Journal of Experimental Psychology: Learning, Memory, and Cognition 2015, Vol. 41, No. 2, 473-481

© 2014 American Psychological Association 0278-7393/15/S12.00 http://dx.doi.org/10.1037/a0038119

Categorical Biases in Spatial Memory: The Role of Certainty Mark P. Holden, Nora S. Newcombe, and Thomas F. Shipley Temple University Memories for spatial locations often show systematic errors toward the central value of the surrounding region. The Category Adjustment (CA) model suggests that this bias is due to a Bayesian combination of categorical and metric information, which offers an optimal solution under conditions of uncertainty (Huttenlocher, Hedges, & Duncan, 1991). A fundamental assumption of this model is that representations of locations are unbiased but uncertain; during combination, greater metric uncertainty results in relatively greater emphasis on categorical information, ultimately leading to increased bias (but also minimizing error across multiple estimates). Sampaio and Wang (2009) have demonstrated that metric information is not lost during this combination process, supporting the CA model’s assumption that underlying spatial representations are undistorted. Here, we examine the 2nd half of the CA model’s central assumption: that increasing metric uncertainty drives the combination process. Participants recognized point locations within visually complex images in a 4-choice task. Our results indicate that individuals recognized the correct location over other, biased alternatives, confirming that metric information is unbiased at the time of retrieval. In addition, we found that, when participants make errors, they are more likely to select locations that are biased toward the category prototype. In Experiment 2, we demonstrate that categorically biased locations are most likely to be chosen under conditions of uncertainty. Indeed, under these conditions, categorically biased locations were chosen more frequently than the correct location. These results suggest that systematic errors are the result of combination across multiple levels of spatial representations that are undistorted but somewhat uncertain. Keywords: category adjustment model, location memory, Bayesian combination, spatial bias, retrieval model

Spatial memory plays a ubiquitous role in our everyday lives. It is required to navigate between homes and workplaces; to find our seats in a theater; and to recall the location of our cell phones, car keys, and countless other items. And yet, despite its pervasiveness and necessity to our functioning, spatial memory not only shows inaccuracies but is often systematically biased in predictable ways. For example, adults regularize irregular spaces (e.g., Glicksohn, 1994; Tversky, 1981), consistently estimate the distance from A to B as shorter or longer than the distance from B to A (e.g., McNamara, 1991; McNamara & Diwadkar, 1997; Newcombe, Huttenlocher, Sandberg, Lie, & Johnson, 1999), and systematically misremember locations as being closer to the center of the sur­ rounding region (e.g., Holden, Curby, Newcombe, & Shipley, 2010; Holden, Newcombe, & Shipley, 2013; Huttenlocher, Hedges, & Duncan, 1991). Some have taken these errors to suggest that human spatial representations are distorted or schematized with respect to the

physical space (e.g., Tversky, 1981; Tversky & Schiano, 1989). In this view, spatial reference frames are assumed to induce percep­ tual illusions that lead to errors in encoding the items within those frames. For example, Tversky (1981) has suggested that memory for the relative latitudes of cities in North America and Europe is distorted because their respective continents are shifted according to the Gestalt principle of alignment. According to this position, then, the common belief that Rome is farther south than Philadel­ phia (when it is in fact farther north) is due to heuristics based in perception. Others, though, have suggested that these errors are best ac­ counted for by Bayesian models in which hierarchically nested spatial cues are combined (e.g., Huttenlocher et al., 1991; New­ combe & Huttenlocher, 2000). For example, to remember where one’s keys are, the fine-grained “metric” estimate of 10 cm from the edge of a table is integrated with the coarser, “categorical” memory that they are within the top left quadrant. This combina­ tion introduces bias toward the center of the spatial category but is optimal under conditions of metric uncertainty in that it minimizes average error across multiple estimates. While there is strong evidence for such a process of combina­ tion, there has been some debate as to when metric and categorical cues are combined (e.g., see Sampaio & Wang, 2009, 2012). According to delay models, such as Spencer and colleagues’ Dy­ namic Field Theory, the metric representation continuously blends with the categorical during the delay period (e.g., Schutte, Spencer, & Schoner, 2003; Spencer & Hund, 2002; Spencer, Simmering, & Schutte, 2006). As a result, the final estimate of the location will be an integrated representation of the true location and of the

This article was published Online First December 22, 2014. Mark P. Holden, Nora S. Newcombe, and Thomas F. Shipley, Depart­ ment of Psychology, Temple University. This research was supported by National Science Foundation Grants SBE-0541957 and SBE-1041707. Portions of this research were presented at the 51st annual meeting of the Psychonomic Society, November 2010. Correspondence concerning this article should be addressed to Mark P. Holden, who is now at the Department of Psychology, University of Western Ontario, London, ON, Canada N5Z 4P4. E-mail: mholde3@ uwo.ca

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category. In contrast, retrieval models suggest that the two repre­ sentations are encoded in parallel and become integrated only at retrieval. For example, Huttenlocher et al.’s (1991) Category Ad­ justment (CA) model proposes that metric and categorical infor­ mation are both retained as separate, unbiased representations throughout the delay period, but that they become less reliable over time. Furthermore, the model assumes that metric information decays relatively more quickly than does categorical information. The final estimate is assumed to be an optimal (Bayesian) combi­ nation of these two cues, each weighted by their relative reliability at the time of recall. Thus, the process of estimation results in systematic biases, even though the underlying representations are themselves unbiased. Sampaio and Wang (2009) demonstrated that, although recalled estimates of locations are systematically biased toward category centers, the underlying spatial memories are not distorted. Partic­ ipants were asked to both recall a spatial location and perform a recognition task in which the same correct locations were pitted against their previously recalled estimates. The results demon­ strated that individuals were able to retain and access the correct, metric location of a target over their own category-biased recalled position of that target. The authors therefore concluded that “category-based errors are due not to a memory [that is] biased by categorical information but to a biasing process that operates on unbiased, yet imprecise [metric] memories” (p. 1336). Interestingly, Sampaio and Wang (2009) found similar results in terms of accuracy in their recognition task, even across different retention intervals (see their Experiments 1 and 3). This is surpris­ ing, especially given the central assumption of the CA model that categorical information is used to adjust increasingly uncertain metric information. That is, a number of studies have suggested that metric information degrades relatively quickly, compared to categorical information (e.g., Allen & Haun, 2004; Intraub, 1997; Postma, Huntjens, Meuwissen, & Laeng, 2006; van der Ham, van Wezel, Oleksiak, & Postma, 2007). The CA model therefore predicts that bias will increase with longer retention intervals, as metric uncertainty increases (e.g., Holden et al., 2013; Hutten­ locher et al., 1991). Sampaio and Wang’s results, however, did not demonstrate any effect of delay. This result runs directly counter to the CA model’s assumption that combination is largely driven by the degree of metric uncertainty. We believe that there are several possible reasons for why Sampaio and Wang (2009) found no effect of increased metric uncertainty. First, it is possible that even their longer retention intervals (5 s) did not lead to sufficient degradation of the metric trace for an effect to be found. That is, the use of a recognition task may provide a strong enough cue as to the veridical (metric) location that categorical information simply does not factor into the recognition estimate. Second, the use of a relatively simple task space (a blank circle) with easily defined categories (defined by the horizontal and vertical axes) may have allowed participants to dedicate relatively greater attentional resources to the encoding of metric information, compared to categorical, than would be the case in more complex instances of location memory (Holden, Duff-Canning, & Hampson, 2014). This may have allowed for relatively strong encoding of the metric location, helping to ame­ liorate the effects of decay. Third, Sampaio and Wang’s foil locations for a given participant were defined by that same partic­ ipant’s recall performance for the same location. Although this

method provides an extremely compelling argument for an unbi­ ased metric trace, it also necessarily means that participants, dur­ ing the recognition portion of a trial, had already viewed that same correct location immediately prior, during the recall portion of the trial (see their Experiments 1 and 3). Again, although we believe it is unlikely, it is possible that this repeated exposure to each correct location led to recognition performance that was spuriously high, thereby masking any effects of metric certainty. Fourth, both the veridical and biased locations were presented within the same frame of reference, which was centrally located during both study and test phases. This may have facilitated the use of alternative cues, such as the edges of the computer monitor, to help define the metric location and protect against its loss over increasing reten­ tion intervals. Finally, participants were required to recognize the correct location over only one alternative location. This may have sufficiently decreased the task difficulty to mask any apparent effects of greater metric uncertainty. Here, we explore the assumption of the CA model that categor­ ical bias in location memory is due to increased metric uncertainty at the time of recall. The experiments presented here address the above explanations for Sampaio and Wang’s (2009) data by pre­ senting participants with a four-choice location recognition task using images of complex, natural scenes. Holden et al. (2010) found that recall of point locations within these scenes is biased toward the category prototype (e.g., the center of the rock), much as in studies using simple geometric shapes. However, to date, no-one has examined predictions of the CA model using a recog­ nition task with such scenes. Furthermore, by including multiple foil options in the recognition task, we were able to address additional questions of theoretical importance (e.g., when errors are made, are all equally likely— indicating guessing— or are some favored?). To preview, in Experiment 1 we replicated Sampaio and Wang’s (2009) primary finding that participants were more likely to choose the correct location over other, biased alternatives, ruling out many of the alternative explanations listed above. In addition, we found that locations that are biased toward the category pro­ totype were more likely to be selected than were locations biased away from the category prototype. Experiment 2 builds upon these results by demonstrating that categorically biased errors are more likely to be selected under conditions of metric uncertainty.

Experiment 1 In Experiment 1, participants were asked to recognize point locations depicted within images of complex, natural scenes. As in Sampaio and Wang’s (2009) study, we hypothesized that if metric information and categorical information are processed in parallel, and combined only at retrieval, then the metric location may be accessible in a task that is less demanding than the traditional recall task. If, however, participants falsely recognize the location that is biased toward the category center, then this would suggest that metric information is either lost through combination during the delay period (e.g., Schutte et al., 2003; Spencer & Hund, 2002) or that our spatial representations are biased during perception (e.g., Tversky, 1981). Importantly, the use of complex, natural scenes allowed us to examine whether the pattern of results reported by Sampaio and Wang (2009) would hold for more complex instances of location memory, as it should if it is to provide an overarching framework

UNCERTAINTY AND LOCATION MEMORY BIAS

for thinking about spatial memory. The task also included three foil options, in addition to the correct location, per trial. The foils were defined by using the average recall error from previous studies using these same images (see below), ensuring that partic­ ipants had not previously viewed the stimulus when they were asked to recognize the location. In addition, the foil and correct options were presented simultaneously, as separate images, all in positions that differed from that of the study image. This (in addition to a cropping procedure described below) eliminated the potential use of cues such as the borders of the screen to help identify metric locations. Finally, by including multiple foil op­ tions, we were able to directly examine error patterns, even in a recognition task.

Method Participants. The participants were 27 undergraduate stu­ dents at Temple University. Participation helped to partially fulfill a course requirement. Three additional individuals participated but were not included in the final analysis. One was omitted due to a computer error in recording the student’s data responses, while the remaining two were omitted because they failed to follow instruc­ tions. Specifically, these participants chose one of the four test image locations (e.g., the image on the upper left of the screen) on more than 50% of the trials. Materials. The presentation of stimuli and collection of data were controlled by the program PsyScope X B46 (Cohen, MacWhinney, Flatt, & Provost, 1993), which ran on a Macintosh computer connected to a large (37 cm wide X 28 cm tall) flatscreen CRT monitor set to a resolution of 1280 X 960 pixels. Stimuli. The stimuli were 60 free downloaded images of natural landscape vistas. Landscapes were approximately evenly distributed between seven types: desert scenes, plains (e.g., grass­ lands), rolling hills, coastal scenes, rocky regions (e.g., hoodoos), lakesides, or mountain regions. Thirty-five of these scenes were identical to those used by Holden et al. (2010). Locations were small yellow dots, which stood out against the natural background colors. In contrast to the case with Holden et al. (2010), the dots were not made to be elliptical (to correspond with the slope of a background object), nor were the edges blended with the background. These changes eliminated the potential use of cues other than location—such as the orientation of an elliptical point—to aid in image recognition. The correct locations were chosen pseudo-randomly, so that the relative direction and distance between the correct locations and category centers (as well as between correct locations and nearby category edges) varied across locations. The only constraints placed on potential locations were that they could not appear in the sky or within 2 cm of any border of the image. This latter constraint was meant to reduce use of the location’s distance from a border, rather than scene content, to recall metric information. All images were 540 pixels (19 cm) in length but varied in height. Study images were cropped by removing 10% of the image from a nearby border, with the constraint that it could not remove any portion of the spatial category. This further prevented partic­ ipants from using cues such as the distance of the location to image borders and encouraged them to rely on the image content. To create the foil images for the test phase, eight additional images were produced. First, a category-biased foil image was

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created by displacing the correct location 18 pixels (6 mm) in the direction of the category center. Then, seven additional foil images were created by displacing the dot 18 pixels (6 mm) from the correct location at angles ±45°, ±90°, ±135°, and 180° relative to the direction of the category prototype. The distance of 18 pixels was chosen based on the mean magnitude of error in location recall for such images in previous studies from our lab (e.g., Holden et al., 2010).1 Finally, we discarded any foil images for which this process resulted in a location that was no longer on the original spatial category, as this would make it a relatively easy option for participants to eliminate in a recognition task. From the remaining foil images, three were randomly chosen and presented (along with the correct location) during the test phase of each trial. Category identification. In order to create the stimuli as outlined above, we needed to identify the spatial categories within our images a priori. Following the methods outlined by Holden et al. (2010), we used the k-means clustering algorithm of a widely available software package (ImageJ; Abramoff, Magelhaes, & Ram, 2004). Briefly, this algorithm randomly chooses k color values (called cluster values) for a given image and calculates the difference between every pixel’s RGB color value and the nearest cluster value. The cluster values are iteratively adjusted to mini­ mize the average difference between every pixel and its nearest cluster value (see Holden et al., 2010). The result of this is an image consisting of k colors. This image is then de-speckled to remove noise. Categories are identified by using the program’s wand tool at the correct location. This tool seeks the nearest edge and follows it until it loops back upon itself. Holden et al. reported that this method has been shown to have high consistency with the categorization scheme of a group of undergraduate students and has the added advantage of being performed relatively quickly. The center of mass of the two-dimensional category surrounding each correct location was used as the category prototype in our study. Procedure. On every trial of the experiment, two study im­ ages— each containing one to-be-remembered location—were pre­ sented serially, in the center of the screen. These were followed by four test versions of the first image (i.e., the correct location and three foil options) presented simultaneously, one in each quadrant of the screen, and then four versions of the second image. The participants’ task was to indicate which of the four test images depicted the same location as its corresponding study image by clicking anywhere on that picture with a mouse. The primary advantage of this procedure is that it doubles the data collected over the course of the experiment compared to a procedure that employs a simple delay between study and test images, while still retaining the characteristic error patterns of bias toward category

1Note that the mean distance value was calculated based on the recall of locations after removing outliers. Specifically, all responses greater than 25% of the image length were automatically eliminated. From the remain­ ing distribution of responses, those that were greater than 2.5 standard deviations of the distance from the correct location were also eliminated. This process prevents large errors from skewing the average distance from the correct location, which could otherwise have over-simplified the dis­ crimination between correct and foil locations in the recognition task. In addition, the mean value for these locations was calculated for images that were 26 cm in length, and proportionally scaled for the present images, which are 19 cm in length. This preserved the relative size of the error but decreased the absolute distance from the correct location.

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prototypes, at least in location recall tasks (e.g., Holden et al., 2010; Huttenlocher et al., 1991). Analyses confirmed that no difference in error patterns was found for locations shown first or second within a trial. Trials began with a 500-ms fixation cross in the center o f the screen. The study locations were then shown for 2,500 ms each, separated by a 750-ms blank screen. Following a 1,000-ms delay, the set of four recognition images was then presented. These remained on-screen until participants made a response. If they were unsure o f the location, they were encouraged to guess. Trials continued until all 60 image-locations had been seen.

Results Because three foil images were chosen randomly for each trial, we separately analyzed those trials that contained the categorybiased foil image (which we refer to as “category trials”) and those that did not (“foil trials”). To facilitate comparison, we averaged the percentage of choices between the two non-category-biased foils for category trials and the three non-category-biased foils for the foil trials. For the foil trials, the correct location was chosen significantly more often than chance (correct: M = 35.28%, SD = 7.56%), t(26) = 7.07, p < 0.01, d = 2.77 (see Figure la). Similarly, for the category trials, the correct location was chosen significantly more often than chance (correct: M = 36.99%, SD = 8.42%), t{26) = 7.41, p < 0.01, d = 2.91 (see Figure lb). Furthermore, the correct location was chosen more frequently than the category-biased location (category-biased: M = 25.23%, SD = 8.54%), t{26) = 4.19, p < 0.01, d = 1.64, and more frequently than the other two foil images in the trial (other/2: M = 18.89%, SD = 4.30%), t(26) = 8.41, p < 0.01, d = 3.30. Finally, when people did err on the category trials, the category-biased location was chosen more often than the other foils in the trial, f(26) = 2.90, p < 0.01, d = 1.14 (see Figure lb). Comparing across the two trials types, there was no difference in the frequency with which participants chose the correct location, f(26) = 0.86, ns. There was also no difference between images seen first or second within a trial, in terms o f the frequency with which the correct location was chosen (in either foil or category trials) or with which the category-biased image was chosen (cat­ egory trials only), all t(26)s < 1.18, ns. In addition, participants showed no preference for any test image position (e.g., the bottom right test image), F(3, 78) = 1.88, ns. In order to determine whether individuals were more likely to choose centrally biased foil options, we analyzed all trials in which participants made an error.2 For this analysis we collapsed across foil and category trials, because this equates the likelihood of seeing the category-biased image and that of seeing any other foil image (e.g., those that were + 4 5 ° from the direction of the category prototype, those that were -4 5 ° ). Furthermore, because two different images contained locations that were biased at an absolute angle of 45°, 90°, or 135° from the direction of the category prototype, while only a single image defined each of the category-biased and 180° biases, we averaged the proportion of choices across each pair o f images with the same absolute differ­ ence angle. There was a significant linear trend, F (l, 26) = 7.19, p = .01, indicating that, when participants erred, they were more

likely to choose locations that were biased in the direction of the category prototype.

Discussion The results from Experiment 1 clearly demonstrate that partic­ ipants were more likely to choose the correct location over other, biased alternatives. Critically, this experiment employed a very different task than that outlined by Sampaio and W ang (2009). For one, the frame of reference in our experiment was derived from complex, natural scenes rather than simple, geometric shapes. Furthermore, the use of three foil options, presented as separate images, increased task difficulty and eliminated any potential use o f screen position or edge cues to help define the metric location. W e believe that these data suggest that memory for metric infor­ mation is still accessible upon retrieval, and that the typical pat­ terns of bias observed in location recall tasks (e.g., Holden et al., 2010; Huttenlocher et al., 1991) are due to the combination of metric and categorical representations at retrieval, rather than to spatial representations that are perceptually distorted. However, an alternative explanation of the data presented in Experiment 1 might propose that the task encouraged participants to simply compare the four choices and choose the location that was most central, relative to the other locations, on each trial. This strategy might result in above-chance performance in choosing the correct location, even in the absence of any memory. We do not believe this to be the case, though, for three reasons. First, Sam­ paio and W ang (2009) demonstrated a similar pattern of choosing the correct location over biased alternatives, even when there were only two choices. Second, this explanation cannot account for the other major finding of Experiment 1— that individuals were more likely to err by choosing the categorically biased location rather than any o f the alternative foils. If participants were choosing locations purely based on perceived centrality, relative to the other options, then there is no reason that this foil would be more likely to be chosen than any other. Finally, this alternative strategy would be viable only if the correct location tended to be centrally situated, relative to the three other foils, and this was not the case. The method by which foil locations were generated produces 56 pos­ sible combinations of foils. O f these, there are only eight combi­ nations that result in the correct location appearing central among the four test images.3 If participants chose locations based on perceived centrality, then they would be more likely to choose the correct location in these trials compared to those in which the correct location was not central with respect to the three foil locations on that trial. However, post-hoc analyses demonstrated that there was no significant difference in the proportion of correct location choices between these types of trials, all 1(25) < 0 .7 1 , ns.

2 Because we discarded foils for which the biased location was no longer on the original category, not all images were associated with eight foils. To prevent these images from affecting the data, only those associated with all eight foil options were included in the following analyses. 3 The correct location was determined to be central among the test images if it was located inside a triangle whose vertices were defined by the locations in the three foil images. If the correct location was located outside the border of the triangle, then that combination was classified as having the correct location not centrally situated. There were eight and 24 such combinations, respectively. The remaining 24 combinations of foils were not included in the post-hoc analysis, as the correct location was located along one of the edges of the triangle.

UNCERTAINTY AND LOCATION MEMORY BIAS

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unbiased metric representation was accessible is demonstrated by the fact that the correct location was chosen more often than chance, and more often than the category-biased location (when present). However, the fact that the category-biased (and nearby) errors were chosen more often than errors in the opposing direction suggests that, at least in some trials, metric information was combined with categorical information. Following Sampaio and Wang (2009), we believe that the correct option in the recognition task served as a cue to the veridical memory trace, and hence performance was fairly accurate. However, in some trials, the metric trace may have been sufficiently degraded or may have been poorly encoded, so that the correct location was no longer a strong enough cue to trigger the correct response. In these cases of metric uncertainty, then, individuals make the optimal estimate (given uncertainty), which combines the metric and categorical representations, leading to biased responses. Note that this explanation of the data suggests that, as metric uncertainty increases, the likelihood of choosing the categorybiased location increases. In contrast, the alternative explana­ tion (outlined above) suggests that participants chose the cor­ rect location at above-chance levels because it was centrally positioned with respect to the other foil locations. According to this position, the less reliable one’s memory for a given loca­ tion, the more likely such a strategy would be employed. Therefore, as memory for the metric location becomes less certain, this alternative explanation would predict— somewhat paradoxically— that participants would be more likely to choose the centrally positioned (i.e., correct) location. We examine these predictions in Experiment 2.

Experiment 2

Figure 1. The percentage of choices made in the recognition task. Foil trials (Panel a) did not contain the categorically biased image, while category trials (Panel b) did contain the category-biased image. Chance is 25% in all trials. Error bars represent the 95% confidence interval (95% Cl) of the mean.

In Experiment 1, the finding that categorically biased errors were more likely than other errors is a critical difference between these results and those of Sampaio and Wang (2009). Although Sampaio and Wang were able to compare the recognition and recall performance, they did not include multiple foil options. This is therefore the first time, to our knowledge, that the bias patterns predicted by the CA model have been identified in a location recognition task, rather than recall or reproduction tasks. We take these results to indicate that recognition errors were not due to a total failure to encode (or the complete loss of) metric information, but rather to the combination of metric and categorical knowledge. Taken together, we believe that the results of Experiment 1 suggest that an unbiased metric representation was accessible to participants, but that it was also somewhat uncertain. That the

Experiment 1 demonstrated that individuals were able to cor­ rectly identify the correct location in a recognition task, even when those locations were depicted in complex, natural scenes. In addi­ tion, when errors were made, those that were biased toward the category prototype were more likely to be chosen than those that were biased away from the category prototype. Bayesian models of spatial cognition state that bias in location memory is the result of uncertain metric information being combined with categorical information. That is, when individuals make errors in the recog­ nition task of Experiment 1, these models suggest that it is due to metric uncertainty about the location (despite the retrieval cue provided by the task itself), leading to combination across the metric and categorical representations of the location. This, in turn, leads individuals to choose centrally biased locations. Following this logic, it would therefore be predicted that participants would be more likely to choose the category-biased location on trials for which they indicate relative uncertainty, compared to trials in which they feel more confident (e.g., Radvansky, CarlsonRadvansky, & Irwin, 1995). Here we explore this prediction by comparing response patterns across trials in which participants are relatively certain of their response versus those in which they are uncertain.

Method Participants. The participants were 35 undergraduate stu­ dents at Temple University. Participation helped to partially fulfill a course requirement.

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Materials, stimuli, and category identification. Materials, stimuli, and methods of identifying categories were identical to those in Experiment 1. Procedure. The procedure was identical to that used in Ex­ periment 1 with one exception. Whereas participants were encour­ aged to guess if unsure in Experiment 1, here they were allowed to skip a trial if unsure by pressing the X key on the keyboard at the time of response. However, 25% of key presses (randomly) would fail to advance to the next stimulus. Participants were informed that this might occur due to a “glitch in the program,” and that they should make a best guess in these instances. Therefore, on trials when participants initially press a key but are forced to still respond, we can assume that their certainty about their response is lower than on trials where no key press preceded a response. Because some participants indicated no uncertainty on any trials, we collected data until 30 participants had indicated at least one trial of uncertainty. Analysis. As in Experiment 1, we separately analyzed cate­ gory and foil trials (i.e., those that did and did not contain the category-biased image, respectively). Again, to facilitate compar­ ison, we averaged the percentage of choices between the two non-category-biased foils for category trials, and the three non­ category-biased foils for the foil trials. We also separated the category and foil trials based on whether they involved forcedchoice (FC) trials (i.e., those for which the participant initially pressed the X key, indicating uncertainty, but was still forced to make a response), or non-forced-choice (NFC) trials (no key press, indicating relative certainty). In addition, although participants were asked to respond by clicking the mouse directly on one of the four response images, a small number of responses in this exper­ iment were located in the negative space off one of the images. All such responses were eliminated from analysis. This amounted to 101 responses, or 4.81% of the data. Participants indicated uncer­ tainty on a total of 393 (19.66%) of the remaining trials, and were forced to make a response on 114 of these. Results Among the NFC foil trials, the correct location was chosen significantly more often than chance (correct: M = 36.71%, SD = 6.74%), t(34) = 10.28, p < 0.01, d = 3.52 (see Figure 2a). Similarly, for the NFC category trials, the correct location was chosen significantly more often than chance (correct: M = 34.24%, SD = 11.72%), t(34) = 4.67, p < 0.01, d = 1.60 (see Figure 2b). Furthermore, the correct location was chosen more frequently than the category-biased location (category-biased: M = 21.98%, SD = 8.61%), r(34) = 4.33, p < 0.01, d = 1.49, and more frequently than the average of the other two foil options (foil/2: M = 21.89%, SD = 5.97%), t(34) = 4.40, p < 0.01, d = 1.51. Interestingly, when people did err on the NFC category trials, the category-biased location was not chosen any more frequently than the other foils, t(34) = 0.05, ns (see Figure 2b). In contrast to these results, for the FC foil trials, the correct location was not chosen more often than chance (correct: M = 25.78%, SD = 37.68%), t(14) = 0.08, ns (see Figure 2c). Nor was the correct location chosen at above chance levels for the FC category trials (correct: M = 16.67%, SD = 38.92%), t( ll) = —0.74, ns (see Figure 2d). However, the category-biased location was chosen at a rate significantly greater than chance

(category-biased: M = 75.00%, SD = 45.23%), f (ll) = 3.83, p < 0.01, d = 2.31, and more frequently than the correct option, f(ll) = 2.55, p = .03, d = 1.54. Furthermore, because we wished to directly assess whether uncertainty led participants to choose the category-biased location, we compared the rates of choosing this image in FC and NFC category trials. Even if we compare only trials in which a participant erred, there was a significant differ­ ence, indicating that participants were more likely to choose the category-biased location in FC trials than in NFC trials, t( ll) = 4.07, p < 0.01, d = 2.45. As in Experiment 1, there was no difference between images seen first or second within a trial, in terms of the frequency with which the correct location was chosen (in any foil or category trials) or with which the category-biased location was chosen (only category trials), all ts(34) < 1.47, ns. Finally, participants showed no preference for any test image position (e.g., the bottom right test image), F(3, 102) < 1, ns. Again, we also examined participants’ errors to determine whether locations that were biased toward the category center were chosen more frequently than those biased in the opposite direction, see Footnote 2. As in Experiment 1, we collapsed across all trials for which an error was made and averaged the proportion of choices across images whose locations were defined by the same absolute angle relative to the direction of the category prototype. Once more, there was a significant linear trend, F (l, 34) = 8.41, p < .01, indicating that, when participants erred, they were more likely to choose locations that were biased in the direction of the category prototype.

Discussion In the discussion of Experiment 1, we suggested that an unbi­ ased metric representation of location was accessible in the test phase of our recognition task, but noted that it was also likely associated with some uncertainty. We further suggested that, al­ though the recognition task may have served as a cue to help individuals access the veridical metric memory trace, in some trials, the metric trace may have been sufficiently degraded or may have been poorly encoded, so that viewing the true location at test was no longer a strong enough cue to trigger the correct response. Bayesian models of spatial cognition suggest that metric informa­ tion that has become degraded over time (i.e., it becomes less certain) is combined with categorical information, leading to sys­ tematic bias toward the center of the category. Because each of these cues is weighted by their relative reliability, greater metric uncertainty will ultimately lead to greater bias (e.g., Huttenlocher et al., 1991). Therefore, it was predicted that participants would be more likely to choose the category-biased location on trials when they are uncertain, compared to trials in which they feel relatively confident in their ability to choose the correct location. The results of Experiment 2 support the conclusions and pre­ dictions derived from our results in Experiment 1. As in Experi­ ment 1, it is clear that the metric representation was still accessible at test, given that the correct location was chosen more often than chance and more often than the category-biased location (when present) in the NFC trials. In addition, we also replicated our previous finding that, when errors were made, those locations that were biased toward the category prototype were more likely to be

UNCERTAINTY AND LOCATION MEMORY BIAS

a) Non-Forced-Choice, Foil Trials

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b) Non-Forced-Choice, Category Trials

0 80

ss in

Correct

Other/3

c) Forced-Choice, Foil Trials

Correct

Other/3

Foil

Figure 2. The percentage of choices made in the recognition task. Panels a and b represent non-forced-choice trials, while Panels c and d represent forced-choice trials. Forced-choice trials were those in which the participant indicated uncertainty but was still required to respond. Panels a and c depict the results for foil trials, which did not contain the categorically biased image, while Panels b and d represent the category trials. Chance is 25% in all trials. Error bars represent the 95% confidence interval (95% Cl) of the mean.

chosen, implying that categorical information was used to adjust imprecise metric estimates. Critically, though, Experiment 2 also demonstrated that uncer­ tainty was strongly associated with choosing locations that are categorically biased. Recall that FC trials essentially involved the participant reporting uncertainty about the correct location, but still making a response. Our results show that on these trials, the category-biased location was chosen significantly more often than chance would suggest, and more often than even the correct location. Furthermore, the percentage of choices of the categorybiased locations was significantly higher for the FC trials than for the NFC trials. This clearly demonstrates that greater cer­ tainty was associated with accurate performance, while uncer­ tainty was associated with categorical biases. In the FC trials, individuals appear to have made the optimal estimate for a location (given metric uncertainty) by combining metric and categorical representations. This led to their choosing the

category-biased locations over the correct locations, even in a recognition task. It is worth noting, however, that the results of the FC trials are necessarily based on a relatively small subset (5.70%) of the total number of trials in Experiment 2. As outlined in the Procedure section, we collected data until 30 participants had indicated un­ certainty on at least one trial. However, a number of these partic­ ipants indicated uncertainty on only a single trial and/or were never forced to make a response due to the randomized nature of the design. The data for the FC trials is therefore based on 114 trials across 19 participants. Although the FC data are based on a relatively small sample, this is a necessary aspect of the experimental design. That is, increasing the difficulty of the task so as to increase the number of trials in which a participant was uncertain is likely to be accom­ panied by an increase in participant frustration, which may affect the validity of the results on either or both of the FC and NFC

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trials. Similarly, increasing the proportion of FC trials from 25% of all trials in which a participant indicated uncertainty might suggest the purpose of the experiment to at least some of the participants in the study, again affecting the potential validity of the results. This was not the case with the current design, though, as exit interviews with the participants confirmed that all who had indi­ cated uncertainty had also believed the cover story of a computer glitch. Last, the use of a set criterion for data collection, coupled with the rather large effect sizes reported for Experiment 2, makes the results unlikely to be due to the effects of a small sample size. Rather, we suggest that the results of Experiment 2 —that greater certainty was associated with accurate performance, while uncer­ tainty was associated with categorical biases— offer support to the CA model’s assumption that systematic errors in spatial memory are due to the combination of categorical information and rela­ tively imprecise metric information. This conclusion may also be bolstered by the somewhat surpris­ ing finding that, in NFC trials, individuals were not more likely to choose the category-biased foil compared to any other foil. That is, the data from Experiment 1 demonstrated that, when individuals erred, they were more likely to choose the category-biased image. We suggested that, on these trials, the metric trace may have been sufficiently degraded or may have been poorly encoded, so that the correct location was no longer a strong enough cue to trigger the correct response. In such cases of metric uncertainty, then, indi­ viduals make the optimal estimate (given uncertainty), which combines the metric and categorical representations, leading to biased responses. In Experiment 2, however, the NFC trials indi­ cated relative metric certainty, as uncertain trials were either eliminated or were analyzed as FC trials. Our data suggest that combination did not take place for the errors in NFC trials. It is possible that, believing the metric information to be accurate, individuals did not combine categorical and metric information in these trials. Instead, these trials may reflect random error in a somewhat certain, unbiased metric representation.

General Discussion There is abundant evidence that metric and categorical repre­ sentations of a remembered location are combined, producing estimates that are systematically biased toward a central categor­ ical value (e.g., Fitting, Wedell, & Allen, 2007; Holden et al., 2010, 2013; Huttenlocher et al., 1991; Huttenlocher, Hedges, & Vevea, 2000; Newcombe et al., 1999; Sampaio & Wang, 2009, 2012; Wedell, Fitting, & Allen, 2007). However, there has tradi­ tionally been some debate as to the point at which these cues are combined— during perception, during the intervening delay, or upon retrieval (e.g., Huttenlocher et al., 1991; Schutte et al., 2003; Spencer & Hund, 2002; Spencer et al., 2006; Tversky, 1981; see also Sampaio & Wang, 2009, 2012). Sampaio and Wang (2009) argued that, if this combination occurs during either perception or across the delay period, then metric information will have been biased by categorical information at the time of retrieval. If, however, combination does not occur until the time of response, then the metric trace would be unbiased and may still be accessi­ ble. Here, in two experiments, we have demonstrated that individu­ als are able to recognize the veridical location at levels signifi­ cantly above chance, and that they selected the correct locations

significantly more frequently than categorically biased foils. These results are consistent with both the results of Sampaio and Wang (2009) and the general formulation of the CA model, which states that systematic biases in spatial memory are due to the combina­ tion of categorical information with imprecise, yet unbiased metric information (e.g., Huttenlocher et al., 1991). Most critically, though, Experiment 2 directly examined this central assumption of the CA model—that combination is driven by imprecise metric information about a location. Experiment 2 assessed the role of certainty by examining recognition perfor­ mance on trials in which participants indicated relatively low certainty. On these trials, participants selected locations that were categorically biased at rates significantly higher than chance, and significantly more frequently than the correct location. Finally, participants were significantly more likely to choose the categor­ ically biased locations on trials in which they indicated low cer­ tainty. These findings are in line with the CA model and support the assumption that systematic errors in spatial memory are due to the combination of categorical information with relatively impre­ cise metric information. There are two other interesting aspects of the data presented here that warrant further attention. First, because our task included multiple foils per trial, we were able to demonstrate that individ­ uals are more likely to err by selecting locations that are biased toward the category prototype. In both experiments, there was a significant trend for individuals to err by choosing categorically biased locations, as opposed to locations biased in another direc­ tion. This is the first time, to our knowledge, that the bias patterns predicted by the CA model have been identified in a location recognition task, rather than in recall or reproduction tasks. Taken with the above results, we believe that the veridical location in the recognition task served as a cue to the metric memory trace, resulting in performance that was fairly accurate. However, in some trials, the metric trace may have been sufficiently degraded or may have been poorly encoded, so that the correct location was no longer a strong enough cue to trigger the correct response. In these cases of metric uncertainty, then, individuals made the op­ timal estimate (given uncertainty), which combines the metric and categorical representations, leading them to choose locations that were categorically biased. Second, the results of Experiment 2 suggest that participants do have available some information concerning the relative contribu­ tions of metric and categorical information to their estimates, as lower confidence responses were generally less accurate than higher confidence responses. However, our data cannot directly speak to the degree to which this information may be available. In Experiment 2, participants were instructed to press the X key only if they were “very unsure” about the location. As such, even though participants made frequent errors on the remaining trials, it is possible that these errors still reflect a fairly high level of uncertainty, and that participants’ confidence ratings would reflect this. On the other hand, it is possible that conscious assessment of confidence is separate from the Bayesian combinatory process outlined by the CA model; participants may have been relatively confident in their responses, yet still combined (uncertain) metric information with categorical knowledge. Relating performance on location memory tasks to explicit ratings of confidence therefore remains an interesting direction for future research.

UNCERTAINTY AND LOCATION MEMORY BIAS

Finally, it is worth noting that the procedure employed in Experiment 2 requires participants to occasionally make a re­ sponse after having indicated their uncertainty on a given trial. This necessarily increases the retention interval for these trials, compared to those in which the participant either responds without indicating uncertainty or indicates uncertainty and continues on to the next trial. However, because it is assumed that increasing a retention interval will lead to greater loss of metric information (e.g., Holden et al., 2013; Huttenlocher et al., 1991; Sampaio & Wang, 2012), this delay would only serve to further decrease metric certainty on those trials. In summary, we have presented two experiments in which individuals were asked to recognize point locations in images of complex, natural scenes. The results clearly demonstrate that in­ dividuals are able to recognize the correct location over other locations, suggesting that metric information is unbiased at the time of retrieval. In addition, we found that, when participants made errors, these errors were more likely to involve selecting categorically biased locations. Finally, and most important, we demonstrated that these biased locations were most likely to be chosen under conditions of uncertainty. These results are consis­ tent with the CA model, which suggests that unbiased (but uncer­ tain) metric information is combined at recall with coarser, cate­ gorical information leading to errors that are systematically biased toward the category prototype.

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