Sample size bias in judgments of perceptual averages (original) (raw)
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Sample size bias in the estimation of means
Psychonomic Bulletin & Review, 2010
The present research concerns the hypothesis that intuitive estimates of the arithmetic mean of a sample of numbers tend to increase as a function of the sample size; that is, they reflect a systematic sample size bias. A similar bias has been observed when people judge the average member of a group of people on an inferred quantity (e.g., a disease risk; see . Until now, however, it has been unclear whether it would be observed when the stimuli were numbers, in which case the quantity need not be inferred, and "average" can be precisely defined as the arithmetic mean. In two experiments, participants estimated the arithmetic mean of 12 samples of numbers. In the first experiment, samples of from 5 to 20 numbers were presented simultaneously and participants quickly estimated their mean. In the second experiment, the numbers in each sample were presented sequentially. The results of both experiments confirmed the existence of a systematic sample size bias.
Obligatory averaging in mean size perception
Vision Research, 2014
The perception of ensemble characteristics is often regarded as an antidote to an established bottleneck in focused attention and working memory, both of which appear to be limited in capacity to a few objects only. In order to test the associative law of summation, observers were asked to estimate the mean size of four circles relative to a reference circle. When there was no time to scrutinize each individual circle, observers discriminated the mean size difference identically, irrespective of whether the same summary size increment or decrement was added to or subtracted from the size of only one, two, or all four circles. Since observers judged the size of individual circles, the position of which was indicated after they were displayed, considerably less accurately than the mean size of the four circles, it is very unlikely that explicit knowledge of the size of the individual elements is the basis of mean size judgments. The sizes of individual elements were pooled together in an obligatory manner before size information had reached awareness. The processing of size information seems to be largely constrained to only one measure at a time, with a preference for mean size rather than the individual measures from which it is assembled.
An almost general theory of mean size perception
Vision Research, 2013
A general explanation for the observer's ability to judge the mean size of simple geometrical figures, such as circles, was advanced. Results indicated that, contrary to what would be predicted by statistical averaging, the precision of mean size perception decreases with the number of judged elements. Since mean size discrimination was insensitive to how total size differences were distributed among individual elements, this suggests that the observer has a limited cognitive access to the size of individual elements pooled together in a compulsory manner before size information reaches awareness. Confirming the associative law of addition means, observers are indeed sensitive to the mean, not the sizes of individual elements. All existing data can be explained by an almost general theory, namely, the Noise and Selection (N&S) Theory, formulated in exact quantitative terms, implementing two familiar psychophysical principles: the size of an element cannot be measured with absolute accuracy and only a limited number of elements can be taken into account in the computation of the average size. It was concluded that the computation of ensemble characteristics is not necessarily a tool for surpassing the capacity limitations of perceptual processing.
The Role of Perceptual Bias in Estimating Quantities
Decision Science Educator: Courses, 2019
A cognitive bias refers to a systematic (that is - a non-random and, thus, predictable) deviation from rationality in judgment or decision-making (Blanco, 2017). This implies that humans tend to deviate from the traditional concept of the ‘homo-economicus’ and can thus be irrational. They can pick an option that defies rational logic as they presume it to be the ‘correct’ option.<br><br>This paper focuses on the existence of one such bias - The Perceptual Bias, which explains how people tend to associate the height of a glass with the quantity of liquid it holds. In other words, a tall glass creates an illusion of greater quantity than a glass that is shorter and wider but holds the same quantity. People associate parameters of the glass, such as the quantity it holds, based on sensory inputs, such as sight. This paper also shows that when a tall glass and a short glass are presented individually, the bias is observed, however, when shown together to the same person, it ...
Research Square (Research Square), 2023
Magnitude perception in the visual domain encompasses enumeration and perceptual averaging. Enumeration involves estimating the number of objects, while perceptual averaging entails perceiving the average value of a feature within an ensemble. This study investigates the interaction between these processes across varied presentation durations. In Experiment 1, participants engaged in two tasks: numerosity comparison and mean size estimation. We familiarized participants with a fixed numerosity (13) and mean size (50px) of a set of black dots. The individual dot sizes and their locations varied in each display. Test stimuli varied in numerosity and mean size. Participants compared either the numerosity or mean size of the set with the reference values. We determined the point of subjective equality (PSE) separately for number and size trials. The PSE for both trials closely approximated 1, indicating a more veridical representation (F (1,42) = 0.04421, p = 0.3917). We attributed this to participants having unrestricted time to respond. In Experiment 2, test stimuli appeared for durations of 68ms, 500ms, and 1s. For both Enumeration and Size, PSE values were close to one at 68ms. A 2-way ANOVA test revealed a statistically significant interaction between enumeration and size at the p = 0.002 level (F (2,80) = 9.96, p ¡ 0.01). Experiment 1, with unrestricted response time, showed greater accuracy 1 compared to Experiment 2, where test stimulus duration was restricted. Both experiments indicate that accurate estimation in numerosity and mean size tasks depends on presentation time.
Journal of Emerging Technologies and Innovative Research, 2020
A cognitive bias refers to a systematic (that is-a non-random and, thus, predictable) deviation from rationality in judgment or decision-making (Blanco, 2017). This implies that humans tend to deviate from the traditional concept of the 'homo-economicus' and can thus be irrational. They can pick an option that defies rational logic as they presume it to be the 'correct' option. This paper focuses on the existence of one such bias-The Perceptual Bias, which explains how people tend to associate the height of a glass with the quantity of liquid it holds. In other words, a tall glass creates an illusion of greater quantity than a glass that is shorter and wider but holds the same quantity. People associate parameters of the glass, such as the quantity it holds, based on sensory inputs, such as sight. This paper also shows that when a tall glass and a short glass are presented individually, the bias is observed, however, when shown together to the same person, it spawns the idea of a comparison, and the effect of the perceptual bias is no longer observed.
Perception of means, sums, and areas
Attention, Perception, & Psychophysics, 2020
In this age of data visualization, it is important to understand our perception of the symbols that are used. For example, does the perceived size of a disc correspond most closely to its area, diameter, circumference, or some other measure? When multiple items are present, this becomes a question of ensemble perception. Here, we compare observers' performance across three different tasks: judgments of (i) the mean diameter, (ii) the total diameter, or (iii) the total area of (N = 1, 2, 3, or 7) test circles compared with a single reference circle. We draw a parallel between Anne Treisman's feature integration theory and Daniel Kahneman's cognitive systems, comparing the preattentive stage to System 1, and the focused attention stage to System 2. In accordance with Kahneman's prediction, average size (diameter) of the geometric figures can be judged with considerable accuracy, but the total diameter of the same figures cannot. Like the total length, the cumulative area covered by circles was also judged considerably less accurately than the mean diameter. Differences in efficiency between these three tasks illustrate powerful constraints upon visual processing: The visual system is well adapted for the perception of the mean size while there are no analogous mechanisms for the accurate perception of the total length or cumulative area. Thus, in visualizing data, using bubble charts proportional to area may be misleading as our visual system seems better adapted to perceive disc size by the radius rather than the area.
How can observers use perceived size? Centroid versus mean-size judgments
Journal of Vision, 2019
statistical representations are aggregate properties of the environment that are presumed to be perceived automatically and preattentively. We investigated two tasks presumed to involve these representations: judgments of the centroid of a set of spatially arrayed items and judgments of the mean size of the items in the array. The question we ask is: When similar information is required for both tasks, do observers use it with equal postfilter efficiency (Sun, Chubb, Wright, & Sperling, 2016)? We find that, according to instructions, observers can either efficiently utilize item size in making centroid judgments or ignore it almost completely. Compared to centroid judgments, however, observers estimating mean size incorporate the size of individual items into the average with low efficiency.
Effects of meaning and symmetry on judgments of size
Frontiers in psychology, 2014
Research has shown that people judge words as having bigger font size than non-words. This finding has been interpreted in terms of processing fluency, with higher fluency leading to judgments of bigger size. If so, symmetric numbers (e.g., 44) which can be processed more fluently are predicted to be judged as larger than asymmetric numbers (e.g., 43). However, recent research found that symmetric numbers were judged to be smaller than asymmetric numbers. This finding suggests that the mechanisms underlying size judgments may differ in meaningful and meaningless materials. Supporting this notion, we showed in Experiment 1 that meaning increased judged size, whereas symmetry decreased judged size. In the next two experiments, we excluded several alternative explanations for the differences in size judgments between meaningful and meaningless materials in earlier studies. This finding contradicts the notion that the mechanism underlying judgments of size is processing fluency.