Is the area measure a historical anomaly?

Green's well-known area theorem establishes an equivalence between the area under the yes-no ROC curve and the percent correct of an unbiased observer in a two-alternative forced-choice (2AFC) task with equivalent stimuli. In this article, we show that this conversion from yes-no detection data to hypothetical performance in a 2AFC task is unnecessary: The same yes-no detection data that are used to compute the area statistic can always be used to compute the percent correct of an unbiased observer in the yes-no detection task itself. We also show that the ROC curve may not be the ideal graphical device for many investigators. A more natural representation of the difficulty of a discrimination task is obtained by plotting the distribution of the posterior betting odds under equal base rates, which can be estimated from their distributions under unequal base rates. Finally, unlike the area measure and other traditional detection theory statistics, both the yes-no percent correct measure and the odds distributions generalize in an obvious and direct way to classification paradigms with more than two responses (e.g., identification).     

Are the Referents Remembered in Temporal Bisection?

In roving-referent bisection, three duration values are presented sequentially on each trial, two referents and then a probe, and the observer is instructed to indicate whether the probe is more similar to the duration of the first or second trial referent. Data from three experiments are reported which consistently indicate that human observers do not compare the probe to the trial referents in roving-referent bisection. Rather, they base their judgment on the absolute value of the probe rather than on its relationship to the trial referents. The data are consistent with Gibbon's (1981) formulation of the decision process in bisection which specifies that the probe is compared to a criterion duration value. Although many studies have used bisection to study temporal memory, the data from the present experiments suggest that referent memory is not a dominant source of variability in human temporal bisection.     

Double bisection of auditory temporal intervals by humans

Scalar Expectancy Theory (SET) has been the leading theory in timing research, and has also influenced research into human timing. However, other timing theories exist, such as Learning to Time (LeT). The double bisection task was designed to test the SET and LeT theories in pigeons. The purpose of this experiment was to verify whether similar results emerge from a human adaptation of the double bisection task. The results indicated that humans perform the double bisection task in the same way as pigeons do. However, the assumptions inherent in LeT cannot be applied to humans. Two other explanations are also assessed here.     

The bisection point across variants of the task

Bisection tasks are used in research on normal space and time perception and to assess the perceptual distortions accompanying neurological disorders. Several variants of the bisection task are used, which often yield inconsistent results, prompting the question of which variant is most dependable and which results are to be trusted. We addressed this question using theoretical and experimental approaches. Theoretical performance in bisection tasks is derived from a general model of psychophysical performance that includes sensory components and decisional processes. The model predicts how performance should differ across variants of the task, even when the sensory component is fixed. To test these predictions, data were collected in a within-subjects study with several variants of a spatial bisection task, including a two-response variant in which observers indicated whether a line was transected to the right or left of the midpoint, a three-response variant (which included the additional option to respond “midpoint”), and a paired-comparison variant of the three-response format. The data supported the model predictions, revealing that estimated bisection points were least dependable with the two-response variant, because this format confounds perceptual and decisional influences. Only the three-response paired-comparison format can separate out these influences. Implications for research in basic and clinical fields are discussed.     

What Is Line Bisection in Unilateral Spatial Neglect?: Analysis of Perceptual and Motor Aspects in Line Bisection Tasks

Three patients with unilateral spatial neglect could detect the difference of length between the right and left segments when a line had a transection mark. To examine the effect of response mode, the manual line bisection task and a new “line bisection task by fixation” were given to the patients. In tasks that used lines with no landmark, they showed apparent rightward errors. The results suggest that line bisection is not a task that examines the ability of patients with neglect to compare the right and left extents of a line. Where to fixate as the subjective midpoint may determine the rightward errors of bisection, whether manual response is used or not.     

Human performance on an analogue of an interval bisection task

Two experiments used normal adult human subjects in an analogue of a time interval bisection task frequently used with animals. All presented durations were defined by the time between two very brief clicks, and all durations were less than 1 sec, to avoid complications arising from chronometric counting. In Experiment 1 different groups of subjects received standard durations of either 0.2 and 0.8 or 0.1 and 0.9 sec and then classified a range of durations including these values in terms of their similarity to the standard short (0.2- or 0.1-sec) and long (0.8- or 0.9-sec) durations. The bisection point (defined as the duration classified as "long" on 50% of trials) was located at 0.43 sec in the 0.2-0.8 group, and at 0.46 sec in the 0.1-0.9 group. Experiment 2 replicated Experiment 1 using a within-subject procedure. The bisection point of both 0.2- and 0.8 sec and 0.1- and 0.9-sec durations was found to be 0.44 sec. Both experiments thus found the bisection point to be located at a duration just lower than the arithmetic mean of the standard short and long durations, rather than at the geometric mean, as in animal experiments. Some other performance measures, such as difference limen, and Weber ratio, were, however, of similar values to those found in bisection tasks with animals. A theoretical model assuming that humans bisect by taking the difference between a presented duration and the short and long standards, as well as having a bias to respond "long", fitted the data well. The model incorporated scalar representations of standard durations and thus illustrated a way in which the obtained results, although different from those found with animal subjects, could be reconciled with scalar timing theory.     

Stimulus Range Effects in Temporal Bisection by Humans

Two experiments with human subjects, using short-duration tones as stimuli to be judged, investigated the effect of the range of the stimulus set on temporal bisection performance. In Experiment 1, six groups of subjects were tested on a temporal bisection task, where each stimulus had to be classified as "short" or "long". For three groups, the difference between the longest (L) and shortest (S) durations in the to-be-bisected stimulus set was kept constant at 400 msec, and the L / S ratio was varied over values of 5:1 and 2:1. For three other groups, the L/S ratio was kept constant at 4:1 but the L-S difference varied from 300 to 600 msec. The bisection point (the stimulus value resulting in 50% 'long' responses) was located closer to the arithmetic mean of L and S than the geometric mean for all groups except that for which the L / S ratio was 2:1, in which case geometric mean bisection was found. In Experiment 2, stimuli were spaced between L and S either linearly or logarithmically, and the L / S ratio took values of either 2:1 or 19:1. Geometric mean bisection was found in both cases when the L / S ratio was 2:1, but effects of stimulus spacing were found only when the L / S ratio was 19:1. Overall, the results supported a previous conjecture that the L / S ratio used in a bisection task played a critical role in determining the behaviour obtained. A theoretical model of bisection advanced by Wearden (1991) dealt appropriately with bisection point shifts discussed above but encountered difficulties with stimulus spacing effects.     

Time and number discrimination in a bisection task with a sequence of stimuli: a developmental approach

Children, aged 5 and 8 years, and adults were tested in a bisection task with a sequence of stimuli in which time and number co-varied. In a counting and a non-counting condition, they were instructed either to process the duration of this sequence while ignoring the number of stimuli (temporal bisection), or to process the number of stimuli while ignoring the duration (numerical bisection). In the temporal bisection task, number interfered with the 5-year-olds' temporal performance, indicating that young children did not process time and number independently in a sequence of stimuli when they had to attend to duration. However, number interference decreased both with age and counting strategy. In contrast, in the numerical bisection task, duration did not interfere with numerical discrimination for any age group.     

Visual distance estimation in static compared to moving virtual scenes

Visual motion is used to control direction and speed of self-motion and time-to-contact with an obstacle. In earlier work, we found that human subjects can discriminate between the distances of different visually simulated self-motions in a virtual scene. Distance indication in terms of an exocentric interval adjustment task, however, revealed linear correlation between perceived and indicated distances but with a profound distance underestimation. One possible explanation for this underestimation is the perception of visual space in virtual environments. Humans perceive visual space in natural scenes as curved, and distances are increasingly underestimated with increasing distance from the observer. Such spatial compression may also exist in our virtual environment. We therefore surveyed perceived visual space in a static virtual scene. We asked observers to compare two horizontal depth intervals, similar to experiments performed in natural space. Subjects had to indicate the size of one depth interval relative to a second interval. Our observers perceived visual space in the virtual environment as compressed, similar to the perception found in natural scenes. However, the nonlinear depth function we found can not explain the observed distance underestimation of visual simulated self-motions in the same environment.     

Prospective memory in the rat

The content of prospective memory is comprised of representations of an action to perform in the future. When people form prospective memories, they temporarily put the memory representation in an inactive state while engaging in other activities, and then activate the representation in the future. Ultimately, successful activation of the memory representation yields an action at an appropriate, but temporally distant, time. A hallmark of prospective memory is that activation of the memory representation has a deleterious effect on current ongoing activity. Recent evidence suggests that scrub jays and non-human primates, but not other species, are capable of future planning. We hypothesized that prospective memory produces a selective deficit in performance at the time when rats access a memory representation but not when the memory representation is inactive. Rats were trained in a temporal bisection task (90 min/day). Immediately after the bisection task, half of the rats received an 8-g meal (meal group) and the other rats received no additional food (no-meal group). Sensitivity to time in the bisection task was reduced as the 90-min interval elapsed for the meal group but not for the no-meal group. This time-based prospective-memory effect was not based on response competition, an attentional limit, anticipatory contrast, or fatigue. Our results suggest that rats form prospective memories, which produces a negative side effect on ongoing activity.     

Visual prediction of collision with natural and nonnatural motion functions

A movement with constant velocity looks fast in the beginning and later slows down, whereas a certain type of accelerated motion (natural motion) looks constant throughout. It was predicted that early occlusion of a constant motion would lead to overestimation of velocity whereas late occlusion would not. With natural motion, there would be no such difference. Constant and natural motions together with constant deceleration and constant acceleration motions were tested in a modified prediction-of-collision experiment. The results agree well with the predictions. It was concluded that the phenomena previously found are operative also in a more complex perceptual task where the observer’s attention is not focused on velocity directly. The visual system seems to achieve perception of partly occluded motion by applying a natural motion function rather than constant velocity. Acquaintance with the phenomena does not seem to alter the way they are perceived.     

Time flies with music whatever its emotional valence

The present study used a temporal bisection task to investigate whether music affects time estimation differently from a matched auditory neutral stimulus, and whether the emotional valence of the musical stimuli (i.e., sad vs. happy music) modulates this effect. The results showed that, compared to sine wave control music, music presented in a major (happy) or a minor (sad) key shifted the bisection function toward the right, thus increasing the bisection point value (point of subjective equality). This indicates that the duration of a melody is judged shorter than that of a non-melodic control stimulus, thus confirming that “time flies” when we listen to music. Nevertheless, sensitivity to time was similar for all the auditory stimuli. Furthermore, the temporal bisection functions did not differ as a function of musical mode.     

Disruptions to number bisection after brain injury: Neglecting parts of the Mental Number Line or working memory impairments?

The aim of this study was to investigate the mechanisms underlying consistent directional number bisection bias in a chronic neuropsychological sample, not selected based on behaviour or lesion definitions. Patients completed a test battery that included measures of number bisection, line bisection, verbal working memory, visual-spatial working memory, egocentric neglect and allocentric neglect. Neither the neglect nor working memory measures were found to significantly correlate with number bisection. Furthermore, when outlier patients with very distinct number bisection biases were compared to patients who did not show any number bisection difficulties, no differences were found between the two groups on any of the other behavioural measures. We conclude that number bisection difficulties are not consistently based on any single deficit, be it neglect or working memory, and biases in number bisection should not be assumed to directly reflect problems in either of these areas.     

The effects of local and global processing demands on perception and action

The line-bisection task, adapted to utilise a wooden rod as the bisection stimulus, has revealed that patients with visuo-spatial neglect may be more accurate at bisection when asked to pick up the rod, compared to pointing to its centre. We recently reported that neurologically intact participants show a similar dissociation on this task-demonstrating a rightward bias when pointing to the centre, which was not present when grasping the rod by the centre. The current paper examined how pointing and grasping responses were affected by adapted rod-bisection tasks that emphasised local or global processing. In Experiment 1, 26 participants completed four rod-bisection tasks. The rods were compound stimuli and the participants directed to focus on either the local or global level. The results demonstrated that when participants focused on the global level, the previous dissociations found for pointing and grasping conditions were evident. However, the perception of centre did change when participants focused on the local level: both the pointing and grasping responses were rightward biased. In Experiment 2, 42 participants completed three bisection tasks which again emphasised either the local or global level, but in different sets of stimuli. The results of this task further support the findings in Experiment 1: the rightward bias in the local-bisection task was again evident and in addition, the global-bisection task resulted in no bias and no difference between the pointing and grasping bisections. These results demonstrate how task demands can similarly affect the pointing and grasping responses, and indicate that local and global processing may be involved in perception/action dissociations on rod bisection.     

Holistic processing in the composite task depends on face size

Holistic processing is a hallmark of face processing. There is evidence that holistic processing is strongest for faces at identification distance 2–10 metres from the observer. However, this evidence is based on tasks that have been little used in the literature and that are indirect measures of holistic processing. We use the composite task—a well validated and frequently used paradigm—to measure the effect of viewing distance on holistic processing. In line with previous work, we find a congruency x alignment effect that is strongest for faces that are close (2 m equivalent distance) than for faces that are further away (24 m equivalent distance). In contrast, the alignment effect for same trials, used by several authors to measure holistic processing, produced results that are difficult to interpret. We conclude that our results converge with previous findings providing more direct evidence for an effect of size on holistic processing.     

Slope estimation and viewing distance of the observer

The overestimation of geographical slant is one of the most sizable visual illusions. However, in some cases estimates of close-by slopes within the range of the observer’s personal space have been found to be rather accurate. We propose that the seemingly diverse findings can be reconciled when taking the viewing distance of the observer into account. The latter involves the distance of the observer from the slope (personal space, action space, and vista space) and also the eye-point relative to the slope. We separated these factors and compared outdoor judgments to those collected with a three-dimensional (3D) model of natural terrain, which was within arm’s reach of the observer. Slope was overestimated in the outdoors at viewing distances between 2 m and 138 m. The 3D model reproduced the errors in monocular viewing; however, performance was accurate with stereoscopic viewing. We conclude that accurate slant perception breaks down as soon as the situation exits personal space, be it physically or be it by closing one eye.     

Numerosities and space; indeed a cognitive illusion! A reply to de Hevia and Spelke (2009)

de Hevia and Spelke (de Hevia and Spelke (2009). Spontaneous mapping of number and space in adults and young children, Cognition, 110, 198–207) investigated the mapping of number onto space. To this end, they introduced a non-symbolic flanker task. Here subjects have to bisect a line that is flanked by a 2-dot and a 9-dot array. Similar to the symbolic line bisection task, a bias towards the larger numerosity was observed. We re-investigated these results both by creating new flanker stimuli that controlled for different (non-numerical) stimulus properties and by developing a new measurement tool. We demonstrate that the bisection bias was caused by the larger area subtended by the 9-dot array compared to the 2-dot array and not numerosity. Our study puts constraints on the results of the study by de Hevia and Spelke. The role of visual cues in numerosity processing in general is discussed.     

Temporal Bisection in Humans with Longer Stimulus Durations

Normal adults were tested in eight temporal bisection conditions, using 500-Hz tones as stimuli. Stimulus lengths matched, or overlapped with, durations normally used in bisection experiments with animals, and chronometric counting was prevented by using a concurrent digit-shadowing task. Four experimental groups were used to investigate any effects of stimulus spacing, and stimuli were logarithmically or linearly spaced between standard 'short' and 'long' durations of 1 and 4, or 2 and 8 sec. A slight leftward shift of the psychophysical function was found in the logarithmic spacing condition, relative to linear spacing. Four other groups tested the conjecture that the ratio of the short and long standards might play some role in determining the location of the bisection point, and conditions with long/short ratios of 2: 1 and 5: 1 were used. In all cases the bisection point was close to the arithmetic mean of the short and long standards, rather than the geometric mean, as in animal studies. Overall, however, smaller long/short ratios (which may indicate more difficult temporal discriminations) produced more sensitive timing. When the long/short ratio was held constant, however, data showed nearly perfect superimposition, indicating conformity to scalar timing. In general, results were similar to those from experiments with humans that used much shorter durations, indicating the animal/human differences in bisection do not depend on the absolute lengths of the stimuli used.     

Stimulus timing by people with Parkinson's disease

Previous literature suggests that Parkinson’s disease is marked by deficits in timed behaviour. However, the majority of studies of central timing mechanisms in patients with Parkinson’s disease have used timing tasks with a motor component. Since the motor abnormalities are a defining feature of the condition, the status of timing in Parkinson’s disease remains uncertain. Data are reported from patients with mild to moderate Parkinson’s disease (both on and off medication) and age- and IQ-matched controls on a range of stimulus timing tasks without counting. Tasks used were temporal generalization, bisection, threshold determination, verbal estimation, and a memory for duration task. Performance of patients was generally “normal” on all tasks, but significant differences from performance of controls were found on the memory for duration task. Among the “normal” effects noted were arithmetic mean bisection, asymmetric temporal generalization gradients, and subjective shortening on the memory for duration task. The results suggest (a) that some previous reports of timing “deficits” in Parkinson’s patients were possibly due to the use of tasks requiring a timed manual response and (b) small differences between patients and controls may be found on tasks where two stimuli are presented on each trial, whether patients are on medication or off it.     

Exocentric pointing to opposite targets

We use an exocentric pointing task to study exocentric visual directions to targets that are opposite to a pointer relative to the observer. (The apparent distance between the target and the pointer always exceeded 90 degrees of visual angle.) All pointing takes place in the horizontal plane at eye height. Observers could not see both target and pointer at a single glance. They had to look back and forth between them, using combinations of eye movements, head turns, twists at the waist and turning on the feet. In the limit of diametrically opposite targets we find that the observers pick either one of two distinct orientations of the pointer as equally "visually correct". Which one results depends on the stance assumed by the observer. The difference between the two equally acceptable pointings is between 5 degrees and 10 degrees. Such a result is predicted from earlier measurements in the context of a model that describes the geometry of the horizon as a Riemannian space with varying intrinsic curvature. The present results thus fit--perhaps surprisingly--very well in such a picture.