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 classification of graphical elements.

In three experiments, participants classified stimuli depicting pie charts and stacked bar graphs on two criteria: a proportion shown in the graph, and the graph's overall size (scaling). Sorting times and errors were measured. For stacked bars, performance was impaired when participants sorted on the proportion and scaling varied. No such impairment occurred for pie charts. Experiment 1 showed that varying scaling produced Garner interference in classification of proportions with stacked bars, but not pies. Experiment 2 showed that this result held when the position of the pie slice was varied; Experiment 3 results showed facilitation for particular combinations of proportion and scaling levels. In general, the results showed that proportion and scaling had an asymmetric integral relation for stacked bar graphs, but were separable dimensions for pie charts.     

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.     

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.     

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.     

Bar graphs depicting averages are perceptually misinterpreted: The within-the-bar bias

Perhaps the most common method of depicting data, in both scientific communication and popular media, is the bar graph. Bar graphs often depict measures of central tendency, but they do so asymmetrically: A mean, for example, is depicted not by a point, but by the edge of a bar that originates from a single axis. Here we show that this graphical asymmetry gives rise to a corresponding cognitive asymmetry. When viewers are shown a bar depicting a mean value and are then asked to judge the likelihood of a particular data point being part of its underlying distribution, viewers judge points that fall within the bar as being more likely than points equidistant from the mean, but outside the bar--as if the bar somehow "contained" the relevant data. This "within-the-bar bias" occurred (a) for graphs with and without error bars, (b) for bars that originated from both lower and upper axes, (c) for test points with equally extreme numeric labels, (d) both from memory (when the bar was no longer visible) and in online perception (while the bar was visible during the judgment), (e) both within and between subjects, and (f) in populations including college students, adults from the broader community, and online samples. We posit that this bias may arise due to principles of object perception, and we show how it has downstream implications for decision making.     

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.     

Graph‐Framing Effects in Decision Making

This study manipulated the graphical representation of options by framing the physical characters in figures and found that preferences could be affected even when the words and numbers of the problem were constant. Based on attribute substitution theory and an equate‐to‐differentiate approach, we proposed a two‐process model of graph‐framing effects. In the first mental process, the graph‐editing process, the physical features (e.g., distance, size) represented in the graph are visually edited, and the perceived numerical difference between the options is judged based on its physical features. The second mental process, the preferential choice process, occurs by an equate‐to‐differentiate approach in which people seek to equate the difference between options on the dimension on which the difference is smaller, thus leaving the greater other‐dimensional difference to be the determinant of the final choice. Four experiments were tested for graph‐framing effects. Experiment 1 found a graph‐framing effect in coordinate graphs resting on the (de)compression of the scales employed in the figures. Experiment 2 revealed additional graph‐framing effects in other question scenarios and showed that preference changes were mediated by perceived numerical distances. Experiment 3 further confirmed the presence of graph‐framing effects in sector graphs similar to those found in coordinate ones. Experiment 4 suggested that such graph‐framing effects could be eliminated when logical processing (e.g., introducing a mathematical operation before a choice task) was encouraged. This paper discusses related research and a possible substrate basis for graph‐framing effects. Copyright © 2011 John Wiley & Sons, Ltd.     

Eye movements reveal distinct search and reasoning processes in comprehension of complex graphs

Hierarchical graphs (e.g. file system browsers, family trees) represent objects (e.g. files, folders) as graph nodes, and relations (subfolder relations) between them as lines. In three experiments, participants viewed such graphs and carried out tasks that either required search for two target nodes (Experiment 1A), reasoning about their relation (Experiment 1B), or both (Experiment 2). We recorded eye movements and used the number of fixations in different phases to identify distinct stages of comprehension. Search in graphs proceeded like search in standard visual search tasks and was mostly unaffected by graph properties. Reasoning occurred typically in a separate stage at the end of comprehension and was affected by intersecting graph lines. The alignment of nodes, together with linguistic factors, may also affect comprehension. Overall, there was good evidence to suggest that participants read graphs in a sequential manner, and that this is an economical approach of comprehension. Copyright © 2010 John Wiley & Sons, Ltd.     

Eye Movements Indicate the Temporal Organisation of Information Processing in Graph Comprehension

Hierarchical graphs (e.g. file system browsers and preference trees) represent objects (e.g. files and folders) as graph nodes and relations between them (e.g. sub‐folder relations) as lines. We investigated the temporal organisation of two processes that are necessary for comprehending such graphs—search for the graph nodes and reasoning about their relation. We tracked eye movements to change graphs while participants interpreted them. In Experiment 1, we masked the graph at a time when search processes had finished but reasoning was hypothetically ongoing. We observed a dramatic deterioration in comprehension compared with unmasked graphs. In Experiment 2, we changed the relation between critical graph nodes after search for them had finished, unbeknownst to participants. Participants mostly based their response on the graph as presented after the change. These results suggest that comprehension processes are organised in a sequential manner, an observation that can potentially be applied to the interactive presentation of graphs. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

Spatial legend compatibility within versus between graphs in multiple graph comprehension

Previous research has shown that spatial compatibility between the data region and the legend of a graph is beneficial for comprehension. However, in multiple graphs, data–legend compatibility can come at the cost of spatial between-graph legend incompatibility. Here we aimed at determining which type of compatibility is most important for performance: global (legend–legend) compatibility between graphs, or local (data–legend) compatibility within graphs. Additionally, a baseline condition (incompatible) was included. Participants chose one out of several line graphs from a multiple panel as the answer to a data-related question. Compatibility type and the number of graphs per panel were varied. Whereas Experiment 1 involved simple graphs with only two lines/legend entries within each graph, Experiment 2 explored more complex graphs. The results indicated that compatibility speeds up comprehension, at least when a certain threshold of graph complexity is exceeded. Furthermore, we found evidence for an advantage of local over global data–legend compatibility under specific conditions. Taken together, the results further support the idea that compatibility principles strongly determine the ease of integration processes in graph comprehension and should thus be considered in multiple-panel design.     

Do seductive details do their damage in the context of graph comprehension? Insights from eye movements

In educational research, interesting but irrelevant materials are often considered seductive details, which are suspected to have detrimental effects on learning. Although seductive details have been mostly examined in the context of text comprehension, such elements are also used in graphs (e.g., depicting data points). In the present experiment, we investigated both seductive text and seductive pictures in the context of graph comprehension as well as the interaction of seductive details with spatial working memory capacity (SWMC). We recorded N = 68 students' eye movements, while they analyzed bar graphs in a within‐subject design. Data were analyzed with linear mixed‐effects models. Results show that seductive details did not affect students' graph reading performance but prolonged the task processing time. Eye‐fixation measures revealed that additional processing time was best explained by attention distraction towards the seductive material. SWMC did not affect the presence or the extent of the seductive details effect.     

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。     

Connectedness underlies the underestimation of the horizontal vertical illusion in L-shaped configurations

L-shaped configuration is a commonly used stimulus configuration in studying horizontal vertical illusion. Here, we report that the horizontal vertical illusion is substantially underestimated when the L-shaped configuration is used for evaluating the illusion. Experiment 1 found that, in a length perception task, the perceived length of a vertical bar was about 10% longer than that of a horizontal bar with the same physical size. Similar amount of HVI was found in a length comparison task, in which the length of a horizontal bar was compared to that of a vertical bar and the two bars were presented separately in space or in time. In contrast, when the length comparison task was conducted with the two bars being arranged in a connected L-shape, the illusion was halved in strength. Experiment 2 and 3 studied what might be the cause of this L-shape induced HVI-underestimation. Two factors were investigated: the connectedness of the two lines, and the 45° absolute orientation or the 45° inner angle information embedded in the upright isosceles L-shape. The results showed that the HVI strength was not much affected when the 45° absolute orientation and the 45° angle information was made useless for the length comparison task. In contrast, the illusion was significantly reduced in strength whenever the two lines were separated as compared to when they were connected. These results suggested that the connectedness of the two lines must underlie the underestimation of the horizontal vertical illusion in the L-shaped configurations.     

The integration of habits maintained by food and water reinforcement through stimulus compounding.

In Experiment 1, a light and a tone were correlated independently with water reinforcement of bar pressing by rats. With different naive subjects in Experiment 2, one of these stimuli was correlated with food and the other with water reinforcement (counterbalanced). In both experiments the absence of tone and light signaled extinction. Tests of stimulus-reinforcer independence in Experiment 2 indicated that tone and light controlled behavior whose rate was specifically affected by deprivation state. In the stimulus-compounding tests of both experiments, response rates were higher to tone-plus-light than to tone or light presented alone (additive summation). This is the first report of additive summation produced through compounding stimuli paired with different reinforcers. The results are discussed in the context of the effects of incentive motivation on operant performance.     

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.     

Visual statistical decisions

To identify variables that underlie intuitive judgments about the sizes of groups of similar objects, we asked people to judge the relative heights of vertical bars briefly shown, two groups at a time, on a computer display. Randomly selected normal deviates determined individual bar height. Average differences in height and group sizes were also randomly varied. Twenty-eight participants judged 250 differences each, which were then submitted to multiple regression analysis and psychophysical inspection. The total number of bars sharpened discrimination, whereas variance dulled it. Critical ratio (CR), the forerunner to the modern t test, emerged as the most important predictor, little additional variance was explained by other factors. The difference in the number of bars was a reliable factor, favoring the greater number of bars. Confidence limits around thresholds, defined as CRs needed to say "possibly greater" surrounded 1.65; as a z value, this corresponded to a one-tailed probability of .05. Judgments about noisy stimuli thus seem to be based on a statistical process and to employ a probability criterion similar to that used in the formal statistical evaluation of experimental findings--namely, p < .05.