(PDF) Reference-Frame Misalignment and Cardinal Direction Judgments: Group Differences and Strategies

Journal of Experimental Psychology: Applied Copyright 2004 by the American Psychological Association 2004, Vol. 10, No. 2, 75– 88 1076-898X/04/$12.00 DOI: 10.1037/1076-898X.10.2.75 Reference-Frame Misalignment and Cardinal Direction Judgments: Group Differences and Strategies Leo Gugerty and Johnell Brooks Clemson University In 3 experiments, the authors examined how misalignment of egocentric and exocentric reference frames affects cardinal direction judgments. Experiments 1 and 2 demonstrated large differences in the accuracy and speed with which 104 less experienced and 7 experienced navigators made cardinal direction judgments. Reference-frame misalignment was associated with large performance decrements. The This article is intended solely for the personal use of the individual user and is not to be disseminated broadly. extent of these decrements diminished as ability and experience increased; however, even experienced This document is copyrighted by the American Psychological Association or one of its allied publishers. navigators showed decrements when reference frames were misaligned. In Experiment 3, the authors used 55 college students to examine the individual subtasks of a common strategy for cardinal direction judgments and to isolate the effects of reference-frame misalignment to a particular subtask of this strategy. The tasks and strategies studied in this article can be applied in the development of navigational training and interfaces. Cardinal direction judgments are made in a variety of navigation processes, in particular the strategies, people use on these tasks, as and transportation tasks, and making these judgments accurately this understanding promises to lead to improvements in training and quickly is an important part of jobs such as piloting, air traffic and interface aids for cardinal direction judgments. We also in- control, and police work. However, previous research has shown vestigated whether individual differences in the ability to make that cardinal direction judgments are more difficult than some these judgments were as wide as suggested in our previous re- other navigational tasks and that even practiced operators (e.g., search (Gugerty & Brooks, 2001), as this would further document pilots and automobile traffic-control operators) experience diffi- the need for improvements in training and interfaces. Therefore, in culty in making these judgments (Draper, Geiselman, Lu, Roe, & the current project, we compared people with a wide range of Haas, 2000; Gugerty & Brooks, 2001). Also, misalignment of ability and experience levels at navigational tasks in terms of their spatial reference frames (e.g., exocentric and egocentric frames), performance and strategies on a cardinal direction task. In addition which degrades performance of a variety of navigational tasks, has to the potential applications of this research project in training and been shown to have an exceptionally strong effect on cardinal interface design, identifying high-level strategies and comparing direction judgments. For example, Gugerty and Brooks (2001) people with differing levels of ability and experience can help in showed that changing from aligned to misaligned reference frames understanding the basic cognitive processes used in cardinal di- can cause the accuracy of cardinal direction judgments to decline rection judgments. by 50% while at the same time response times double. Finally, Thus, the current research project had two goals. First, we prior research has found preliminary evidence of wide individual sought to document the extent of individual differences in differences in the ability to make cardinal direction judgments cardinal direction judgments among a group of relatively inex- (Gugerty & Brooks, 2001). perienced navigators and also measure the extent of differences Given that cardinal direction judgments are an important navi- in these judgments between less experienced and experienced gational task that some experts and many novices find difficult, we navigators. In exploring these individual and group differences, attempted in these experiments to further understand the cognitive we paid particular attention to any differences in how reference- frame misalignment affected cardinal direction judgments, be- cause misalignment has such a large effect on these judgments. Leo Gugerty and Johnell Brooks, Psychology Department, Clemson Second, we sought to understand the strategies that less expe- University. rienced and experienced navigators use in making cardinal This research project was partially funded by a grant from the U.S. Air direction judgments. Force Office of Scientific Research (work unit numbers 1123A117, One of the most salient characteristics of human spatial cogni- 2313HM15, and 2313T154), awarded to Ellen Hall and Wes Regian. tion is that people perceive and think about their environment in Opinions, interpretations, conclusions, and recommendations are those of terms of particular perspectives or frames of reference, such as the the authors and are not necessarily endorsed by the U.S. Air Force. egocentric, or person-centered frame, and the exocentric, or world- The authors thank Richard Walker for developing the cardinal direction centered frame. During navigational tasks, people often need to task, Dewayne Moore for providing statistical advice, Jennifer Lee for coordinate information in multiple reference frames, as when they developing the tasks used in Experiment 3, and Janice Hereford, Jennifer Lee, Rebecca Morley, and Joseph Jenkins for helping with data collection. use information in the exocentric reference frame (which may be Correspondence concerning this article should be addressed to Leo shown on a map) to help determine an egocentric navigation action Gugerty, Psychology Department, 418 Brackett Hall, Clemson University, such as whether to turn right or left at a road intersection. Con- Clemson, SC 29634. E-mail:

siderable research has shown that when information in spatial 75 76 GUGERTY AND BROOKS reference frames is not coordinated, or is misaligned, performance on a variety of navigational tasks suffers. According to Hutchins (1995), Klatzky (1998), and Wickens (1999), the three top-level goals of navigation are the following: (a) specifying paths from one’s own location to a destination (route finding), (b) identifying one’s own location (localization), and (c) identifying the location of other objects in the environment. Re- search using route finding tasks—in which participants use maps to plan or follow routes— has shown that response times and errors in pointing, walking, or right–left decisions increased as the par- ticipant’s heading was more misaligned with the top of the map (Aretz, 1991; Hintzman, O’Dell, & Arndt, 1981; Levine, Jankovic, & Palij, 1982; Presson, DeLange, & Hazelrigg, 1989; Presson & Hazelrigg, 1984; Shepard & Hurwitz, 1984; Sholl, 1987). In ad- This article is intended solely for the personal use of the individual user and is not to be disseminated broadly. This document is copyrighted by the American Psychological Association or one of its allied publishers. dition, Werner and colleagues (Werner & Jaeger, 2002; Werner & Schmidt, 1999) found that if participants studied a map in which the orientation of a rectilinear road network (an exocentric refer- ence frame) is misaligned with the top of the map (an egocentric reference frame), then participants were less accurate at using the remembered map to point to targets in the mapped world. Thus, route finding performance suffers when the participants’ map heading is misaligned with the top of the map (Shepard & Hurwitz, Figure 1. Map display used in the cardinal direction task. The triangular 1984) and when the exocentric reference frame provided by the icon shows the aircraft. The line from the aircraft shows the heading of a map’s road grid is misaligned with the top of the map. camera mounted on the front of the aircraft and always facing forward. The A task related to localization (the second navigational goal) is circle shows where the camera is pointing on the ground (the ground navigational checking, in which the navigator compares a potential footprint). In this map, the aircraft and camera face southeast, toward current location and heading on the map with the forward three- Target 1. The actual displays were in color, and objects were easily dimensional (3D) view to see if they match. Aretz and Wickens discriminable. (1992) and Eley (1988) found that for a navigational checking task, response times and errors were highest when the participant’s view from the aircraft showing the ground target, a building, and heading was toward the bottom of the map. One task involving four parking lots surrounding the building (Figure 2). For each identifying the locations of objects in the environment (the third cardinal direction problem, one of the four parking lots had vehi- navigational goal) involves specifying the bearing between two cles in it, and the participants’ task was to determine whether the objects. For example, Gugerty and Brooks (2001) had participants parking lot with the vehicles was north, south, east, or west of the judge the bearing from a building to another object using a 3D building. The heading of the aircraft, as shown by the map icon, view and a map showing their current heading. Both errors and was varied across problems. response times on this task increased as the participant’s heading In Experiments 1 and 2 of the current project, we focused on became more misaligned with the exocentric reference direction of intergroup differences in an attempt to document the extent of north. This task involves misalignment of egocentric and exocen- individual differences in cardinal direction judgments, and to un- tric reference frames because when the participant is heading in derstand in more detail how these judgments are made. We com- any direction but north, the egocentric reference heading of for- pared performance of a group who had more experience at navi- ward (which can be applied both to the 3D view and the map gational tasks (i.e., jet pilots with an average of 13 years of flying heading icon) is misaligned with the exocentric reference heading experience; Experiment 2) with a group of less experienced nav- of north. igators (i.e., Air Force recruits with almost no flying experience; The studies mentioned above show that for tasks focusing on all Experiment 1). In Experiment 3, we investigated a common strat- three types of navigational goals—route finding, localization, and egy participants use to coordinate reference frames in the cardinal identifying object locations—navigation performance is degraded direction task. when information in spatial reference frames is misaligned. In the direction-of-turn (Shepard & Hurwitz, 1984) and navigational- Experiments 1 and 2 checking (Eley, 1988) tasks, the participant’s heading is mis- aligned with the top of a visible map, and both the participant’s Because prior research has shown a bimodal distribution of heading and the map’s top are probably represented egocentrically. accuracy scores on the cardinal direction task in a group of Air In the Werner and Jaeger (2002) and the cardinal-direction- Force trainees (Gugerty & Brooks, 2001), and because we tested judgment (Gugerty & Brooks, 2001) tasks, egocentric representa- Air Force trainees in Experiment 1, we expected a similar bimodal tions are misaligned with exocentric ones. distribution. We also expected that the experienced pilots in Ex- The cardinal direction task used in the current experiments is periment 2 would perform better on the cardinal direction task than shown in Figures 1 and 2. Participants saw a north-up map indi- the trainees, because even better performing trainees in the cating the location and heading of their aircraft, and a ground Gugerty and Brooks (2001) study were performing suboptimally target ahead of the aircraft (Figure 1). They also saw the forward (i.e., 78% correct), and the jet pilots in Experiment 2 passed REFERENCE FRAMES AND CARDINAL DIRECTIONS 77 pad and then saw a problem with the forward-view 3D display on the left (Figure 2) and the map (Figure 1) on the right. The 3D display was described to participants as the view from a camera looking forward from the nose of the participant’s aircraft. The actual displays were in color and were 10.2 cm on a side. Below these displays, the following text message was shown: Which parking lot has vehicles in it? Participants used unla- beled keys on the number pad to respond, pressing 8 for north, 2 for south, 6 for east and 4 for west. Textual feedback was displayed concerning response correctness, response time, the participant’s answer, and, if needed, the correct answer. The feedback and the 3D and map displays remained visible until the participant initiated the next trial. Twelve aircraft headings were presented across trials, from 0° (facing north) to 330°, in 30° increments. For each heading, there were problems with the vehicles in each of the four parking lots (north, south, east, and west). This yielded 48 trials in a block; these were presented in random This article is intended solely for the personal use of the individual user and is not to be disseminated broadly. order. All of the map displays showed north as up. Summary feedback This document is copyrighted by the American Psychological Association or one of its allied publishers. about the number of correct answers was presented after each block. The instructions for the cardinal direction task were presented via computer. They clearly explained that the camera display always pointed ahead of the aircraft and showed the forward view from the aircraft, and explained how to read the information about the aircraft (or camera) heading on the map. Participants were instructed to answer the questions as quickly as possible without making mistakes. Figure 2. Three-dimensional display from the aircraft’s forward-facing nose camera, as used in the cardinal direction task. The display shows four parking lots surrounding a building, with cars in the lower right lot (in this Procedure example). The actual displays were in color, and objects were easily Participants were tested in groups of about 50 but worked at individual discriminable. workstations. Participants read the instructions and performed three blocks of 48 trials in the cardinal direction task, which took about 25 min. extensive selection procedures and received rigorous training re- lated to spatial skills. In addition to these differences in overall cardinal direction Method for Experiment 2 performance, we predicted that increasing reference-frame mis- Participants alignment would degrade performance most for the poorer per- forming novices and least for the experienced pilots. We made this The 7 participants (6 men; 1 woman) ranging in age from 28 –39 years prediction because we felt that group performance differences (M ⫽ 33.6), were Air National Guard jet fighter pilots from McEntire Air would be weaker when reference frames were aligned (because all Force Base, SC, who participated in the experiment voluntarily. The participants could apply the well-learned north-up reference frame number of aircraft flight hours for the group ranged from 500 –5,500 (M ⫽ 2,601; Mdn ⫽ 2,010), and the years of flying experience ranged from 3–22 to the 3D scene on these problems), but would be strongest when (M ⫽ 13). reference frames were misaligned. Because prior performance on the cardinal direction task was sometimes poor, and because we were interested in assessing Materials and Tasks whether performance on this task can improve via training, we The cardinal direction task was the same as in Experiment 1 except that investigated whether performance improved over the three trial the task was presented on a laptop computer with an LCD screen, and blocks of this study. We predicted that both accuracy and speed participants pressed the H key to start each trial, and responded using would improve. Because the data from Experiments 1 and 2 are labeled keys on the keyboard (Y as north, J as east, N as south, and G as compared, the methods for these experiments are described west). The feedback after each trial was the same as for Experiment 1 together. (correctness of answer and response time), except that participants did not receive feedback about the answer they had given or the correct answer. Method for Experiment 1 Procedure Participants Participants were tested individually. Participants first read through the The 104 participants (79 men; 25 women), ranging in age from 17 to 27 instructions. Participants’ questions concerning the instructions were an- years (M ⫽ 19.0), were Air Force recruits at Lackland Air Force Base, TX, swered only by repeating information in the instructions. (One participant who participated in the experiment as part of their basic training. The asked a single question.) Then participants performed three blocks of 48 number of aircraft flight hours for the group ranged from 0 to 200 (M ⫽ trials in the cardinal direction task, which took about 25 min. 3.6, Mdn ⫽ 0). Materials and Tasks Results and Discussion for Experiments 1 and 2 The cardinal direction task was presented using personal computers with An alpha level of .05 was used for statistical significance deci- CRT monitors. On each trial, participants pressed the 5 key on the number sions. Cohen’s (1988) f was used to indicate effect size; f values of 78 GUGERTY AND BROOKS 0.10, 0.25, and 0.40 correspond to small, medium, and large effect and better performing novices into separate groups for further sizes, respectively. analyses of the cardinal direction task, using an accuracy score of 56.7% to divide the groups. Cardinal Direction Task Accuracy Data An analysis of variance (ANOVA) was performed with heading (12) and trial block (3) as within-subjects factors, group (3) as a Figure 3 is a histogram showing how overall accuracy at the between-subjects factor, and accuracy as the dependent variable. cardinal direction task was distributed for the 104 less experienced The effects of heading, block, and group were significant, and navigators in Experiment 1. As we predicted, the figure showed a there was a significant interaction of Heading ⫻ Group (see Table bimodal distribution of accuracy scores, with one group of 53 1). The three groups differed significantly in overall accuracy, as averaging 35% correct (SE ⫽ 1.3) and another group of 51 described above. As predicted, the experts were most accurate averaging 78% correct (SE ⫽ 1.5). The excess mass test of (94%), and the 16% difference in accuracy between experts and modality (Cheng & Hall, 1998) supported the conclusion that the the better performing novices showed a large effect size, f ⫽ 0.77. distribution was significantly bimodal ( p ⬍ .01). This bimodal The 59% accuracy difference between the experts and the poorer distribution, and its negative kurtosis value of ⫺1.39, suggests a performing novices showed a large effect size, f ⫽ 3.24. Also as This article is intended solely for the personal use of the individual user and is not to be disseminated broadly. relatively wide range of individual differences for novices on the This document is copyrighted by the American Psychological Association or one of its allied publishers. predicted, accuracy increased significantly across trial blocks, cardinal direction task. The experienced pilots in Experiment 2 had from 54% (SE ⫽ 2.4), to 59% (SE ⫽ 2.5), to 61% (SE ⫽ 2.5) on an overall accuracy of 94% correct (SE ⫽ 1.4). Blocks 1–3, respectively. We investigated demographic characteristics of the novice Figure 4 shows that for all three groups, accuracy was strongly group to see what might underlie this unusual distribution. The affected by aircraft heading.1 Accuracy was highest when the poorer performing (M ⫽ 18.8, SE ⫽ 0.2) and better performing aircraft faced north, and thus the participant’s heading and the (M ⫽ 19.3, SE ⫽ 0.3) novice groups did not differ in age, t(103) ⫽ exocentric reference direction were in alignment. Accuracy de- 1.36, ns. The poorer (M ⫽ 0.6, Mdn ⫽ 0, SE ⫽ 0.3) and better clined as the aircraft heading moved away from north, that is, with (M ⫽ 6.8, Mdn ⫽ 0, SE ⫽ 4.6) groups also did not differ in flight increasing heading misalignment. However, accuracy increased hours, Mann–Whitney U ⫽ 1,292, ns. There were proportionally again near south, which probably reflected the use of the south- more women in the poorer performing group, ␹2(1, N ⫽ 104) ⫽ reversal strategy, in which participants determine the answer they 11.1, p ⬍ .05, with 20 women and 33 men in this group and 5 would give if the aircraft were facing north, and then reverse this women and 46 men in the higher performing group. However, the answer. One other effect of aircraft heading was evident only in the group of 79 men still clearly showed a bimodal distribution of data for the better performing novice group. Accuracy at east and cardinal direction accuracy scores, so gender is not the main cause west aircraft headings, as well as north and south, was greater than of the bimodal distribution. Thus, the differences between the nearby headings; we called this the cardinal direction advantage cardinal direction scores of the two groups did not seem to be due effect. to age, gender, or flight experience. In the conclusion of this The data in Figure 4 and the significant Heading ⫻ Group article, we discuss other possible reasons for these individual interaction suggest that the effect of heading misalignment on differences. In any case, we followed Hartwig and Dearing’s accuracy decreased as expertise increased, as we had predicted. (1979) advice regarding bimodal distributions and put the poorer We investigated the size of the three different effects of heading on accuracy— heading misalignment, south reversal, and cardinal di- rection advantage— by forming linear contrasts representing these effects, and then testing how well various combinations of these contrasts fit the mean data in Figure 4. We created two contrasts to represent misalignment effects. The first, called misalignment north (MN) involved a linear decrease in accuracy from north to south headings, as would be expected if participants used only the north heading as a reference direction and did not use the south- reversal strategy (i.e., 1, 0.67, 0.33, 0, ⫺0.33, ⫺0.67, ⫺1, ⫺0.67, ⫺0.33, 0, 0.33, 0.67 for headings 0° to 330°, respectively). The 1 The standard error bars in all figures were calculated using the follow- ing pooled-mean-square within-cells variation, 冘冘 n k MSW ⫽ 共Aji ⫺ SGMj兲 2 /n共k ⫺ 1兲, j⫽1 i⫽1 to calculate the standard error 共冑MSW/n兲, Figure 3. Histograms of average accuracy at cardinal direction task for where n is the number of participants, k is the number of treatments, Aji is participants in Experiments 1 and 3 and a prior experiment (Gugerty & a participant’s cell mean, and SGMj is a participant’s grand mean, as Brooks, 2001; Experiment 1, N ⫽ 263). Exp. ⫽ experiment. described in Estes (1997). REFERENCE FRAMES AND CARDINAL DIRECTIONS 79 second contrast, called misalignment north–south (MNS) involved a linear decrease in accuracy from north to about 120° (or 240°), and then a linear increase approaching south, as would be expected if participants used both the north and south headings as reference directions and did use the south-reversal strategy (i.e., 1.12, 0.62, 0.12, ⫺0.38, ⫺0.88, ⫺0.25, 0.38, ⫺0.25, ⫺0.88, ⫺0.38, 0.12, 0.62). In the MNS contrast, the size of the misalignment effects relative to north and south headings was based on the cardinal direction task data for 501 Air Force trainees in Experiments 1 and 2 of Gugerty and Brooks (2001). The third contrast, for the cardinal direction advantage effect (C), used high weights (1.0) for headings facing cardinal directions, and low weights (– 0.5) for other headings. For each group of participants in Experiments 1 and 2, we This article is intended solely for the personal use of the individual user and is not to be disseminated broadly. This document is copyrighted by the American Psychological Association or one of its allied publishers. compared two regression models (see Table 2). In the first regres- sion model, the MNS and C contrasts were regressed on the mean cardinal direction task accuracy data for the 12 headings. In the second, the MN and C contrasts were regressed on the same data.2 For the three groups, the difference in R2 values between the MNS Figure 4. Effect of heading on average accuracy for the poorer (n ⫽ 53) and C model and the MN and C model ranged from .21 to .59; and better (n ⫽ 51) performing novices in Experiment 1, and the pilots (n ⫽ 7) in Experiment 2, with standard error bars. these R2 differences represented medium to large effect sizes (Cohen, 1988). This suggests that participants in each group used the south-reversal strategy, as this was the only factor that differ- greater than for the experts (f ⫽ 0.40, for the difference). Thus, as entiated the two models. For the models with the higher R2 values, predicted, the effect of misalignment from the north and south the unique variance accounted for by each of the two contrasts was reference directions decreased with increasing ability and calculated (e.g., by subtracting the R2 for a model with only C as expertise. a predictor from the model with both MNS and C to obtain the Given the low accuracy level (35% correct) of the poor- unique variance accounted for by MNS). Table 2 shows that most performing group on the cardinal direction task, it is important to of the unique variance in accuracy in each group is accounted for discuss whether this group understood the instructions and whether by MNS contrast, with the C contrast accounting for little variance. they were simply guessing. Two points are relevant here. First, the The unstandardized regression coefficients for the best fitting average accuracy for the poorer performing group was above models represent the relative sizes of the different effects. The chance (with above-chance accuracy defined by a chi-square test MNS coefficient was larger for the poorer novices (21), than for the as greater than 46 of the 144 problems correct), and 55% of the better novices (14), or for the experts (6). The coefficient for the individuals in this group showed overall performance above poorer novices was greater than for the better novices (f ⫽ 0.23, chance. Second, the strong misalignment and south-reversal ef- for the difference); and the coefficient for the better novices was fects demonstrate that the poorer performing novices were not simply guessing on the cardinal direction problems. If these par- ticipants were guessing on all problems, then their accuracy would Table 1 be near 25% for all aircraft headings, and Figure 4 shows that this ANOVA Table for Analysis of Accuracy (Percentage Correct) was clearly not the case. Many of these participants made fairly Dependent Variable for Experiments 1–3 accurate, above-chance cardinal direction judgments for some aircraft headings. A chi-square test showed that above-chance Variable df MSE F f performance for a particular heading required being correct on Experiments 1 and 2 more than 5 of the 12 problems. The group average for the poorer performing novices was above chance for the headings 330°, 0°, Heading (12) 11, 1188 1,015.0 17.9** 0.35 30°, and 180°; and 77% of the group was above chance for heading Block (3) 2, 216 1,132.4 4.0* 0.09 0° and 60% for heading 180°. Thus, when the aircraft was headed Group (3) 2, 108 3,581.4 289.1** 0.42 Heading ⫻ Block 22, 2376 500.0 0.7 0.09 Heading ⫻ Group 22, 1188 1,015.0 4.5** 0.16 2 Block ⫻ Group 4, 216 1,132.4 2.3 0.06 Instead of fitting these 2 two-factor models, it might seem more Heading ⫻ Block ⫻ Group 44, 2376 500.0 0.8 straightforward to separate the misalignment north–south (MNS) contrast into two contrasts, the MN contrast as defined above, and a misalignment Experiment 3 from south (MS) contrast which had high values near south and low values for all other headings. Then one could fit the MN, MS, and C contrasts in Heading (cardinal direction task) 11, 583 621.1 12.5** 0.40 a single model. This three-factor model was not feasible because the MN Heading (subtasks) 7, 378 327.4 27.7** 0.29 and MS contrasts were of necessity negatively correlated, which led to Task (subtasks) 2, 108 612.9 45.5** 0.24 Heading ⫻ Task (subtasks) 14, 756 241.6 9.5** 0.26 suppression effects that made it impossible to accurately estimate the contributions of these three factors. In the two-factor models considered Note. ANOVA ⫽ analysis of variance. here, there is no problem of suppression or multicollinearity, because the * p ⬍ .05. ** p ⬍ .01. correlation of MNS and C is .23, and the correlation of MN and C is 0. 80 GUGERTY AND BROOKS Table 2 was 6.0 s (SE ⫽ 0.5) for the poorer performing novices, 5.8 s Contrast-Based Models of the Effect of Aircraft Heading on (SE ⫽ 0.4) for the higher performing novices, and 3.8 s (SE ⫽ 0.3) Accuracy (Percentage Correct) for the Cardinal Direction Task for the experts. Response time was strongly affected by heading and the Heading Referencing Subtasks in Experiments 1–3 for all three groups. Response time was lowest when the aircraft faced north, increased as the aircraft heading moved away from R2 full models Unique, ⌬R2 north (misalignment effect), and decreased again near south Experiment and Group/Task MNS, C M N, C MNS MN C (south-reversal effect). Finally, response time for east and west aircraft headings was lower than nearby headings (cardinal direc- Experiment 1 tion advantage). An ANOVA with heading, block, and group as Poor/CDIR .90 (.38) .74 .04 factors, and response time for all responses as the dependent Better/CDIR .94 (.73) .63 .13 variable showed significant effects of heading, block, and group Experiment 2 Pilots/CDIR .68 (.09) .66 .00 (see Table 3). Mean response times for Trial Blocks 1, 2, and 3 Experiment 3 were 7.6 s (SE ⫽ 0.5), 5.9 s (SE ⫽ 0.4), and 4.7 s (SE ⫽ 0.3), Students/CDIR .98 (.68) .59 .19 respectively. Figure 5 shows how heading affected response time This article is intended solely for the personal use of the individual user and is not to be disseminated broadly. Students/map .48 (.35) .12 .18 This document is copyrighted by the American Psychological Association or one of its allied publishers. for all responses for each group. Students/Step 3 (.78) .89 .42 .47 Students/Step 4 .98 (.96) .05 .67 The effect of heading on response time was similar regardless of whether response time to all responses or to correct responses was Note. R2 values are shown for two models, with either the misalignment used. Also the ANOVAs for these two variables revealed the same north–south (MNS) and cardinal direction advantage effect (C) contrasts or pattern of significant effects. This suggests that using response the misalignment north (MN) and C contrasts as predictors (with the lesser time to all responses or to correct responses will lead to similar R2 in parentheses). CDIR ⫽ full cardinal direction task. conclusions about participants’ cognitive processes for this task. Given this, and given the problems associated with analyzing near north or south, the poorer performing group was relatively response time for correct responses in this task (e.g., data loss accurate. Their relatively high accuracy at the south heading is resulting from incomplete cells), we used response time to all particularly important because it rules out the possibility that these responses in further analyses in this article. participants simply did not understand the instructions and there- Table 4 shows the results of the contrast-based modeling per- fore assumed that the 3D view always showed the view facing formed on the response time data for each of the three groups. For north. Many of the poorer performing novices seemed to use the each group, the small difference in R2 values between the MNS and south-reversal strategy, which is a useful strategy that better nov- C model and the MN and C model (.03 to .06) suggests that the ices and experienced navigators also used. Thus, although some of south-reversal strategy, which is what differentiates the two mod- the poorer performing group may have been unclear as to how to els, did not affect response time much. The unique ⌬R2 values perform the cardinal direction task, more than half of this group demonstrated a reasonable understanding of the task and applied some effective strategies for accomplishing it. Table 3 ANOVA Table for Analysis of Response Time (in seconds) Cardinal Direction Task Response Time Data Dependent Variable for Experiments 1–3 Response times to correct responses are usually used to assess Variable df MSE F f cognitive processes, and so these were used in analyzing Experi- Experiments 1 and 2–Correct responses ments 1 and 2. However, Bethell-Fox and Shepard (1988) pointed out that when investigating processes such as mental rotation, Heading (12) 11, 594 11.9 3.8** 0.26 response times to correct responses are less informative when task Group (3) 2, 54 36.5 4.2* 0.14 accuracy is less than 90% and is affected by the angle of rotation. Heading ⫻ Group 22, 594 11.9 0.7 0.11 Both of those conditions were met in Experiments 1 and 2. One Experiments 1 and 2–All responses problem with using response times to correct responses when accuracy is low is loss of data as a result of participants with no Heading (12) 11, 726 8.5 15.5** 0.31 correct responses for some cells of the design. Only 34 of the 53 Block (3) 2, 132 26.1 18.7** 0.18 Group (3) 2, 66 64.0 3.9* 0.10 poorer performing novices had at least one correct response time Heading ⫻ Block 22, 1452 7.3 1.1 0.09 for each heading; therefore 19 of these participants could not be Heading ⫻ Group 22, 726 8.5 0.6 0.07 included in a two-way ANOVA analyzing heading effects for the Block ⫻ Group 4, 132 26.1 0.9 0.04 three groups. Because of these difficulties, we also used response Heading ⫻ Block ⫻ Group 44, 1452 7.3 0.6 time to all responses as a dependent variable. For both of these Experiment 3–All responses response time variables, variance was not homogeneous across the three groups. Therefore, following Wilcox and Keselman (2003), Heading (cardinal direction task) 11, 583 21.7 20.5** 0.44 ANOVAs for both variables were conducted using trimmed means Heading (subtasks) 7, 378 4.5 70.9** 0.40 (trimming the top and bottom 20% of observations in each group). Task (subtasks) 2, 108 7.7 166.3** 0.49 Heading ⫻ Task (subtasks) 14, 756 3.9 25.8** 0.79 An ANOVA with heading and group as factors showed that the only significant effects on response time to correct responses were Note. ANOVA ⫽ analysis of variance. for heading and group (see Table 3). The average response time * p ⬍ .05. ** p ⬍ .01. REFERENCE FRAMES AND CARDINAL DIRECTIONS 81 Because some participants in Experiments 1 and 2 experienced considerable difficulty with the cardinal direction task, and even experts experienced difficulty when reference frames were mis- aligned, in Experiment 3 we investigated the strategies people use to coordinate reference frames on this task. Gugerty and Brooks (2001) identified a number of strategies that participants used on the cardinal direction task. These included strategies that had been previously identified in the navigation literature, such as mental rotation and south reversal. However, the most frequently used strategy was a more analytic strategy that did not seem to involve much mental rotation, which we called heading referencing. For the problem in Figures 1 and 2, the heading referencing strategy involves: (a) identifying on the map that the aircraft is headed southeast; (b) noticing that forward (i.e., toward the top) in the 3D This article is intended solely for the personal use of the individual user and is not to be disseminated broadly. This document is copyrighted by the American Psychological Association or one of its allied publishers. view corresponds to southeast; (c) determining that the top left and right parking lots in the 3D view are the east and south lots, respectively; and (d) determining that the bottom right lot in the 3D view is the west lot. Figure 5. Effect of heading on average response time (in seconds) to all In Experiment 3, we capitalized on the step-by-step nature of responses for the poorer (n ⫽ 53) and better (n ⫽ 51) performing novices heading referencing and developed separate subtasks representing in Experiment 1, and the pilots (n ⫽ 7) in Experiment 2, with standard error most of the steps of the strategy. Then we tested less experienced bars. navigators’ ability to perform each of these subtasks. Thus, we had participants perform subtasks involving reading headings from a suggest that the C and MNS contrasts both accounted for signifi- map (Step 1), making inferences about the bearings of 3D target cant variance. objects using the map heading (Step 3), and making inferences about the bearings of 3D target objects using bearings of other 3D objects (Step 4). We did not create a separate subtask for Step 2 of General Discussion of Experiments 1 and 2 the heading referencing strategy, which involves realizing that the Experiments 1 and 2 compared three groups with different aircraft’s map heading coincides with forward in the 3D view. This levels of ability and experience at making cardinal direction judg- subtask was omitted because it seemed that people using the ments. In terms of overall accuracy of cardinal direction judg- heading referencing strategy would perform it with very high ments, the less experienced groups, who were Air Force basic accuracy, and thus measuring this accuracy was deemed trainees, exhibited a bimodal distribution, as predicted. As shown unnecessary. in Figure 3, this bimodal distribution of accuracy judgments has In the first phase of Experiment 3, participants performed the been replicated in another large group of Air Force trainees (N ⫽ complete cardinal direction task. In this phase, participants also 263; Gugerty & Brooks, 2001). Experienced pilots were more completed a standardized test of spatial orientation ability, the accurate than both groups of novices, as predicted. Another difference among the three groups was in the degree to Table 4 which heading misalignment degraded the accuracy of cardinal Contrast-Based Models of the Effect of Aircraft Heading on direction judgments. When focusing on accuracy, the contrast- Response Time (for All Responses, in Seconds) for the Cardinal based modeling supported our hypothesis that poorer performing Direction Task and the Heading Referencing Subtasks in novices would be most affected, and experienced pilots least Experiments 1–3 affected, by reference-frame misalignment. This finding suggests that an important characteristic of increasing expertise in cardinal R2 full models Unique, ⌬R2 direction judgments is lessening the negative effects of reference- frame misalignment. However, it is not clear yet whether better Experiment and Group/Task MNS, C M N, C MNS MN C methods of handling misalignment are a cause or an effect of Experiment 1 increasing expertise. Poor/CDIR .96 (.90) .20 .56 Although effects of reference-frame misalignment decreased Better/CDIR .94 (.91) .28 .45 with expertise, they did not disappear altogether, as even the Experiment 2 experienced pilots were negatively affected by heading misalign- Pilots/CDIR .88 (.85) .24 .45 ment. Thus, degraded performance in making cardinal direction Experiment 3 Students/CDIR .96 (.91) .22 .54 judgments in the face of reference-frame misalignment seems to be Students/map (.78) .79 .03 .76 a universal characteristic of human performance. Students/Step 3 (.77) .88 .26 .62 A significant improvement in cardinal direction performance Students/Step 4 .99 (.95) .16 .50 over the three blocks was found for both accuracy, f ⫽ 0.09, and 2 Note. R values are shown for two models, with either the misalignment speed, f ⫽ 0.18, as predicted. This small practice effect is tentative north–south (MNS) and cardinal direction advantage effect (C) contrasts or evidence that cardinal direction judgments would improve with the misalignment north (MN) and C contrasts as predictors (with the lesser training. R2 in parentheses). CDIR ⫽ full cardinal direction task. 82 GUGERTY AND BROOKS Guilford–Zimmerman (1981) Spatial Orientation Test. In the sec- the number of correct answers minus 25% of the number of incorrect ond phase of the experiment, participants completed three separate answers. blocks of trials, with each block consisting of one of the subtasks Cardinal direction task and subtasks. The complete cardinal direction of heading referencing. task and the three cardinal direction subtasks were all performed using a The part-task technique in Experiment 3 allowed us to investi- PC. The response keys for all of these tasks consisted of the horizontal row of number keys on the keyboard, which were labeled as follows: 1 key gate a puzzling question from our earlier studies. Given our con- labeled N (for north), 2–NE (for northeast), 3–E (for east), 4 –SE (for clusion that heading referencing is frequently used but does not southeast), 5–S (for south), 6 –SW (for southwest), 7–W (for west), and involve much mental rotation, why does the cardinal direction task 8 –NW (for northwest). The horizontal response key arrangement was used repeatedly show strong effects of heading misalignment? In other because the usual ⫹ arrangement used in previous studies would have words, what aspect of heading referencing could be causing errors allowed the use of artificially unrealistic strategies in some of the subtasks and response times to increase with heading misalignment? This (e.g., map reading). For each of these four tasks, participants received question arises because mental rotation is a reasonable and com- computer-based instructions and practice trials and were asked to answer as mon explanation for misalignment effects in navigation tasks (e.g., quickly as possible without making mistakes. Summary feedback about the Hintzman et al., 1981; Shepard & Hurwitz, 1984), and we have number of correct answers was provided after each task. The three heading This article is intended solely for the personal use of the individual user and is not to be disseminated broadly. referencing subtasks were not described as parts of a strategy for perform- This document is copyrighted by the American Psychological Association or one of its allied publishers. advanced no explanation for why misalignment effects should be expected when heading referencing is used for the cardinal direc- ing the complete cardinal direction task. Rather, each subtask was pre- sented as an isolated task, and the subtasks were completed in a variety of tion task. The part-task technique allowed us to explore this orders across participants. question by isolating which steps of heading referencing were Complete cardinal direction task. The complete cardinal direction task most affected by heading misalignment. In the complete cardinal was the same as in Experiment 1, except the response keys were arranged direction task and each of the subtasks of Experiment 3, heading of horizontally. Participants used only the N, E, S, and W keys in performing the aircraft was varied across trials so that we could investigate the complete cardinal direction task. Participants completed one block of how heading misalignment affected performance. Because partic- 48 trials. ipants could apply the well-learned north-up reference frame to the Heading referencing, Step 1: Map reading. On each trial of this task, map without rotating it, we predicted that map reading (Step 1) participants saw a map of the type shown in Figure 1, with the following would be less affected by heading misalignment than the Step-3 or question displayed: In which direction is the plane headed? After indicat- Step-4 tasks. ing their response by pressing a key labeled N, NE, E, SE, S, SW, W, or NW, The part-task technique also allowed us to look for converging participants saw the same type of feedback after each trial as in the evidence that heading referencing is used frequently. By measur- complete cardinal direction task. All of the map displays showed north as up; and participants were instructed that this would be the case. Participants ing the speed and accuracy with which participants performed each completed one block of 40 trials. There were 5 trials for each of the plane subtask of heading referencing, we could use these data to predict headings 0°, 90°, 180°, and 270°; for these headings, the correct answers participants’ speed and accuracy on the complete cardinal direc- were N, E, S, and W, respectively. There were 5 trials with a plane heading tion task when using heading referencing. We were able to test of 30° or 60°, 5 trials of 120° or 150°, 5 trials of 210° or 240°, and 5 trials whether the predictions based on the subtasks fit the data for the of 300° or 330°; for these headings, the correct answers were NE, SE, SW, complete task because we also measured participants’ speed and and NW, respectively. accuracy at the complete task. We predicted that the estimates Heading referencing, Step 3: From 3D reference heading to nearby from the subtask data would fit the complete task data well, bearings. In this step of heading referencing, participants use exocentric because we expected a high frequency of heading referencing use heading information that has been integrated into the 3D view (e.g., on the complete task. Straight ahead is southeast) to make inferences about the bearings of objects near that reference heading. To represent this heading to partici- pants in the current task, on each trial, participants were shown a 3D Experiment 3 perspective display like the one in Figure 2. The current heading of the participant’s plane was shown by the letters N, NE, E, SE, S, SW, W, or NW Method along with an upward pointing arrow in the top central portion of the 3D display (e.g., SE 1). One of the parking lots in the display had vehicles in Participants it. Below the 3D display, the question, Which parking lot has vehicles in it? was displayed. After indicating their response by pressing a key labeled N, The 55 participants (23 men; 32 women), ranging in age from 18 to 36 NE, E, SE, S, SW, W, or NW, participants saw the same type of feedback years (M ⫽ 19.1), were undergraduates at Clemson University who re- after each trial as in the complete cardinal direction task. ceived extra credit in a psychology class for their participation. None of the In Step 3 of heading referencing, participants use the reference heading participants had any piloting experience. to make inferences about the parking lots near the reference direction. Therefore, in the current task, the parking lots with cars were always near the top of the 3D view. For example, if the 3D display in Figure 2 were Materials and Tasks used in this task, a reference heading like SE 1 would be shown at the top Spatial orientation task. This task is Part 5 (spatial orientation) of the of the display, and the parking lot with the cars would be either the upper Guilford–Zimmerman Aptitude Survey (Guilford & Zimmerman, 1981). right (south) or the upper left (east) lot (also see Figure 6). Participants On each problem of this paper-and-pencil task, participants saw two 3D completed one block of 48 trials. Six trials were presented at each of the perspective scenes as if they were looking over the prow of a boat, and then reference headings N, NE, E, SE, S, SW, W, and NW. For each heading, the they were to indicate how the boat moved between the two views (e.g., parking lot with the cars was in the upper right of the 3D display for two whether it moved right or left, pitched up or down, or rolled right or left) trials, in the upper left for two trials, and in the upper center for two trials. by selecting from five diagrams. Participants completed as many of 60 Heading referencing, Step 4: Inferences between 3D bearings. Prior to problems as they could in a 10-min period, and they were scored based on Step 4 of heading referencing, participants have determined the bearing REFERENCE FRAMES AND CARDINAL DIRECTIONS 83 direction task because the labels for the response keys were ar- ranged incorrectly. Overall accuracy on the full cardinal direction task did not show a bimodal distribution as found in Experiment 1. However, the accuracy scores had a kurtosis of ⫺0.63, indicating a flattened distribution. Also, as shown in Figure 3, there was a better per- forming group of participants and a poorer performing group, although the size of the poorer performing group relative to the better performing group was smaller in this sample than in Exper- iment 1. In contrast, the spatial orientation task showed a kurtosis of 2.04, indicating a peaked distribution and suggesting a narrower range of individual differences than on the cardinal direction task. Overall accuracy on the complete cardinal direction task showed a moderate correlation with accuracy on the spatial orientation This article is intended solely for the personal use of the individual user and is not to be disseminated broadly. task, r ⫽ .29, p ⬍ .05. The order of performing the cardinal This document is copyrighted by the American Psychological Association or one of its allied publishers. direction task and the spatial orientation task did not significantly affect accuracy on the cardinal direction task, t(52) ⫽ 0.59, f ⫽ 0.08, or on the spatial orientation task, t(53) ⫽ 1.34, f ⫽ 0.19. Figure 6. Display for heading referencing Step-3 subtask. Complete Cardinal Direction Task As shown in Figures 8 and 9, accuracy and response time in the full cardinal direction task were affected by heading in the same between two objects in the 3D scene, for example, from the central way as in the previous experiments. The effect of heading was building to one of the parking lots near the top of the 3D display. In Step significant for accuracy (see Table 1), and for response time for all 4, they use the known bearing to determine the bearing to one of the other parking lots in another part of the scene, that is, the lot with the cars. On responses (see Table 3). Contrast-based modeling, following the each trial of this task, participants saw a display like in Figure 2, except that same procedure as Experiments 1 and 2, showed that the misalign- one of the parking lots near the top of the scene had the letters N, NE, E, ment north–south effect accounted for much of the unique variance SE, S, SW, W, or NW in it, to indicate the bearing from the central building in accuracy related to heading (⌬R2 ⫽ .59, see Table 2). Contrast- to that lot. One of the parking lots near the bottom of the display had based modeling for the response time data showed the cardinal vehicles in it. Below the 3D display, the question, Which parking lot has direction advantage (⌬R2 ⫽ .54) and misalignment north–south vehicles in it? was displayed. After indicating their response by pressing a effect (⌬R2 ⫽ .22) accounted for much of the unique variance key labeled N, NE, E, SE, S, SW, W, or NW, participants saw the same type related to heading (see Table 4). These effects of heading on of feedback after each trial as in the complete cardinal direction task. accuracy and response time were very similar to those found in Participants completed one block of 48 trials. On half of the trials, the four parking lots were oriented in a “⫻” configuration, as in Figure 2. For Experiments 1 and 2. these trials, the bearing letters were always in the upper right or left lots, and the lot with the cars could be any of the other three lots. On the other half of the trials, the four parking lots were oriented in a “⫹” configuration (see Figure 7). For these trials, the bearing letters were always in the top lot, and the lot with the cars could be any of the other three lots. Procedure Participants were tested in groups of about 10, although they worked at individual computer workstations. Participants first completed the demo- graphic questionnaire. Then they completed the complete cardinal direction task and the spatial orientation task, in counterbalanced order, with 36 participants completing the spatial orientation task first, and 19 completing the cardinal direction task first. Finally, participants completed the map- reading task (Step 1), the heading-to-bearing inference task (Step 3), and the bearing-to-bearing inference task (Step 4). Each participant was ran- domly assigned to complete these three tasks in one of the six possible orders; between 8 and 11 participants were assigned to each order. The entire experimental session took about 1.5 hr. Results and Discussion The results for the spatial orientation and cardinal direction tasks are presented first, followed by those for the three heading referencing subtasks. One participant could not do the cardinal Figure 7. Display for heading referencing Step-4 subtask. 84 GUGERTY AND BROOKS Overall accuracy was 97% correct (SE ⫽ 0.7) for the map-reading task (Step 1), 86% (SE ⫽ 1.8) for the heading-to-bearing inference task (Step 3), and 83% (SE ⫽ 1.9) for the bearing-to-bearing inference task (Step 4). Response time was 2.31 s (SE ⫽ 0.09) for the map-reading task, 4.50 s (SE ⫽ 0.21) for the Step-3 task, and 5.59 s (SE ⫽ 0.22) for the Step-4 task. Figure 10 shows that accuracy varied with heading for each of the subtasks, but the heading effect seemed stronger for the Step-3 and Step-4 tasks than for map reading. A significant heading by subtask interaction supported this conclusion (see Table 1). A similar pattern was evident for the effect of heading on response time. Figure 11 shows that the effect of heading on response time seemed stronger for the Step-4 task than for the other two tasks. A significant heading by subtask interaction supported this conclu- This article is intended solely for the personal use of the individual user and is not to be disseminated broadly. This document is copyrighted by the American Psychological Association or one of its allied publishers. sion (see Table 3). We were interested in characterizing in more detail the effect of heading on accuracy and speed at performing these heading ref- erencing subtasks. Therefore, for each of the heading referencing Figure 8. Effect of heading on average accuracy on the complete cardinal subtasks, we conducted contrast-based modeling as was done in direction task for participants in Experiment 3, with standard error bars. Experiments 1 and 2 to assess how accuracy and speed were The circles show the accuracy on the complete cardinal direction task affected by misalignment from north and south headings, misalign- predicted on the basis of accuracy at performing Steps 1, 3, and 4 of the heading referencing strategy. ment from north only, and the cardinal direction advantage effect. The MNS, MN, and C contrasts used to represent these effects were similar in shape to the ones used for the full cardinal direction task. Subtasks of the Heading Referencing Strategy The MNS contrast was 1.09, 0.43, ⫺0.24, ⫺0.91, 0.35, ⫺0.91, ⫺0.24, 0.43 for headings from 0° to 315°, respectively. For the The order of completing the three subtasks did not significantly same respective headings, the MN contrast was 1.0, 0.5, 0, ⫺0.5 affect overall performance on the tasks, regardless of whether ⫺1.0, ⫺0.5, 0, and 0.5; and the C contrast was 1.0, ⫺1.0, 1.0, performance was measured via accuracy or response time, and task ⫺1.0, 1.0, ⫺1.0, 1.0, and ⫺1.0. Like before, we fit two regression order did not significantly interact with type of task or heading. models to the mean performance data for the 8 headings, one with Therefore, task order was not included in further analyses. the MNS and C contrasts as predictors and one with the MN and C ANOVAs with subtask type and heading as within-subjects contrasts as predictors. The best fitting models were used to factors showed that subtask type significantly affected accuracy characterize participants’ performance. (see Table 1) and response time for all responses (see Table 3). The results of this modeling are shown in Table 2 for the accuracy data, and in Table 4 for the response time data. For the map-reading task, the largest unique portion of the variance with heading was accounted for by the cardinal direction advantage effect, both for accuracy and response time. As predicted, the Figure 9. Effect of heading on average response time (in seconds) on the complete cardinal direction task for participants in Experiment 3, with standard error bars. The circles show the response time on the complete cardinal direction task predicted on the basis of response times when Figure 10. Effect of heading misalignment on accuracy for each of the performing Steps 1, 3, and 4 of the heading referencing strategy. subtasks of heading referencing, with standard error bars. REFERENCE FRAMES AND CARDINAL DIRECTIONS 85 southeast) is aligned with egocentric forward. In other words, people may rotate a mental compass in the 3D scene until the desired exocentric heading aligns with forward. Thus, the contrast- based modeling suggests that Step 3 of heading referencing may involve some mental rotation. Given this description, it seems plausible that Step 3 involves mental rotation of an abstract exocentric reference frame; and the misalignment effects for both accuracy and speed on this task provide some evidence for this. It also seems plausible that mental rotation is not needed for the map-reading and Step-4 tasks, which fits with the smaller misalignment effects for these tasks. Mental rotation of the exocentric reference frame is not needed during map reading because all the maps were north up, and this canonical orientation of the exocentric reference frame is the best one for This article is intended solely for the personal use of the individual user and is not to be disseminated broadly. This document is copyrighted by the American Psychological Association or one of its allied publishers. accomplishing the map-reading task. Mental rotation also seems less necessary in the Step-4 task, because here people are some- times making judgments like West is the opposite of east and Figure 11. Effect of heading misalignment on response time (in seconds) Southwest is the opposite of northeast, and these judgments also for each of the subtasks of heading referencing, with standard error bars. can be made by consulting an unrotated, north-up exocentric reference frame. This analysis leads to the conclusion that heading referencing misalignment effect accounted for little variance. Thus, partici- may involve some mental rotation, but primarily in the Step-3 pants found map headings facing cardinal directions easier to read subtask. Although heading referencing may involve some mental than others. rotation, it still seems a quite different strategy than the mental For the Step-3 subtask, the cardinal direction advantage effect rotation strategies reported from previous research on cardinal also accounted for the largest unique portion of the variance, both direction tasks, which involve the mental rotation of images of the for accuracy and response time. However, the misalignment-north participant’s aircraft and/or the configuration of objects in the 3D effect also accounted for a considerable portion of variance, with view (Gugerty & Brooks, 2001; Gunzelmann & Anderson, 2002). ⌬R2 ⫽ .42 for accuracy, and ⌬R2 ⫽ .26 for response time. Thus, In contrast, any rotation in Step 3 of heading referencing seems to inferring bearings relative to a reference direction is easier when involve the abstract exocentric reference frame. Also, heading the reference direction is a cardinal direction, and harder when the referencing is a more analytic strategy, in that it involves four reference direction is misaligned with north. distinct steps, and three of these do not seem to involve much The Step-4 task was like the map-reading task in that the mental rotation. cardinal direction advantage effect accounted for the largest por- In a final analysis of the Experiment 3 data, we tested our tion of unique variance in accuracy and response time with head- hypotheses that performance on the heading referencing subtasks ing, and misalignment with north or south accounted for little would predict accuracy and speed on the complete cardinal direc- variance. Thus, determining one bearing from another is easier tion task. If participants were using the heading referencing strat- when the bearings align with cardinal directions. egy while performing the complete cardinal direction task, and if One important conclusion from the contrast analysis is that they performed the map-reading, Step-3, and Step-4 subtasks of heading misalignment degraded accuracy and speed for the Step-3 heading referencing with the error rates shown in Figure 10, then task, but led to much less degradation for the map-reading or their accuracy (proportion correct) for each heading in the com- Step-4 tasks. These findings supported our hypothesis of a greater plete cardinal direction task would be predicted by multiplying the misalignment effect for Step 3 than map reading, but not our proportion-correct values for that heading from the three subtasks. hypothesis of a greater misalignment effect for Step 4 than map This multiplication was done at the group level; that is, the three reading. Thus, to the extent that participants used the heading group-level proportion correct values shown in Figure 10 were referencing strategy on the complete cardinal direction task, the multiplied for each heading. These predictions were based on the strong heading misalignment effect found in the complete task simplifying assumption that the probability of an error at one step occurred mainly when executing Step 3 of the strategy. of heading referencing is uncorrelated with the probability of Why might Step 3 show the strongest heading misalignment errors at other steps, and the assumption that participants do not effect of any heading referencing subtask? To answer this ques- make any errors in Step 2 of heading referencing (which involves tion, first recall that Step 3 involves reasoning from an exocentric recognizing that the aircraft heading read from the map coincides reference heading in the 3D view (e.g., Ahead is southeast) to the with forward in the 3D view). Note that the heading referencing bearings of the objects near this reference direction (e.g., Upper subtasks were performed after the complete cardinal direction task; left lot is east of the building). In the misalignment-north effect, thus, experience on the subtasks did not influence the strategies this task becomes increasingly difficult as the exocentric reference participants used on the complete task. heading changes from north to south. A possible reason for this Figure 8 shows the accuracy levels for each heading predicted misalignment effect may be that performing this task involves a by the multiplicative procedure, along with the actual accuracy mental rotation of the canonical, north-up (or north-forward) exo- levels for the complete cardinal direction task. The accuracies centric reference frame until the desired reference heading (e.g., predicted by the use of heading referencing follow the pattern of 86 GUGERTY AND BROOKS the actual accuracies closely. To assess the degree of fit of these ices in Experiment 1. In a sample of college students, Experiment predicted and actual data, we first used linear interpolation to 3 also found wider individual differences on the cardinal direction estimate the accuracy level at headings of 45°, 135°, 225°, and task as compared with another spatial orientation test, the 315° for the complete cardinal direction task (e.g., accuracy at 45° Guilford–Zimmerman (Guilford & Zimmerman, 1981), as evi- interpolated from 30° and 60°). Then we calculated R2 and root- denced by the different kurtosis values for these two tests. mean-squared error (RMSE) using the predicted accuracies (on the These experiments also allowed us to identify some of the basis of the multiplicative procedure) and the actual (and interpo- factors underlying these individual and group differences in car- lated) accuracy levels for the eight headings. The R2 was .73 and dinal direction judgments. One important difference among the the RMSE was 6.9% correct. This RMSE can be compared with poorer and better performing novices and also the experienced the actual standard error of the mean for the complete cardinal navigators was in the extent to which reference-frame misalign- direction task data, 3.3%. As the RMSE is greater than the SEmean, ment degraded accuracy of cardinal direction judgments. Contrast- the fit is not optimal. However, the predicted accuracies account based modeling supported the conclusion that poorer performing for 73% of the variance in the actual accuracies on the complete novices had the most difficulty in handling reference-frame mis- cardinal direction task, suggesting that heading referencing is used alignment, and experienced navigators had the least difficulty. This article is intended solely for the personal use of the individual user and is not to be disseminated broadly. This document is copyrighted by the American Psychological Association or one of its allied publishers. frequently in the complete task. Thus, we suggest that a key factor underlying group differences in We made similar predictions using the response time data from cardinal direction judgments is the need to coordinate misaligned the three heading referencing subtasks. In the case of response reference frames and that a key element of expertise in cardinal times, we made predictions for each heading of the complete direction judgments involves minimizing the effects of this cardinal direction task by adding the response times for each misalignment. subtask at that heading. Before comparing these summed times In Experiment 2, we also showed that although experienced with the actual data for the complete task, we subtracted a constant navigators (aircraft pilots) are affected less by reference-frame amount (4.0 s) from the summed times, because the summed misalignment than are novices, even the more experienced group response times included three responses, and the times for the was slower and less accurate when reference frames were mis- complete task included only one response. The predicted response aligned than when they were not. Thus, it seems that degraded times, shown in Figure 9, fit the actual (and interpolated) response cardinal direction judgments in the face of reference-frame mis- time data well. Using the same procedure as for the accuracy data, alignment is a universal characteristic of human performance that the R2 was .96 and the RMSE was 0.64 s, while the SEmean for the can be reduced but not eliminated by selection and training. complete task data was 0.55 s. We suggest that all of the above findings—the greater difficulty This analysis provides evidence that the effects of aircraft head- of the cardinal direction task relative to other navigational tasks, ing on accuracy and response time for the complete cardinal the relatively wide individual differences on this task, the associ- direction task that were observed in Experiment 3 and in previous ation of reference-frame misalignment with the difficulty of the experiments could be produced by participants using the heading task, and the fact that even expert navigators experience difficulty referencing strategy. In conjunction with the verbal protocol data with the task—stem from the fact that the cardinal direction task from Gugerty and Brooks (2001), the data from Experiment 3 requires coordination of information in egocentric and exocentric provide further evidence that heading referencing is an important reference frames. Before justifying this claim, we present some strategy used to coordinate exocentric and egocentric information theoretical context for the idea that coordination of reference during cardinal direction judgments. frames is an important part of the cardinal direction task by describing how the task fits within the structural alignment theory General Discussion of Gentner and colleagues (Gentner & Gunn, 2001; Markman & Gentner, 1997). This theory has been used to explain basic cog- In the introduction, we noted that cardinal direction judgments nitive processes of analogy and metaphor, and has been applied to are used in a variety of navigational tasks but are more difficult spatial judgments involving maps and models (Uttal, Greg, Tan, than some other navigational tasks and seem to be particularly Chamberlin, & Sines, 2001). difficult for some novice navigators. Given this, we sought in the Structural alignment theory suggests that the process of com- current studies to quantify the extent of individual and group parison is central to tasks like cardinal direction judgments, and differences in making cardinal direction judgments and to under- that comparison involves first finding commonalities between two stand the strategies people use in making these judgments. In representations, then finding alignable differences, and finally investigating cardinal direction judgments, we were particularly making inferences about the representations that are based on the interested in understanding how reference-frame misalignment common structure. For example, in the heading referencing strat- affects these judgments, because misalignment has been shown to egy, the commonalities between the 3D view and the map would have a strong affect on cardinal direction judgments and other involve the matching target object in both representations and the navigational judgments. matching representations of current heading. Key alignable differ- Experiment 1 documented relatively wide differences in the ences include the fact that current heading on the map can be ability to make cardinal direction judgments within a group of less represented by an exocentric direction (e.g., southeast) and that experienced navigators, in that accuracy for these judgments was current heading in the 3D view can be represented egocentrically distributed bimodally and showed a large negative kurtosis. Ex- as “ahead.” The inference that “ahead” in the 3D view is also periment 2 provided more evidence of group differences by show- “southeast,” which is the second step in heading referencing, then ing that a group of more experienced navigators, aircraft pilots, follows from the commonalities and alignable differences. This performed more accurately than even the better performing nov- analysis suggests that coordination of egocentric and exocentric REFERENCE FRAMES AND CARDINAL DIRECTIONS 87 reference frames during cardinal direction judgments may involve nal direction judgments can be modeled on the effective strategies basic processes of comparing and aligning structured representa- identified in these studies. Using the heading referencing strategy tions that are used in a variety of cognitive tasks. as a model, a heads-up display can superimpose labeled arrows Couching cardinal direction judgments in terms of structural indicating the current compass heading and/or the north heading alignment theory also helps explain our finding that these judg- on the ground plane. This interface integrates exocentric informa- ments may involve wider individual differences than other navi- tion into the 3D view. Alternatively, using a mental rotation gational tasks (e.g., the Guilford–Zimmerman [1981] spatial ori- strategy (Gugerty, Brooks, & Treadaway, in press) as a model, a entation task), and are more difficult. For example, noticing dynamic map display can superimpose letters symbolizing top (T) commonalities among objects in the 3D and map views may be and right (R) ahead of the moving map icon indicating vehicle more difficult in the cardinal direction task because matching position. This second interface was suggested by an uninhabited- objects are more perceptually dissimilar in these two views; aerial-vehicle operator who used imagery like this to perform whereas noticing commonalities between the two views of the spatial orientation tasks (Gugerty, 2004). It integrates egocentric Guilford–Zimmerman task may be easier because these objects information into the map and thus should facilitate the rotating of look perceptually similar in its two 3D scenes. Furthermore, higher spatial configurations that is part of mental rotation. This article is intended solely for the personal use of the individual user and is not to be disseminated broadly. This document is copyrighted by the American Psychological Association or one of its allied publishers. order spatial relations are represented in different terms in the cardinal direction task (e.g., “southeast” vs. “ahead”) and must be References treated as alignable differences, whereas higher order relations can Aretz, A. (1991). The design of electronic map displays. Human Factors, be represented in similar terms in the Guilford–Zimmerman (e.g., 33, 85–101. A is above B) and thus treated as commonalities. Thus, coordinat- Aretz, A. J., & Wickens, C. D. (1992). The mental rotation of map displays. ing egocentric and exocentric reference frames in cardinal direc- Human Performance, 5, 303–328. tion judgments may be difficult because of the difficulty of match- Bethell-Fox, C., & Shepard, R. (1988). Mental rotation: Effects of stimulus ing and aligning elements in these disparate representations. complexity and familiarity. Journal of Experimental Psychology: Hu- In addition to the findings in the present experiments regarding man Perception and Performance, 14, 12–23. Cheng, M. Y., & Hall, P. (1998). Calibrating the excess mass and dip tests individual and group differences in cardinal direction judgments, of modality. Journal of the Royal Statistical Society, Part B, 60, 579 – we also provided evidence that heading referencing is a common 589. strategy used in making these judgments. Experiment 3 provided Cohen, J. (1988). Statistical power analysis for the behavioral sciences. evidence of heading referencing use by showing that the accuracy Mahwah, NJ: Erlbaum. and timing of novices’ cardinal direction judgments was predicted Draper, M. H., Geiselman, E. E., Lu, L. G., Roe, M. M., & Haas, M. W. well by the accuracy and timing with which they performed the (2000). Display concepts supporting crew communication of target steps of heading referencing. Experiment 3 also clarified the nature location in unmanned air vehicles. In Proceedings of the XIV Triennial of the cognitive processes used in this strategy by showing that the Congress of the International Ergonomics Association and 44th Annual misalignment effects in the complete cardinal direction task are Meeting of the Human Factors and Ergonomics Society, Vol. 3 (pp. found most strongly in Step 3 of heading referencing (in which the 85– 88). Santa Monica, CA: Human Factors and Ergonomics Society. Eley, M. G. (1988). Determining the shapes of land surfaces from topo- exocentric reference heading is extrapolated to nearby bearings in graphical maps. Ergonomics, 31, 355–376. the 3D view). Estes, W. (1997). On the communication of information by displays of The research presented here has a number of applications to standard errors and confidence intervals. Psychonomic Bulletin & Re- navigational practice. First, the considerable difficulty experienced view, 4, 330 –341. by a large percentage of novice navigators suggests the need for Gentner, D., & Gunn, V. (2001). Structural alignment facilitates noticing of training to improve performance on this task. Our findings regard- differences. Memory & Cognition, 29, 565–577. ing the strategies used by novice and experienced navigators can Gugerty, L. (2004). Using cognitive task analysis to design multiple suggest options for effective instruction in cardinal direction judg- synthetic tasks for uninhabited aerial vehicle operation. In S. Schiflett, ments. In addition to being a preferred strategy, heading referenc- L. Elliott, E. Salas, & M. Coovert (Eds.), Scaled worlds: Develop- ing is a step-by-step strategy that is amenable to training using ment, validation, and applications (pp. 240 –262). London: Ashgate Publishing. part-task training techniques. Gugerty, L., & Brooks, J. (2001). Seeing where you are heading: Integrat- Conceptualizing the cardinal direction task as involving pro- ing environmental and egocentric reference frames in cardinal direction cesses of comparison and analogy between a map and a 3D scene, judgments. Journal of Experimental Psychology: Applied, 7, 251–266. as in structural alignment theory, is potentially useful because it Gugerty, L., Brooks, J., & Treadaway, C. (in press). Individual differences suggests other methods of training cardinal direction judgments. in situatuion awareness for transportation tasks. In S. Banbury & S. Loewenstein and Gentner (2001) found that comparing two mod- Tremblay (Eds.), A cognitive approach to situation awareness: Theory, els of a room helped preschoolers use one of the models to find measures and application. London: Ashgate Publishing. objects in a new room. This finding suggests that training to Guilford, J. P., & Zimmerman, W. S. (1981). The Guilford–Zimmerman improve cardinal direction judgments should include tasks such as Aptitude Survey: Manual of instructions and interpretations. Palo Alto, comparing pairs of maps, and comparing maps and 3D scenes to CA: Consulting Psychologists Press. Gunzelmann, G., & Anderson, J. (2002). Strategic differences in the find the common structure. coordination of different views of space. In W. D. Gray & C. D. In addition to training applications, this research project pro- Schunn (Eds.), Proceedings of the 24th Annual Conference of the vides a better understanding of how people coordinate map infor- Cognitive Science Society (pp. 387–392). Cincinnati, OH: Cognitive mation and information in the forward field of view when making Science Society. cardinal direction judgments, and this understanding can improve Hartwig, F., & Dearing, B. (1979). Exploratory data analysis. Beverly the design of navigational interfaces. Interfaces to improve cardi- Hills, CA: Sage. 88 GUGERTY AND BROOKS Hintzman, D., O’Dell, C., & Arndt, D. (1981). Orientation in cognitive Shepard, R., & Hurwitz, S. (1984). Upward direction, mental rotation, and maps. Cognitive Psychology, 13, 149 –206. discrimination of left and right turns on maps. Cognition, 18, 161–193. Hutchins, E. (1995). Cognition in the wild. Cambridge, MA: The MIT Sholl, M. J. (1987). Cognitive maps as orienting schemata. Journal of Press. Experimental Psychology: Learning, Memory, and Cognition, 13, 615– Klatzky, R. (1998). Allocentric and egocentric spatial representations: 628. Definitions, distinctions, and interconnections. In C. Freksa, C. Habel, & Uttal, D., Gregg, V., Tan, L., Chamberlin, M., & Sines, A. (2001). K. Wender (Eds.), Spatial Cognition: An interdisciplinary approach to Connecting the dots: Children’s use of a systematic figure to facilitate representing and processing spatial knowledge (pp. 1–17). New York: mapping and search. Developmental Psychology, 37, 338 –350. Springer. Werner, S., & Jaeger, M. (2002). Intrinsic reference systems in map Levine, M., Jankovic, I. N., & Palij, M. (1982). Principles of spatial displays. In Proceedings of the 46th Annual Meeting of the Human problem solving. Journal of Experimental Psychology: General, 111, Factors and Ergonomics Society (pp. 1628 –1632). Santa Monica, CA: 157–175. Human Factors Society. Loewenstein, J., & Gentner, D. (2001). Spatial mapping in preschoolers: Werner, S., & Schmidt, K. (1999). Environmental reference systems for Close comparisons facilitate far mappings. Journal of Cognition and large-scale spaces. Spatial Cognition and Computation, 1, 447– 473. Development, 2, 189 –219. Wickens, C. (1999). Frames of reference for navigation. In D. Gopher & A. This article is intended solely for the personal use of the individual user and is not to be disseminated broadly. Koriat (Eds.), Attention & performance XVII: Cognitive regulation of This document is copyrighted by the American Psychological Association or one of its allied publishers. Markman, A., & Gentner, D. (1997). The effects of alignability on mem- ory. Psychological Science, 8, 363–367. performance: Interaction of theory and application (pp. 113–144). Cam- Presson, C. C., DeLange, N., & Hazelrigg, M. D., (1989). Orientation bridge, MA: MIT Press. specificity in spatial memory: What makes a path different from a map Wilcox, R., & Keselman, H. (2003). Modern robust data analysis methods: of the path? Journal of Experimental Psychology: Learning, Memory, Measures of central tendency. Psychological Methods, 8, 254 –274. and Cognition, 15, 887– 897. Presson, C. C., & Hazelrigg, M. D. (1984). Building spatial representations Received June 5, 2003 through primary and secondary learning. Journal of Experimental Psy- Revision received December 10, 2003 chology: Learning, Memory, and Cognition, 10, 716 –722. Accepted December 11, 2003 䡲