Global-scale location and distance estimates: common representations and strategies in absolute and relative judgments

The authors examined whether absolute and relative judgments about global-scale locations and distances were generated from common representations. At the end of a 10-week class on the regional geography of the United States, participants estimated the latitudes of 16 North American cities and all possible pairwise distances between them. Although participants were relative experts, their latitude estimates revealed the presence of psychologically based regions with large gaps between them and a tendency to stretch North America southward toward the equator. The distance estimates revealed the same properties in the representation recovered via multidimensional scaling. Though the aggregated within- and between-regions distance estimates were fitted by Stevens's law (S. S. Stevens, 1957), this was an averaging artifact: The appropriateness of a power function to describe distance estimates depended on the regional membership of the cities. The authors conclude that plausible reasoning strategies, combined with regionalized representations and beliefs about the location of these relative to global landmarks, underlie global-scale latitude and distance judgments.     

Scaling techniques for modeling directional knowledge

A common way for researchers to model or graphically portray spatial knowledge of a large environment is by applying multidimensional scaling (MDS) to a set of pairwise distance estimations. We introduce two MDS-like techniques that incorporate people’s knowledge of directions instead of (or in addition to) their knowledge of distances. Maps of a familiar environment derived from these procedures were more accurate and were rated by participants as being more accurate than those derived from nonmetric MDS. By incorporating people’s relatively accurate knowledge of directions, these methods offer spatial cognition researchers and behavioral geographers a sharper analytical tool than MDS for studying cognitive maps.     

The representation and integration in memory of spatial and nonspatial information

A series of experiments investigated whether people could integrate nonspatial information about an object with their knowledge of the object's location in space. In Experiments 1 and 3, subjects learned the locations of cities on a fictitious road map; in Experiments 2, 4, and 5, subjects were already familiar with the locations of buildings on a campus. The subjects then learned facts about the cities on the maps or the buildings on the campus. The question of interest was whether or not these nonspatial facts would be integrated in memory with the spatial knowledge. After learning the facts, subjects were given a location-judgment test in which they had to decide whether an object was in one region of the space or another. Knowledge integration was assessed by comparing levels of performance in two conditions: (a) when a city or a building name was primed by a fact about a neighboring city or building, and (b) when a city or a building name was primed by a fact about a distant city or building. Results showed that responses in Condition a were faster or more accurate, or both faster and more accurate, than responses in Condition b. These results indicate that the spatial and nonspatial information were encoded in a common memory representation.     

Avoiding the dangers of averaging across subjects when using multidimensional scaling

Ashby, Maddox and Lee (Psychological Science, 5 (3) 144) argue that it can be inappropriate to fit multidimensional scaling (MDS) models to similarity or dissimilarity data that have been averaged across subjects. They demonstrate that the averaging process tends to make dissimilarity data more amenable to metric representations, and conduct a simulation study showing that noisy data generated using one distance metric, when averaged, may be better fit using a different distance metric. This paper argues that a Bayesian measure of MDS models has the potential to address these difficulties, because it takes into account data-fit, the number of dimensions used by an MDS representation, and the precision of the data. A method of analysis based on the Bayesian measure is demonstrated through two simulation studies with accompanying theoretical analysis. In the first study, it is shown that the Bayesian analysis rejects those MDS models showing better fit to averaged data using the incorrect distance metric, while accepting those that use the correct metric. In the second study, different groups of simulated ‘subjects’ are assumed to use different underlying configurations. In this case, the Bayesian analysis rejects MDS representations where a significant proportion of subjects use different configurations, or when their dissimilarity judgments contain significant amounts of noise. It is concluded that the Bayesian analysis provides a simple and principled means for systematically accepting and rejecting MDS models derived from averaged data.     

Learning fine-grained and category information in navigable real-world space

Spatial judgments are affected by both fine-grained and categorical knowledge. We investigated whether, and how, the two forms of knowledge are learned in real-world, navigable space, as well as the time course of learning each type of knowledge. Participants were Northwestern University undergraduates who estimated the locations of buildings and other landmarks on campus. The Northwestern campus is roughly divided into three regions whose borders are not easy to discern, either from a map or by navigation. Nevertheless, students often refer to these regions linguistically and use them when making housing decisions, choosing classes, and so forth. We found that knowledge of both the fine-grained configuration of locations and the regional distinctions increased with time. However, regional influences on judgments occurred later in students’ time on campus. Consequently, computed distances across the nonexistent border between north and south campus locations became more biased with time. The results have implications for understanding how spatial representations develop in navigable environments.     

The role of instructions and familiar size in absolute judgments of size and distance.

The effects of familiar size and instructions (apparent, objective) on direct reports of size and distance were evaluated. Subjects estimated the size and distance of two different-sized playing cards or two unfamiliar stimuli under either apparent or objective instructions. The stimuli were presented successively at a distance of 5.48 m under reduced-cue conditions. The form of the instructions selectively influenced the effect of familiar size on absolute judgments of size and distance, with apparent instructions minimizing, and objective instructions promoting, familiar-size effects. The ratio of the distance judgments of the first to the second presented stimuli approximated the relative retinal sizes of the two objects under both apparent and objective instructions, while the ratio of size judgments tended to be either influenced by or independent of the object's relative retinal sizes under apparent and objective instructions, respectively. These results are consistent with Gogel's theory of off-size perception and, in particular, with the claim that, in comparison with apparent instructions, objective instructions are more likely to direct observers to base their judgments on cognitive, as opposed to perceptual, sources of spatial information.     

The role of instructions and familiar size in absolute judgments of size and distance

The effects of familiar size and instructions (apparent, objective) on direct reports of size and distance were evaluated. Subjects estimated the size and distance of two different-sized playing cards or two unfamiliar stimuli under either apparent or objective instructions. The stimuli were presented successively at a distance of 5.48 m under reduced-cue conditions. The form of the instructions selectively influenced the effect of familiar size on absolute judgments of size and distance, with apparent instructions minimizing, and objective instructions promoting, familiar-size effects. The ratio of the distance judgments of the first to the second presented stimuli approximated the relative retinal sizes of the two objects under both apparent and objective instructions, while the ratio of size judgments tended to be either influenced by or independent of the object’s relative retinal sizes under apparent and objective instructions, respectively. These results are consistent with Gogel’s theory of off-size perception and, in particular, with the claim that, in comparison with apparent instructions, objective instructions are more likely to direct observers to base their judgments on cognitive, as opposed to perceptual, sources of spatial information.     

Memory for the spatial layout of the everyday physical environment: Differential rates of acquisition of different types of information

The hypothesis that the relative locations of the landmarks in a town is not accurately remembered before the paths between them have been learned was refuted in the present study showing that the reverse may in fact be true. In two of the three experiments carried out, undergraduates were found to give accurate estimates of the relative directions to different landmarks in an average-sized Swedish town (Umeå with about 80 000 residents), even if the subjects had been living there no more than two to four months. However, for some reason which could not be disentangled relative distance estimates turned out to be less accurate. In the third experiment, undergraduates who had lived for two months in the town by contrast hardly remembered which places among designated ones they would pass by the most direct path, whereas those who had been one year longer in the town were much better although not perfect. Finally, no sex differences were observed and there were no important differences depending on whether memory was tested for the central area of the town or for the whole town including the outskirts.     

Differences in spatial knowledge acquired from maps and navigation

Models of the spatial knowledge people acquire from maps and navigation and the procedures required for spatial judgments using this knowledge are proposed. From a map, people acquire survey knowledge encoding global spatial relations. This knowledge resides in memory in images that can be scanned and measured like a physical map. From navigation, people acquire procedural knowledge of the routes connecting diverse locations. People combine mental simulation of travel through the environment and informal algebra to compute spatial judgments. An experiment in which subjects learned an environment from navigation or from a map evaluates predictions of these models. With moderate exposure, map learning is superior for judgments of relative location and straight-line distances among objects. Learning from navigation is superior for orienting oneself with respect to unseen objects and estimating route distances. With extensive exposure, the performance superiority of maps over navigation vanishes. These and other results are consonant with the proposed mechanisms.     

Spatial knowledge of geographical globes: Evidence of vertical alignment effects

This study investigated human spatial memory of geographical globes. In two experiments, participants studied locations presented on a three‐dimensional globe. Subsequently, participants' knowledge of the locations was tested employing two types of pointing task. Directional judgments from imagined locations on the globe were performed either vertically through the ground (as if digging a straight tunnel between the locations) or horizontally along the surface of the globe (the shortest distance for an aircraft to fly to a given destination). In the vertical pointing task, judgments originating from imagined locations in the upper hemisphere were superior by comparison with those originating from imagined locations in the lower hemisphere. Performance in the horizontal pointing task was more variable, with a tendency for superior judgments originating from imagined locations in the lower hemisphere. The results provide evidence of a novel alignment effect involving vertical judgments.     

Direct versus indirect tests of memory for source: judgments of modality

We studied the relation between performance on direct versus indirect tests of memory for modality. Subjects read or heard words in a mixed list and then were tested by visual perceptual identification (the indirect test) and direct report of items as read, heard, or new. There was a dependent relation between perceptual identification performance and modality judgments, in accord with the hypothesis that subjects base their judgments of modality on relative perceptual fluency. In Experiment 2, we attempted to change the degree of dependence by providing subjects with an alternative basis for modality judgments. Subjects given a mnemonic to encode modality exhibited less dependence between perceptual identification performance and modality judgments than did subjects who encoded modality incidentally. The relation between direct and indirect tests of memory for source characteristics depends on the basis used for each.     

Direct and indirect measures of frequency monitoring in young and elderly adults

Memory for frequency of occurrence of novel material (Turkish words) was investigated in young and elderly adults via direct (absolute and relative frequency judgments) and indirect (reading speed) measures. Both young and elderly adults showed increased reading speed as a function of frequency of occurrence (Experiment 1). However, when asked explicitly to identify how often a word occurred (Experiment 1) or which word occurred more often (Experiment 2), elderly subjects were less accurate than young adults. These results support and extend research on age-related dissociations in memory.     

Structure mapping in spatial reasoning

Four experiments examined whether spatial reasoning about non-spatial concepts is based on mapping concepts to space according to similarities in relational structure. Six- and 7-year-old children without any prior graphing experience were asked to reason with graph-like diagrams. In Experiments 1 and 2, children were taught to map time and quantity to vertical and horizontal lines, and then were asked to judge the relative value of a second-order variable (rate) or a first-order variable (quantity) represented in a function line. Children’s judgments indicated that they mapped concepts to space by aligning similar relational structures: quantity judgments corresponded to line height, and rate judgments corresponded to line slope. These correspondences entail a mapping of first-order concepts to first-order spatial dimensions and second-order concepts to second-order spatial dimensions. Experiments 3 and 4 investigated the role of context in establishing relational structure. Children were taught to map age and rate (Experiment 3) or age and size (Experiment 4) to vertical and horizontal lines, and were then asked to judge the rate or the size represented by a function line. In this context, both rate and size were first-order variables, and children’s judgments corresponded to line height, also a first-order variable. The results indicate that spatial reasoning involves a structure-sensitive mapping between concepts and space.     

Static and dynamic factors in the perception of rotary motion

Direction of rotation and static slant judgments were collected for a series of outline plane forms in four experiments with 106 subjects. Direction was judged more accurately for forms displaying the same perspective gradients as trapezoids, but with right-angled contours, than for trapezoids. There were no consistent differences among these forms in judged slant. Direction of rotation judgments were affected by a static false interposition cue, with interposition increasing the proportion of veridical judgments when placed in conflict with a relative size gradient and decreasing this proportion when a size gradient was absent. Both a dynamic factor (contour angle change) and a static factor (misperceived relative distance of the vertical sides) were found to affect perceived direction of rotation, with direction judgments based primarily on the dynamic factor.     

Effect of distance instructions on size judgments

The proposition that in a reduced-cue setting subjects could use cognitive information about an object's distance to make accurate judgments of its size was tested. An improved paradigm was used to determine the effects of distance instructions per se. This paradigm also allowed independent tests of the effectiveness of cue reduction. The data indicated that cue reduction was successful and that the specific distance tendency governed size judgments when there were no distance instructions. When distance instructions were given, they produced size judgments in precisely the ratio predicted by the size-distance invariance hypothesis. However, there was a large constant error, which reflects a tendency of college students to overestimate the amount of distance signified by a verbal instruction. Hence, cognitive information in the form of verbal distance instructions has precise effects on size judgments, but the latter are not veridical, even in the absence of anchor effects from the specific distance tendency and residual perceptual cues.     

On the interdependence of temporal and spatial judgments

Three experiments are reported on the tau and kappa effects, the dependence of judgments of distance upon duration (tau) and of judgments of duration upon distance (kappa). In Experiment 1, three lights in a horizontal sequence were used to define two temporal and two spatial intervals over a total duration of 160 msec. The subject was required to choose the shorter of either the two durations or the two distances. The results confirmed Collyer’s (1977) findings that the two effects are inconsistently observed across subjects when the display duration is brief. In Experiment 2, display duration was systematically manipulated from 160 to 1,500 msec. It is argued that relative temporal judgments should become easier as the total display duration is increased and that, hence, the kappa effect should become less marked. On the other hand, relative spatial judgments should become more difficult as the total duration of the display is increased, and the tau effect should become more marked. The data were in conformity with the hypothesis. In Experiment 3, data are presented for a tau experiment which fit the assumption that the effect depends upon a weighted average of distance and the expected distance which would be traversed in the given time at constant velocity.     

Learning to perceive the relative mass of colliding balls: the effects of ratio scaling and feedback

The theory of direct perception holds that competent observers are able to detect optical patterns that specify the relative mass of colliding balls. Heuristic theorists, on the other hand, claim that judgments of relative mass are based on variables that do not specify relative mass. We contrasted these views with an experiment in which participants were given feedback on their ratio-scaled estimates of the relative mass of simulated colliding balls. Correlations between judged relative mass and various kinetic and kinematic measures of the collisions revealed that (1) judgments of relative mass become more accurate with feedback, (2) different observers use different variables, (3) during training, many observers change which variables they use, (4) before training, observers tend to use nonspecifying variables or combinations thereof, (5) after a minimal amount of training, at least some observers seem to detect mass-specifying information, and (6) the judgments do not support a generalization of the heuristic model of Gilden and Proffitt (1989, 1994). These findings suggest that direct perception of relative mass is a skill that can be developed through appropriate training.     

Developmental Changes in Young Children's Spatial Memory and Language in Relation to Landmarks

Two experiments investigated how young children and adults understand whether objects are by a landmark and remember their locations. Three- and 4-year-old children and adults were asked to judge whether several blocks were by a landmark. The blocks were arranged so that their absolute and relative distances from the landmark varied. Later, the blocks were removed, and participants were asked to place them in their original locations. All ages relied on relative distance between objects and a landmark when making by judgments; however, older children and adults showed systematic judgments. Relative distance also affected block placement, and systematicity increased across development. Children's understanding of the relative nature of by and their ability to remember locations precisely increased during the preschool years, indicating developmental changes in the adaptive combination of location cues for spatial language and memory.     

The role of verbal labels in the judgment of orientation and location

In an earlier study it was found that judgments of right-left orientations and locations were more difficult than judgments of up-down only when spatial words were used in the tasks. Experiments are reported in which pictures of many objects were presented to eliminate the possibility that subjects in previous studies had used strategies specific to single-stimulus tasks. In experiment 1, right-left orientations were judged more slowly than up-down orientations both when the spatial words were used and when arbitrary letters replaced the spatial words. In experiment 2, judgments of the right-left locations of pictures took longer than judgments of their up-down locations only when spatial words were used in the task; the right-left difficulty was eliminated when arbitrary letters replaced the words. The differential effect of words and letters in location judgments seems to be due to the different coding strategies adopted by subjects under the two conditions. It is concluded that a right-left difficulty does not depend on the use of spatial terms: word and letter conditions yield different results only when the task permits different judgments to be made under the two conditions.     

The role of categorical information in processing relational attributes

In two experiments, the effect of knowledge about relevant common taxonomic categories on judgments of relative magnitude was investigated. In Experiment 1, subjects judged the relative size of objects that belonged to the categoriesbuilding andanimal. The symbolic distance effect was smaller for between-category pairs (e.g.,horse-cabin) whose members could be classified more quickly into the two categories. This result strongly suggests that subjects used category membership to determine relative size on at least some portion of the trials. In Experiment 2, a similar attenuation of symbolic distance was obtained when subjects judged the relative height of furniture and vehicles. A simple explanation of the reduced symbolic distance effect for between-category pairs is that subjects occasionally fail to categorize the items into different categories and have to compute relative magnitude from the magnitudes of the two items. Fits to the data using the bootstrap technique suggest that more involved assumptions are required.