Abstract
Directional pointing tasks—particularly judgments of relative direction (JRDs)—have advanced research on spatial memory. However, overreliance on a single measurement task like JRDs may miss nuances in how spatial information is processed and represented. Therefore, we compare JRDs with object-based judgments (OBJs). While these measures seem to reflect different cognitive processes, a parameter-free measurement model suggests they assess the same underlying memory representations. This model, grounded in two key assumptions, allows point estimates of JRD absolute angular error to be calculated from specific OBJ responses. Across two experiments (N = 96), we found support for two conclusions: (a) JRDs and OBJs access the same memory representations, and (b) JRDs combine the absolute angular error from two different sources, while OBJs isolate a single source, making OBJs more specific.
Keywords
Introduction
As a fundamental aspect of human cognition, spatial knowledge supports our ability to represent, navigate, and reason about the structure of our environment. In this work, we define spatial knowledge as memory for the angular and distance relations among objects within an environment, with a particular emphasis on angular relations. To study how angular relations are learned and represented in memory, researchers rely on a variety of behavioral tasks that serve as measurement tools. One approach uses participant-drawn maps of the learned environment to study memory representations of distance and angular relationships. Beyond sketch maps, two widely used directional pointing tasks—the judgment of relative direction (JRD) and the object-based judgment (OBJ)—offer complementary methods for assessing angular spatial memory. Our aim is to examine particularly the JRD and OBJ tasks in depth to clarify what each measure, and how they relate to the underlying memory representations and cognitive processes they are presumed to assess.
In addition to the judgment type, several physical methods exist for collecting participants’ angular responses. In the present study, participants reported their responses using direction circles. We chose this method because it allows for angle estimation while minimizing introducing additional cues or dimensions that may not be directly relevant to spatial memory representations—or that could prompt extraneous or unnecessarily complex memory processes such as placing participants back in the original environment, pointing with their hands or moving their bodies, or creating sensorimotor alignment effects (Kelly et al., 2007; Rieser, 1989). In this way, the current work can address a key gap in the literature: although JRD and OBJ tasks are widely used, it remains unclear whether they assess the same or distinct components of spatial memory, which limits our ability to interpret findings across studies and hinders theoretical integration. By empirically testing a parameter-free measurement model linking these two measures, we clarify their relationship and deepen our understanding of what spatial pointing tasks reveal about the structure of spatial memory (van Fraassen, 2012).
Literature Review
Judgments of Relative Direction
The JRD is a directional pointing task in which participants respond to a spatial query by selecting an angle. Queries request participants to imagine themselves at one object (the base or standing-at object), facing a second object (the facing object), and then indicating the direction to a third object (the target object). For example: “Imagine that you are standing at the book. Now, imagine facing the toaster. Point to the ashtray.” When using a direction circle, the center of the circle corresponds to the standing-at (base) location, and the 0° mark (typically at the top) represents the direction of the facing object. Participants indicate the direction of the target object by selecting a point on the circle. The primary dependent measure is the mean absolute angular error between the participant’s target response and the correct angular difference between the target and the facing object. Conceptually, the JRD response captures the remembered angle between the facing and target objects. Because the facing direction is fixed at 0° on the circle, it does not need to be represented algebraically in computing the absolute angular error. Thus, a JRD could be a cognitive difference score. If so, they should act as external difference scores act in data sets. They should report the combined absolute angular error of both the facing object and the target object, not just the target object’s absolute angular error.
While the JRD has been applied in a variety of research contexts, it is particularly relevant to more recent theories that emphasize spatial frames or coordinate systems (McNamara, 2013; McNamara et al., 2003; Mou & McNamara, 2002; Newman et al., 2021). These theories conceptualize memory representations as points within a coordinate system (Carlson et al., 2010). The JRD naturally maps onto this structure by requiring participants to generate an angle in a query, represented by three objects that define the angle.
Earlier spatial memory research also employed JRD tasks to investigate spatial knowledge acquisition, although from a wide variety of theoretical perspectives. For example, Moar and Bower (1983) tested the critical symmetry assumption of mathematical coordinates. Gärling et al. (1981) examined Siegel and White’s (1975) then-dominant landmark-route-configural model. Thorndyke and Hayes-Roth (1982) (who tested women working for different durations in the Rand building) tested a theory that participants made JRD judgments by mentally simulating navigating through the environment with JRDs based on the number of cognitive operations. Ruddle et al. (1997) replicated this work in a virtual version of the Rand building, but despite many successful replications of key findings, participants in their study struggled to perform the JRD task consistently. Hintzman et al. (1981) tested a theory that angular relations between objects in 3D space could be mentally rotated, akin to simple visual object rotations. Presson and Hazelrigg (1984) arranged four objects along a path on the floor—defined by start, turn1, turn2, and end points. Participants either viewed the path from a single fixed perspective or walked the path blindfolded. The two groups were then compared using JRD tasks. Collectively, these examples illustrate that the JRD has served as a general-purpose tool for probing how individuals acquire and represent spatial information from their environments—albeit through diverse theoretical lenses and experimental designs.
Object-Based Judgments
Colle and Reid (1998) developed a new task, later called the OBJ task. The OBJ task uniquely incorporated a feature common to large, relatively immovable objects—distinctive “front sides” of these objects. Colle and Reid thought that when people navigate through an environment, they pay attention to the front sides and learn the object's rotational orientation (its yaw) with respect to other objects and the environment's spatial plane. The OBJ used the perpendicular to the vertical plane of the base object as one leg of the angle, and that juncture to the target object as the second leg. A typical OBJ query might be phrased as follows: “Imagine that you are standing directly in front of and facing the front of the Pepsi machine (base object), at arm’s length away. Point to the ATM (target object).” In this case, an angle is formed by two legs, one of them being perpendicular to the front of the Pepsi machine (defining a spatial plane that includes the vertical dimension of 3D objects). The OBJ response can then be compared with the actual correct angle to compute absolute angular error.
Notice that the OBJ task’s query uses only two objects, but they do not just identify locations. With knowledge of the orientation of the front side of the base object, the OBJ’s two-object angle can be formed. Thus, OBJ tasks measure only the absolute angular error for their target object, whereas the JRD task may measure the combined absolute angular error for both its facing and target objects, depending on the nature of the underlying cognitive processes. If cognitive differences are confirmed, this result could change the way some experimental results are interpreted. The experiments described below address this issue and provide evidence supporting the distinction between the OBJ and JRD tasks in terms of one source versus two sources of absolute angular error, respectively.
Although Colle and Reid (1998) were the first to experimentally use OBJs, the concept of OBJs predates their work. In Hintzman et al. (1981, p. 151), the following passage was cited: In arguing for an analog representation of the environment, Attneave presents the following casual experiment: 'I say to a friend, “Imagine yourself standing in front of the library, about to enter. Now, from that position, point at the Law School.” Most people will point without hesitation in the general direction that would be correct if they were in the position indicated. “The Law School” was almost certainly not present in consciousness when the observer assumed his imaginary position, but its location, relative to his body, seems immediately available on demand’ (Attneave, 1972, p. 305).
Two prominent cognitive psychologists implicitly endorsed the OBJ task. Attneave’s (1972) description aligns closely with the OBJ task, and Hintzman et al. (1981) accepted this idea, demonstrating that the concept of object-based spatial relations was present.
Colle and Reid (1998) used the two-object advantage of the OBJ to identify a result they called the room effect. When a base object and a target object were experienced in the same virtual room, the OBJ absolute angular error was smaller for these queries than when two objects were experienced in different rooms. Like others, we initially thought that the availability of direct viewing for within-room pairs was responsible, but Colle and Reid (2003) found that when walls were removed (replaced with narrow tape) between rooms, the absolute angular error between rooms showed only slight or no decrease. Objects in other rooms could be identified, as tests in the virtual environment showed. Thus, direct viewing was not sufficient. It was also not necessary. When participants could travel directly from room to room without using hallways, absolute angular error decreased substantially, although participants could not see objects in different rooms (Colle & Reid, 2003; Saffell et al., 2012). In these and other research, it was found that participants could use front-side orientation to make their judgments; within-room queries typically had small OBJ absolute angular error. OBJs have been used in many experiments (Colle & Reid, 1998, 2000, 2003; Couture et al., 2005; Gauthier et al., 2008—though they referred to their OBJ task as a JRD; Ishikawa & Montello, 2006; May & Colle, 2018; Saffell et al., 2012). As we will describe in the general discussion, this was across boundaries and between-room absolute angular error was better than chance, although participants were not given instruction to learn spatial knowledge, there were four rooms with objects randomly placed and oriented and participants only experience the environment once, unlike results from studies of global spatial knowledge acquisition (e. g., Han & Becker, 2014; Kelly et al., 2007; Lei et al., 2020; Meilinger et al., 2014).
Measurement Models: An Approach to Compare JRDs and OBJs
Although OBJs and JRDs are likely to differ on the number of sources they measure, we also wanted to learn if they differed in the underlying memory representations they measured. JRDs only use objects to identify locations in space. OBJs must use object orientation. Are these differences dependent on different memory representations?
To evaluate this question, we used a measurement model approach proposed by van Fraassen (2012). His examples were from modern physics, but we present an example more relevant to psychology. Although not Hilgard’s (1958) original intent, he provided a useful illustration of the advantages of a measurement model when he sought to clarify the concept of intervening variables and the benefits of using specific equations for each measurement task, as opposed to simply comparing tasks using correlation and regression (or other measures of just similarity). He used typical equations for gravity, such as the distance of a falling body, d = ½gt2, and the time for one complete cycle of a pendulum, T = 2π(L/g)1/2. From van Fraassen’s approach, these equations and tasks represent two measurement models for the same underlying concept—gravity. Importantly, both equations use the underlying variable g, and you can solve for the unobservable g in both equations using observable variables. Hilgard argued that these specific equations (measurement models) were far more informative than the more general ones obtained through regression, such as d = k1 t2 and T = k2L1/2, because regression equations do not measure g directly or show the relationship between the two measurement tasks. The specific equations serve as two distinct measurement models for gravity across two tasks. The two measurement models should yield the same point estimate of g in a given environment, using the same units. While both models estimate g, they do not control or explain it; they merely show the relationships between the measurement tasks. The measurement models, however, can be tested, but they are not theories explaining gravity. For example, if both measurement tasks were conducted at higher altitudes, the measurement models should still agree on point estimates of g, since gravity varies with altitude, even though altitude itself is not part of the measurement models. Thus, while measurement models can be tested, they do not attempt to explain the underlying variables they measure.
The k-parameter regression approach is commonly used in psychology to evaluate the convergence of measures, effectively assuming alternative linear forms of a single underlying dimension. For example, Huffman and Ekstrom (2019) primarily used regression and correlation methods with different dependent variables to demonstrate the relationship between the JRD directional pointing task and a map task. Although they also conducted additional analyses of signed errors, which could be seen as initial steps toward developing a measurement model, their approach still largely relied on traditional regression techniques. When it is explicit, a measurement model approach not only shows how tasks are related but also reveals how they differ, providing a deeper understanding of the underlying constructs.
Thus, we adopted a measurement-model approach similar to that described by van Fraassen (2012) and Hilgard (1958). Hilgard’s examples involved two measurement models—one for falling bodies and another for pendulums—both of which used the same gravity parameter. Our aim was to develop a measurement model for OBJs and test whether it would fit JRDs. If the OBJ model did not fit JRDs, we planned to develop a second measurement model specifically for JRDs (if that was the issue), while keeping the learning experience equivalent for both tasks. Although we varied the amount of learning as a theoretical variable, analogous to Hilgard’s manipulation of mountain height to test gravity measurement models, we anticipated that the OBJ model might fail for JRDs. Angular object-orientation judgments based on the distinctive front sides of solid objects suggest that objects themselves may be part of spatial memory representations, rather than merely indicators of locations or points in space. Research on visuospatial working memory has shown complex interactions between object and location processing across various tasks (Jiang et al., 2009). Since the OBJ task may incorporate object information, while the JRD focuses solely on location information, we had to consider the possibility that the OBJ measurement model might not adequately describe JRD performance.
The OBJ Measurement Model
The angular judgment measurement model based on OBJ processing has two main assumptions. One main assumption is that its memory representations are those underlying the OBJ query, and that its cognitive judgment processes parallel the angles described in the experimental spatial queries for both OBJ and JRD.
Figure 1 illustrates the model’s representation of both JRD and OBJ queries in generic terms. “B” represents the base object (the red vertical bar represents its front side), “F” represents the facing object, and “T” represents the target object. The JRD query is “Imagine standing at the B object, facing the F object, and pointing to the T object.” As shown in the figure, the spatial arc labeled “JRD” represents the angle of the JRD query. This angle reflects the participant’s cognitive judgment, not necessarily the correct angle or the correct representation of the F and T angles. Note that the legs of the JRD angle are at different angles because the base object for a JRD is only an indicator of location.
Hypothetical cognitive processes between OBJs and JRDs.
Figure 1 also shows how the measurement model represents OBJ queries and estimates JRD queries. An OBJ query begins with “Imagine that you are standing directly in front of and facing B at arm’s length.” The B object has its front side intersected by the long dashed horizontal line, which represents the participant’s judgment of the perpendicular to B. The dashed line is extended in the figure for clarity in displaying angular arcs. Using the same B object, two OBJ queries can estimate the JRD response angle: one OBJ target query directed to the JRD’s F object and the second directed to the JRD’s T object. The first OBJ query is represented by the angular arc labeled “OBJ-F” in Figure 1, while the second is represented by the angular arc labeled “OBJ-T.” As shown, the angular arc of the JRD is equal to the difference of the angular arcs of OBJ-T and OBJ-F. This equivalence depends on both tasks using the same underlying memory representations. It is important to note that the difference between T and F in the JRD query is assumed to be a cognitive difference in mental operations that represents all of the participant’s spatial cognitive processing. In contrast, each OBJ query for the F and T objects is seen as a distinct cognitive processing step, and the combination of their absolute angular errors is the experimenter’s mathematical operation. Although Figure 1 focuses on participants’ response angle to show which OBJ angles are relevant for a JRD angle, the model’s important measures are angular error magnitudes and absolute angular errors, which are typically used by both JRDs and OBJs. The F and T OBJ queries share the same heading, but as shown in Figure 1, it is typically different from the heading of the JRD, whose absolute angular error they are estimating.
The second main assumption of the OBJ angular judgment measurement model is the Component Error Assumption, which posits that absolute angular error is attributed to individual components. Components are the objects involved in the experimental queries, so that the absolute angular error is associated with each object in a query. To make judgments, participants must remember the spatial relationship of an object with respect to at least one other object or aspect of the environment. For both types of judgments, the base object (B), which the participant thinks of it as typically very close to her or him, so the measurement model assumes that B is a known component with little or no absolute angular error. The measurement model reflects participants’ thinking that they know where the B object is because it is next to them. The OBJ query has only one other source of absolute angular error—its target object. However, in the JRD, both the facing and target objects may each introduce absolute angular error, depending on their positions within the environment and its overall structure. As shown in Figure 1, both the facing and target objects can contribute to the JRD absolute angular error, which nominally is the difference between them. This angular arc represents the measurement model’s JRD angle, attributing absolute angular error to each object (both F and T).
The dependent variable used in previous JRD and OBJ experiments is the absolute angular error (the absolute value of the response angle minus the correct angle). This choice is crucial for the analysis. Angular responses are circular measures that require specialized descriptive and inferential statistics (Batschelet, 1981). Arithmetic means derived from object angles measure the means of circular chords, not the mean distance around the perimeter of the circle (arcs). However, absolute angular error scores are not circular; they are linear and confined to the closed interval [0, 180], making them suitable for typical means and statistical analyses (Batschelet, 1981). Note that, cognitively, both F and T contribute to the absolute angular error in JRDs. The two equations for OBJs also contribute to the absolute angular error from both F and T.
Sketch Maps: An Alternate Measurement Task
Colle and Reid (1998) had participants sketch maps of experienced environments, an allocentric measurement task. Maps were scored in a novel way. OBJ queries were measured using a protractor on the maps. Participants sketched maps and simply placed rectangles on them to represent landmark objects. They named each rectangle and identified its front side, which were used by experimenters to determine OBJ response angles. Importantly, both JRDs and OBJs can be scored with appropriate queries. We also collected sketch map data.
Experiment 1
This experiment addressed two issues. First, to evaluate empirically if the OBJ task estimates the absolute angular error from single target objects, while the JRD’s target response includes absolute angular error from the facing object as well as the target object. Second, whether JRD and OBJ tasks measure the same underlying memory representations.
To make these comparisons, we used a specific set of JRD queries. The base and target objects were always in the same room. The JRD’s facing object was manipulated. It was in the same room for half of the trials and in a different room from the base and target objects for the other half. Previous research found that both OBJs and JRDs were sensitive to a room location effect, a within-room versus between-room manipulation (Douglas, 2008). Participants learned more about the layout of objects in the same room than they did about those in different rooms, a theoretical variable manipulation that is not part of the measurement model. This is analogous to Hilgard’s use of varying heights on a mountain to test gravity measurement models.
The First Issue
The first issue has two parts. The first part concerns how the component error assumption of the OBJ measurement model implies that absolute angular error is attributed to individual objects. The second part addresses whether the JRD task also measures the absolute angular error between a single target object and its target response on the direction circle, or is it a cognitive difference process in which its target response is affected by both the facing and the target objects? If the OBJ individually measures its target objects, then when the JRD’s facing object is the OBJ’s target object, absolute angular error should increase when the facing object, the OBJ’s target object, changes from within-room to between-room. However, if the OBJ’s target object does not change rooms, as was the case when the JRD’s target object was the OBJ’s target object, then its absolute angular error should not change when the facing object changes rooms.
In this experiment, the JRD’s facing object was not only in the same room as the base object, but it also changed to a different room. The JRD’s target object did not change rooms. It was always in the room with the base object. Therefore, when the JRD task is used instead of the OBJ task, it should show little or no change if it only measures target absolute angular error. The JRD target response should not be affected by the manipulation of the facing object. If it is affected by the change in the facing object, that result implies that the JRD’s target response includes absolute angular error from the facing object.
The Second Issue
To address the second issue, the OBJ measurement model was used. Pairs of OBJ queries were used to estimate the equivalent absolute angular error of JRD queries according to the OBJ measurement model. These estimated JRD absolute angular errors were compared with the actual JRD absolute angular errors. If the OBJ estimates match the actual JRDs, then the results would be consistent with the OBJ measurement model. The implication would be that both the OBJ and the JRD tasks measure the same underlying memory representations. The point estimates could be directly compared. If the equivalence holds when JRD absolute angular error increases because of the room location effect, this is additional evidence in favor of the OBJ `measurement model, similar to Hilgard’s validation of gravity measurement models when it was measured at different altitudes.
Method
Participants
Thirty-five self-identified females and 13 self-identified males (N = 48) from introductory psychology courses participated in the experiment for course credit, with ages ranging from 18 to 29 years (M = 19.2). Participants reported having normal or corrected-to-normal vision and hearing, normal upper body motor control, and English as their first language. The experiment was approved by the Institutional Review Board for human participants at the university of the first author, and all students provided informed consent before participating by signing a paper document.
DualOBJs: Our Approach to Comparing JRDs and OBJs
Comparisons of JRDs and OBJs rely on the assumption that “all other things are equal.” Therefore, we made efforts to match the conditions under which OBJs were collected as closely as possible to those for JRDs. In JRDs, the base, facing, and target information are presented together on a single trial. However, OBJ pairs for base-to-facing and base-to-target objects are typically presented on separate trials. To address this, we developed an alternative OBJ query called the dual object-based judgment (DualOBJ). In the DualOBJ procedure, participants saw both a base-to-facing object query and a base-to-target object query on the same trial and provided OBJ responses to each. While this approach is uncommon in contemporary spatial research, similar methods were used in older studies, such as Trowbridge’s (1913) work. By placing both responses on the same directional circle for the same trial, we minimized potential confounding variables, such as differences in short-term or working memory processing, that could impact spatial cognitive processes and experimental results. Muffato et al. (2020) found that spatial ability tests were important for JRD performance. Although a working memory task did not influence memory when participants learned via navigation, this test was based on imagery. We thought it best to be cautious. Using DualOBJs, the main dependent variables and comparisons focused on the absolute angular error of estimated JRDs from DualOBJs, compared to the absolute angular error of actual JRDs.
The Room Location Effect
Arguments for the convergence of measures are stronger if the convergence can be shown to hold across a wider range of performance. To test this, we used a manipulation known to produce large absolute angular error differences in previous spatial memory research, particularly when participants navigated from room to room using hallways—a phenomenon referred to as the room location effect (Colle & Reid, 1998, 2000, 2003; Couture et al., 2005; May & Colle, 2018; Saffell et al., 2012). When tested from memory, the OBJ absolute angular error was greater for a base and target object originally experienced in different rooms than for those experienced in the same room. The room location effect suggests that participants acquire more spatial knowledge (better memory representations) about within-room objects than about between-room objects, potentially involving different spatial processes.
The angular relationship between the base and the facing objects is an important variable in research on spatial reference systems, where alignment effects have been observed (Schultheis, 2021; Shelton & McNamara, 2001). Shelton and McNamara (2001) and subsequent studies showed that differences in object angular orientation affected target absolute angular error. Consequently, we kept the angle between the base and facing objects constant (i.e., the same heading) while manipulating the room location of the facing object (within-room versus between-room). As shown in Figure 2, the arrow from the refrigerator to the dryer (in the same room) extends as a dashed line to the Gatorade machine in a different room. The mean absolute angular difference between within-room and between-room facing angles was a maximum of 3.68° (M = 1.92, standard deviation [SD] = 1.26). Each JRD had a yoked specific within-room facing object paired with a specific between-room facing object, as illustrated in Figure 2. The within-room versus between-room facing angles occurred on different randomly ordered trials.
The virtual environment participants navigated in Experiments 1 and 2.
The Virtual Environment
A simulated virtual environment was created using Trimble’s SketchUp three-dimensional modeling program (SketchUp 2020.2; Trimble Inc., 2020). As shown in Figure 2, the environment consisted of four rooms separated by walls and a hallway wrapping around three sides of the environment. The following measurements are in virtual units. The environment measured 14.63 m × 14.63 m, with each room measuring 7.32 m × 7.32 m, and the hallway measuring 2.44 m in width. Each of the four doorways connecting the hallway to the rooms measured 1.22 m in width. These doorways were always open and placed near the midpoint of each room’s wall. The doorways were the only entrances and exits to each of the four rooms and are marked with an asterisk in the hallways of Figure 2. The walls were a textured gray, and a wood-colored parquet floor was used in both rooms and hallways. There were no windows in any of the rooms, and the ceilings were blue.
A total of 16 objects were imported from SketchUp’s 3D Warehouse and grouped semantically, with four objects per room. The appliance room contained a refrigerator, stove, dryer, and dishwasher. The furniture room contained a dresser, a writing desk, a sofa, and an armchair. The vending machine room contained a water machine, a Gatorade machine, a lemonade machine, and a coffee machine. The arcade room contained a Super Smash Bros. game, a deer-hunting game, a racing game, and a dancing game. Figure 3 shows the perspective from the doorway into the vending machine room. Each of the 16 landmark objects was placed randomly in the rooms and had a clear, distinguishable front. The orientation of the front sides of the 16 landmark objects was determined randomly, with the following restrictions: (a) no more than 2 objects in the same room could have the same facing direction (a mistake was made in one room where 2 pairs faced the same direction), and (2) each of the 4 facing directions was used equally often when summed across all rooms.
A room example in the virtual environment.
SketchUp was used to create a first-person perspective, displaying the environment from a virtual eye height of 157.5 cm. While most of our previous research allowed participants to self-navigate through the virtual environment, the present research used the same defined pathway for all participants to control the learning experience. To accomplish this, an electronic video recorded from a first-person perspective while navigating the environment was created in SketchUp for participants to watch. The navigation pathway began in the hallway just outside the vending machine room, where participants entered the room, approached each object in a predefined order, and stood perpendicular to its front at about arm’s length. After visiting each landmark object in a room, navigation exited the room through the doorway, continued down the hallway, and then entered the doorway to the next room. The order in which each within-room landmark object was visited was randomly determined. All navigation paths were sweeping curves designed to maximize viewing of the landmark objects and the room. The number of right and left turns was also randomly determined and balanced. In other words, all navigation was controlled, and all participants received the same virtual learning experience. The objects were visited in the following order: (a) coffee vending machine, (b) Gatorade vending machine, (c) lemonade vending machine, (d) water vending machine, (e) stove, (f) dryer, (g) refrigerator, (h) dishwasher, (i) sofa, (j) armchair, (k) dresser, (l) writing desk, (m) racing game, (n) dancing arcade game, (o) deer hunting game, and (p) Super Smash Brothers game.
Apparatuses and Measurement Tools
Up to six participants were tested simultaneously, each under different randomly assigned conditions at one of six workstations separated by black dividers. The experiment was conducted on Apple iMac computers (Model 7.1), configured via Boot Camp to run Windows 7. Each monitor measured 42.3 cm by 27.1 cm with a resolution of 1,680 × 1,050 pixels and a refresh rate of 60 Hz. Displays were powered by ATI Mobility Radeon HD 2,400 XT video cards, which used a 32-bit color palette. Each computer was connected via USB to a 12-inch-by-9-inch MonoPrice graphic drawing tablet, which participants used to sketch maps of the virtual environment. Participants used MonoPrice wireless electronic pens for their drawings. Headphones were provided at each workstation and connected to the computer’s audio port. Volume was set to a comfortable listening level that was not audible to other participants.
Directional Pointing
A directional pointing program was developed to present queries and record responses for both the new DualOBJ task and the JRD tasks. Figure 4 illustrates the directional circle used in the program. Participants responded by dragging labeled boxes from a sidebar onto the circle to indicate the direction in which they would point. As a box was dragged, a green line extended from the center of the circle to the box, and when this line crossed the circle’s edge, one of the segments would turn red, indicating the selected direction. For the DualOBJ task, participants placed two boxes, each representing a directional response; for the JRD task, only one box was placed. Each box was labeled with the name of the relevant object. Once satisfied with their placements, participants clicked the on-screen Enter key with the mouse. In DualOBJ trials (as shown in Figure 4), participants were presented with four lines of instruction corresponding to two queries: (a) “you are standing in front of the stove,” (b) “point to the dishwasher,” (c) “you are standing in front of the stove,” and (d) “point to the refrigerator.” Participants were instructed to complete the first two lines before proceeding. In JRD trials, two lines were displayed: (a) “you are standing at the stove, facing the dishwasher,” and (b) “point to the refrigerator.” All trials were presented in random order.
A directional circle is used for pointing tasks.
Sketch Maps
We also collected data not directly related to the equivalence of the two directional pointing tasks, but with broader implications for spatial memory and directional judgment. Colle and Reid (1998) demonstrated a strong relationship between directional circle judgment tasks when using a novel method of scoring sketch maps. In this method, an OBJ query was applied directly to a participant’s sketch map. A protractor was used to measure angles based on the positions and front side orientations of the drawn objects, and these response angles were compared with the correct angles to compute absolute angular error—similar to the output of directional pointing tasks. This approach differs from traditional sketch map scoring methods (Blades, 1990; Blaser, 2000; Coluccia et al., 2007; Golledge & Stimson, 1997; Kitchin, 1996; Lynch, 1960) and bidimensional regression techniques (Gardony et al., 2016), which primarily rely on distance metrics or experimenter ratings. As Montello (1991) noted, distance-based measures can be complex and nonlinear, whereas angular measures—as used in JRD and OBJ tasks—are treated as linear. Previous research has shown that sketch maps can yield results comparable to those from directional pointing tasks in multiple OBJ experiments (see Colle et al., in preparation; Douglas & Colle, 2010). Therefore, in the present study, we also collected both sketch map and directional pointing data from participants to extend the potential generalizability of the measurement model beyond directional pointing tasks alone.
The sketch map testing software was designed with a layout similar to that of the directional circle software, providing participants with all the necessary tools and instructions to complete their electronic sketch maps. As illustrated in Figure 5, participants used the Drag tool to place boxes representing objects on the map and to assign labels by dragging landmark names onto those boxes. The Front tool allowed participants to designate the front side of each object. A Pen tool, represented by a colored bar, was used to draw structural elements, such as walls and doorways, in rooms and hallways. To support larger or more complex layouts, the Paper tool enabled participants to expand the drawing space in any direction, while the Zoom tool allowed them to view the entire sketch map within a single, monitor-fitting display. The program automatically recorded and saved the sketch maps, capturing key data including each object’s name, its (x, y) coordinates, and the orientation of its front side. These coordinates and orientations were then used to compute angular values, which were analyzed in the same manner as responses in the directional pointing tasks.
Sketchpad toolbar participants used to create sketch maps of the virtual environment.
Procedure
Before participants explored the virtual building environment, they were given a scenario to guide their experience. They were asked to imagine working in a warehouse where their job was to inventory objects. Participants were instructed to ensure that no objects were missed, as company policy required items to be checked off in the exact order presented on an inventory list. They were also informed that the objects had been delivered at different times by different people, so they should be prepared to explore the entire environment to locate all items. Instructions indicated that participants should be aware that they might be asked to find the objects again later. However, the specific nature of the upcoming tests was not disclosed. After receiving these initial instructions, each participant completed the following sequence of tasks:
Spatial exploration of the virtual warehouse, where their primary task was to inventory landmark objects.
A free recall test of landmark object names.
One of the two directional pointing tasks (DualOBJ or JRD), with judgment type manipulated between subjects to avoid carry-over effects.
The electronic sketch map task.
Directional pointing and sketch map tasks were not counterbalanced, as they had been in prior studies, because the primary focus of the present research was on directional pointing. Moreover, earlier research had not found significant order effects for these tasks.
Spatial learning of the environment occurred during approximately 12 min of viewing a first-person point-of-view video. As participants navigated through the virtual space, relevant audio played through their headphones to guide the experience. The narration named and described the target objects, clearly identifying each one and highlighting its key features. For instance, when the next object on the inventory list was the coffee vending machine, participants would hear, “Okay, looking for a coffee vending machine now.” Upon reaching the object, the narration continued with, “Seems like the one. This thing sure has a lot of options.” Transitional audio was also included to accompany movement between rooms and hallways. For example, after all objects in a room were located, the narrator would say, “Alright, looks like we found everything in this room, let’s move on to the next one.” This audio provided status updates and helped participants transition to the next object or room, supporting continuity and engagement during spatial learning.
After experiencing the virtual warehouse, all participants completed a free-recall task by typing the names of remembered objects on a keyboard during a fixed recall period. Following this, participants completed their assigned directional pointing task—either the JRDs or the Dual Object (DualOBJ) task. On-screen video and audio instructions explained how to use the directional circle interface to complete their judgments. To ensure task comprehension, participants completed a set of practice trials using objects physically located in the experimental room. They were encouraged to look around the room while making judgments, and the experimenters provided corrective feedback as needed. Once participants demonstrated understanding, they proceeded to the experimental trials. There were 32 JRD trials: 16 involved a facing object in the same room as the base and target objects, and 16 involved a facing object in a different room, positioned at the same angle. Similarly, there were 32 DualOBJ trials. Each DualOBJ trial consisted of two sequential queries: the first used a facing-object query, and the second used a target-object query that matched a JRD-facing and target-object query. The queries were yoked to those in the JRD task to allow direct comparison in data analyses.
After completing the directional pointing tasks, participants moved on to the sketch map task. They first received instruction and practice by drawing the physical experimental room using an electronic sketch pad and pen. Once the practice maps were reviewed by the experimenter, participants then drew the virtual warehouse building and the landmark objects from memory. JRD and DualOBJ groups both received the same instructions and practice.
Results and Discussion
The First Issue
To address the first part of the first issue, the OBJ needs to be evaluated to determine if it measures each of its target objects individually. We analyzed the OBJ dependent variable using a 2 × 2 repeated-measure ANOVA. The two repeated-measures factors were object type (facing object, target object) and facing object room location (within-room, between-room). Each target object was yoked to a specific facing object, so while the location of the facing object varied, the target object was always in the same room as the base object and paired with its respective facing object.
Let E denote the absolute value of the angular difference between a participant’s response to a query and the correct angle, going the shortest way around the circle. The equation is Min(Abs(R-C), 360-Abs(R-C)), where R is a participant’s response on the direction circle and C is the environmental correct response for that judgment task and query. R and C are in the semi-closed interval [0, 360). This allows the use of linear statistics, as the shortest way around the angular circle is a magnitude that keeps linear measures within the closed interval [0, 180], unlike signed errors, which require the use of circular descriptive and inferential statistics (Batschelet, 1981). Abs is the absolute value, and Min is the minimum value of the two arguments. Ef and Et are the OBJ absolute angular errors for the JRD’s facing and target objects, respectively. Using E allows the use of linear statistics, and taking measures as the shortest way around the angular circle is a magnitude that also keeps the linear measures in the closed interval [0, 180].
If the OBJ measures objects individually, then the OBJ absolute angular error for the JRD’s facing object, Ef, should increase when the facing object changes its location from within-room to between-room. In contrast, the absolute angular error for the target object, Et, should not increase as the facing object changes from within-room to between-room, because the target object should not be affected by another object’s absolute angular error if OBJs measure objects individually. However, if the target object’s absolute angular error, Et, does combine with the facing object’s absolute angular error, and if OBJs do not measure objects individually, then an increase in the OBJ absolute angular error for the facing object, Ef, should be accompanied by an increase in the OBJ absolute angular error of the target object, Et. This target object increase would indicate that the OBJ does not measure its target objects individually.
As shown in Figure 6, the results indicated that the OBJ mean absolute angular error for facing objects, Ef, was 47.4 ° in the within-room condition and increased to 73.6° in the between-room condition. For the OBJ mean absolute angular error of the target object, Et, there was relatively little change. As shown in Figure 6, the mean absolute angular error for the target object, Et, when its yoked facing object was in the same room was 48.5°, which decreased slightly to 48.1° when the yoked facing object was in the between-room condition. The interaction of Object Type × Facing Object Location was statistically significant, F(1, 23) = 34.5, Mean square error [MSE] = 122, ηp² = .600, p < .0001. These results were consistent with the expectation that the OBJ measures its target objects individually.
OBJ absolute angular error for facing and target objects.
Follow-up ANOVAs for each object type supported the above results. For the facing object condition, the difference between within-room and between-room conditions was statistically significant, F(1, 23) = 58.9, MSE = 149, ηp² = .719, p < .0001. For the target object condition, the difference when the facing object changed to between-room was not statistically significant, F(1, 23) = 0.83, MSE = 69, ηp² = .001, p = .87. These analyses substantiate the conclusions, supporting that the OBJ task measures its target object individually, consistent with the OBJ measurement model.
These findings have implications for the interpretation of JRD results, addressing the second part of the first issue. Ej denotes the JRD task absolute angular error measure of the JRD’s target response minus the correct angle between the target and facing objects. If Ej, is found to be sensitive to the facing object room location (within-room versus between-room), while participants nominally select the target object angle on the direction circle, then these results imply that the JRD’s target response was primarily influenced by the facing object’s absolute angular error, Ef, with little to no influence from the target object’s absolute angular error, Et. This pattern of results suggests that the JRD may be misinterpreted, as it represents a combination of both the facing object and the target object absolute angular errors contributing to the target’s response.
As Figure 7 shows, the JRD group had a 17.4° increase in absolute angular error, Ej, from facing object within-room (M = 57.9°) to between-room (M = 75.3°). This difference was significant, implying that the JRD target response combined the absolute angular error of both the facing and target objects.
Absolute angular error for DP measures in experiment 1.
JRD absolute angular error (E’j = |Et-Ef|) as separate lines, across facing object location conditions (within room versus between room) on the x axis. The right-side interval shows 95% CI for between-subjects comparisons; intervals around individual points show 95% CI for within-subjects comparisons. OBJ = Object-based judgment; JRD = Judgments of relative direction; CI = Confidence interval; DP = Directional pointing.
Second Issue: Do OBJ and JRD Tasks Measure Same Underlying Memory Representations?
To evaluate performance across the JRD and OBJ tasks, absolute angular error estimates based on the OBJ measurement model were obtained from the DualOBJ trials. Estimated JRD absolute angular error is denoted as E’j and actual JRD absolute angular error obtained from participants’ JRD trials is denoted as Ej. For the DualOBJ group, the dependent variable was the estimated JRD absolute angular error, E’j, calculated based on both the JRD facing and target objects as OBJ target responses, and assumptions of the OBJ measurement model. E’j = Etf(Et-Ef), where Etf denotes the absolute angular difference between the two OBJ absolute angular error measures inside the parentheses. The OBJ measurement model deals with unsigned magnitudes as does most spatial research using JRDs and OBJs.
Figure 7 shows that the OBJ’s estimates using its facing and target object absolute angular errors were equal to the JRD’s target response absolute angular error, or E’j = Ej . Note that E’j is the OBJ measurement model’s mathematical difference score’s absolute angular error, which estimates the assumed JRD’s cognitive difference score’s absolute angular error.
These Ej and E’j values were analyzed as a single dependent variable across the two groups. A 2 × 2 mixed factorial ANOVA was conducted with judgment type (DualOBJ, JRD) as a between-subjects factor and facing object room location type (within-room, between-room) as a within-subjects factor. MSE is reported to assess test sensitivity. Although partial eta squared (ηp²), a variance accounted-for measure, is reported, it was not interpreted in detail due to its extreme variance accounted-for values, which were closely aligned with significance levels.
Figure 7 displays the mean absolute angular error on the vertical axis, with JRD (DP-JRD), the Ej group, and DualOBJ (DP-DualOBJ), the E’j group, represented by separate lines. The horizontal axis represents the facing object’s room location conditions (within-room, between-room). Two types of 95% confidence intervals are shown, following Loftus and Masson (1994). The interval on the right side indicates the 95% confidence interval for the overall means per group, a between-subjects’ error, while 95% intervals around individual data points, a repeated-measure error, should only be compared within the same line. As shown in Figure 7, the JRD group demonstrated substantially greater absolute angular error when the facing object was located in a different room (between-room) compared to when it was in the same room (within-room) as the base and target objects. This suggests that JRD absolute angular error inherently combines both facing and target absolute angular error sources.
The two tasks were analyzed using a 2 × 2 mixed ANOVA with a between-subject factor of measurement task and a repeated-measure factor of room location type. Comparing the two tasks, the mean estimated JRD absolute angular error from the DualOBJ task, E’j, was 64.8°, closely aligning with the observed JRD mean absolute angular error, Ej, of 66.6°. This 1.8° difference was not statistically significant, F(1, 46) = 0.09, MSE = 895, ηp² = .002, p = .77, suggesting that the DualOBJ estimated absolute angular error, E’j, closely approximated actual JRD response absolute angular error, Ej. A robust main effect of facing object room location was observed, with an average increase of 19.2° in absolute angular error when the facing object changed from the same room to a different room, F(1, 46) = 48.4, MSE = 182, ηp² = .513, p < .0001. This within-subjects effect was highly sensitive, as reflected by its much smaller MSE—approximately 4.5 times smaller than the between-subjects MSE.
As shown in Figure 7, the mean JRD absolute angular errors, Ej, in the within-room and between-room conditions were closely mirrored by the estimated DualOBJ mean absolute angular errors, E’j, for JRD. This pattern was confirmed by the non-significant interaction between the measurement task and the room location facing the object, F(1, 46) = 0.40, MSE = 182, ηp² = .009, p = .53. The interaction was tested with the same high sensitivity as the within-subject main effect. Specifically, the JRD group showed a 17.4° increase in absolute angular error from within-room (M = 57.9°) to between-room (M = 75.3°), while the DualOBJ group showed a comparable 20.9° increase (from M = 54.3° to M = 75.2°), an interaction difference of only 3.5°. This result is analogous to Hilgard's use of “mountain height” to test his gravity-measurement models, in which non-significant differences in model estimates indicate equivalent performance. Overall, the absence of a significant interaction supports the conclusion that the DualOBJ-derived absolute angular error, E’j, is a valid and reliable estimate of JRD angular error, Ej, regardless of the overall level of performance. This outcome is consistent with expectations of the OBJ measurement model.
In the above analyses of absolute angular error, we calculated group means as usual. However, individual angular judgments can occasionally be quite large, leading to positively skewed distributions that may distort the means. To address this, we averaged each participant’s absolute angular error over 16 trials per condition to reduce the impact of outliers. Additionally, we applied a log transformation to the absolute angular error values and then repeated the 2 × 2 mixed-factorial ANOVA. The results were consistent with the original findings. Neither the main effect of measurement task, F(1, 46) = 0.05, MSE = 0.054, p = .83, nor the Measurement Task × Facing Object Location interaction, F(1, 46) = 0.34, MSE = 0.015, p = .56, were statistically significant. The main effect of facing-object room location remained large and significant, F(1, 46) = 45.5, MSE = 0.015, p < .0001. These results further reinforce the robustness of the findings.
While these analyses demonstrated that the DualOBJ estimates of JRD absolute angular error were statistically indistinguishable from actual JRD absolute angular errors, additional evidence was collected to show that the two types of judgments’ absolute angular errors were positively related. Although JRD and DualOBJ were from separate participant groups—precluding within-subject correlation—we leveraged the fact that both groups responded to the same set of 32 queries. For each query, we calculated the mean absolute angular error across participants within each group. This yielded 32 pairs of average absolute angular errors (one from each group), which we then correlated. The resulting Pearson correlation coefficient was r = .61, indicating a substantial positive relationship between the DualOBJ estimates and actual JRD performance across queries. This strengthens the conclusion that DualOBJ is a valid estimator of JRD absolute angular error. Also, the correlation was not confounded by trials because each participant’s trials were randomly ordered.
Sketch Maps: DualOBJ versus JRD
As mentioned previously in the introduction, the sketch map analyses do not directly relate to the two directional pointing tasks, but they are of more general interest. To measure the relevant angles between sketched objects on participants’ maps, we apply judgment queries called map angle queries (MAQs). MAQs can be performed using DualOBJs and JRDs, with the distinction that there is no need for a sequential query order on a sketched map, as there is no inherent order between queries. Therefore, all the analyses conducted for directional pointing tasks in the previous sections can also be applied to MAQs.
As shown in Figure 8, the results were similar to those found for directional pointing. For the JRD group, the mean absolute angular error, Ej, from MAQs was 53.7°. For the DualOBJ group, the estimated JRD mean absolute angular error, E’j, from the appropriate pairs, according to the OBJ measurement model, was 53.1°. This 0.6° difference in absolute angular error was not statistically significant, F(1, 46) = 0.007, MSE = 964, ηp2 = 0.002, p = .93. There was also a large difference in absolute angular error performance for the repeated-measure main effect of facing object room location type, which was statistically significant, F(1, 46) = 17.9, MSE = 276, ηp2 = 0.473, p < .0001. Additionally, the JRD estimated from MAQ DualOBJ queries, E’j, agreed with MAQ JRD queries, Ej, for both within-room and between-room conditions. The interaction of judgment × facing object room location type was not statistically significant, F(1, 46) = 0.40, MSE = 276, ηp2 = 0.009, p = .53. It is worth noting that this interaction had the same MSE as the other repeated-measure effect, indicating similar sensitivity. The mean absolute angular error for the JRD queries, Ej, in the within- and between-room conditions were 47.0° and 59.2°, respectively. For the DualOBJ-estimated JRD absolute angular error, E’j, the comparable means were 45.4° and 61.9°, producing non-significant increases of 12.2 and 16.5°, respectively, with an interaction difference of only 4.3°.
Absolute angular error for sketch map measures in experiment 1.
Landmark Name Free Recall
We analyzed the free recall of landmark object names. There were no significant differences in correct recall between OBJ and JRD conditions, and almost all the names were recalled. A more complete analysis landmark recall in both experiments is presented after Experiment 2.
Experiment 2
The results of Experiment 1 supported the conclusion that the OBJ measurement model could also describe JRD data. So, that result implies that both the OBJ and the JRD tasks measured the same underlying memory representations. However, the JRD’s target response measured the absolute angular error from both the facing and target objects, while the OBJ only measured absolute angular error from its target object.
Experiment 2 further tested the task differences and the OBJ measurement model by providing participants with a different spatial experience that could influence the way they approached the task queries. In this experiment, participants moved directly from one room to another, bypassing hallways. As described earlier in the introduction, prior research indicated that navigating in this manner improved between-room performance. Participants gained more spatial knowledge (memory representations) of the objects in different rooms, and direct viewing was not necessary. One possible explanation for this improvement is that participants used room structural relations. To move directly from one room to another, the rooms must be adjacent and share a common wall. A distinctive part of the wall, such as a corner, could be recognized from both sides. Therefore, an object in one room could be referenced to its corner, and the same corner in the adjacent room could be used to reference another object in that room. These inferences could change how judgments are made. Hence, we argue that this provided another test of the OBJ measurement model. If participants were induced into making relational judgments not just on individual landmark objects, then the component error assumption of the OBJ measurement model could fail.
Method
The method was nearly identical to Experiment 1 in almost all aspects, except for changes to the doorway locations, which allowed participants to navigate directly from room to room without having to go through a hallway. The new doorway locations are indicated with a “#” in Figure 2, and the hallway doorways were removed. The doors were always open, allowing participants to partially see into the next room as they approached the doorway; however, the navigation track never turned to look backward. To keep within-room navigation as consistent as possible with Experiment 1, once a new room was entered, the navigation turned and navigated along the walls until reaching the location where the doorway had been in Experiment 1. Afterward, within-room navigation proceeded as in Experiment 1. After visiting the last landmark object in a room, the navigation moved directly to the doorway leading to the next room. Virtual building navigation was followed by a free recall test, a directional pointing task, and a sketch map task. The queries were identical to those used in Experiment 1.
Participants
The student participants from introductory psychology classes identified their genders as 15 male and 33 female, with ages ranging from 18 to 29 years old (M = 18.9). They met all the other criteria for participation as in Experiment 1, but none of them had participated in Experiment 1. The experiment was approved by the Institutional Review Board for human participants at the university of the first author, and all students provided informed consent before participating by signing a paper document.
Results and Discussion
First Issue
In this part of the first issue, data were analyzed using the same sequence of ANOVAs, and dependent variables as in Experiment 1. As in Experiment 1, the OBJs dependent variable was used to examine the absolute angular error of the facing and target objects individually. The OBJ measurement model assumes that absolute angular error can be attributed individually to each object. If judgments become relative because participants travel directly from room to room, then the component error assumption may be violated.
A 2 × 2 repeated-measure ANOVA with factors of object type (facing object, target object) and facing object room location type (within-room, between-room) was performed. The dependent variable was the OBJ absolute angular error. The interaction of object type × facing object room location was statistically significant, F(1, 23) = 19.3, MSE = 85, ηp² = .456, p < .0001. As Figure 9 shows, for facing objects, the mean absolute angular error, Ef, was 52.1° for the within-room condition, but it increased to 68.4° for the between-room condition. In contrast, for the target object, mean absolute angular error, Et, was 51.1° when the facing object was in the same room, but changed little to 50.09° for the between-room condition. These are the results expected if the OBJ response measured its target object absolute angular error individually.
OBJ absolute angular error for facing and target objects.
Follow-up ANOVAs on each object type separately confirmed this interpretation. For facing objects, the within-versus-between difference was statistically significant, F(1, 23) = 31.1, MSE = 102, ηp² = .575, p < .0001. For target objects, that difference was not statistically significant, F(1, 23) = 0.01, MSE = 47, ηp² = .0005, p = .91. These results support that the OBJ target response measures absolute angular error of its target objects individually, and support the results found in Experiment 1.
Addressing the second part, JRDs behaved as they did in experiment 1. The JRD target response increased when its facing object changed its location from within room to between room. This change was significant. As Figure 10 shows, the within-room (M = 62.3°) to between-room (M = 68.9°) increase of 6.64° of mean absolute angular error, Ej, for the JRD target response queries.
Absolute angular error for DP measures in experiment 2.
Second Issue: Do OBJ and JRD Tasks Use the Same Underlying Memory Representations?
As in Experiment 1, estimates of JRD absolute angular error, E’j, were obtained from pairs of OBJ queries as prescribed by the OBJ measurement model, obtained from the DualOBJ group. For the JRD group, the dependent variable was the absolute angular error, Ej, of its target response. The mean absolute angular error for the JRDs estimated by the DualOBJ pairs, E’j, using the OBJ measurement model was 58.5°, compared with the actual JRD absolute angular error, Ej, of 65.6°. This main effect of judgment was not statistically significant, F(1, 46) = 1.32, MSE = 928, ηp² = .028, p = .26.
As Figure 10 shows, the facing-object room location increased the mean absolute angular error. It increased by 7.23° when the facing object was in the same room as the base and target objects, compared with when it was in a different room. This main effect difference was statistically significant, F(1, 46) = 8.32, MSE = 151, ηp² = .153, p = .006. The facing location produced a substantial change in performance. However, although the Measurement Task × Facing Object room location effect had the same statistical sensitivity (small MSE) as the main effect increase, it was not statistically significant, F(1, 46) = 0.06, MSE = 151, ηp² = .001, p = .81. Note that the slight vertical separation of the overall DualOBJ and JRD data points in Figure 10 is within the 95% confidence interval on the right side of the data. As noted in Experiment 1, the interaction indicates if the increases were similar. Therefore, the within (M = 62.3°) to between (M = 68.9°) increase of 6.64° of mean absolute angular error for the JRD queries was comparable to the within (M = 54.6°) to between (M = 62.4°) increase of 7.83° for the DualOBJ’s estimated JRD mean absolute angular error using the OBJ measurement model. The difference between these two increases, the interaction effect, was only 1.19°.
As we did for Experiment 1, we log-transformed the data in the 2 × 2 mixed factorial ANOVA to assess whether the results were sensitive to the distribution. The log-transformed data produced comparable results. The measurement task main effect and the Measurement Task × Facing Object Location interaction were not statistically significant, F(1, 46) = 0.15, MSE = 0.062, p = .86, and F(1, 46) = 2.56, MSE = 0.010, p = .09, respectively. Of course, the main effect of facing object room location type was statistically significant, F(1, 46) = 4.03, MSE = 0.010, p = .05.
As in Experiment 1, we used queries from both judgment groups to evaluate the relationship between the groups. Each of the 32 queries was present in both judgment groups. The mean absolute angular error across the 24 participants in each group was used as the paired scores. The Pearson correlation was r = .57, again supporting the conclusion that DualOBJ estimated absolute angular error was substantially related to JRD absolute angular error, supporting the validity of the OBJ measurement model.
Sketch Maps: DualOBJ versus JRD
Figure 11 shows the sketch map data for Experiment 2. The sketch map MAQ OBJ estimated JRD absolute angular error, E’j, from the DualOBJ group was 52.3° compared with the actual MAQ JRD absolute angular error, Ej `, of 49.6°. This 2.7° difference was not statistically significant, F(1, 46) = 0.69, MSE = 977, ηp² = .015, p = .41. The repeated-measure main effect of facing object room location was statistically significant, F(1, 46) = 12.2, MSE = 168, ηp² = .210, p = .001. However, the interaction of measurement task × facing object room location was not statistically significant, F(1, 46) = 0.34, MSE = 168, ηp² = .007, p = .56. Again, note that this repeated-measure interaction was as sensitive as the facing object location main effect.
Absolute angular error for sketch map (MAQ) measures in experiment 2.
The within- and between-room absolute angular error, Ej, means were 51.0° and 58.8° for JRD queries. The comparable means for the estimated JRD queries, E’j, using the OBJ measurement model for the DualOBJ task were 44.2° and 55.0°, respectively. So, the interaction difference in increases was only 3.00°, a non-significant interaction. These results were consistent with experiment 1 under these new conditions, providing additional support for the OBJ measurement model.
Experiment 2 evaluated the effects of the relative judgment hypothesis. Between-room absolute angular error was reduced compared with Experiment 1. As described in the introduction, this increase in spatial knowledge occurred without additional direct viewing from one room to another, most likely some new aspect of the environment was responsible. This new aspect changed memory representations, improving spatial performance. It could have caused difficulties for the OBJ measurement model such as the relative judgment hypothesis, but it did not. Instead, experiment 2 broadened the generality of the OBJ measurement model.
Landmark Name Free Recall
Participants’ free recall of the landmark object names was analyzed with a 2 × 2 between-subjects ANOVA (Experiment × Measurement Task). There were no statistically significant effects. The main effects of experiment (1 vs. 2) and measurement task (JRD vs. DualOBJ) and their interaction all were not significant. The respective medians, means, and SDs of the number of object names correctly recalled for the 4 groups were 15, 14.6, 1.61 for DualOBJ and 15, 13.2, 3.66 for JRD of experiment 1, and 14.5, 14.1, 1.91 for DualOBJ and 15. 14.5, 1.84 for JRD of experiment 2. For all groups, the median was 15 out of the 16 objects (M = 13.8, SD = 2.47). Therefore, it is unlikely that differential recall of landmark knowledge or low levels of recall affected the absolute angular error results.
A Methodological Check
This experiment was conducted because we were concerned that the new direction circle task used in the above experiments was too complex. Therefore, we completed this methodological experiment before starting the above experiments. It compared our new direction circle task with our older, standard task in which participants simply selected a location on the circle to make their response. These two groups each had 24 participants (none of whom participated in experiments 1 and 2) and came from the same subject pool with the same requirements. The experiment used a previously used L-shaped environment with two rooms along each leg of the hallways with four objects in each room (16 objects). Hallways in the environment had a right or left turn, balanced across participants. Queries were OBJs with both within-room and between- room queries. Navigation was aided by an auditory script. Data were analyzed using mixed ANOVA statistics. There were no main effects of the type of direction circle task used and no interactions with that factor. Therefore, we proceeded with the use of the new direction circle task.
General Discussion
OBJ Angular Judgment Measurement Model
Both critical experimental tests in Experiments 1 and 2 supported the assumptions of the OBJ measurement model. A direct implication of these findings is that both the JRD and the OBJ tasks measure the same underlying angular spatial memory representations. Importantly, the measurement model yielded the correct point estimates, not just correlations, and both tasks were in the same units, degrees. This strong relationship was found, although the JRD task uses only locations for measurement, whereas the OBJ task uniquely uses the orientation of the front sides of objects, supporting the idea that both tasks measure the same underlying memory representations. In addition, this suggests that the JRD task is not uniquely useful for measuring memory representations related to spatial reference frame theory.
However, while the two tasks measure the same underlying representations, they differ in their focus. The JRD task measures the combined absolute angular error from two sources: the facing and target objects, likely as a cognitive difference judgment. A possible adjunct to this double absolute angular error issue is to use a placement task to estimate facing absolute angular error of JRDs, as was used by Du et al. (2021). In contrast to JRDs, the OBJ task measures the absolute angular error of only one source, its target object. Therefore, while both tasks measure absolute angular error, they differ because the JRD task measures the combined angular error of two objects, while the OBJ task measures the absolute angular error of only one object, its target object. The implication is that the OBJ task provides more specific measurements.
Another important implication of the OBJ task is that participants were able to use the front sides of objects to make judgments. Therefore, objects—or at least a recognition of their front side orientations—should be considered an important component of human spatial memory representations.
Measurement Models
Finally, this exercise demonstrates how a measurement model has advantages over simple correlation or regression approaches. Although the OBJ and JRD tasks are correlated, they are not merely alternate forms of the same underlying dimension. When both tasks are used to measure people’s knowledge of a target, they may yield different results, even though they measure the same underlying memory, because they assess different sources. Measurement models reveal both the similarities and the differences between measurement tasks. To illustrate, Hilgard’s (1958) falling body and pendulum tasks both measure the same underlying gravity, yet they are very different measurement tasks.
Although we designed the experiments to be sensitive tests of the OBJ measurement model’s assumptions while avoiding carryover effects, they were the first and only tests conducted thus far. Further research is needed to broaden its applicability. For example, in our experiments, the fronts of the objects were always parallel to a wall. The model could be tested in scenarios where the fronts of the objects are at 45° angles to the walls, or in environments without walls (May & Colle, 2018). All models have boundary conditions that should be explored. As van Fraassen (2012) argued, understanding the relations between measurements in the context of measurement models and the theories they test is crucial for interpreting scientific concepts. However, while measurement models describe the relationships between measurement tasks and the variables important for those tasks, they do not explain the phenomenon being measured. That explanation falls within the domain of a theory of the phenomenon.
The current OBJ measurement model is also significant because there are relatively few examples of measurement models in psychology, especially in spatial memory research. One well-known measurement model in psychology is signal detection theory (SDT), which has been applied in recognition memory as well as in psychophysical detection experiments. The SDT measurement model allowed the separation of stimulus differences from response biases (Green & Swets, 1966). Moreover, it produced measures that were shown to be equivalent according to the measurement model, such as the relationship between the area under a yes/no task ROC curve and the percent correct in a two-alternative forced-choice judgment task. This led to tests of that measurement relationship (Lapsley Miller et al., 2002) and to more psychological theories that were at least partially based on that measurement model (Wixted, 2020). While the SDT measurement model had a profound impact on psychological measurement, it did not emerge solely from examining coherences using correlations and linear regressions—approaches that have historically dominated the field. The measurement model presented here could potentially have a similar impact on spatial memory research.
Headings Versus Objects
An alternative approach for OBJ pointing judgments is that they are essentially JRDs where the front of the object defines a heading, just as a facing object would, making the task an implicit JRD. While this contrasts with the object interpretation, it is unlikely to change the consequences of the measurement model results. Importantly, it is clear that the typical JRD’s target response includes absolute angular error from the facing object. The “implicit JRD” measures only one source of absolute angular error, the target object. However, the results suggest that the task we call an OBJ has different properties and implications than the typical JRD. Not only is the OBJ task a more specific measure, but it also implies that object front knowledge is a component of spatial memory, not just locations. Calling both tasks by the same name confuses these differences.
The Base Object
It could be noted that the OBJ suffers from a similar issue of combined absolute angular error. The base object also has absolute angular error that could combine with its target absolute angular error. The measurement model made the no absolute angular error assumption because it was simulating human thinking, which was assumed that in memory, the person is positioned by the base object. The omission of base object absolute angular error did not affect the interpretation of the results because the base objects for JRDs could also have absolute angular error. So, both sides of the equivalence were affected similarly. However, base absolute angular error complicates the interpretation of JRDs more than OBJs. To form an angle, you need at least two objects. An OBJ satisfies this minimum. The absolute angular error is between a single base-target object pair. However, a JRD has three possible paired relations: Base-Facing, Base-Target, and Facing-Target.
Egocentric versus Allocentric
Our working hypothesis favors an object interpretation. One reason for this preference goes beyond directional pointing, which is nominally an egocentric task. When people make directional judgments, they may think about directions in space with respect to their bodies or some other reference point that can be referred back to it. However, we also had participants create sketch maps. They placed boxes for objects, labeled them, indicated fronts, and drew lines for walls, etc. There was no need for symbols representing a person or a heading. Yet, this allocentric task produced results very similar to the pointing task. The maps were scored mathematically using the objects, with judgments made according to the OBJ measurement model. This suggests that memory representations may capture object relations, and when people are asked to make egocentric judgments, they can process them similarly to how we calculated sketch maps.
Theory: A Speculation
Our laboratory’s conceptualization and theoretical orientation of spatial layout memory is that it is a form of episodic memory (not a specialized memory like the one originally proposed by Brown and Kulik, 1977), with objects serving a role roughly analogous to words. Learning occurs in part when, through experience, objects become spatially related to some other objects. These spatial relationships consist primarily of angles and distances. We have chosen to focus on angles, as they are simpler to analyze.
In addition to object-to-object relations, spatial memory learning includes learning about structures. Examples include walls, doorways, and more complex arrangements such as the relative positions of multiple rooms. These room relations are analogous to Lynch’s (1960) concept of “districts.” During navigation, people may concurrently learn about districts (or other structural features) as well as landmark objects as was implied by the measurement models for the relationships between pointing DP-OBJs and sketch map MAQ-OBJs described by Colle et al. (in preparation). Errors in learning and representations of this structural spatial knowledge (district relations) likely contribute to the observation that absolute angular error between rooms is typically greater than angular error within-rooms. Structures may serve as organizing elements in spatial memory, much like semantic or ad hoc categories organize verbal memory.
This framework presents an intriguing speculative possibility: if we constrain spatial layout learning and memory to purely visual learning—such as in some virtual environments—then memory representations could consist of just a few fundamental spatial relations (angles, distances, physical structures). This contrasts with the complex, multidimensional nature of verbal episodic memory, which encompasses semantic, lexical, phonological, orthographic, and grammatical factors. Such a streamlined approach may allow us to describe and formalize spatial memory phenomena and episodic memory theories with greater precision and simplicity. While this reductionist method is not ideal for studying human navigation in all its richness, it offers a promising avenue for understanding the structure and mechanisms of episodic learning and memory.
Footnotes
Funding
The authors received no financial support for the research, authorship, and/or publication of this article.
Declaration of Conflicting Interests
The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.