External Cue Effects on Memory for Spatial Location within a Rotated Task Field

Abstract

Fitting, Wedell and Allen (2007) demonstrated that although memory for location within a small two-dimensional task field is largely independent of cues when orientation is fixed, it is highly dependent on cues when orientation varies by rotating the task field on a majority of trials. Their analysis focused only on 0° rotation trials. The current investigation aimed to understand the spatial estimation process under conditions of actual rotation and thereby analyzed the cue effects for the 30°, 90°, and 160° rotation trials of that experiment. Results indicated strong cue-based angular bias effects, which were modeled as resulting from use of cues as category prototypes. Unique to rotation trials, the number of inferred protypes did not generally correspond to the number of cues. In the one-cue condition, there was evidence that an additional prototype was generated at a location opposite the single cue, representing a “phantom” prototype. In the three-cues condition, there was evidence that only two cues served as prototypes biasing estimation. Absolute error in spatial memory was also strongly reduced as a function of proximity to cues, implicating the role of cues in anchoring fine-grain memory. In contrast to the bias measure, effects on absolute error were more directly tied to actual cue locations.

Keywords:

• spatial memory
• place memory
• categorical coding
• fine-grain memory
• external cues
• mental rotation

Notes

¹In Equation 3, c is a constant. In fitting different versions of this model to the data, we allowed c to vary with stimulus (long and short radius) or with prototype. These distinctions are described in detail when we report the model fitting procedures in the Results section.

²In modeling the actual data, we include “virtual” prototypes for the lowest and highest categories so that recruitment may be conducted in a clockwise or counter-clockwise fashion in the same way for each quadrant.

³. In Equation 5, the probabilistic recruitment function essentially falls out of the equation if c is fixed at 0.0. In this case, the equation becomes a simple regression equation on the different log distances. We describe the use of this variation of Equation 5 later in the Results section.

⁴. Because missing data points increase with increases in degree of rotation, as shown in Table 1, a potential confound arises for the analyses we report. Namely, the differential amounts of missing data mean that the more accurate subjects may be overrepresented in high rotation conditions compared to low rotation conditions, potentially confounding interpretation of effects of rotation. Note that this confound would likely work against finding rotation effects that we report, because bias and error increase with rotation. To investigate this issue, we conducted ANOVAs on a restricted set of subjects who showed less than 7% missing data for the three rotation conditions in a given cue condition. This resulted in restricting the analyses to 13 participants in the one-cue-first condition, 13 in the one-cue-second condition, 17 in the three-cues-first condition, and 18 in the three-cues-second condition. These analyses then look only at one group of subjects across the three rotation conditions, namely, the ones who perform the best on this spatial task. In these analyses, the number of extreme data points that have been replaced by the mean of remaining subjects' data was much smaller and distributed more equally across rotation conditions. Overall, percentages of missing data were 3.49% (30° rotation), 4.21% (90° rotation) and 6.85% (160° rotation) in the one-cue condition, and 2.57% (30° rotation), 3.82% (90° rotation), and 2.97% (160° rotation) in the three-cues condition.

We conducted parallel 2 (Cues) × 3 (Rotation) × 2 (Radius) × 16 (Angle) mixed factorial ANOVAs on this restricted data set, separately for the first cue-set encountered and the second cue-set encountered (thus, cue was a between subjects factor in these analyses). The patterns of significance from these ANOVAs were quite similar to those reported for the whole data set, despite the much lower power due to fewer subjects and cues being analyzed as a between subjects factor. We summarize these below.

For angular bias, nine significant effects were reported for the within subjects analysis of the full data set (Table 2). Five of these were replicated in the cues-first restricted set and eight were replicated in the cues-second restricted set. Each restricted data set had one significant effect that was not significant in the full data set. For absolute error, 10 significant effects were reported in Table 2. Six of these were replicated in both the cues-first and the cues-second sets, with the latter set producing one significant effect not found in the full set. For radial bias, five significant effects were reported in Table 2. Two of these were replicated in the cues-first set and three in the cues-second set, with each restricted set producing two significant effects not found in the full data set.

Table 2 Degrees of freedom and F-values for 2 (cues) × 3 (rotation) × 2 (radius) × 16 (angle) within factorial ANOVAs

Overall, the effects most critical to our hypotheses and modeling in the full data set were replicated in analyses for both restricted data sets. These critical effects include the effect of rotation on absolute error, the effect of angle, the Cue × Angle interaction effect, and the Rotation × Cue × Angle interaction effect on both angular bias and absolute error, and the radius effect on radial bias. In conclusion, the patterns of significance were quite similar for analyses of the restricted and full data sets. Therefore, we are confident that the reported results are not due to a potential confound resulting from differential mortality across rotation conditions.

∗∗p < .01

∗∗∗p < .001.

∗∗p < .01

∗∗∗p < .001.

^a ∗∗p < .01

^a ∗∗∗p < .001.

⁵. Although response times were collected, a programming error led to a substantial loss of response time data. Therefore, we have chosen not to report analyses for response times in the main text. However, an ANOVA that was conducted on the available response times indicated highly significant effects for rotation, with response times increasing as expected from 30° to 90° to 160° rotation. Because of the incomplete nature of the data set, we do not feel it worthwhile to pursue further analyses on these data.