A model of rotated mirror/normal letter discriminations

Rotated mirror/normal letter discriminations are thought to require mental rotation in order to determine the direction of facing of the stimulus. The response time (RT) function over orientation tends to be curved, rather than the linear function found for other mental rotation tasks. The present study investigated the possibility that the curved RT function is a result of a mixture of trials requiring and not requiring mental rotation. The results suggested that the frequency of mental rotation is also a linear function of stimulus orientation. Moreover, the relationship between an individual's rate of plane rotation and the mean difference in RT between mirror and normal stimuli was replicated, supporting the suggestion that mirrored stimuli are flipped after they are spun (Hamm, Johnson, & Corballis, 2004). On the basis of the present findings, the entire RT function can be modeled by using only the mean RTs for upright and inverted stimuli.     

Evidence for Mixed Processes in Normal/Mirror Discrimination of Rotated Letters: A Bayesian Model Comparison Between Single- and Mixed-Distribution Models1

When determining whether a rotated letter is normal or mirrored, an observer mentally rotates the letter to its canonical orientation. To account for patterns of response times (RTs) for the normal/mirror discrimination of rotated letters, previous research formulated a model that postulated a mixture of trials with and without mental rotation. While this model could explain the curvilinear relationship that has been found between averaged RT and letter orientations, the curved RT function is still open to alternative explanations without assuming mixed processes. To address this issue and test the mixed-process hypothesis more directly, we analyzed trial-by-trial RT data instead of averaged RTs by employing a Bayesian model comparison technique. If rotation and non-rotation trials are mixed, trial-by-trial RTs for letters in a particular orientation should not follow a single distribution but a mixed one formed from the superposition of two separate distributions, one for rotation and one for non-rotation trials. In the present study, we compared single- and mixed-distribution models. Bayes-factor analysis showed decisive support for the mixed-distribution model over the single-distribution model. In addition, using the widely applicable information criterion (WAIC), the predictive accuracy of the mixed-distribution model was found to be as high as that of the single-distribution model. These results indicated the involvement of mixed processes in normal/mirror discrimination of rotated letters. The usefulness of statistical modeling in psychological study and necessary precautions to take in the interpretation of the parameters of unconfirmed models are also discussed.     

Effects of object asymmetry on visual attention

Unilateral neglect has been demonstrated relative to the intrinsic left side of objects, even when presented in the preserved hemispace. These results have been interpreted as evidence of an object-centered reference frame. In the present study, neurologically normal individuals were presented with letter stimuli having distinguishing features to the right (R) or left (J) of their intrinsic midline, shown in normal and mirror parity, and in six angle rotations. RTs confirmed that participants rotated the letters to the upright to decide parity: such rotation would align the object-centered and viewer-centered frames of reference, suggesting that not controlling for mental rotation would confound this effect. In addition, a dot, presented lateral to the main letter stimulus, resulted in quicker parity decisions when on the maximally-informative side of the letter. Together, the results suggest that apparent object-centered neglect may arise from the combined effects of mental rotation and within-object information asymmetries.     

GLOBAL PROCESSING-TIME COEFFICIENTS CHARACTERIZE INDIVIDUAL AND GROUP DIFFERENCES IN COGNITIVE SPEED

Abstract— Forty participants performed seven different information processing tasks (choice reaction time, letter classification, visual search, abstract matching, line-length discrimination, mental rotation, and mental paper-folding) Slow (top quartile) and fast (bottom quartile) processors were selected based on their mean z scores Response times (RTs) of the slow and fast groups in the 21 conditions of the seven tasks were linear functions of the mean RTs of the entire group (both r²s = 99) In addition, individuals' RTs were well described by linear functions (median r²= 93) When tasks were ranked in order of complexity, the odd-even reliability of the ratio of an individual's RT to the average RT was 80, indicating that such ratios remain relatively stable across tasks Taken together, these findings indicate that the performance of an individual on diverse tasks can be predicted on the basis of a single processing-time coefficient Such coefficients may provide useful indices of the efficiency with which different individuals process information     

Asymmetric response time functions during left-/right-facing discriminations of rotated objects: The short and the long of it

When deciding if a rotated object would face to the left or to the right, if imagined at the upright, mental rotation is typically assumed to be carried out through the shortest angular distance to the upright prior to determining the direction of facing. However, the response time functions for left- and right-facing objects are oppositely asymmetric, which is not consistent with the standard explanation. Using Searle and Hamm’s individual differences adaption of Kung and Hamm’s Mixture Model, the current study compares the predicted response time functions derived when assuming that objects are rotated through the shortest route to the upright with the predicted response time functions derived when assuming that objects are rotated in the direction they face. The latter model provides a better fit to the majority of the individual data. This allows us to conclude that, when deciding if rotated objects would face to the left or to the right if imagined at the upright, mental rotation is carried out in the direction that the objects face and not necessarily in the shortest direction to the upright. By comparing results for mobile and immobile object sets we can also conclude that semantic information regarding the mobility of an object does not appear to influence the speed of mental rotation, but it does appear to influence pre-rotation processes and the likelihood of employing a mental rotation strategy.     

Attention and the processing of emotional words: Dissociating effects of arousal

There is debate as to whether emotionally charged words receive preferential attentional processing in normal individuals. Using a digit-parity task, Harris and Pashler (2004) found that threat-related words captured attention on only the first trial, suggesting no attention capture for emotional words aside from an initial surprise reaction. We examined whether sexually explicit words would be more effective at capturing attention in a similar task. Our results with threat words replicated those of Harris and Pashler in that threat words did not lead to an increase in reaction time (RT) on the parity task, relative to emotionally neutral words. However, sexual words led to a marked increase in RTs for over 100 trials. Words’ arousal ratings, but not their valence ratings, predicted the amount of interference. Parity RTs for individual words were also related to memory for the word on a surprise memory test. Sexually explicit words may have more potential to capture attention than do threat-related words. The words presented here as distractors in the digit-parity task, along with their corresponding valence ratings, arousal ratings, and digit-parity RTs, can be downloaded from www.psychonomic.org/archive.     

复合字母刺激心理旋转加工中的整体优先效应

采用复合字母材料结合正镜像判断任务,首次揭示了心理旋转加工中的整体优先效应。实验一延长复合字母材料的呈现时间,检验心理旋转实验常用的正/镜像判断任务中的视知觉整体优先效应;实验二将实验一的复合字母材料旋转一定角度,考察心理旋转加工中的整体优先效应。结果发现：（1）延长复合字母呈现时间后的字母正镜像判断任务中,被试判断大字母和判断小字母的时间没有显著差异,并且大小字母是否一致对大字母判断和小字母判断的影响无显著差异;（2）在排除了视知觉的整体优先效应存在的情况下,发现心理旋转加工中存在明显的整体优先效应,大字母（整体）旋转条件下的反应时显著短于小字母（局部）旋转条件下的反应时;（3）旋转角度一致性对大字母旋转和小字母旋转条件下的反应时均无显著影响,表明心理旋转的整体优先效应模式可能有别于视知觉加工的整体优先效应模式     

Winding one's ps and qs: mental rotation and mirror-image discrimination

Subjects were timed as they made judgments about ps and qs (also interpretable as ds and bs) in different angular orientations. Whether these judgments were left-right mirror-image discriminations (b vs. d or p vs. q) or up-down mirror-image discriminations (b vs. p or d vs. q), the subjects' reaction times increased sharply with the angular departure of each letter from its designated normal upright orientation, a fact implying mental rotation. This was so whether the subjects responded with the letter labels themselves (e.g., b vs. d) or with the labels left versus right or top versus bottom. It was again the case when the letters were replaced by nonletter forms, in which event there was also a left visual-field advantage in reaction time. This study is therefore the first to demonstrate a mental-rotation strategy when the canonical forms to be discriminated are up-down mirror images as well as when they are left-right mirror images. In both cases, however, the task requires the ability to tell left from right, and we suggest that this is the critical ingredient that induces mental rotation.     

Mental rotation performance in primary school age children: Are there gender differences in chronometric tests?

In contrast to the well documented male advantage in psychometric mental rotation tests, gender differences in chronometric experimental designs are still under dispute. Therefore, a systematic investigation of gender differences in mental rotation performance in primary-school children is presented in this paper. A chronometric mental rotation task was used to test 449 second and fourth graders. The children were tested in three separate groups each with different stimulus material (animal drawings, letters, or cube figures). The results show that chronometric mental rotation tasks with cube figures – even rotated in picture plane only – were too difficult for children in both age groups. Further analyses with animal drawings and letters as stimuli revealed an overall gender difference in response time (RT) favoring males, an increasing RT with increasing angular disparity for all children, and faster RTs for fourth graders compared to second graders. This is the first study which has shown consistent gender differences in chronometric mental rotation with primary school aged children regarding reaction time and accuracy while considering appropriate stimuli.     

Mental rotation and the frame of reference in blind and sighted individuals

Mental rotation in the congenitally blind was investigated with a haptic letter-judgment task. Blind subjects and blindfolded, sighted subjects were presented a letter in some orientation between 0° to 300° from upright and timed while they judged whether it was a normal or mirror-image letter. Both groups showed an increasing response time with the stimulus’s departure from upright; this result was interpreted as reflecting the process of mental rotation. The results for the blind subjects suggest that mental rotation can operate on a spatial representation that does not have any specifically visual components. Further research showed that for the sighted subjects in the haptic task, the orientation of a letter is coded with respect to the position of the hand. Sighted subjects may code the orientation of the letter and then translate this code into a visual representation, or they may use a spatial representation that is not specifically visual.     

The impact of extended practice on rate of mental rotation

9-, 13-, and 20-year-olds were tested on 3840 trials of a mental rotation task in which they judged if pairs of stimuli presented in different orientations were identical or mirror images. Response time increased linearly as a function of the difference in orientation of the stimuli, and the slope of this function was used to estimate rate of mental rotation. At all ages, mental rotation became faster over trials. Age differences in rate of mental rotation were eliminated after approximately 1500 trials. At all ages the influence of practice was well characterized by hyperbolic and power functions. Furthermore, children's and adolescents' data were well fit by hyperbolic and power functions in which most of the parameters of those functions were constrained to adults' values. These results are discussed in terms of possible mechanisms underlying the impact of practice.     

Developmental functions for speeds of cognitive processes

In Experiment 1, 8- to 21-year-olds were tested on a visual search task in which they determined whether a target digit was present in a set of one to five digits and a memory search task in which they determined whether a target digit was a member of a previously presented set of one to five digits. Increases with age in speeds of visual and memory search were both described well by exponential functions, and the rate of developmental change was similar for the two processes. In Experiment 2, 8- to 22-year-olds were tested on a memory search task, a mental rotation task in which they judged whether a stimulus presented in various orientations was a letter or a mirror image of a letter, an analogical reasoning task in which they judged whether sets of pictures were related to one another according to the same rule, and a mental addition task in which they judged the accuracy of problems such as 2 + 3 = 6. Here, too, for three of the four tasks developmental change was described well by exponential functions with a common rate of change. Results are interpreted in terms of a central mechanism that limits speeded performance and that changes with age.     

Let’s twist again! Embodiment effects in spatial judgments on human figures rotated along a vertical axis

We investigated whether individuals used mental rotation and embodiment for arm laterality judgments of human figures that were stepwise rotated from back view to front view along a vertical axis. In Experiment 1, figures’ heads were always shown in profile, while only the bodies were rotated. Judgments were faster and more correct when figures were presented in back view compared to front view, but the relation between reaction times (RTs) and rotation angles was not strictly linear. In addition, judgments on figures in anatomically possible postures were better than on figures in impossible postures. In Experiment 2, figures’ heads were turned together with their body. RTs and rotation angles were linearly related. Results suggest that individuals use both mental rotation and a more direct matching between their own body and that of the figures, when making arm laterality judgments of human figures that are rotated along a vertical axis.     

Two- vs. three-dimensional presentation of mental rotation tasks: Sex differences and effects of training on performance and brain activation

The well-documented sex difference in mental rotation favoring males has been shown to emerge only for 2-dimensional presentations of 3-dimensional objects, but not with actual 3-dimensional objects or with virtual reality presentations of 3-dimensional objects. Training studies using computer games with mental rotation-related content have demonstrated training effects on mental rotation performance. Here, we studied the combined effect of a two-week mental rotation (MR) training on 2-dimensional vs. 3-dimensional presentations of a classic Shepard–Metzler task (presented in a pretest–training–posttest design) and their accompanying cortical activation patterns assessed via EEG in a sample of 38 male and 39 female adolescents of about 15 years of age. Analysis of one performance parameter (reaction times) displayed only main effects of dimensionality (with shorter RTs on the 3D vs. 2D version of the MR task) and of training (significant shortening of RTs), but no significant sex difference. Analysis of the other performance parameter (scores) in the MR task revealed a sex difference favoring males that first, appeared only in the 2D version, but not in the 3D version of the MR task and, secondly, diminished after training. Neurophysiologically we observed a complex sex × dimensionality × training × hemisphere interaction showing that the hypothesized decrease of brain activation (increase in neural efficiency) with training emerged for males in both 2D and 3D conditions, whereas for females this decrease was found only in the 3D but not with the 2D version of the MR task.     

Using visual codes for comparisons of pictures

In two experiments, Ss indicated for a series of trials whether or not two pictures of common objects had the same name (a positive or negative response, respectively). The pictures were separated by one of three interstimulus intervals (ISis), and reaction time (RT) was recorded. In Experiment I, positive trials involved pictures that were identical (identity match), mirror images (mirror match), or physically different but had the same name (name match). The stimuli came from either an S set, in which name-match pairs were physically similar, or a D set, in which name-match pairs were physically dissimilar. The mean RTs for mirror and identity matches were virtually the same but faster than name-match RTs, an advantage that decreased with increasing ISI. It was expected that name-match RT for the S set would be less than for the D set, indicating a facilitative effect of physical similarity; however, the identity-match RTs showed the expected difference. These results were extended in Experiment II, which involved only the identity and name matches, in pure sessions (which included positive trials of just one type) or mixed sessions (which included both types of positive trials). For mixed sessions, name- as well as identity-match RTs differed between the S and D sets. These results provide evidence for the use of visual codes in comparing nonidentical pictures, codes that apparently vary with experimental context and task demands.     

Mental rotation of mirrored letters: evidence from event-related brain potentials

Event-related brain potentials (ERPs) were recorded while participants (n=13) were presented with mirrored and normal letters at different orientations and were asked to make mirror-normal letter discriminations. As it has been suggested that a mental rotation out of the plane might be necessary to decide on mirrored letters, we wanted to determine whether this rotation occurs after the plane rotation in mirror rotated letters. The results showed that mirrored letters in the upright position elicited a negative-going waveform over the right hemisphere in the 400-500 ms window. A similar negativity was also present in mirrored letters at 30 degrees, 60 degrees, and 90 degrees, but in these cases it was delayed. Moreover, the well-known orientation effect on the amplitude of the rotation-related negativity was also found, although it was more evident for normal than for mirrored letters. These results indicate that the processing of mirrored letters differs from that of normal letters, and suggest that a rotation out of the plane after the plane rotation may be involved in the processing of mirror rotated letters.     

Attentional capture by motion onsets is modulated by perceptual load

The onset of motion captures attention during visual search even if the motion is not task relevant, which suggests that motion onsets capture attention in a stimulus-driven manner. However, we have recently shown that stimulus-driven attentional capture by abruptly appearing objects is attenuated under conditions of high perceptual load. In the present study, we examined the influence of perceptual load on attentional capture by another type of dynamic stimulus: the onset of motion. Participants searched for a target letter through briefly presented low- and high-load displays. On each trial, two irrelevant flankers also appeared, one with a motion onset and one that was static. Flankers defined by a motion onset captured attention in the low-load but not in the high-load displays. This modulation of capture in high-load displays was not the result of overall lengthening of reaction times (RTs) in this condition, since search for a single low-contrast target lengthened RTs but did not influence capture. These results, together with those of previous studies, suggest that perceptual load can modulate attentional capture by dynamic stimuli.     

Impact of practice on speed of mental rotation

We tested 11- and 20-year-olds on 3360 trials of a mental rotation task in which they judged if stimuli presented in different orientations were letters or mirror images of letters. Children's and adults' processing times decreased substantially over practice. These changes were well characterized by hyperbolic and power functions in which most of the parameters of those functions were constrained to adults' values. Performance on two transfer tasks, mental rotation of letter-like characters and memory search for numbers, indicated that the practiced skill did not generalize to other domains. The results are discussed in terms of different mechanisms that might be responsible for the impact of practice.     

Processing two tasks with varying task order: central stage duration influences central processing order

In a recent study, Sigman and Dehaene (2006, PLoS Biology, 4, 1227–1238) reported that perceptual processing duration influences processing order of two tasks in the psychological refractory period paradigm (PRP). The present study examines whether the duration of central processes also influences processing order. For this purpose, we employed letter tasks with different central processing durations and varied task order in the PRP. In one part of the experiment, a tone discrimination task was combined with a similar time-consuming letter discrimination task. In the other part, the tone task was combined with a more time-consuming letter task, which required a mental rotation of the letter thereby prolonging central processing. If the duration of central processes influences processing order, participants should perform the tone task first more often when it is presented with the more time-consuming mental rotation task, than when it is presented with the similar time-consuming letter task. The results clearly confirm this prediction and thus show that not only perceptual processing duration but also central processing duration affects processing order in a dual-task situation. We suggest that the reported effect mirrors a tendency of participants to minimize total reaction time to both tasks by reducing slack time.     

Age and individual differences in visuospatial processing speed: Testing the magnification hypothesis

Forty young adults and 40 older adults performed seven visuospatial information processing tasks. Factor analyses of the response times (RTs) yielded a single principal component with a similar composition in both age samples. For both samples, regressing the mean RTs of fast and slow subgroups for the seven tasks (18 conditions) on the corresponding mean RTs for their age group accounted for 99% of the variance. Taken together, these findings suggest that individual differences in processing time were largely task independent. The magnification hypothesis, a simple mathematical model of the interaction between age and ability, is presented. This model correctly predicts the finding that in both the young and the older adult groups, individual differences increased systematically with task difficulty. The magnification hypothesis also explains the regression parameters describing individual differences among young adults and predicts correctly that equivalent parameters describe individual differences among older adults. According to the magnification hypothesis, the RTs of slower individuals are more affected by aging than those of faster individuals, and slower individuals may be more at risk with respect to other biological insults (e.g., changes in health status) as well.