Understanding bias in proportion production

The Stevens exponent (beta) can be obtained from proportion estimation judgments using the power model. In this article, the authors extend that model to proportion production, in which the relative magnitudes of 2 stimuli are adjusted to correspond to a numeric proportion (e.g., 1/4 or .25). The model predicts that when beta < 1, small proportions are underproduced, and large proportions are overproduced, but it predicts the reverse when beta > 1, which is the opposite of the predicted patterns for estimation. Eight participants estimated and produced magnitudes and proportions with spatial volume (beta < 1; Experiment 1) and color saturation (beta > 1; Experiment 2). The model's predictions were generally supported. An extension of the model using reference points can account for multicycle patterns shown by some participants.     

Bias in proportion judgments: the cyclical power model

When participants make part-whole proportion judgments, systematic bias is commonly observed. In some studies, small proportions are overestimated and large proportions underestimated; in other studies, the reverse pattern occurs. Sometimes the bias pattern repeats cyclically with a higher frequency (e.g., overestimation of proportions less than .25 and between .5 and .75; underestimation otherwise). To account for the various bias patterns, a cyclical power model was derived from Stevens' power law. The model proposes that the amplitude of the bias pattern is determined by the Stevens exponent, beta (i.e., the stimulus continuum being judged), and that the frequency of the pattern is determined by a choice of intermediate reference points in the stimulus. When beta < 1, an over-then-under pattern is predicted; when beta > 1, the under-then-over pattern is predicted. Two experiments confirming the model's assumptions are described. A mixed-cycle version of the model is also proposed that predicts observed asymmetries in bias patterns when the set of reference points varies across trials.     

Coordination of Eye and Leg Movements During Visually Guided Stepping

In the present study, 2 related hypotheses were tested: first, that vision is used in a feedforward control mode during precision stepping onto visual targets and, second, that the oculomotor and locomotor control centers interact to produce coordinated eye and leg movements during that task. Participants' (N = 4) eye movements and step cycle transition events were monitored while they performed a task requiring precise foot placement at every step onto irregularly placed stepping stones under conditions in which the availability of visual information was either restricted or intermittently removed altogether. Accurate saccades, followed by accurate steps, to the next footfall target were almost always made even when the information had been invisible for as long as 500 ms. Despite delays in footlift caused by the temporary removal (and subsequent reinstatement) of visual information, the mean interval between the start of the eye movement and the start of the swing toward a target did not vary significantly (p > .05). In contrast, the mean interval between saccade onset away from a target and a foot landing on that target (stance onset) did vary significantly (p < .05) under the different experimental conditions. Those results support the stated hypotheses.     

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.     

Androgyny on the TV screen? An analysis of sex-role portrayal

Characters in a random sample of dramatic television programs representative of family time and later viewing time in 1975 and equivalent time periods in 1976 were rated on sex-role portrayal, using traits from the Bem Sex-Role Inventory (BSRI). The family time concept, which eliminated violence and sex from programs shown between 7:00 and 9:00 p.m. during 1975, had a significant effect on sex-role portrayal. Male characters were portrayed in a more realistic, though still highly masculine, way than their counterparts in other time periods. Female characters were portrayed as somewhat more feminine during family time than during other viewing hours. A significant interaction effect among viewing time, type of program, and sex of character suggested that content considered acceptable for younger viewers emphasized the stereotypical female role.This research was reported in part at the meeting of the Western Psychological Association, Seattle, April 1977. The author expresses appreciation to all those individuals who assisted with the project by serving as judges and as critics, and to the anonymous reviewer who made many helpful suggestions.     

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.     

Human Eye Movements During Visually Guided Stepping

Visually guided locomotion was studied in an experiment in which human subjects (N = 8) had to accurately negotiate a series of irregularly spaced stepping-stones while infrared reflectometry and electrooculography were used to continuously record their eye movements. On average, 68% of saccades made toward the next target of footfall had been completed (visual target capture had occurred) while the foot to be positioned was still on the ground; the remainder were completed in the first 300 ms of the swing phase. The subjects' gaze remained fixed on a target, on average, until 51 ms after making contact with it, with little variation. A greater amount of variation was seen in the timing of trailing footlift relative to visual target capture. Assuming that subjects sampled the visual cues as and when they were required, visual information appeared most useful when the foot to be positioned was still on the ground.     

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.