO) and lower on emotional stability (ES). Each scale consisted of 20 items. Participants indicated the degree to which a trait word described them on a 9-point scale ranging from not at all (1) to extremely (9). Sample items for agreeableness, conscientiousness, and emotional stability are (a) ‘‘helpful,’’ (b) ‘‘practical,’’ and (c) ‘‘moody’’ (reverse coded), respectively. Note that a positivity bias might be expected for such scales, but such a bias would predict high correlations across all three scales, and this was not observed. We intended to measure spatial ability by including a computerized mental rotation task with Shepard and Metzler (1971) shapes (Peters & Battista, 2008). There is a great deal of evidence for sex diﬀerences in spatial tasks (e.g., D. Voyer, S. Voyer, & Bryden, 1995) including those related to slope (Nardi, Holmes, Newcombe, & Weisberg, 2015; Nardi, Meloni, Orlandi, & Olivetti-Belardinelli, 2014). However, data from this reaction time task, which involved judging whether each of two imaged shapes was the same or diﬀerent from another, were reliably correlated both with age and with conscientiousness. This rendered its value as a measure of spatial ability questionable; it was not used for analysis. Participants were next asked whether they had prior experiences or special knowledge that was relevant to the evaluation of hill slant (we gave as examples experience with skiing, measuring a slant with an inclinometer, or having had a driveway repaved); 36 participants listed some form of such experience. We also asked participants whether they used any particular strategies in making their judgment, though this data were intended simply to screen for unusual approaches to the task and were not included in statistical analyses. Finally, we collected demographic information such as sex and age, and also self-reported weight and height, which was used to estimate body mass index (BMI ). BMI has been used SR previously as a marker of ﬁtness by proponents of embodied perception (e.g., Bhalla & Proﬃtt, 1999; Sugovic & Witt, 2011). We used de-identiﬁed self-report of weight to avoid privacy concerns where some of our participants were peers of the experimenters. Because we wondered if high-heeled footwear might inﬂuence slant judgments, we also asked them to indicate the height of the heels of their shoes, though there turned out to be insuﬃcient variance in this measure to use it as a predictor. The correlations among our various predictor variables are shown in Table 1. It can be seen that the personality traits we expected to be sex-linked did not strongly covary with sex 6 i-Perception Table 1. Correlation Coefficients Between Individual Difference Measures. Knowledge Age Sex AG CO ES Age 0.061 Sex –0.042 0.077 AG 0.249 0.205 0.086 CO 0.081 0.204 –0.054 0.060 ES 0.026 0.379* –0.072 0.221 0.238 BMI –0.123 0.223 –0.037 0.055 0.022 0.097 SR Note. AG¼ agreeableness; CO ¼ conscientiousness; ES¼ emotional stability; BMI ¼ body mass index. *p< .0001. in our sample, but that they did all tend to covary with age, with a particularly strong correlation (r¼ .38) between age and emotional stability, (p< .0001). Procedure Once participants arrived at the lab, they signed a consent form and were paid in advance for their time. All participants were ﬁrst involved in a separate study of distance perception and height perception in a ﬁeld near the Psychology building (Oh et al., 2015). Following this, participants were driven in a golf cart by an experimenter to a diﬀerent part of campus where they stopped at each of the three hills, made their ﬁve judgments (three at the ﬁrst hill and one at each of the other two) and were then driven back to the Psychology building where the individual diﬀerence measures were collected. Analysis As has been reported previously (Shaﬀer, McManama, Swank, et al., 2014; Stigliani et al., 2013), all three of the slant measures were reliably correlated with each other, suggesting a common underlying representation: MMR and VMR, r ¼ 0.50, p< .001; MMR and NER, r ¼ 0.29, p¼ .003; VMR and NER, r ¼ 0.54, p< .001. The three types of measure were 104 104 therefore averaged to produce a single estimate of perceived hill slant for the 9 hill for each participant (note that separate analyses are also reported for each measure below for completeness). We then used simultaneous multiple linear regression modeling to look at all of the data from the ﬁrst hill using the individual diﬀerence scores as predictors. Results In previous studies (e.g., Durgin & Li, 2011), prior experiential knowledge relevant to slant estimation (e.g., experience with skiing) has been a predictor of slant estimates, and the present data replicate this observation. A simultaneous multiple linear regression model was tested that included knowledge, conscientiousness, agreeableness, emotional stability, age, sex, and BMI as predictors, as well as all two-way interactions between them (all SR variables were ﬁrst centered). This analysis showed main eﬀects of knowledge, sex, and BMI : Those reporting some knowledge gave lower (more accurate) estimates, SR ¼5.12 , t(74)¼ 2.52, p¼ .014, R ¼ 0.05; female participants gave higher slant estimates, ¼ 4.15 , t(74) ¼ 2.32, p¼ .023, R ¼ 0.04; and participants with higher BMI SR gave higher slant estimates, ¼ 0.50 , t(74)¼ 2.35, p¼ .022, R ¼ 0.06. However, the Dean et al. 7 analysis also showed that knowledge interacted both reliably with conscientiousness, t(74)¼ 2.77, p¼ .007, and marginally with BMI , t(74)¼ 1.83, p ¼ .072. We therefore split SR the data according to whether the participants reported having knowledge relevant to slant (N¼ 39) or not (N¼ 67). Reliable Predictors in the Presence of Knowledge: Conscientiousness A simultaneous multiple linear regression model of the responses of those reporting any experiential knowledge relevant to slant (with age, sex, all three personality factors, and BMI as predictors) is shown in Table 2. The only reliable predictor of estimates among SR knowledgeable people was conscientiousness, which predicted reliably lower (and thus more accurate) slant estimates, ¼3.53, t(30)¼ 4.00, p< .001, R ¼ 0.23. Although this result was not anticipated, this pattern is consistent with the idea that knowledgeable people scoring higher in conscientiousness were more likely to take the trouble to use their knowledge (rather than merely their perceptual experience) when asked to provide a slant estimate. A plot depicting the interaction between conscientiousness and knowledge is shown in Figure 2. Table 2. Model for Those With Knowledge About Slant (N¼ 39). Estimate Standard error t value p value Intercept 20.44 1.08 18.937 <.0001*** Age 0.08 0.07 1.194 .2420 Sex 3.03 2.03 1.490 .1466 AG 1.94 1.52 1.280 .2105 CO –3.53 0.88 4.003 .0004 *** ES –1.48 0.89 1.673 .1047 BMI –0.13 0.27 0.501 .6203 SR Note. AG ¼ agreeableness; CO¼ conscientiousness; ES¼ emotional stability; BMI¼ body mass index. ***< .001 Figure 2. Interaction between conscientiousness and knowledge on estimates of 9 hill. 8 i-Perception Figure 3. Age effect on estimates of 9 hill among is present among those without knowledge, but not among those reporting experiential knowledge. Table 3. Model for Those With No Knowledge of Slant (N¼ 67). Estimate Standard error t value p value Intercept 23.41 1.03 22.686 <.0001*** Age –0.20 0.07 2.928 .0049** Sex 4.23 2.09 2.028 .0471* AG –0.35 1.22 0.290 .7729 CO 0.17 1.02 0.163 .8713 ES 0.46 1.04 0.440 .6617 BMI 0.69 0.20 3.372 .0013** SR Note. AG ¼ agreeableness; CO¼ conscientiousness; ES¼ emotional stability; BMI¼ body mass index. *< .05, **< .01, ***< .001 Reliable Predictors in the Absence of Knowledge For those who reported no particular knowledge about slant (N¼ 67), a simultaneous multiple linear regression model, shown in Table 3, indicated three reliable predictors: age, sex, and BMI . We will consider each of these observations in turn. SR Age. As shown in Figure 3, older participants gave estimates that were lower than those of younger participants by about 2 per decade, ¼0.20 /year, t(59)¼ 2.93, p¼ .005, R ¼ 0.084. The direction of this eﬀect diﬀers from the claims of Bhalla and Proﬃtt (1999) who argued that older people saw hills as steeper. However, for a hill of a similar magnitude to this one (as well as for all lower hills they tested), Bhalla and Proﬃtt found a similar pattern: Older adults in their study gave lower estimates than younger observers (see also Norman et al., 2009). Thus, we have replicated the ﬁnding that older adults are more accurate than are younger adults in slant estimation of a typical walkable slope. It remains possible that these eﬀects reﬂect an accumulation of world knowledge that is not detected by our experiential knowledge probe. Dean et al. 9 We note that measured visual acuity was, of course, correlated with age, but the age eﬀect found here remained even when visual acuity was included in the model as a covariate. Sex. Consistent with previous reports, female participants gave estimates that were 4.2 higher than male participants, t(59)¼ 2.03, p¼ .047, R ¼ 0.034. The present data suggest that these eﬀects are not due to sex-linked personality diﬀerences (which were included in the model), nor by the forms of experiential knowledge measured by our probe. Note that excluding sex as a factor in this model did not unmask any eﬀects of sex-linked personality traits. BMI . As shown in Figure 4, participants with higher BMI gave higher slant estimates, SR SR ¼ 0.69, t(59) ¼ 3.37, p¼ .001, R ¼ 0.132. This appears to lend support to the claim that behavioral potential (i.e., ﬁtness) aﬀects slant perception. However, a closer look at the data here shows that the eﬀect is limited to obese women, which may support the alternative perspective that knowingly having a particularly high BMI may inﬂuence how participants make their estimate. Of the 67 people in the no-knowledge condition, seven can be classiﬁed as obese, and it is a subset of these seven that drive the BMI eﬀect: If we eliminate the seven obese participants SR (without knowledge) from our analysis, not only does BMI cease to be predictive, SR t(52)¼ 0.13, but sex is no longer predictive either, t(52)¼ 1.10. Thus it seems possible that greater salience of body image among females is responsible for at least a portion of the sex diﬀerences found in previous studies. Among the nine obese participants in our overall sample, the six females gave reliably higher average estimates of the 9 hill (M¼ 38.3 ) than did the three males (M¼ 18.6 ), Welch t(6.3)¼ 4.08, p¼ .006. If the inﬂuence of obesity on slant judgment is sex-linked, this would seem consistent with the idea that eﬀects of obesity are based on sociocognitive factors rather than perceptual eﬀects. Differences between measures? There is a controversial claim in the literature that the three measures we used tap into diﬀerent underlying representations (e.g., Creem & Proﬃtt, 1998, 2001; but see Durgin, Hajnal et al., 2010). In particular, Creem and Proﬃtt suggested that manual measures tap into dorsal (‘‘accurate’’) processing streams, whereas visual and verbal measures reﬂect conscious perception. Shaﬀer et al. (Shaﬀer, McManama, & Durgin, 2015; Shaﬀer, McManama, Swank, et al., 2014) have argued that manual measures are just more susceptible to anchoring eﬀects. To address this issue here, we tested whether manual measures were immune to individual diﬀerences. As we expected, however, given that the three measures are typically correlated, regression models computed for each of the three measures individually showed evidence of eﬀects of age and of BMI among those without knowledge of slant. SR The pattern among those with knowledge of slant diﬀered somewhat for the manual measure in a manner that might also indicate a role of sex-linked personality traits. The ﬁrst estimate given by each participant was the manual estimate. When the manual estimates were analyzed separately, they showed evidence of an interaction between knowledge and agreeableness (rather than between knowledge and conscientiousness). In fact, among those reporting some knowledge of slant, manual estimates tended to increase with agreeableness, ¼ 3.98 , t(30)¼ 2.02, p ¼ .052, R ¼ 0.115. Although only a marginal result, statistically, this is exactly the sort of pattern (an interaction of knowledge and agreeableness) that one would predict of participants who might be trying to co-operate with what they expect the experiment to be about (Durgin et al., 2009). Insofar as their knowledge gave them some awareness that hill slant tends to be overestimated, those participants who were more 10 i-Perception Table 4. Model for those with no knowledge of slant (N¼ 67) for the steep (22.5 ) embankment. Estimate Standard error t value p value Intercept 45.78 1.80 25.393 <.0001*** Age –0.25 0.12 –2.163 .0346* Sex 7.26 3.65 1.991 .0512 AG 1.84 2.13 0.862 .3923 CO 1.08 1.78 0.609 .5451 ES –1.66 1.82 0.914 .3646 BMI 0.35 0.36 0.977 .3324 SR Note. AG ¼ agreeableness; CO¼ conscientiousness; ES¼ emotional stability; BMI¼ body mass index *< .05, **< .01, ***< .001. agreeable tended to give higher estimates in their very ﬁrst estimate, perhaps believing that the experimenters wished to measure overestimation of hill slant. This evidence that agreeable participants were tempted to ‘‘help’’ initially, is not inconsistent with the further observation, that, when ﬁnally asked to give a verbal estimate, the conscientious participants (among those who had knowledge) now gave reliably lower verbal estimates, ¼7.06 , t(30)¼ 4.46, p< .001, R ¼ 0.258. That is we see evidence that both agreeableness and conscientiousness interact with the presence of some knowledge about hill slant overestimation in determining responses. Because the order in which the diﬀerent types of estimates were collected was ﬁxed, we cannot draw strong conclusions about whether this is indeed an order eﬀect or an eﬀect of the manual nature of the measure. However, the present data are consistent with the idea that personality variables can interact with background knowledge of participants both to elevate estimates (including manual estimates) and to rein them in. Replication with the steep embankment. For the 22.5 embankment, a preliminary analysis of verbal estimates showed a similar pattern to the data from the primary hill. There was a marginal eﬀect of knowledge, ¼2.81 , t(74)¼ 1.83, p ¼ .071, and a reliable interaction between knowledge and conscientiousness, t(74)¼ 2.02, p¼ .048. A separate analysis of the participants reporting some knowledge about hill slant indicated a marginal eﬀect of conscientiousness, ¼4.76 /unit, t(30)¼ 1.93, p¼ .064, consistent with the results for the primary hill. The analysis of those without knowledge (Table 4) replicated the eﬀects of age, ¼0.25 /year, t(59)¼ 2.16, p¼ .035, found for the primary hill, as well as (marginally) the higher estimates of females than males, ¼ 7.26 , t(59)¼ 1.99, p¼ .051. However, the eﬀect of BMI was not reliable for this hill, ¼ 0.34 , t(59) ¼ 0.98, p¼ .332. Given that the same SR participants gave judgments at the primary hill ﬁrst, the replication of most of the patterns is reassuring, but perhaps unsurprising since participants were likely trying to remain consistent with their previous estimate. Replication with the shallow path. For the 4.5 path, analysis of verbal estimates again showed a reliable interaction between knowledge and conscientiousness, t(74) ¼ 2.34, p¼ .022. However, a separate analysis of the participants reporting some knowledge about hill slant did not detect any reliable main eﬀects. The analysis of those who reported no knowledge showed a marginal eﬀect of BMI , ¼ 0.34 /unit, t(59)¼ 1.86, p¼ .068, while no other main SR eﬀects were reliable. It seems likely that individual diﬀerence eﬀects from the previous Dean et al. 11 Figure 4. BMI effect on estimates of 9 hill among those without knowledge is driven by obese SR participants (i.e., BMI> 30). BMI¼ body mass index. analyses were not detectable at this hill simply because the mean estimates were compressed relative to the variance. One way of expressing diﬀerential proportional variance is the coeﬃcient of variation (CoV), which is the standard deviation of a measure divided by the mean. For the verbal estimates of the 4.5 hill, the CoV was 0.69, which was substantially greater than the 0.36 CoV for verbal estimates of the 22.5 hill, F(105, 105)¼ 3.69, p< .001, and also much higher than the 0.38 CoV of the combined estimates for the 9 hill, F(105, 105) ¼ 3.37, p< .001. Note that CoVs of the individual measures for the 9 hill were somewhat higher than those of the combined response: They ranged from 0.43 for the visual matches to 0.52 for the verbal estimates, whereas combining these correlated measures eﬀectively produced a more sensitive measure by reducing proportional variance. Durgin, Hajnal et al. (2010) have discussed diﬀerential proportional variance as an artifactual source of apparent dissociation between diﬀerent types of slant measure. The current result illustrates how diﬀerential proportional variance can also aﬀect analysis of data from diﬀerent hills. The results also indicate the advantage of combining correlated measures into a single measure for the purpose of reducing error variance. How does aging affect slant perception? A comparison to the findings of Bhalla and Proffitt (1999). Bhalla and Proﬃtt (1999) collected hill slant estimation data from older participants (age 60 and above). Each older participant in their study saw four hills. They compared these data with normative data collected in a prior study (Proﬃtt et al., 1995) with diﬀerent sets of hills, a diﬀerent design, and diﬀerent instructions. They concluded from this comparison that older adults saw hills as steeper. However, their own data seem to contradict this conclusion for the majority of hill slants tested, and their design leaves the comparisons between the two groups risky overall. The verbal estimation data used by Bhalla and Proﬃtt are replotted in Figure 5. It can be seen that for hill slants of 4 ,5 , and 10 , their older participants gave lower estimates than were provided in the normative data. Proﬃtt and Bhalla adopted the rather unusual statistical approach of comparing estimates that were averaged across the entire range of 2 to 10 and reported a null statistical eﬀect. 12 i-Perception Proffitt et al. (1995) normative data Bhalla and Proffitt (1999) older adults (> 59 years old) 0 5 10 15 20 25 30 35 Actual slant of hill (deg) Figure 5. Verbal estimation data published by Bhalla and Proffitt (1999; Table 2) arguing that older adults see hills as steeper than do younger adults. Note that their conclusion appears to be contradicted in the range from 4 to 10 . Standard errors of the means are shown. Figure 6. Verbal estimation data for the three hills we tested, divided into older and younger adults. Standard errors of the means are shown. For comparison with their results, we computed average verbal estimates at each of the three hills we tested for all participants older than 59 years old (N¼ 11) as well as for participants younger than 23 years old (N¼ 70). These data are shown in Figure 6 along with standard error bars. At each of the three hills we tested, the estimates of the older participants (M¼ 6.5 , 14.6 , 31.4 ) are less than the estimates of the younger participants (M¼ 10.3 , 25.0 , 46.0 ), Welch t(16.1) ¼ 2.30, p¼ .035, Welch t(16.0) ¼ 3.57, p¼ .003, Welch t(13.7)¼ 3.08, p¼ .008, respectively. In summary, older adults gave lower (more accurate) estimates than younger adults for all the hills we tested including a very steep embankment. Note that there is evidence that older Average verbal estimate (deg) Dean et al. 13 adults are also more accurate at estimating egocentric distance (Bian & Anderson, 2013) and exocentric depth extents (Norman, Adkins, Norman, Cox, & Rogers, 2015), and knowledge eﬀects have also been implicated for estimates of distance (Durgin, Leonard-Solis, Masters, Schmelz, & Li, 2012). The present age eﬀect on slant estimation is consistent with cognitive factors playing a signiﬁcant role in slant estimation. We did not see any evidence that older adults gave higher slant estimates, as had been proposed by Bhalla and Proﬃtt (1999). Even for our steepest hill (22.5 ), the older adults gave lower estimates than did the younger adults. It might be objected that our sample was self-selected and thus cannot support strong conclusions about eﬀects of aging. For example, Bhalla and Proﬃtt recruited some of their older participants from a senior living community, and their participants may have diﬀered from ours in health and ﬁtness. These concerns, however, ought to be mitigated by the observation that our data seem to agree with the majority of the data of Bhalla and Proﬃtt (as well as the data of Norman et al., 2009 collected for small surfaces) in suggesting that older adults are generally more accurate at estimating slant than are younger adults. The two hills where the data of Bhalla and Proﬃtt suggest otherwise were not tested with younger participants and were tested with potentially biasing instructions. Discussion Our study sought to evaluate individual diﬀerences in slant estimation in order to diﬀerentiate between cognitive (e.g., modularist; Firestone & Scholl, 2016) and perceptual (e.g., embodied perception; Bhalla & Proﬃtt, 1999) interpretations of such individual diﬀerences. Two of the strongest and most consistent predictors we observed were age and experiential knowledge. Experiential knowledge could involve a variety of activities, such as skiing, that might allow one to learn about the mismatch between perceived and actual slant. More than a third of our population reported some experiential knowledge, and these participants gave lower, more accurate, estimates of hills. Age acted similarly in that older participants gave lower, more accurate judgments that were similar to those who explicitly reported having experiential knowledge (see Figure 3). Of particular importance, we found that conscientiousness could have a substantial role in estimating slant: Among participants explicitly indicating some experiential knowledge concerning slant, conscientiousness seemed to predict whether they would use that knowledge to lower (improve) their estimates both for the steep path and for the steep embankment. This observation helps to show that cognitive eﬀects of experience play an important role. We found only circumstantial evidence that sex diﬀerences in slant estimation might be due to personality diﬀerences in our study. First, for those with some knowledge, agreeableness seemed to elevate initial manual slant estimates. This is consistent with the idea that participants who suspected that we wanted to get overestimates tried to oblige us to the extent that they were agreeable. Although agreeableness was not strongly correlated with sex in our study, it is generally regarded as a sex-linked trait, such that females tend to score higher on measures of agreeableness than males. A combined role of agreeableness and knowledge might be a pathway whereby females would end up giving higher estimates than males even though their perceptual experience might not diﬀer on average. A second hypothesis for explaining sex-diﬀerences in hill slant estimation was suggested by our ﬁndings related to obesity. Obesity was a predictor of slant estimates among those who did not report having any special knowledge of slant. However, this eﬀect was limited to female participants. Future investigations may want to consider whether obese female participants are more likely to provide particularly high estimates for social reasons or 14 i-Perception because they actually perceive hills as geometrically steeper. That is, it seems unlikely that these participants really meant that the 9 hill appeared to be tilted half way to vertical; perhaps their exaggerated estimates reﬂect stereotype threat or consciously taking imagined eﬀort into consideration (Woods et al., 2009). Overall, our data suggest that age, knowledge, and personality diﬀerences produced cognitive rather than perceptual eﬀects in this study. The eﬀect of age, in particular, went contrary to the widely cited claims of embodied perception. We have suggested that those claims probably ought not to have been made in the ﬁrst place given that the original data for older participants were collected under such diﬀerent circumstances than the data of younger participants to which it was compared. The eﬀect of experiential knowledge, by seeming to remove age and ﬁtness eﬀects, strongly suggests that the age eﬀects we have documented are more cognitive than perceptual. That is, experiential knowledge did not simply act as an additional factor, nor did it produce particularly accurate estimates on average, but it seemed to replace these other factors rather than combine with them. Although there may additionally be individual diﬀerences in the perceived slant of hills, it is hard to measure such individual diﬀerences because cognitive factors can easily overwhelm perceptual variation. The subject-wise correlations across measures we replicated here might mean that participants are reporting their individual and unique percept by each of the measures. However, correlations could also emerge as the result of individual diﬀerences in the cognitive translation processes from perception to a reportable impression. More striking to us than these possible individual diﬀerences is the success of recent quantitative models of hill perception, such as the angular scale expansion model proposed for hill perception (Li & Durgin, 2010, 2012). This model uses one ﬁxed parameter (an angular gain of 1.5, estimated across a variety of studies; Durgin & Li, 2011) and one free parameter that accounts for an additional logarithmic eﬀect (see also Bridgeman & Hoover, 2008) of viewing distance on slant perception measures both for explicit slant estimation (e.g., the classic hill data of Proﬃtt et al., 1995) and implicit (shape-based) measures of perceived slant (Li & Durgin, 2010, 2012). These models propose that the striking overall bias observed in slant perception may represent a species-wide functional (eﬃcient) perceptual coding strategy that eﬀectively exaggerates the (shallow) range of slants most often encountered in perceptual experience. The present ﬁndings regarding eﬀects of age, knowledge, and personality suggest that a complete model of cognitive processes of slant estimation might proﬁtably include a variety of postperceptual transformations and adjustments. These postperceptual processes clearly involve cognitive eﬀects of experience and knowledge that appear to interact with personality variables such as conscientiousness and agreeableness. Depending on context, estimation may additionally be susceptible to social and cognitive biases including anchoring, stereotype threat, and experimental demand characteristics—which may also interact with personality variables. Acknowledgements The authors express their gratitude to Ruth Talbot, Kailyn Witonsky, and Violet Brown for their contribution to this project. Declaration of Conflicting Interests The author(s) declared no potential conﬂicts of interest with respect to the research, authorship, and/or publication of this article. 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Magnitude of sex diﬀerences in spatial abilities: A meta- analysis and consideration of critical variables. Psychological Bulletin, 117, 250–270. Woods, A. J., Philbeck, J. W., & Danoﬀ, J. V. (2009). The various perceptions of distance: An alternative view of how eﬀort aﬀects distance judgments. Journal of Experimental Psychology: Human Perception and Performance, 35, 1104–1117. Author Biographies Abigail M. Dean earned her degree in Psychology at Ursinus College. She is currently research manager in the Department of Psychology at Swarthmore College. Jaehyun Oh graduated from Swarthmore College with High Honors in Psychology and Education in 2015. She is now at Harvard Law School. Christopher J. Thomson graduated from Swarthmore College in 2015. 18 i-Perception Catherine J. Norris is professor of Psychology at Swarthmore Psychology with a specialization in Social Neuroscience. Frank H. Durgin has been a professor of Psychology at Swarthmore College since 1994.
i-Perception – SAGE
Published: Jul 18, 2016
Keywords: 3D perception; slant perception; spatial cognition; individual differences; aging
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