![]() Next, the central assumption of the estimation techniques-that numbers can be assigned to perceived magnitudes in a consistent way-is problematic, leading to the possibility of unstable or context-dependent estimates (Ellermeier & Faulhammer, 2000) (this may help explain why inconsistent results are sometimes encountered-see e.g., Doherty et al., 2007.) Third, there was little investigation of systematicity-the extent to which connections exist between precision and accuracy, not to mention with the rest of visual perception. First, they paid relatively little attention to the precision of the process-the extent to which the same estimate results when the same stimulus is presented. However, although these studies were important, they had limitations. Thus, although knowledge and expertise can influence the more sophisticated aspects of this process (Freedman & Smith, 1996 Lewandowsky & Spence, 1989), there nevertheless seems to exist a distinct basic stage of correlation perception-a rapidly-acting initial phase that can be considered purely perceptual, with similar characteristics for most observers. They also showed that much of this process is carried out rapidly, with results largely independent of the statistical expertise of the observer (Lane, Anderson, & Kellam, 1985 Meyer & Shinar, 1992 Meyer et al., 1997 Strahan & Hansen, 1978) indeed, particular neural systems appear to be involved (Best, Hunter, & Stewart, 2006). Results showed that perceived correlation g( r) tends to underestimate physical correlation r (especially at intermediate levels), with little correlation perceived when | r | < 0.2 (Bobko & Karren, 1979 Boynton, 2000 Cleveland, Diaconis, & McGill, 1982 Strahan & Hansen, 1978). Most were based on numerical estimation-asking observers for a number that describes the magnitude of the correlation perceived. Historically, the perception of correlation has been investigated in several ways (for reviews, see Boynton, 2000 Doherty et al., 2007). Another reason is that this domain is simple enough to explore systematically, while still being rich enough to raise interesting questions about the mechanisms involved. In part, this is because much of the estimation of r appears to be a perceptual process, one to which existing techniques of vision science can be readily applied (e.g., Doherty, Anderson, Angott, & Klopfer, 2007 Meyer & Shinar, 1992 Meyer et al., 1997). It has been argued (Rensink & Baldridge, 2010) that a good test-bed for this approach is the estimation of Pearson correlation r in scatterplots. The perception of such graphical representations therefore has considerable potential to help us investigate various aspects of our visual intelligence (Rensink, 2014 see also Cleveland & McGill, 1987 Meyer, Taieb, & Flascher, 1997). If a graphical representation is designed well, analysis can be rapid, accurate, and precise in such situations the visual system of the analyst perceives structure in a dataset in much the same way as it perceives structure in the physical world. An important part of such analysis is the use of graphical representations, which can be highly effective when datasets are large, messy, and complex (see e.g., Card, Mackinlay, & Shneiderman, 1999 Thomas & Cook, 2005). The analysis of data is important in many aspects of life. It is suggested that this reflects the ability of observers to perceive the information entropy in an image, with this quantity used as a proxy for Pearson correlation. The generality and form of these laws suggest that what underlies correlation perception is not a geometric structure such as the shape of the dot cloud, but the shape of the probability distribution of the dots, likely inferred via a form of ensemble coding. Performance was found to be similar in all conditions. Three other conditions were also examined: a dot cloud with 25 points, a horizontal compression of the cloud, and a cloud with a uniform distribution of dots. In addition, these laws were linked, with the intercept of the JND line being the inverse of the bias in perceived magnitude. Consistent with earlier results, just noticeable difference (JND) was a linear function of the distance away from r = 1, and the magnitude of perceived correlation a logarithmic function of this quantity. The first had 100 points with equal variance in both dimensions. To cast light on these, four different distributions of datapoints were examined. The underlying perceptual mechanisms, however, remain poorly understood. ![]() ![]() ![]() For scatterplots with gaussian distributions of dots, the perception of Pearson correlation r can be described by two simple laws: a linear one for discrimination, and a logarithmic one for perceived magnitude (Rensink & Baldridge, 2010). ![]()
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