Judging proportion with graphs: the summation model

People take longer to judge part-to-whole relationships with bar graphs than with pie charts or divided bar graphs. Subjects may perform summation operations to establish the whole with bar graphs, which would be unnecessary for other graph types depicting the whole with a single object. To test this summation model, the number of components forming the whole was varied with bars, divided bars, reference bars, and pies in three experiments. Response time increased with the number of components for bar graphs but there was little increase for other graph types in Experiment 1. An accuracy emphasis in Experiment 2 produced generally longer response times, but had little effect on the time per summation. The summation operation was not used when graphs were displayed briefly in Experiment 3, although subjects still took longer with bars. The estimated time for a summation operation is consistent with estimates derived from other research. In general, the bar graph is not effective for proportion judgments, and its disadvantage becomes potentially greater as the number of components increases. © 1998 John Wiley & Sons, Ltd.     

The discrimination of graphical elements

A model is proposed to account for how people discriminate quantities shown in pie charts and divided bar graphs (i.e. which proportion is larger, A or B?). The incremental estimation model assumes that an observer sequentially samples from the available perceptual features in a graph. The relative effectiveness of sampled perceptual features is represented by the spread of probability distributions, in the manner of signal detection theory. The model's predictions were tested in two experiments. Participants took longer with pies than divided bars and longer with non‐aligned than aligned proportions in Experiment 1. In Experiment 2, participants took longer with divided bars than pies when graphs were of unequal size. Generally, graphical formats producing longer response times incurred a greater time penalty when the difference between proportions was reduced. These results were in accordance with the model's predictions. Implications for graphical display design are discussed. Copyright © 2001 John Wiley & Sons, Ltd.     

The effect of emergent features on judgments of quantity in configural and separable displays

Two experiments investigated effects of emergent features on perceptual judgments of comparative magnitude in three diagrammatic representations: kiviat charts, bar graphs, and line graphs. Experiment 1 required participants to compare individual values; whereas in Experiment 2 participants had to integrate several values to produce a global comparison. In Experiment 1, emergent features of the diagrams resulted in significant distortions of magnitude judgments, each related to a common geometric illusion. Emergent features are also widely believed to underlie the general superiority of configural displays, such as kiviat charts, for tasks requiring the integration of information. Experiment 2 tested the extent of this benefit using diagrams with a wide range of values. Contrary to the results of previous studies, the configural display produced the poorest performance compared to the more separable displays. Moreover, the pattern of responses suggests that kiviat users switched from an integration strategy to a sequential one depending on the shape of the diagram. The experiments demonstrate the powerful interaction between emergent visual properties and cognition and reveal limits to the benefits of configural displays for integration tasks.     

The representation of auditory source characteristics: Simple geometric form

Two experiments examined listeners’ ability to discriminate the geometric shape of simple resonating bodies on the basis of their corresponding auditory attributes. In cross-modal matching tasks, subjects listened to recordings of pairs of metal bars (Experiment 1) or wooden bars (Experiment 2) struck in sequence and then selected a visual depiction of the bar cross sections that correctly represented their relative widths and heights from two opposing pairs presented on a computer screen. Multidimensional scaling solutions derived from matching scores for metal and wooden bars indicated that subjects’ performance varied directly with increasing differences in the width/height (WIH) ratios of both sets of bars. Subsequent acoustic analyses revealed that the frequency components from torsional vibrational modes and the ratios of frequencies of transverse bending modes in the bars correlated strongly with both the bars’ WIH ratios and bar coordinates in the multidimensional configurations. The results suggest that listeners can encode the auditory properties of sound sources by extracting certain invariant physical characteristics of their gross geometric properties from their acoustic behavior.     

Self‐framing of risky choice

Previous research on framing effects has largely focused on how choice information framed by external sources influences the response of a decision maker. This research examined how decision makers framed choice options and how the hedonic tone of self‐framing influenced their risk preference. By using pie charts and a complementary sentence‐completion task in Experiment 1, participants were able to interpret and frame the expected choice outcomes themselves before making a choice between a sure option and a gamble in either a life–death or a monetary problem. Each of these self‐frames (phrases) was then rated by a group of independent judges in terms of its hedonic tone. The hedonic tone of self‐frames was mostly positive and was more positive in the life–death than the monetary context, suggesting a motivational function of self‐framing. However, positive outcomes were still more likely to be framed positively than negative outcomes. In Experiment 2, choice outcomes were depicted with a whole‐pie chart instead of a pie slice in order to emphasize positive and negative outcomes equally. The results showed that the hedonic tone of self‐framing was still largely positive and more positive in the life domain than the monetary domain. However, compared to Experiment 1, the risk preference in the life–death domain was reversed, showing an outcome salience effect: when the pie‐slice chart emphasized only survival outcomes, participants were more risk taking under positive hedonic frames whereas when the whole‐pie chart depicted both survival and mortality outcomes, they became risk averse under positive frames. In sum, self‐framing reflected a positive bias in encoding risk information and affected the risk preference of the decision maker. Like the tone of voice used in communication, the hedonic tone of self‐framing, either positive or negative, can affect risk perception of a choice problem. Copyright © 2003 John Wiley & Sons, Ltd.     

Neuroscientific information bias in metacomprehension: The effect of brain images on metacomprehension judgment of neuroscience research

In the present study, we investigated how brain images affect metacomprehension judgments of neuroscience research. Participants made a prereading judgment of comprehension of the text topic and then read a text about neuroimaging findings. In Experiment 1, participants read text only or text accompanying brain images. In Experiment 2, participants read text accompanying bar graphs or text accompanying brain images. Then participants were asked to rate their comprehension of the text. Finally, they completed comprehension tests. The results of Experiment 1 showed that the text accompanying brain images was associated with higher metacomprehension judgments than was the text only, whereas the performance of the comprehension test did not differ between each condition. The results of Experiment 2 showed that the text accompanying brain images was associated not only with credibility of the text, but also with higher metacomprehension judgments than was the text accompanying the bar graphs, whereas the performance of the comprehension test did not differ between each condition. The findings suggest that the readers’ subjective judgments differ from actual comprehension.     

Proportional Reasoning in 5- to 6-Year-Olds

There have been mixed results in studies investigating proportional reasoning in young children. The current study aimed to examine whether providing visual scaling cues and structuring the reasoning process can improve proportional reasoning in 5- to 6-year-old children. In a series of computerized tasks, children compared the sweetness of 2 mixtures. Each mixture was represented by a juice rectangle stacked on top of a water rectangle. Two rectangles shared the same width but were of same or different heights. The mixtures were scaled by either changing their widths or their heights. In Experiment 1, children’s performance was poor when judging equivalent proportions. In Experiment 2, the 2 mixtures were individually previewed to encourage individual estimation of each mixture and thereby allow participants to strategically reason about the relative proportions. Children performed significantly better than in Experiment 1. In Experiment 3, children explicitly rated the sweetness of each preview mixture. Performance did not improve relative to Experiment 2. Throughout all 3 experiments, children were more sensitive in detecting equivalence when scaling occurred along the width compared with the height, demonstrating the effectiveness of visual-spatial scaling cues. Together, these experiments suggested that visuospatial scaling cues and structuring the 2-step reasoning process using previews can improve 5- to 6-year-olds’ proportional reasoning with certain limitations.     

The structure of frontoparallel haptic space is task dependent

In three experiments, we investigated the structure of frontoparallel haptic space. In the first experiment, we asked blindfolded participants to rotate a matching bar so that it felt parallel to the reference bar, the bars could be at various positions in the frontoparallel plane. Large systematic errors were observed, in which orientations that were perceived to be parallel were not physically parallel. In two subsequent experiments, we investigated the origin of these errors. In Experiment 2, we asked participants to verbally report the orientation of haptically presented bars. In this task, participants made errors that were considerably smaller than those made in Experiment 1. In Experiment 3, we asked participants to set bars in a verbally instructed orientation, and they also made errors significantly smaller than those observed in Experiment 1. The data suggest that the errors in the matching task originate from the transfer of the reference orientation to the matching-bar position.     

Nonretinotopic processing is related to postdictive size modulation in apparent motion

The present study briefly examined how the perceived size of a leading flash would be modulated by trailing motion signals. Observers were presented with two vertical green bars that were followed by white bars with different lengths, which were presented at different locations from the green bars. The task of observers was to discriminate which of the green bars was shorter than the other (Experiment 1) or whether the lengths of the green bars were equal or not (Experiments 2 and 3). One green bar producing apparent motion with the following shorter white bar was reported to be shorter than the other green bar producing apparent motion with the following longer white bar, not only when motion correspondence was determined on the basis of retinal proximity (Experiments 1 and 2),but also when motion correspondence was determined on the basis of nonretinotopic information-that is, a relative location within each perceptual group of bars (Experiment 3). These results indicate that motion processing involving object updating or motion deblurring in the nonretinotopic frame of reference is related to postdictive size modulation.     

On apparent misalignment of collinear edges and boundaries

In two experiments, subjects adjusted various pairings of the top and bottom boundaries of two obliquely oriented outline bars (Experiment 1) and those of two similarly oriented complete and incomplete squares (Experiment 2) to apparent alignment. The data from the first experiment showed that the misalignment effects were determined jointly by the directional properties of the bar ends (vertical, oblique, and semicircular) and the pair of boundaries that were aligned (both top boundaries, top of upper bar with bottom of lower bar, bottom of upper bar with top of lower bar). The results from the second experiment showed that the misalignment effects were the same for the oblique boundaries of solid and outline squares and persisted when the squares were reduced to two parallel lines. The effect was undiminished when the ends of the parallels were aligned, but was markedly reduced when pairs of parallels themselves were aligned. The outcomes of the two experiments are explained in terms of the apparentpositions of the oblique boundaries. It is proposed that these vary with the positions of the elements (bar or square) relative to the visual field, the position of the boundaries relative to the stimulus elements, and the positions of the boundaries relative to axes that are delineated by the parallel adjacent ends of bars and sides of squares. This relative-position basis for apparent misalignment is held to be the basis of misalignment effects in other figures.     

时距长度和速度变化对进度条时距知觉的影响

进度条在人机交互界面中具有广泛应用。本研究运用单任务的预期式范式和口头估计法,探究速度变化对不同时距长度进度条的时距知觉的影响,为进度条的智能化设计提供参考。研究表明：（1）时距长度影响个体的时距估计,时距长度与时距估计比率分数成反比关系;（2）进度条的不同速度变化趋势影响进度条时距知觉,在持续时间相同的匀速、减速、加速和先加后减四种进度条类型中,加速进度条的时距知觉最短,而匀速进度条时距估计最长。     

Effects of spatial compatibility on integration processes in graph comprehension

A precondition for efficiently understanding and memorizing graphs is the integration of all relevant graph elements and their meaning. In the present study, we analyzed integration processes by manipulating the spatial compatibility between elements in the data region and the legend. In Experiment 1, participants judged whether bar graphs depicting either statistical main effects or interactions correspond to previously presented statements. In Experiments 2 and 3, the same was tested with line graphs of varying complexity. In Experiment 4, participants memorized line graphs for a subsequent validation task. Throughout the experiments, eye movements were recorded. The results indicated that data-legend compatibility reduced the time needed to understand graphs, as well as the time needed to retrieve relevant graph information from memory. These advantages went hand in hand with a decrease of gaze transitions between the data region and the legend, indicating that data-legend compatibility decreases the difficulty of integration processes.     

Displaying proportions and percentages

Pie and bar charts are commonly used to display percentage or proportional data, but professional data analysts have frowned on the use of the pie chart on the grounds that judgements of area are less accurate than judgements of lenth. Thus the bar chart has been favoured. When the amount of data to be communicated is small, some authorities have advocated the use of properly constructed tables, as another option. The series of experiments reported here suggests that there is little to choose between the pie and the bar chart, with the former enjoying a slight advantage if the required judgement is a complicated one, but that both forms of chart are superior to the table. Thus our results do not support the commonly expressed opinion that pie charts are inferior. An analysis of the nature of the task and a review of the psychophysical literature suggest that the traditional prejudice against the pie chart is misguided.     

Visual binding in the standing wave illusion

When two video frames are alternated at the appropriate rate, one with a central bar and the other with two flanking bars, the central bar becomes invisible. Competing explanations for this standing wave illusion are examined, with the results showing an influence of higher level shape representations on lower level edge processes. In Experiment 1, flanking bar duration was found to be more important to masking than central bar duration. Experiment 2 showed strong nonlocal effects in that masking of the central bar depended critically on whether it appeared in the same video frame as other visible bars. Experiments 3 and 4 showed that the contour shared by bars in separate frames was a less important factor than shape and surface similarity. This illusion is therefore an excellent tool for studying recursive interactions between higher level object representations and lower level contour processes.     

An analysis of the time course of attention in preview search

We used a probe dot procedure to examine the time course of attention in preview search (Watson & Humphreys, 1997). Participants searched for an outline red vertical bar among other new red horizontal bars and old green vertical bars, superimposed on a blue background grid. Following the reaction time response for search, the participants had to decide whether a probe dot had briefly been presented. Previews appeared for 1,000 msec and were immediately followed by search displays. In Experiment 1, we demonstrated a standard preview benefit relative to a conjunction search baseline. In Experiment 2, search was combined with the probe task. Probes were more difficult to detect when they were presented 1,200 msec, relative to 800 msec, after the preview, but at both intervals detection of probes at the locations of old distractors was harder than detection on new distractors or at neutral locations. Experiment 3A demonstrated that there was no difference in the detection of probes at old, neutral, and new locations when probe detection was the primary task and there was also no difference when all of the shapes appeared simultaneously in conjunction search (Experiment 3B). In a final experiment (Experiment 4), we demonstrated that detection on old items was facilitated (relative to neutral locations and probes at the locations of new distractors) when the probes appeared 200 msec after previews, whereas there was worse detection on old items when the probes followed 800 msec after previews. We discuss the results in terms of visual marking and attention capture processes in visual search.     

Just noticeable differences in 2D and 3D bar charts: a psychophysical analysis of chart readability

The comparative readability of 2-dimensional (2D) and 3-dimensional (3D) bar charts was assessed using the method of constant stimuli, and the corresponding Weber constants and just-noticeable-differences were computed. It was predicted that the just-noticeable-difference for 3D charts would be larger than for 2D charts. 36 bar charts (18 2D and 18 3D) were prepared for individual presentation on an overhead projector. Each chart contained two bars, one of standard size (25 units) and a second that varied in size from 24 to 26 units in increments of 0.25 units (1% of the standard). 57 undergraduates in psychology were shown the 36 charts in a random sequence for 3 sec. each, separated by 3-sec. intervals. Participants recorded comparative size judgements of bars for each chart. Multivariate analyses identify an advantage in accuracy (in the order of magnitude of approximately 10%) for 2D rather than 3D bar charts, after controlling for sex, age, and use of corrective lenses. The computed Weber constants for these judgements were similar to those computed for visual intensity over 100 years ago, but--as predicted--the just-noticeable-difference for 3D charts was larger (implying that larger differences are needed on 3D charts to distinguish closely related bars). Furthermore, the use of traditional psychophysical approaches (such as the method of constant stimuli) in assessing graphical aids would appear to be justified.     

Visual psychophysics of simple graphical elements

The accuracy with which graphical elements are judged was assessed in a psychophysical task that parallels the real-life use of graphs. The task is a variant of the Metfessel-Comrey constant-sum method, and an associated model based on Stevens's law is proposed. The stimuli were horizontal and vertical lines, bars, pie and disk slices, cylinders, boxes, and table entries (numbers). Stevens's law exponents were near unity for numbers and 1-dimensional elements but were also close to 1 for elements possessing 2 or 3 apparent dimensions--subjects accommodate extraneous dimensions that do not carry variation, changing the effective dimensionality of the stimulus. Judgment errors were small, with numbers yielding the best performance; elements such as bars and pie slices were judged almost as accurately; disk elements were judged least accurately, but the magnitude of the errors was not large.     

Do irrelevant depth cues affect the comprehension of bar graphs?

Eight participants decided whether two‐ or three‐dimensional bars embedded within two‐ or three‐dimensional frames were semantically consistent with written inequalities of the form ‘A>B’. Inequalities were presented either before (Experiment 1) or after the graphs (Experiment 2). In Experiment 1, irrelevant depth cues were associated with slower decision times and there was no processing cost associated with an inconsistency between the dimensionalities of bars and frames. Memory encoding and retrieval times in Experiment 2 were affected by both graph complexity and consistency. Neither a depth consistency heuristic nor the maximum ink–data ratio principle can account for these results. More appropriate guidance for graph design will come from elaborating the working memory component of current cognitive models of graph processing. Copyright © 2000 John Wiley & Sons, Ltd.     

Working memory and stroop interference: an individual differences investigation

We investigated the claim that individual differences in working-memory capacity reflect limitations on the ability to inhibit task-irrelevant information and/or to maintain activation in the face of distracting or interfering events. Specifically, we investigated whether high- and low-capacity individuals differed in their susceptibility to interference on the Stroop task and whether high-capacity individuals employed a strategy for minimizing Stroop interference. In Experiment 1, we found that high-capacity participants showed substantial interference when conflict trials were infrequent, but almost no interference when conflict trials were frequent. In contrast, low-capacity participants showed substantial interference irrespective of the proportion of conflict trials. In Experiment 2, we found that high-capacity participants experienced substantial negative priming, slow responses when the to-be-named color was the irrelevant word on the previous trial. We discuss these results and their implications for high-capacity individuals' ability to reduce Stroop interference in light of both inhibitory and noninhibitory accounts of negative priming.     

Does crossmodal correspondence modulate the facilitatory effect of auditory cues on visual search?

The ??pip-and-pop effect?? refers to the facilitation of search for a visual target (a horizontal or vertical bar whose color changes frequently) among multiple visual distractors (tilted bars also changing color unpredictably) by the presentation of a spatially uninformative auditory cue synchronized with the color change of the visual target. In the present study, the visual stimuli in the search display changed brightness instead of color, and the crossmodal congruency between the pitch of the auditory cue and the brightness of the visual target was manipulated. When cue presence and cue congruency were randomly varied between trials (Experiment 1), both congruent cues (low-frequency tones synchronized with dark target states or high-frequency tones synchronized with bright target states) and incongruent cues (the reversed mapping) facilitated visual search performance equally, relative to a no-cue baseline condition. However, when cue congruency was blocked and the participants were informed about the pitch?Cbrightness mapping in the cue-present blocks (Experiment 2), performance was significantly enhanced when the cue and target were crossmodally congruent as compared to when they were incongruent. These results therefore suggest that the crossmodal congruency between auditory pitch and visual brightness can influence performance in the pip-and-pop task by means of top-down facilitation.