The Impact of the Landmark Attraction Effect and Central Tendency Bias on Spatial Memory Distortions

The successful communication of spatial information with maps allows correct spatial memory retrieval. Space-referencing map elements like grid pattern lead to a higher spatial accuracy in memory performance. We studied the influence of the landmark attraction effect and the central tendency bias predicted by the categorical adjustment model. While landmark attraction effect would lead to an attraction toward the landmark for the recalled object location, central tendency bias would lead to a deviation toward the center of a given field. The effects of these distortions were investigated on two different kinds of grid pattern, continuous grid lines and grid crosses, superimposed on a map or on a blank background. Results showed higher object-location memory accuracy for grid crosses. As expected, a clear central tendency bias was observed for the continuous grid lines according to the expected central tendency bias. However, there was no clear landmark attraction effect or central tendency bias for the grid crosses. We suspect a partial cancellation of the two opposing effects in this case. Overall results, central tendency bias seems to be stronger than the landmark attraction effect. In our experimental design, the landmark attraction effect seems not to be able to eliminate the central tendency bias, but to mitigate its strength. We suggest a correcting influence of map elements on object-location memory as the spatial distortions caused by the central tendency bias of the complete grid are significantly reduced in the grid cross condition. Future studies have to show more exactly how different shifting effects of recalled object positions can be used cartographically to reduce distortions of the mental representation of space.


Theoretical Background
Maps are commonly used to communicate spatial information from the real environment to people and to build mental representations of space, called cognitive maps.The accomplishment of orientation and navigation tasks in everyday life requires useful cartographic media that support people in solving their tasks in an efficient and effective way.The decisive factor is how the map-based information and their perception can contribute to the formation of the cognitive map.
However, findings from cognitive psychology have shown that cognitive maps can be distorted in various ways when people encode spatial information via maps (Dickmann et al. 2013;Okabayashi and Glynn 1984;Stevens and Coupe 1978;Tversky 1981).These distortions impair the efficient transfer of information significantly, that is intended with the creation and use of maps.For example, the size and position of objects, as well as the distances between them, are not distorted randomly in recall (e.g., Hirtle and Jonides 1985;McNamara et al. 1984).The results of numerous cognitive and cartographic studies have rather indicated that spatial judgements based on information from maps are systematically distorted (e.g., Kosslyn et al. 1974;Newcombe and Liben 1982;Thorndyke and Stasz 1980).Individuals tend to regularize irregular spaces in spatial memory tasks (Glicksohn 1994;Holden et al. 2013;Tversky 1981) or recall map elements more horizontally or vertically aligned to other map elements than presented (Tversky 1992).In addition, distances between two locations are underestimated when presented within the same (administrative) region, while distances are overestimated across regions (Hirtle and Jonides 1985).With regard to distances, it has also been demonstrated that Euclidian distances between two locations connected by a street are estimated to be shorter than distances between unconnected objects as a result of the Gestalt psychology (law of proximity or law of continuity), the so-called route effect (Klippel et al. 2005;McNamara et al. 1984).
Landmarks play an important role causing distortions in maps.Experimental studies showed that landmarks with different salience lead to an impaired distance estimation between them (Newcombe et al. 1999).Concretely, the distance from a less salient object toward a more salient object is underestimated.From the map reader's perspective, landmarks are more prominent than the surrounding objects (Bestgen et al. 2017;Hamburger and Röser 2014).Thus, landmarks are considered to be visual anchors that provide a spatial reference frame for the formation of mental models of the environment (Golledge 1993).Numerous studies confirm various effects of landmarks on navigation, orientation, and the mental representation of space (Deakin 1996;Denis and Loomis 2007;Kiefer et al. 2014;Lovelace et al. 1999;May et al. 2003;Ohm et al. 2014;Peters et al. 2010;Schwering et al. 2013;Steck and Mallot 2000).According to Bryant and Subbiah (1994), the so-called landmark attraction effect describes a systematic distortion of the spatial representations.This interferes with encoding the exact positions of map elements located in the areas between landmarks.Map elements in the vicinity of salient landmarks are remembered closer to the landmark then they actually were.
Such systematic distortions of cognitive maps show that the creation on modern maps should consider the cognitive processing by the map user.This presupposes suitable cartographic methods.
To prevent or at least reduce the distortions in the recall of spatial information, the effect of regular grid geometries superimposed on maps has been already repeatedly tested (Bestgen et al. 2017;Edler et al. 2015Edler et al. , 2019)).Grids are commonly used in maps for search tasks and practical reading of coordinate data.However, grids on maps have also been shown to improve performance in memory of object locations by providing an additional (artificial) layer of information structure (Edler et al. 2014) (Fig. 1).Especially, this is the case for maps with low and medium visual complexity.Due to the reduced number of spatial reference points in maps of low visual complexity, grids seem to be an important graphic reference element for users learning the positions of map objects (Edler et al. 2019;Keil et al. 2020).
Learning or recall might be enhanced by the grid fields, because they divide the map into regular areas that presumably are processed separately in the brain.
The grid or grid fields provide further information for spatial referencing of map elements.Previous studies have already shown that superimposed grids improve the distance estimation performance in maps (Bestgen et al. 2017;Dickmann et al. 2019).One reason for this effect might be the regularity of the grid pattern.Thus, grids seem to counteract the attraction of salient map elements, such as landmarks.
The term landmark, in this study, is understood as a salient point object in a map.We emphasize its geometrical function rather than any semantical expression within the represented topography.Grids that are reduced to small grid crosses (i.e., a regular point pattern) presumably contribute less to distortion prevention in object-location memory or distance estimation performance compared to full grid pattern.Single grid crosses, not connected by lines, may be perceived more as distinct, single map features (geometric landmarks) than as being part of a grid.This landmarklike character of grid crosses could result in diminishing of the stabilizing effect of grid lines.Additionally, due to the presumed perception as distinct single map features, grid crosses could act as landmarks, and therefore cause a landmark attraction effect.Thus, in maps only superimposed by grid crosses, the remembered object locations are assumed to be drawn closer to the nearest grid cross (landmark) than in maps with full grid lines.
In case of complete grids superimposed on maps (i.e., not only single grid crosses), no such attraction effect is expected.It seems even likely that an opposite distortion process will be dominant in this case.For visually delimited areas created in a map by grid fields, a central tendency bias as presented by Huttenlocher et al. (1991;2000) could affect memory processes.This distortion effect can be described by the categorical adjustment model (CAM) (Huttenlocher et al. 1991).According to this model, objects placed within a map area (here the area framed by complete grid lines), will be shifted toward the center of the superordinate area when recalled from memory (Fig. 2).The CAM describes the assumption that people use two types of spatial representations.The categorical spatial representation reflects the coarse spatial relations of objects to superordinate areas, e.g., a city within the borders of the belonging state.The other type of spatial representation is called coordinative, and emphasizes precise metric distances (Hurts 2005;van Asselen et al. 2008).In contrast to the coarse spatial representation, this fine-grained relationship refers to the position of an object to a neighboring object on the same representation level, e.g., the position of a building at a road intersection.If grid lines are used, which divide the map into regular areas, the spatial referencing is carried out according to the CAM on two different levels of spatial representation (cf.Huttenlocher et al. 1991).
According to this model, people who are worse in remembering fine-grained spatial positions rely more on the categorical representations, e.g., the affiliation of an object to a large area (Montello 2009;Wilton 1979).The spatial information seems to be hierarchically structured, i.e., the categorical information nests metric information (Holden and Newcombe 2013).The separate processing of these two qualities of spatial information is supported by studies suggesting that categorical relations are primarily processed by brain areas in the left hemisphere, while metric coordinate representations are encoded by the right hemisphere (Kessels et al. 2002;Kosslyn et al. 1989;Postma et al. 2004;van Asselen et al. 2008).
For map user, the recall of positions on the categorical level (superordinate area) is easier than on the precise fine-grain level (cf.Stevens and Coupe 1978).Due to the CAM, an estimation of an object's position is a cross-level combination of both estimations that are balanced according to their reliabilities.Under a Bayesian framework, both sources of spatial information are combined by weighting them, each source according to its reliability (expressed in smaller variances) (Cheng et al. 2007;Holden and Newcombe 2013;Huttenlocher et al. 1991).The weighting depends on the memory uncertainty to maximize the average accuracy of the estimate (Duffy et al. 2010; but see Duffy and Smith 2018).It can be assumed that the position of an object is estimated primarily on the basis of the location of the associated grid field (area framed by grid lines), to which the map object coarsely belongs.The position of the spatial object is assigned to the (superordinate) category grid field, and thus tends to be assigned to the center of the grid field when remembered.The probability of remembering the approximate position of the superordinate unit (i.e., the grid field as such) is expected to be significantly higher (cf.Stevens and Coupe 1978).This effect is probably more pronounced in less complex maps, e.g., maps depicting rural areas, because these maps show fewer map elements in the vicinity of the to-be-learned object position.This leads to fewer visual anchor points for the map user, reducing corrective effects.Studies have already shown the effect of decreasing memory for the precise object position with decreasing map complexity (Bestgen et al. 2017;Edler et al. 2014).In the case of map grids, it is expected that the position within the grid unit (categorical/coarse unit) leads to a shift of the remembered map elements toward the center of the grid field.The recalled object position (R) is then shifted toward the center of the grid field (category center).It can be assumed that this effect also arises within areas framed by grid lines.This spatial distortion is directed in the opposite direction of the landmark attraction effect.Thus, overlaid grids in maps could reduce the spatially interfering landmark attraction effect.
In addition to the memory processes, perception-based studies suggest that grid lines in maps already lead to push effects when map elements are fixated with the eyes.Dickmann et al. (2015) and Kuchinke et al. (2016) showed with  2010).The CAM describes the shift of remembered object position (from M to R) toward the center of the coarser (superordinate) map area to which the object is assigned eye-tracking experiments that eye movements seem to be pushed away from the grid lines, when a to-be-learned object is fixated (Fig. 3).It can, therefore, be assumed that grid lines already have a structuring function at the perceptual level, leading to a systematic deflection of gaze behavior away from the grid lines.The gaze is, thus, moved to the center of the area (grid field).This perceptual process could reflect or even supports the memory processes according to the CAM.
It seems there are two opposing grid-based biasing processes affecting memory performance during map reading.Due to the landmark attraction effect, the recall of object positions should be shifted toward salient objects, such as landmarks or grid crosses, during memory encoding and retrieval.On the other hand, the boundary lines of areas could lead to repulsion processes toward the center of the respective area.Both distortion processes could occur at the same time, thus causing distortions in memory.This could result in incorrect object positions recalled from memory.Object positions might be remembered too close to the landmark as predicted by the landmark attraction effect, whereas in the case of grids, the remembered object positions are shifted toward the center of the superordinate area they cartographically are part of.

Study Aim
The aim of the presented study is to examine the interaction of these opposing cognitive distortion processes for spatial learning and to improve the understanding of the underlying effects from a cartographic perspective.The focus of this empirical investigation is on the landmark attraction effect (Bryant and Subbiah 1994;Hubbard 2005) and the opposing push effect induced by grid lines according to the CAM (Huttenlocher et al. 1991).Using regular grid patterns plotted on maps in this study is interesting because previous studies have shown their memory enhancing effect.So far, it has not been clarified how both effects interact when reading a map.Insights into the effect and intensity of these cognitive biases could help to understand the mechanisms influencing spatial memory performance.
We assume that the influence of the respective type of bias depends on the design of the grids (see Fig. 4).If the landmark-like character of the grid superimposed on a map predominates the design as it is the case for grid crosses, the landmark attraction effect might lead to biased remembered object location toward the nearest grid cross.As the individual grid crosses are regarded as graphic elements in the sense of a geometric landmark, they might serve as visual anchor points to which objects in the immediate vicinity can be referred in terms of direction and distance.Therefore, the described landmark attraction effect set in, which leads to remembered object positions being recalled too close to the nearest grid cross.
The central tendency bias associated with delimitated areas would induce an opposite process.According to the CAM, map users adjust their estimation of object position to the average value of the fine-grained memory and the category center.
For grid crosses, we expect effects in the opposite direction.The extremely reduced grids, which appear as small single crosses in a regular pattern within the map area, reflect the character of landmarks.Therefore, the landmark attraction effect is expected, causing objects to be remembered closer to the nearest landmark than the correct location of the object.
Insights into the strength of the opposing distortion processes would make it possible to evaluate and predict distortions of object positions learned by map.Furthermore, the controlled use of one effect in a map might neutralize or at least reduce other effects.The arrangement of landmarks and grid in a map considering balanced push or pull effects could then prevent distortions in spatial memory.

Methods
The study was conducted in accordance with the Declaration of Helsinki (World Medical Association 2013).The used study design has been reviewed and approved by the ethics committee of the Faculty of Geosciences at the Ruhr University Bochum.All participants gave their written consent before inclusion in the study.Participation was rewarded with a payment of 5.00 €.

Participants
A total of 94 participants, mostly students, were tested, but three subjects had to be excluded from the analysis because two of them were not familiar with the German alphabet, so Fig. 3 Push effect of grid lines on gaze behavior in maps (Dickmann et al. 2015, p. 277) they could not solve the distractor task properly.One participant was excluded because remaining trials for analysis were more than three standard deviations away from mean.Ninety-one participants (thirty-four females, fifty-seven males) were left for analysis.The age ranged between 19 and 41 years (M = 25.52;SD = 3.80).All participants reported having normal or corrected-to-normal vision.

Materials
Sixteen different digital maps were created as study material.The scale of each map was 1/25,000.The maps represented the topography of 16 different places in Germany and were randomly assigned to the different trials.Map complexity was determined by lossless JPEG compressed file length (Donderi and McFadden 2005;Rosenholtz et al. 2007).Only rural maps were selected for the experiment, the average jpg file size was 622 kb (range 468-852 kb).
Two types of grids, continuous grid (full grid pattern) and discontinuous grids (single grid crosses), were added as an additional layer to the map (Fig. 5).The spacing between the horizontal and vertical lines of the presented full grid pattern and the grid crosses was 7 cm each.The offset of the presented grids to the border of the screen was randomized in each trial to prevent transfer effects between the different trials.

Procedure
Participants were invited after completing a questionnaire due to restrictions and health issues regarding the Covid-19 pandemic.Before the experiment, participants were informed about the procedure and were asked to give their written informed consent.The participants were randomly assigned to one of two groups at the beginning of the experiment.One half of the participants did the object-location memory task on rural maps, while the other half did the same task on blank backgrounds (no map, between-subject condition).In a within-subject condition, half of the participants within each group first saw eight trials with the full grid pattern and then eight trials with the grid crosses, while the grid patterns were presented the other way around for the other half of participants.The whole task was shown on a 24-inch computer screen.
All participants first did a practice run of the object-location memory task to get familiar with the experiment.In the practice trial, the object-location memory task was presented with a different spacing of grid or crosses with respect to the upcoming experiment on a map with a scale of 1/5000 or a blank background.The presentation of full grid pattern or grid crosses and map or blank background depended on the first trial of the upcoming experiment.The procedure in the practice run was the same as in the following test trials.
At the beginning of each trial, participants saw a fixation cross in the middle of the screen with a random presentation time between 2 and 3 s.Then the map or the blank background with the full grid pattern or the grid crosses was presented for 6 s in total.After 3 s, a red dot with a diameter of 0.4 cm with a black border was presented for 3 s.The minimum distance of the red dot to the map borders was 3.5 cm (half grid width).The dot represented the object location for the object-location memory task.Participants were instructed to remember the position of the dot as correct as possible.The presentation of the dot on the map/the blank background was followed by an alphabetical distractor task.Participants had to solve two trials where they had to press the button with the letter which followed a given letter in the alphabet by a given number of digits.Trials with incorrect answers were repeated.The experiment continued directly after the second trial was solved correctly.Then the blank background/map with the full grid pattern/grid crosses was presented again and participants had to recall the position of the presented dot as precise as possible using the computer mouse.Participants were allowed to correct the position as many times as they wanted.This phase of the experiment ended after 15 s.The end of the phase was indicated 3 s earlier with a beep tone allowing participants to (re-)place the dot and to prevent missing trials.Participants were allowed to end the phase self-paced by pressing the space button if they did not want to change the recall location anymore.The experiment consisted of 16 test trials, with a total experiment duration of about 15-20 min.

Statistical Analyses
All statistical analyses were done with jamovi 2.2.5.For all analyses, trials without any response of the participant were excluded.Trials with a recall position outside the grid field of the correct object location were excluded as well, because participants were assumed to be inattentive in these trials.Due to this criterion, 200 trials (13.8%) were excluded from analyses, 1,245 trials remained.Three different linear mixed models fit by REML were calculated.Post hoc tests were Bonferroni corrected and marginal means were calculated.The α-level was set to 0.05.
At first, the position error was calculated as the Euclidian distance between recalled and correct object location.Distance error served as the dependent variable and participant as the cluster variable (random coefficient).Grid condition (full grid pattern/grid crosses), map condition (map/no map), and the closest grid corner with respect to the correct object location (up left/up right/down left/down right) served as factors in the model.All possible interactions between these three factors were also fitted in the model.To check for ageand sex-related differences in performance, this model was calculated separate with and without the covariates sex and age.Normal distribution of residuals was tested with Kolmogorov-Smirnov tests.
Second, the impact of grid corners on the accuracy of the recalled object was analyzed to examine the push or pull effect of grid corners in full grid pattern and grid crosses.The error caused by the grid condition was calculated as the difference between the distance of the correct object location to the nearest grid corner and distance between the recalled object location and the nearest grid corner, hereafter referred to as grid error.Values below zero would indicate an attraction of the recalled object position toward the nearest grid corner with respect to the correct object location (pull effect).Values above zero would mean a greater distance between the recalled object location and the nearest grid corner than the distance between the correct object location and the nearest grid corner (push effect).The grid error served as the dependent variable in this linear mixed model.Cluster variable and factors were the same as in the position error model.This second analysis was also calculated separately with and without the covariates sex and age.The procedure was the same as in the model before.
Third, the center error was calculated for an exploratory linear mixed model.The center error was calculated similar to the grid error in the second model.While the nearest grid corner served as the reference point in the grid error model, the center of the associated grid field served as the reference point in this model.The grid error, therefore, was calculated as the difference between the distance of the recalled object location and the center of the grid field and the distance of the correct object location and the center.The center error served as dependent variable in the linear mixed model, participants as cluster variable.Grid condition, map condition, closest grid corner, and their possible interactions served as factors in the mixed linear model.The procedure was the same as in the position and grid error model.

Position Error
The mixed linear model on the position error (R 2 marginal = 0.138) revealed, in the fixed effect omnibus tests, significant main effects of grid condition (F(1,1147.8)= 13.538,p < 0.001) and map condition (F(1,85.9)= 66.033, p < 0.001), as well as a trend for closest grid corner (F(3,1204.7)= 2.596, p = 0.051).In addition, two different significant two-way interactions were observed: grid condition*map condition (F(1,1147.8)= 4.654, p = 0.031, see Fig. 6) and grid condition*closest grid corner (F(3,1197.7)= 3.610, p = 0.013).Post hoc comparisons showed significantly higher position error for full grid pattern compared to grid crosses (d (grids-crosses) = 0.2024, T(1147.8)= 3.679, p < 0.001), as well as a significantly higher position error for trials with blank background compared to a map (d (no map-map) = 0.6932, T(85.9) = 8.126, p < 0.001).No significant post hoc comparisons were found for closest grid corner.Post hoc comparisons revealed significant differences between all interactions of grid and map condition except the comparison of grid crosses and full grid pattern presented on a map (Table 1).
The post hoc comparisons for the significant grid condition*closest grid corner interaction revealed significant differences between grid conditions with respect to the closest grid corner.Additionally, it shows a significant difference between the closest grid corner down left and the closest grid corner up right for the grid condition (d (down lef-up right) = 0.34944, SEM = 0.108, T(1198) = 3.24269, p corr = 0.029).For the three-way interaction, many post hoc comparisons reached the level of significance.The intraclass correlation (ICC) for the random components (participants) was 0.0944.The residuals in this model were not normally distributed, as indicated by the Kolmogorov-Smirnov test (p < 0.001).As we have a relatively big sample size with 91 participants and focus on the unbiased fixed regression coefficients as well as variance components, biases in these coefficients and components are unlikely (Maas andHox 2004, 2005).The same model was also calculated with the additional covariates sex and age, which did not improve the R 2 marginal = 0.138.Moreover neither age (F(1,86.6)= 0.0139, p = 0.907) nor sex (F(1,84.6)= 0.5434, p = 0.463) reached the level of significance.Age and sex did not have any impact on the performance in this task.

Grid Error
The mixed linear model on the grid error (R 2 marginal = 0.0522) revealed, in the fixed effect omnibus tests, significant main effects of grid condition (F(1,1150.7)= 16.03,p < 0.001) and closest grid corner (F(3,1224.8)= 7.64, p < 0.001).Main effect of map condition was not significant (F(1,81.9)= 2.61, p = 0.110).In this model, only the two-way interaction between map condition and closest grid corner was significant (F(3,1224.8)= 3.62, p = 0.013).The three-way interaction as well as the both interactions with grid condition were not significant.Post hoc comparisons revealed a significantly higher grid error for full grid pattern compared to grid crosses (d (grids-crosses) = 0.2471, SEM = 0.0617, T(1150.7)= 4.003, p < 0.001) while both grid errors exhibited positive marginal means, as shown in Fig. 7.In both conditions, recalled object location tends to be distracted farther from the closest grid corner.
Post hoc comparisons for closest grid corner revealed significant differences between the grid corner down left and up left (d (down left-up left) = 0.2843, SEM = 0.0874, T( 1223   The ICC for participants was relatively low with 0.0328.With violations of the normal distribution, assumption of residuals was proceeded as described in the model with distance error.As in the analysis of distance error, we calculated a model with the covariates age and sex, too.We cannot see any impact of these two variables on the model (R 2 marginal = 0.0527; age: (F(1,83.8)= 0.209, p = 0.648; sex: (F(1,80.7)= 0.337, p = 0.563).

Center Error
As we did see a push effect of the full grid pattern, but not an attraction effect of grid crosses, we decided to calculate another (exploratory) mixed linear model on the center error to check for an attraction error of recall location toward the center of a grid field.The exploratory mixed linear model on the center error (R 2 marginal = 0.0337) revealed, in the fixed effect omnibus tests, significant main effects of grid condition (F(1,1149.3)= 11.126,p < 0.001) and closest grid corner (F(3,1224.6)= 5.353, p = 0.001).Map condition did not reach significance ((F(1,80.6)= 1.985, p = 0.163).The two-way interaction between map condition and closest grid corner showed a trend ((F(1,1224.6)= 2.563, p = 0.053).Post hoc comparisons revealed a significant lower center error for full grid pattern compared to grid crosses (d (grid-crosses) = -0.1524,SEM = 0.0457, T(1149.3)= − 3.336, p < 0.001), which means that recalled positions of objects showed higher attraction to the center in the continuous grid condition.Center error of full grid pattern exhibited negative marginal mean and center error of grid crosses exhibited a slightly positive marginal mean, as shown in Fig. 9.In the full grid condition, the object location was recalled closer to the center, while this was not the case for the grid crosses condition.
Post hoc comparisons for the significant main effect of closest grid corner revealed significant differences between the grid corner down right and the grid corner up left (d (down right-up left) = − 0.20987, SEM = 0.0664, T( 1227  Marginal means showed a push error toward the center of a grid field of recalled object locations for object locations placed in the bottom half.This was not the case for object locations in the upper two quadrants, which revealed slightly positive marginal means (Fig. 9).
The ICC of participants was relatively low with 0.0332.With violations of the normal distribution, assumption of residuals was proceed as described in the models above.As in the previous analyses, we also calculated a model with the covariates sex and age for the center error (R 2 marginal = 0.0344).Neither age (F(1,82.9)= 0.0499, p = 0.824) nor sex (F(1,79.9)= 0.6776, p = 0.641) revealed significance in the fixed effect omnibus tests.

Discussion
The results show that the distortions caused by both the landmark attraction effect and the central tendency bias seem to vary greatly in intensity.With respect to errors made by participants in this object-location memory task, it becomes clear that the landmark attraction effect and the central tendency bias do not affect spatial memory performance to the same extent.
With regard to central tendency bias, the analysis of position error shows significant differences in the strength of object-location memory distortions between the full grid condition and the grid crosses condition (landmark-like condition).The spatial memory performance is characterized by less distortions in the grid crosses condition compared to the full grid condition.This effect was predominantly driven by the blank background condition (no map) and, thus, can be clearly related to the grids that have been superimposed onto the maps in the experiments.In the full grid condition, a clear push effect of the nearest grid corner toward the grid field center can be observed, as predicted by the central tendency bias according to the CAM (Huttenlocher et al. 1991(Huttenlocher et al. , 2000)).The observed tendency for recalled object positions in the grid corner condition is not as clear as the push effect in the full grid condition.We could see a small push effect from the nearest grid corner and the center of the grid field as well.Therefore, we do not see any clear push effect toward the center for the recalled object location in this condition.
The studies on central tendency bias provide insights into the effect of grids on the level of detailed cartographic information, i.e., for the precise position of objects in a subarea of a map.On the one hand, superimposed grids in maps support position memory (Edler et al. 2014(Edler et al. , 2019) ) and distance estimation over larger map areas (Dickmann et al. 2019).On the other hand, they also seem to impair the learning and recall of absolute object positions within grid fields, especially on the fine-grain level.These problems that occur within the grid fields remain largely without consequences for distance estimation over large map distances, because the central tendency bias only affect the end points (object positions) of the given distance and not the whole route.However, the larger the estimated distance in the map (e.g., over many grid fields), the less the distortions in the estimation of end points locations affect the distance estimation result proportionally.
The requirements for the accuracy of the cognitive map are different, when the focus is on detailed cartographic information, e.g., when clarifying the distance from an intersection to the entrance of a multi-store car park.Within the same map at the same scale, encoding and recall take place on a smaller map area, e.g., within a grid field.The results show that the central tendency bias within the grid fields of the full grid pattern condition significantly impairs the absolute (coordinative) position determination of recalled object positions.This is especially the case when only a few other map elements are available as visual anchor points.As described by the CAM, it can be assumed that recalled location (R) will be distorted toward the center of a grid field (p) (Fig. 2).In such tasks, superimposed grids might have a negative effect on object-location memory.In the grid crosses condition, however, the central tendency bias cannot be found.The absence of complete grid lines and the use of grid crosses could be an advantage for object-location memory in the small-scale perception of map information.
In contrast to our hypothesis of an attraction error toward the nearest grid cross (corresponding to the landmark attraction effect), we instead found a push effect away from the nearest grid corner in the grid cross condition.In this condition, no direct evidence for a pure landmark attraction effect as described by Bryant and Subbiah (1994) could be found.However, it is noticeable that the (unexpected) push effect is significantly weaker than in the condition with a complete grid.Therefore, it cannot be ruled out that this significantly less pronounced push effect in the grid crosses condition might arise due to a mixture of the landmark attraction effect and the central tendency bias.The significantly lower push effect compared to the full grid condition is possibly the result of the two opposing shift effects.The intensity of the landmark attraction effect (if any) seems not to be able to eliminate the central tendency bias, but to mitigate its strength.The results of our study suggest that the two opposing cognitive effects partially cancel each other out.These assumptions are supported by the better spatial memory performance of the participants in the grid cross condition and the observed push effect away from the grid center in the center error analysis for grid crosses.Compared to the spatial distortions caused by the central tendency bias in the full grid condition, the distortions in the grid cross condition are much smaller.One possible reason for the absence or weakness of the landmark attraction effect is probably the lack of perception of the grid crosses as landmarks.Due to their uniform and insufficiently (semantically) salient appearance (Keil 2021), the grid crosses seem to be graphically no more conspicuous than the surrounding topographic objects on the map (Bestgen et al. 2017;Hamburger and Röser 2014).This seems to weaken potential landmark attraction effects.Obviously, the grid crosses in our experimental design only serve as visual anchors.They can only take on the function of landmarks to a limited extent, which prevents the emergence of a more intensive attraction effect.The perception of the geometrically arranged grid crosses as map symbols may then be based more on principles of Gestalt psychology (Dickmann 2021, p. 131;MacEachren 2004, p. 69).According to the Gestalt principles (law of closure), the regular rectangular pattern of the grid crosses might lead to the perception of a full grid, even if the grid is in fact incomplete (Dickmann et al. 2017).Then four grid crosses might be perceived more as a closed grid field and are less considered as single landmarks.This would prevent the emergence of a more pronounced attraction effect in favor of the central tendency bias.Future studies would have to test this assumption with the help of more salient landmarks.
The observed bias effects seem to be influenced by the complexity of the maps, as the comparison between the map condition and the blank background condition (no map) shows.Position errors are significantly higher in trials with a blank background.The object-location memory performance increased when a map is displayed in the background, presumably, because further visual clues are available.The results, thus, replicate the findings of other studies investigating the impact of map complexity (Bestgen et al. 2017;Edler et al. 2014).In principle, distortions for the mental representation of space seem to be reduced when a larger number of (topographic) elements are represented in a map.
Another surprising result concerns the unevenly occurring push effects regarding the different positions of the nearest grid corner in both grid conditions.The push effects of the lower corners are significantly higher compared to the two upper corners.A comparison between the left and the right corners revealed no significant differences regarding the push effect from the sides of these corners.This effect might be due to the reading direction of participants or due to the horizontal grouping of spatial information in the absence of other visual cues (Eastman 1985).This effect would have to be investigated in further studies to be able to derive conclusions for the map design.

Conclusion
Cognitive biases such as the central tendency bias or the landmark attraction effect influence the learning and recall of map information, especially for small-scale information.
The results of our study show how the use of complete grids or simple grid crosses has different effects on object-location memory.The expected attraction toward the nearest grid corner-according to the landmark attraction effect (Bryant and Subbiah 1994;Newcombe et al. 1999)-could not be proven in this study.The use of grid crosses leads to less systematic distortions regarding the recalled object position compared to the continuous grid pattern, but the expected attraction toward the grid crosses cannot be seen.When grid crosses are perceived as a complete grid pattern, no landmark attraction effect can be detected that is capable of causing a shift of a recalled object position toward a landmark (grid cross), because the central tendency bias is dominant.Therefore, the results can only partially confirm the assumptions, that two opposing distortion processes can be induced in the mental representation of space using different grid designs (complete grids vs. grid crosses).Results show a strong influence of the central tendency bias, even in the grid cross condition.
Nevertheless, the landmark attraction effect can have an influence on the accuracy of the remembered object position.Even if the expected reversal of the position shift in the direction of the grid crosses could not be demonstrated, the results of the investigation show that the use of (landmarklike) grid crosses instead of complete grids is accompanied by a clear mitigation of the position errors.It cannot, therefore, be completely ruled out that an opposing mechanismsuch as the landmark attraction effect-does not contribute to significantly less pronounced distortions.
In any case, the results show that in cartographic methods, such as the insertion or omission of grids in maps, it is possible to influence the accuracy with which spatial information is perceived and remembered.The exact conditions for the containment of distortions must be worked out in further studies.
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Fig. 2
Fig. 2 Modified categorical adjustment model (CAM) according to Duffy et al. (2010).The CAM describes the shift of remembered object position (from M to R) toward the center of the coarser (superordinate) map area to which the object is assigned

Fig. 4
Fig. 4 Visualization of the direction of the hypothesized distortion effects caused by the different designs

Fig. 5
Fig.5Stimulus conditions.Background type (map or blank background) was a between-subject condition.Grid type (full grid or grid crosses) was a within-subject condition.The offset of the grids to the screen borders was randomized

Fig. 6
Fig. 6 Interaction effect of grid and map condition in the position error model visualized by marginal means.All comparisons except map*grid/ map*crosses are significant.***p < 0.001.
) = 3.252, p corr = 0.007) and a trend between the grid corner down left and up right (d (down left-up right) = 0.2248,

Table 1
Comparisons for interaction effect of grid and map condition