Underestimating Correlation from Scatterplots

Strahan, Robert F.; Hansen, Chris

doi:10.1177/014662167800200409

Cited by 30 publications

(30 citation statements)

References 7 publications

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“…For jnd‐above data over the same range, corresponding values are m =–0.25 and a = 0.282, with R 2 = .964. This is consistent with earlier reports [SH78, CDM82] that precision is greatest at higher correlations. Note that jnd is proportional to the distance of the base correlation from the intersection with the x‐axis; in this way, performance can be described in terms of a Weber fraction (–m).…”

Section: Resultssupporting

confidence: 93%

The Perception of Correlation in Scatterplots

Rensink

Baldridge

2010

Computer Graphics Forum

148

197

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We present a rigorous way to evaluate the visual perception of correlation in scatterplots, based on classical psychophysical methods originally developed for simple properties such as brightness. Although scatterplots are graphically complex, the quantity they convey is relatively simple. As such, it may be possible to assess the perception of correlation in a similar way. Scatterplots were each of 5.0° extent, containing 100 points with a bivariate normal distribution. Means were 0.5 of the range of the points, and standard deviations 0.2 of this range. Precision was determined via an adaptive algorithm to find the just noticeable differences (jnds) in correlation, i.e., the difference between two side-by-side scatterplots that could be discriminated 75% of the time. Accuracy was measured by direct estimation, using reference scatterplots with fixed upper and lower values, with a test scatterplot adjusted so that its correlation appeared to be halfway between these. This process was recursively applied to yield several further estimates. (1 -b). The values of b found via discrimination closely match those found via direct estimation. As such, it appears that the perception of correlation in a scatterplot is completely described by two related performance curves, specified by two easily-measured parameters. Results of the discrimination tests show jnd(r) = k (1/b -r), where r is the Pearson correlation, and parameters 0 < k, b < 1. Integration yields a subjective estimate of correlation g(r) = ln(1 -br) / ln

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Section: Resultssupporting

confidence: 93%

The Perception of Correlation in Scatterplots

Rensink

Baldridge

2010

Computer Graphics Forum

148

197

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“…Pollack first observed the varying levels of sensitivity between low and high C R values in a study with 6 participants [Pol60]. The underestimation when 0 < C R < 1 was subsequently confirmed by many others (e.g., [Erl66, SH78, BK79, DAAK07]). Some have also observed overestimation when −1 < C R < 0 [Erl66, BK79].…”

Section: Related Workmentioning

confidence: 88%

“…We hope to establish how the variations of these conditions impact human perception in relation to the statistical measure PPMCC. If the impact were insignificant, it would suggest that human perception of correlation might be modelled by a relatively simple function, such as the ones proposed in [SH78, MS92, BK79, CDM82, DAAK07], and more recently in [RB10, HYFC14, KH16]. If the impact were significant, an appropriate underlying model would have to encode the functional dependency of humans’ perceived correlation on many visual features of datasets in addition to their PPMCC indicators.…”

Section: Introductionmentioning

confidence: 99%

An Empirical Study on the Reliability of Perceiving Correlation Indices using Scatterplots

Sher

Bemis

Liccardi

et al. 2017

Computer Graphics Forum

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Scatterplots have been in use for about two centuries, primarily for observing the relationship between two variables and commonly for supporting correlation analysis. In this paper, we report an empirical study that examines how humans’ perception of correlation using scatterplots relates to the Pearson's product‐moment correlation coefficient (PPMCC) – a commonly used statistical measure of correlation. In particular, we study human participants’ estimation of correlation under different conditions, e.g., different PPMCC values, different densities of data points, different levels of symmetry of data enclosures, and different patterns of data distribution. As the participants were instructed to estimate the PPMCC of each stimulus scatterplot, the difference between the estimated and actual PPMCC is referred to as an offset. The results of the study show that varying PPMCC values, symmetry of data enclosure, or data distribution does have an impact on the average offsets, while only large variations in density cause an impact that is statistically significant. This study indicates that humans’ perception of correlation using scatterplots does not correlate with computed PPMCC in a consistent manner. The magnitude of offsets may be affected not only by the difference between individuals, but also by geometric features of data enclosures. It suggests that visualizing scatterplots does not provide adequate support to the task of retrieving their corresponding PPMCC indicators, while the underlying model of humans’ perception of correlation using scatterplots ought to feature other variables in addition to PPMCC. The paper also includes a theoretical discussion on the cost‐benefit of using scatterplots.

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“…There are also a number of studies that have presented relatively sophisticated subjects with scatter diagrams and asked them to estimate the correlation coefficient or in some cases degree of linear relationship (e.g., Bobko & Karren, 1979;Cleveland, Diaconis, & McGill, 1982;Strahan & Hansen, 1978). These studies arenot considered here.…”

Section: Notesmentioning

confidence: 99%

Prediction and judgment as indicators of sensitivity to covariation of continuous variables

et al. 1988

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The present study used both judgments of strength of relationship and measures of the ability to predict one variable from another to assess subjects' sensitivity to the covariation of two continuous variables. In addition, one group of subjects judged strength of relationship after merely observing the presentation of 60 pairs of two-digit numbers, and a second group made strength judgments after being actively engaged in predicting one member of a pair when given the other. The prediction and judgment data provide different pictures of subjects' sensitivity to covariation. The subjects were quite poor at estimating strength of relationship but, by some measures, good at predicting one variable from another. Judgments were not strongly influenced by whether subjects had previously engaged in overt prediction. The implications of these results for the literature on covariation estimation are discussed.The ability to detect relationships between events in the environment and to use knowledge about these relationships to make predictions has come to be regarded as an important component of human intelligence. As Crocker (1981, p. 272) pointed out, "knowing whether events are related, and how strongly they are related, enables individuals to explain the past, control the present, and predict the future."The large literature that is concerned with people's ability to judge the degree to which imperfectly related events covary has often been characterized as indicating that people are poor at assessing covariation (e.g., Nisbett & Ross, 1980). Most research in the field has dealt with binary variables (e.g., presence or absence of symptom and presence or absence of disease), so that all cases fall into one of the cells of a 2 X 2 table. Empirical studies and theoretical analyses have been aimed at exploring reasons why performance is often poor and at delineating circumstances under which subjects tend to be more or less accurate according to some statistical measure of relationship (for reviews, see Alloy & Tabachnik, 1984;Crocker, 1981).The ability to estimate covariation between variables that can take on more than two values has also been characterized as being quite poor (e.g., Nisbett & Ross, 1980), despite the fact that few estimation studies have employed nonbinary variables and the fact that the older studies cited as providing evidence of conservatism (Beach & Scopp, 1966; Edick & Mills, 1967) by Beach and Scopp (1966) was a rating of degree of confidence that the relationship was positive or negative, whereas subjects in the Edick and Mills (1967) study made more than 1,000 covariationjudgments over 10 sessions.Jennings, Amabile, and Ross (1982) had subjects make covariationjudgments for several types of "theory-free" bivariate distributions in which the product-moment correlation (r) varied between 0 and 1. In one condition, after briefly studying 10 number pairs, subjects first judged whether the relationship between members of pairs was positive or negative, then indicated their subjective impression ...

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Underestimating Correlation from Scatterplots

Cited by 30 publications

References 7 publications

The Perception of Correlation in Scatterplots

The Perception of Correlation in Scatterplots

An Empirical Study on the Reliability of Perceiving Correlation Indices using Scatterplots

Prediction and judgment as indicators of sensitivity to covariation of continuous variables

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