Acta Psychologica 64 (1987) 151-166 North-Holland

151

MEMORY FOR SPATIAL LOCATION IN TWO-DIMENSIONAL ARRAYS *

Erik LINDBERG and Tommy GARLING University of Umeb, Sweden

Accepted December 1985

Memory for spatial location in a two-dimensional display was studied in two experiments by means of a recognition task. The fist experiment investigated the effects of presenting multiple reference points at the same time as sequentialIy shown to-be-remembered (TBR) locations. In the second experiment, the TBR locations were presented either one by one or four at a time with and without multiple reference points. The reference points tended to decrease the false alarm rate during acquisition, rather than to increase the hit rate, which suggests that they affected the precision rather than the amount of systematic bias in memory for the locations. Similar effects were obtained when the TBR locations were presented four at a time. The reference points were also found to serve as effective retrieval cues in a final recognition test. Reference points may thus facilitate both acquisition and retrieval of information about spatial location.

Acquiring information about the spatial location of objects and places is an important psychological ability which comes into play in many of our everyday transactions with the environment. The extensive literature on cognitive mapping (see Evans 1980, Russel and Ward 1982, for reviews) has been dealing with the internal representation of locational information about the large-scale physical environment. This type of research, together with research on visual imagery (e.g., Cooper and Shepard 1978; Kosslyn 1980; Shepard 1975), and laboratory experiments on memory for spatial location in two-dimensional stimu- lus displays (e.g., Attneave and Curlee 1977; Finke and Pinker 1982; Mandler et al. 1977; Nelson and Chaiklin 1980), has shown that people

* The present research was supported by grants No. F186/79 and F83/81 from the Swedish Council for Research in the Humanities and Social Sciences. Thanks are due to Jot&o S&8 for assistance in collecting the data.

Requests for reprints should be sent to E. Lindberg, Dept. of Psychology, University of Ume&, S-901 87 Urn&, Sweden.

0001-6918/87/$3.50 8 1987, Elsevier Science Publishers B.V. (North-Holland)

152 E. Lidberg, T. Giirling / Memory for spatial location

are able to acquire and manipulate information about locations in three-dimensional as well as in two-dimensional space.

A major issue in the study of spatial knowledge concerns the degree of accuracy with which spatial locations are represented in memory. That internally represented spatial relations may be distorted when compared to their external counterparts is witnessed both in studies of cognitive mapping (Milgram and Jodelet 1976; Stevens and Coupe 1978; Tversky 1981) and of perception (Indow 1968). One factor which has been found, or assumed, to affect the accuracy with which spatial locations are recalled, both in cognitive mapping studies (Sadalla et al. 1980) and in studies of short-term memory for spatial location in two-dimensional displays (Nelson and Chaiklin 1980), is the presence of reference points (or ‘landmarks’). According to Sadalla et al. (1980), spatial reference points provide an organizational structure which facilitates the localization of adjacent points in space. Similarly, the Weighted-Distortion theory of Nelson and Chaiklin (1980) postulates that the accuracy of spatial memory is a monotonically decreasing function of the physical distance between the to-be-remembered (TBR) spatial location and a reference point. Empirical evidence in support of this contention is, however, at least partly, still lacking. Whereas the experiments of Sadalla et al. (1980) demonstrate a number of func- tional differences between reference and non-reference points, they do not provide any data showing that the reference points actually facili- tate the recall of spatial location. Further, although their theory is not, the empirical work by Nelson and Chaiklin (1980) is limited to a short-term memory condition with only one reference point. In ad- dition, localization accuracy could in the latter study vary only towards or away from the reference point along a straight line, making the study one of memory for spatial location in one rather than two dimensions.

The aim of the present study was to investigate the role of reference points for memory for spatial locations on a two-dimensional surface. The present research adds to the findings of Nelson and Chaiklin (1980) by representing a true two-dimensional case, by studying both acquisition and retrieval, and by including multiple reference points. Whereas those authors used a reproduction method and avoided arbi- trary metric assumptions about the nature of spatial representations by considering only ordinal aspects of their data, the present study avoids such assumptions by using a recognition method. Further, since

E. Un&rg, T. Gdrling / Memory for spatial location 153

spatial-memory performance has been found to be influenced by gen- eral knowledge of everyday spatial relations among objects (Mandler and Parker 1976), and since the focus of the present study is on basic spatial processes, abstract dots with no preassigned meaning were used as stimuli. This kind of stimuli should also eliminate possible effects of linguistic factors, such as those indicated by the finding that recall of building locations in a scale model of a city could be improved by pairing each building with a verbal label (Pezdek and Evans 1979).

Experiment 1

This experiment was designed to investigate whether reference points facilitate the acquisition and retrieval of other spatial locations. Different locations, denoted by small asterisks, were presented sequentially on the screen of a computer terminal. Some of these locations were presented several times (TRR locations), others only once (hues). The subject’s task was to decide on each trial whether the location presented had been seen before. In one condition, each location was presented alone except for a small circle denoting the center of the stimulus display; in another condition, four additional reference points were presented with each stimulus location.

If reference points have the facilitating effect suggested by Sadalla et al. (1980) and Nelson and Chaiklin (1980), the TBR locations should be easier to learn in the condition with the larger number of reference points. More precisely, increasing the number of reference points (and distributing their locations across the display) reduces the average distance between each TBR location and the nearest reference point, which, according to the theory of Nelson and Chaiklin (1980), should lead to a more accurate memory representation of the TBR locations.

In the present experiment, the reference points were presented on every trial and they were arranged symmetrically along the principal axes of the stimulus display at equal distances from the center. They could therefore be expected to become well-known to the subjects, and removing them from the stimulus display after the TRR locations have been learned might not affect recognition performance. However, if the reference point locations are remembered inaccurately, the presentation of the reference points may provide extra retrieval cues and removing them should in the case lead to a decrement in performance. In order to test this suggestion, the subjects in experiment 1 were given a final recognition test in which the additional reference points were removed for half of the subjects who saw these reference points in the first phase. As a precaution against the possibility that the additional reference points may introduce some kind of response bias (by, e.g., causing the subjects to believe that the TBR locations are in some way systematically related to them), they were also presented to half of the subjects in the condition without these reference points in the first phase of the experiment.

In line with the prediction concerning the first phase of the experiment, recognition performance in the second phase should be better in the two conditions with multiple

154 E. Lindberg T. Giirling / Memory for spatial location

reference points in the first phase. The very best performance could be expected in the condition with multiple reference points in both phases, since the reference points in the second phase in that condition should serve as retrieval cues to the memory representation acquired in the first phase. For the subjects without additional reference points in the first phase, finally, the conditions with and without these reference points in the second phase were not expected to differ.

Method

Apparatus and materials The experiment was run on-line on a PDP 11/44 computer. The subject was seated

in a light-proof booth with a Volker-Craig VC4152 CRT-terminal in front of him/her. The lighting in the booth was reduced and directed to the keyboard of the terminal. The terminal display was tilted so that the subject was looking at it at a right angle from a distance of 45 cm. A black mask, in which a circle with 6.5 cm radius had been cut out, was mounted on the display. Within this circular frame, a large number of perceptually clearly separable locations were defined as shown in fig. 1, the shortest

. l .

. . l l . . . . .

. . . . . . . . . .+.y.. . .

. . . . . . . . . . 0 l . .o* . .

. . l . . .*.* . . . . .

. . . . . . . . . . . . . . . . . . .

. l . . . .*(t*. . . .

l . . 0 . . . . . . . . .

Fig. 1. Locations of the reference points, TBR items, and lures in the display.

E. Litulberg, T, Giirling / Memory for spatial locution 155

distance between any pair of locations being 0.7 cm. From this set, 16 locations distributed across a large portion of the display were defined as TBR locations. The remaining locations (except for the reference point locations) were used as lures in the recognition tests of the TBR locations. The TBR locations and the lures were presented as asterisks, the center of the display and the additional reference points (also shown in fig. 1) as small circles.

Procedure Twenty trials were given in order to familiarize the subjects with the general

procedure of the experiment. On each trial, the word ‘Yes’ or ‘No’ appeared in the display, and the subject responded by pressing one of two keys in the keyboard. The subject pressed the ‘No’-key and the ‘Yes’-key with his/her right index and middle finger, respectively.

After these preliminary trials, the 16 TBR locations and 52 randomly selected lures were presented one at a time in the display. Each TBR location was presented five times, the lures only once. The five presentations of each TBR location were separated by 0, 1, 4, and 16 intervening trials on which either other TBR locations or lures were presented. The number of intervening trials was balanced across,different numbers of previous presentations. The presentation order of the lures was randomized individu- ally for each subject. For each location presented, the subjects had to decide whether or not they had seen it before and then give a ‘Yes’ or ‘No’ response in the same way as in the preliminary trials. The subjects were instructed to try to learn as exactly as possible the locations which appeared more than once, and they were also told that they would subsequently be tested for these locations.

The beginning of each trial was signalled by a tone. Immediately thereafter the midpoint of the display and either a TBR location or a lure appeared in the display. In the condition with additional reference points, these appeared at the same time as the midpoint. The presentation lasted for 4 set, then went off for 2 set before the next trial was initiated, thus giving the subject 6 set to respond. In all, this phase of the experiment lasted for about 13 minutes. After the first phase of the experiment proper, the subjects were given a one-minute pause. They were during that time given more detailed instructions about the final recognition test. The 16 TBR locations and 16 new lures (not previously used) were then presented once. The presentation order was randomized individually for each subject. The subjects were told in advance that half of the locations would be those which they had seen several times before and that the remaining half would be entirely new ones. The presentation was self-paced, but otherwise the procedure was the same as in the preceding phase. For each of the two conditions in the first phase (with/without multiple reference points), half of the subjects were presented the reference points in the second phase whereas the remaining half were not. Depending on how fast the subjects responded, the second phase of the experiment lasted for between 1 and 5 minutes.

Subjects Forty-eight high-school students and undergraduates participated as subjects. Six

men and six women were randomly assigned to each of the four conditions (with/without multiple reference points in phase I x with/without multiple reference points in phase II).

156 E. L.inakg, T. GWng / Memory for spatial location

Results

The proportion of failures to respond within the 6-set time limit in the first phase of the experiment, was less than 0.005 in all conditions.

The numbers of hits and false-alarms were analyzed separately for each phase of the experiment. The interpretation of the results for these dependent variables is, however, complicated by the fact that yes/no-recognition procedures confound memory perfor- mance with effects due to the response criterion. What is needed, then, is a measure that assesses performance uncontaminated by criterion effects (like, e.g., d’ in Signal Detection Theory). In a recent article, Nelson (1984) compares different measures purporting to accomplish this and clearly identifies the Goodman-Kruskal gamma correlation as the most appropriate for the present type of data (if A = hit rate x true-rejection rate, and B = miss rate X false-alarm rate, Gamma is obtained as (A - B)/(A + B)). Unlike d’, for instance, this measure does not require assumptions about the underlying distributions. Gamma correlations were therefore computed for each subject in each phase and subjected to analyses parallelling those for the hits and false-alarms.

The number of hits in phase I was subjected to an ANOVA (with/without multiple reference points in phase I x with/without multiple reference points in phase II x sex x number of intervening items X number of presentations, with repeated measures on the last two factors). As revealed by a significant interaction between the reference point conditions in phase I and II, F(1,40) = 6.44, p < 0.05, the hit rates in phase I were not quite comparable for the groups treated identically in that phase but differently in phase II. Tests of simple effects showed tbat only the two groups without multiple reference points in phase I differed reliably (p < 0.05), the group which was later given these reference points in phase II having somewhat fewer hits than the other group (hit rates = 0.83 and 0.87, respectively).

The subjects with multiple reference points in phase I had slightly higher hit rates than those without (hit rates = 0.87 and 0.85, respectively), but the difference did not reach significance (F(l, 40) = 1.95, p < 0.25). The reference point conditions in phase I did, however, affect the hit rates at the second presentation of the TBR locations for 4 and 16 intervening items, F(9, 360) = 1.93, p < 0.05, but the differences disappeared with additional presentations of the TBR locations (see fig. 2). Hit rate increased with the number of presentations, F(3, 120) = 43.55, p i 0.001, and with decreasing num- bers of intervening items, F(3, 120) = 70.78, p c 0.001. These two factors also inter- acted, F(9, 360) = 4.76, p < 0.001, due to the fact that the effect of the number of presentations was strongest for 16 and 4 intervening items (p c 0.001) and did not reach significance when there were no intervening items.

Another two ANOVAs with the same between-subjects factors were carried out for the number of false-alarms and the gamma correlations in phase I. The subjects with multiple reference points in phase I produced significantly fewer false-alarms than those without, F(1, 40) = 16.11, p < 0.001 (false-alarm rates = 0.25 and 0.37, respec- tively), and had also significantly higher gamma correlations, F(1, 40) = 19.60, p <

0.001, (0.90 as compared to 0.82). The number of hits and falsealarms and the gamma correlations in phase II were

subjected to ANOVAs with the same between-subjects factors as in the preceding

E. Lindberg, T. Giirling / Memory for spatial location 157

One Reference Point

1 ’ I I I I 2 3 4 5

Number of

Multiple Reference Points

I I I I I J

2 3 4 5

Presentations

o---O no intervening items

6--Q , II II

o+) 4 II I,

-16 ” ”

Fig. 2. Hit rate in phase I (experiment 1) as a function of number of presentations for different numbers of intervening items in the conditions with and without multiple reference points.

analyses. As can be seen in table 1, the subjects with multiple reference points in both phases performed best on all three measures. The reference point conditions in phases I and II interacted for the number of hits, F(l, 40) = 6.08, p < 0.05, the hit rate being

Table 1 Hit rates, false-alarm rates and gamma correlations in phase II (experiment 1).

Multiple Multiple reference points in phase II reference points in phase I

Yes No

Hits

Yes

0.74 0.63

No

0.58 0.66

False-alarms Gamma

Yes No Yes No

0.39 0.47 0.63 0.23 0.55 0.56 0.18 0.22

158 E. Linak-& T. Giirling / Memory for spatial location

raised reliably by multiple reference points in phase II when these reference points had also been presented in phase I (p < 0.01). The number of false-alarms was significantly lower in the conditions with multiple reference points in phase I, F(l, 40) = 8.15, p < 0.001, and was also reliably affected by the interaction between the reference. point conditions in phases I and II and the sex of the subject, F(1, 40) = 4.16, p < 0.05. In the conditions with multiple reference points in phase I, the women had more false-alarms than the men when only one reference point was presented in phase II (false alarm rates = 0.55 and 0.39, respectively), whereas the reverse was true when the multiple reference points were presented in that phase (false-alarm rates = 0.32 and 0.45, respectively). The analysis of the gamma correlations, finally, yielded a significant effect of reference point condition in phase I, F(1, 40) = 6.54, p < 0.05, which was modified by reference point condition in phase II, F(1, 40) = 6.11, p -Z 0.05. Post-hoc tests by the Tukey method showed that the group with multiple reference points in both phases had significantly higher gammas than the remaining three groups, and that the latter groups did not differ reliably.

Discussion

The prediction that multiple reference points should facilitate the acquisition of the TBR locations was confirmed by the gamma correlations in the first phase of experi- ment 1. The notions of Sadalla et al. (1980) and Nelson and Chaiklin (1980) concerning the role of reference points for spatial memory thus received general support from the present phase I data.

The facilitating effect of multiple reference points on performance, as indicated by the gamma correlations, was matched by a decrease in false-alarm rate but not by an increase in hit rate. This may in part have been due to a ceiling effect for hit rate, but at least for the cases with 4 and 16 intervening trials there should have been room for further improvement. In interpreting this result, it may be fruitful to distinguish between two aspects of spatial memory (e.g., GXrling et al. 1981; Lindberg 1984; Lindberg and GKrling 1982, 1983). The first of these aspects, which will be referred to as ‘bias’, concerns the degree of mismatch between the memory representation of a given TBR location and the true location of that TBR item in space. The second aspect, here termed ‘precision’, refers to the degree of exactness with which a location is represented in memory. The degree of precision could be thought of as (inversely related to) the size of an area within which the subject is unable to discriminate between a subjective TBR location and lures and hence responds ‘Yes’ to all occurring stimuli, the amount of bias as the extent to which the center of gravity of this area deviates from the true TBR location. A high hit rate could then be due either to small bias, low precision, or both, whereas a low false-alarm rate would seem to presuppose a high degree of precision. The present fmding that the multiple reference points reduced the false-alarm rate without increasing the hit rate therefore indicates that the precision of the memory representation was increased without the degree of bias being notably affected. However, since a less precise representation makes it possible to have large biases but still obtain a large number of hits, bias may also have been decreased somewhat by the multiple reference points.

The notion that reference points may act as retrieval cues received support from the

E. Lidberg, T. Giirling / Memoy for spatial location 159

results in the second phase of the experiment. As shown by a general decrement in performance, some forgetting undoubtedly occurred from the first to the second phase in all conditions. This decrement was however, at least partially, counteracted in the condition with multiple reference points in both phases. In contrast, when the multiple reference points were removed in the second phase, the gamma correlations did not differ from those in the condition without multiple reference points in phase I. A possible explanation of this result could be that the TBR locations were learned relative to the reference point locations with little bias and a high degree of precision in phase I, but that the locations of the reference points themselves were remembered impre- cisely and/or with some bias (in spite of their symmetrical spatial arrangement). If the locations of the reference points were misjudged when the latter were removed in the second phase, this would bias the ‘subjective’ TBR locations and therefore decrease the number of hits, and, to the extent that the lures happened to coincide with the subjective (erroneous) TBR locations, increase the number of false-alarms.

Finally, the false-alarm rates in phase II suggest that the performance of the female subjects may to a larger extent than that of the males be dependent on the presence of multiple reference points. It could be speculated, that this finding may be related to the fact that sex differences indicating a slight male superiority are often found in studies of memory for spatial location in two-dimensional displays (where multiple reference points are rarely provided), whereas most research on the cognitive mapping of large-scale environments (where, at least potentially, the number of reference points may be quite large) has found no sex differences (Evans 1980).

Reference points thus seem to play an important role for the acquisition and retrieval of information about spatial location. The present experiment is however limited to the case with sequentially presented TBR locations. Another case, which should also be of interest, is when several TBR locations are presented simultaneously, since some of these TBR locations may be easier to learn and may therefore act as reference points for the representation of the remaining ones.

Experiment 2

If, as indicated by the results of experiment 1, single TBR locations are learned relative to the locations of reference points which are simultaneously present in the stimulus array, multiple TBR locations which are presented at the same time could be assumed to be learned relative to one another in a similar fashion. Simultaneously presented TBR locations may thus, like multiple reference points, be expected to yield a more precise (and perhaps, although not necessarily, a less biased) representation of the individual TBR locations. As compared to a condition in which these locations are presented one by one without multiple reference points, the number of false-alarms should therefore be expected to be lower, whereas the hit rate may not show the same advantage.

The assumption that simultaneously presented TBR locations have an effect similar to that of multiple reference points further suggests that the latter would be more or less redundant and that their effects therefore should be reduced as compared to the case in which only one TBR location is presented at a time. Thus, whereas multiple

160 E. Lindberg, T. G&ling / Memory for spatial location

reference points were found to increase the precision with which singly presented TBR locations are represented, the same needs not be the case with simultaneously presented ones. Similarly, the effectiveness of multiple reference points as retrieval cues may be reduced after the simultaneous presentation of multiple TBR locations.

In order to test these hypotheses, TBR locations were in experiment 2 presented four at a time in two conditions, one with and one without multiple reference points. The procedure was otherwise similar to that of experiment 1.

Method

Materials and procedure The TBR locations and the lures were the same as in experiment 1, but they were

now presented four at a time, thus forming 4 different patterns of TBR locations and 13 different patterns of lures. The individual locations which were presented simulta- neously were selected so as to form irregular patterns with at least a moderate degree of spatial dispersion.

The experiment comprised the same two phases as experiment 1. On each trial in ‘the first phase, a TBR or a lure pattern was presented for 16 set, then went off for 2 set before the next trial. Thus, whereas the number of trials was reduced to one fourth of that in the preceding experiment, the time allowed for inspection of each individual TBR location in the patterns was the same. In the condition with multiple reference points, the same reference point locations as in experiment 1 were presented together with the patterns. In all, this phase of the experiment lasted for about 10 minutes.

In the second phase, recognition of individual TBR locations was tested in the same way as in the preceding experiment. The subjects with multiple reference points in the first phase were presented these reference points in this phase as well, whereas the remaining subjects were not. The procedure was in all other respects identical to that of experiment 1.

Subjects Another 24 high-school students and undergraduates served as subjects. Six men

and six women were randomly assigned to each of the two conditions (with/without multiple reference points in both phases of the experiment).

Results

In order to test whether simultaneously presented TBR locations and multiple reference points have similar effects, hit and false-alarm rates and gamma correlations were analyzed together with those of the two conditions with and without multiple reference points in both phases of experiment 1. ANOVAs were carried out with three between-subjects factors (number of reference points x number of locations presented at a time in phase I x sex), the within-subject factors being the same as in the preceding experiment.

The proportion hits in phase I is shown in fig. 3. Multiple reference points and sex had no reliable effects, and the data in the figure have therefore been collapsed across

E. findberg T. Giirling / Memory for spatial location 161

One TBR Location

1 1 I I

2 3 4 5

Number of

o--O no intervening items

- , II 1,

o-_o 4 II 1,

-16 ” ”

Four TBR Locations

2 3 4 5

Presentations

Fig. 3. Hit rate in phase I (experiment 2) as a function of presentations for different numbers of intervening items in the conditions with one and four TBR locations at a time.

these factors. When the TBR locations were presented one at a time, the proportion hits was higher, F(l, 40) = 27.41, p -Z 0.001, but this effect became weaker with increasing numbers of presentations, F(3, 120) = 3.50, p < 0.05, and failed to reach significance after the final presentation. As in experiment 1, hit rate increased with increasing numbers of presentations and with decreasing numbers of intervening items, F(3, 120) = 24.00 and 33.42, p < 0.001. The effects of the latter factor decreased with increasing numbers of presentations, F(9, 360) = 2.22, p < 0.05. A three-way interac- tion between these two factors .and the number of simultaneously presented TBR locations was also obtained, F(9, 360) = 2.18, p < 0.05, due to the two-way interaction between the first two factors being reliable only in the condition with presentation of four TBR locations at a time.

As shown in table 2, the false-alarm rate in phase I was lower and the gamma correlations were higher in the condition with simultaneously presented TBR locations, F(l, 40) = 50.92,. p < 0.001, and F(l, 40) = 4.70, p < 0.05. Multiple reference points also tended to reduce the false-alarm rate, but this effect did not reach significance, F(1, 40) = 3.67, p < 0.10. The two factors did, however, interact reliably, F(l, 40) =

162 E. Lidberg. T. Giirling / Memory for spatial location

Table 2 False-alarm rates and gamma correlations in phase I (experiment 2).

Multiple Number of TBR locations presented at a time reference points

False-alarms

One Four

Gamma

One Four

Yes 0.24 0.09 0.92 0.92 No 0.38 0.07 0.84 0.95

Table 3 Hit rates, false-alarm rates and gamma correlations in phase II (experiment 2).

Multiple reference points

Number of reference points presented at a time in phase II

Hits FalZ3e-aknl.Y Gamma

One Four One Four One Four

Yes 0.74 0.56 0.39 0.35 0.63 0.40 No 0.66 0.62 0.56 0.42 0.22 0.38

6.21, p < 0.05, due to the fact that the multiple reference points reduced the false-alarm rate when the TBR locations were presented one by one (p < 0.01) but not otherwise. Finally, the effect of multiple TBR locations on the gamma correlations tended to be restricted to the conditions without multiple reference points, F(l, 40) = 3.96, p < 0.06.

In phase II, the hit rate was higher when the TBR locations had been presented one by one in the first phase, F(l, 40) = 12.86, p < 0.01, but this effect was modified by the multiple reference points, F(l, 40) = 5.85, p < 0.05, reaching signitkance only when the latter were presented (p < 0.001) (see table 3). The false-alarm rate was lower both when four TBR locations had been presented at a time, F(l, 40) = $24, p < 0.05, and when multiple reference points were presented, F(l, 40) = 7.76, p < 0.01. The gamma correlations, finally, were higher when multiple reference points were presented, F(l, 40) = 5.84, p < 0.05, but this effect was restricted to the conditions in which the TBR locations were presented one by one, F(1, 40) = 4.69, p < 0.05.

Discussion

The gamma correlations in phase I confirmed the prediction that the simultaneous presentation of multiple TBR locations facihtates the acquisition of these locations. The prediction that multiple TBR locations would reduce the effects of multiple reference points also received some support in that the latter tended to affect perfor- mance only when the TBR locations were presented one by one. Like in the precedmg experiment, the effects obtained for the gamma correlations were matched by similar effects on falssalarm rates but not on hit rates, which, as argued previously, indicates that the precision of the memory representation is affected.

E. Lindberg T. Giirling / Memory for spatial location 163

The learning curve for hit rates in phase I (see fig. 3) looked quite different for the conditions with presentation of one and four TBR locations at a time. Although they reached about the same proportion of hits after the final presentation, initial hit rates were substantially lower in the latter condition. It is, however, difficult to compare the proportion hits in phase I in the conditions with presentation of one and four locations at a time. Missing a few TBR locations in the former condition would, of course, lower the hit rate somewhat, but the same number of missed locations could in the latter condition have lead to several whole TBR patterns being missed, thereby yielding a more dramatic decrease in hit rate. Thus, if the subjects had a strict criterion for giving ‘yes’ responses to the TBR patterns, possibly involving recognition of all four locations in each pattern, this may have accounted for the superiority of the individually presented TBR locations.

As predicted, presenting four TBR locations at a time in phase I reduced the falsealarm rate in phase II without increasing the hit rate, which indicates that the TBR locations in this case were represented with a higher degree of precision than when they were presented individually. In this respect then, multiple TBR locations seem to have had an effect similar to that of multiple reference points. In contrast, the effects on the hit rate in phase II differed, the multiple TBR locations tending to decrease the proportion hits, the multiple reference points to increase it. This finding should not be surprising, however, since the TBR locations were always presented one by one during the recognition test in phase II. A similar decrease in hit rate was found in experiment 1 when the multiple reference points were removed in the second phase, and the explanation in terms of a precise but biased representation which was offered for that finding should be equally applicable to the present case.

The hypothesis that multiple TBR locations would reduce the effectiveness of multiple reference points as retrieval cues received support from the gamma wrre- lations in phase II. The phase II hit rate was also significantly lower in the condition with both multiple reference points and multiple TBR locations than in the condition with the former only. The finding that the reduction in phase II false-alarm rate with the presentation of multiple reference points tended to be less when the TBR locations had been presented four at a time in phase I did, however, not reach significance. Thus, whereas the effectiveness of multiple reference points as retrieval cues seems to be reduced by the simultaneous presentation of multiple TBR locations, they may still contribute to the degree of precision with which TBR locations are represented in memory.

General discussion

The paradigm employed in the present study has made it feasible to extend the findings of Nelson and Chaiklin (1980) to a true two-dimen- sional case and to conditions involving multiple reference points and multiple simultaneously presented TBR locations. The results of the study generally supported the notion that reference points play an

164 E. Lindberg, T. Gsirling / Memory for spatial location

important role in memory for spatial location (Nelson and Chaiklin 1980; Sadalla et al. 1980). The finding that the reference points tended to decrease the number of false-alarms during acquisition, rather than to increase the number of hits, further suggests that this role may mainly be one of increasing precision rather than decreasing bias in memory for location. The reference points were also found to serve as efficient retrieval cues in the final recognition test. Reference points thus seem to facilitate both acquisition and subsequent retrieval of information about spatial location. The function of the reference points may be similar to that ascribed to the ‘skeletal’ image in the theory of Kosslyn (1980) about the internal representatipn of visual images. According to that theory, one constructs a visual image by first retrieving the ‘skeleton’ (i.e., a set of reference locations) and then adding finer details (by retrieving additional features, or TBR loca- tions, and placing them in their appropriate locations relative to the skeletal image). Similarities may also be found between the role of reference points in spatial memory, that of ‘schemata’ in memory for goal-directed actions (Brewer and Dupree 1983; see also Brewer and Treyens 1981), and that of semantic-category cues in memory for verbal material (Tulving 1974; Tulving and Pearlstone 1966), which may be indicative of a general class of memory phenomena related to the integration of isolated facts into supraordinate units.

Although the Weighted-Distortion Theory of Nelson and Chaiklin (1980) received general support from the present results, no attempt was made to test the more specific postulates of that theory. Such a test should be possible to perform by systematically varying the distances between the reference points and the TBR locations in the present paradigm. To do this with multiple reference points would, however, require a much larger number of possible TBR and lure locations and was therefore beyond the scope of the present study. It should never- theless be a worthwhile enterprise for future research to pursue this issue, since it seems somewhat unlikely that a pure physical distance model like that of Nelson and Chaiklin (1980) would be able to fully account for the effects of reference points on memory for spatial location. It is for instance known that orientation and other structural factors may affect spatial memory (e.g., Attneave and Curlee 1977). In the present experiments an attempt was made to minimize the effects of such factors (by not allowing TBR locations on the same vertical or horizontal axes as the reference points, see fig. 1, and by using irregular

E. Lindberg. T. Giirling / Memory for spatial location 165

TBR patterns in experiment 2), but they should be worthy of study in their own right. The observed patterns of hits and false-alarms in the present study also make it seem less plausible that a fully satisfactory account of spatial memory performance will be arrived at unless not only the degree of bias but also the precision of the memory representa- tion is taken into account (cf. G%rling et al. 1981; Lindberg 1984; Lindberg and Gtiling 1982, 1983).

It should finally be noted that the effects of multiple TBR locations and multiple reference points were not found to be additive in experi- ment 2. In general, there should not be any reason why memory for spatial location could not be organized by linking a reference point location to one of the locations in a TBR pattern, then linking the latter to another TBR location, and so on. Such an organization may, however, have been counteracted if the subjects perceived the TBR locations and the reference points as two distinct patterns. An analogy would be to perceive, e.g., a face against a background, in which case reference points in the face presumably are related to each other but not to reference points in the background. Perceptual principles of organization are likely to be at work in this case, but other organiza- tional principles may be found under conditions in which, e.g., scene schemata play a role (Mandler and Parker 1976).

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