Jing Li and Jean-Bernard Martens and Jarke J van Wijk.
Judging Correlation from Scatterplots and Parallel Coordinate Plots.
In Information Visualization, vol. 9, no. 1, pp. 13--30, 2010.


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Abstract:

Scatterplots and parallel coordinate plots (PCPs) that can both be used to assess correlation visually. In this paper, we compare these two visualization methods in a controlled user experiment. More specifically, 25 participants were asked to report observed correlation as a function of the sample correlation under varying conditions of visualization method, sample size and observation time. A statistical model is proposed to describe the correlation judgment process. The accuracy and the bias in the judgments in different conditions are established by interpreting the parameters in this model. A discriminability index is proposed to characterize the performance accuracy in each experimental condition. Moreover, a statistical test is applied to derive whether or not the human sensation scale differs from a theoretically optimal (that is, unbiased) judgment scale. Based on these analyses, we conclude that users can reliably distinguish twice as many different correlation levels when using scatterplots as when using PCPs. We also find that there is a bias towards reporting negative correlations when using PCPs. Therefore, we conclude that scatterplots are more effective than parallel plots in supporting visual correlation analysis.

Bibtex:

@Article{        li:2010:JCSP,
  Author = 	 {Jing Li and Jean-Bernard Martens and Jarke J van Wijk},
  title = 	 {Judging Correlation from Scatterplots and Parallel Coordinate Plots},
  journal = 	 {Information Visualization},
  year = 	 {2010},
  volume = 	 {9},
  number = 	 {1},
  pages = 	 {13--30},
}

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References:

1 Amar, R., Eagan, J. and Stasko, J. (2005) Low-level components of analytic activity in information visualization. Proceedings of the IEEE Symposium on Information Visualization (InfoVis'05); Minneapolis, USA, Washington, DC: IEEE Computer Society Press, pp. 111-117.
2 Anderson, T.W. and Finn, J.D. (1996) The New Statistical Analysis of Data. New York: Springer-Verlag, p. 139.
3 Inselberg, A. and Dimsdale, B. (1990) Parallel coordinates: A tool for visualizing multidimensional geometry. Proceedings of the IEEE Visualization Conference (VIS'90); San Franscisco, CA, Los Alamitos, CA: IEEE Computer Society Press, pp. 361-378.
4 Inselberg, A. (1985) The Plane with Parallel coordinates. The Visual Computer 1(4): 69-91.
5 Wegman, E.J. (1990) Hyperdimensional data analysis using parallel coordinates. Journal of the American Statistical Association 85(411): 664-675.
6 Slocum, T.A., McMaster, R.B., Kessler, F.C. and Howard, H.H. (2005) Thematic Cartography and Geographic Visualization, 2nd edn. Prentice Hall Series in Geographic Information Science. New Jersey: Pearson Prentice Hall, p. 40.
7 Sirrtola, H. (2000) Direct manipulation of Parallel coordinates. Proceedings of International Conference on Information Visualization (IV'00); London, UK, London: IEEE Computer Society Press, pp. 373-378.
8 Loh, W.Y. (1987) Does the correlation coefficient really measure the degree of clustering around a line? Journal of Educational Statistics 12: 235-239.
9 Cleveland, W.S., Diaconis, P. and McGill, R. (1982) Variables on Scatterplots look more highly correlated when the scales are increased. Science, New Series 216: 1138-1141.
10 Strahan, R.F. and Hansen, C.J. (1978) Underestimating correlation from Scatterplots. Applied Psychological Measurement 2(4): 543-550.
11 Erlick, D.E. and Mills, R.G. (1967) Perceptual quantification of co- nditional dependency. Journal of Experimental Psychology 73: 9-14.
12 Best, L.A., Hunter, A.C. and Stewart, B.M. (2006) Perceiving relationships: A physiological examination of the perception of Scatterplots. In: D. Barker-Plummer, R. Cox and N. Swoboda (eds.) Diagramatic Representation and Inference, Proceedings of Fourth International Conference, Diagrams (LNAI 4045); Berlin,Heidelberg: Springer-Verlag, pp. 244-257.
13 Kareev, Y. (1995) Positive bias in the perception of covariation.Psychological Review 102, 490-502.
14 Johansson, J., Forsell, C., Lind, M. and Cooper, M. (2008) Perceiving patterns in parallel coordinates: Determining thresholds for identification of relationships. Information Visualization (advance online publication 31 January 2008, http://www.palgrave- journals.com/ivs/journal/vaop/ncurrent/abs/9500166a.html, accessed 11 March 2008.
15 Forsell, C. and Johansson, J. (2007) Task-based evaluation of multi-relational 3D and standard 2D parallel coordinates. Proceedings of Electronic Imaging; San Jose, CA, Bellingham, WA: Copublished by SPIE and IS&L, pp. 64950C-1-12.
16 Wegenkittl, R., Loffelmann, H. and Groller, E. (1997) Visualizing the behavior of higher dimensional dynamical systems (VIS'97). Proceedings of the 8th conference on Visualization '97; Phoenix, AZ, Washington, DC: IEEE computer Society Press, pp. 119-125.
17 Fanea, E., Carpendale, S. and Isenberg, T. (2005) An interactive 3D integration of parallel coordinates and star glyphs. Proceedings of the IEEE Symposium on Information Visualization (INFOVIS'05); Minneapolis, MN, USA, Washington, DE: IEEE Computer Society Press, pp. 149-156.
18 Tory, M., Potts, S. and Moller, T. (2005) A parallel coordinates style interface for exploratory volume visualization. IEEE Transactions on Visualization and Computer Graphics 11: 71-80.
19 Ellis, G. and Dix, A. (2006) Enabling automatic clutter reduction in parallel coordinate plots. IEEE Transactions on Visualization and Computer Graphics 12: 717-723.
20 Novotny, M. and Hauser, H. (2006) Outlier-preserving Focus + Context visualization in parallel coordinates. IEEE Transactions on Visualization and Computer Graphics 12(5): 893-900.
21 Johansson, J., Ljung, P., Jern, M. and Cooper, M. (2005). Revealing structure within clustered parallel coordinates displays.
Proceedings of the IEEE Symposium on Information Visualization (INFOVIS'05); Minneapolis, MN, Washington, DC: IEEE Com- puter Society Press, pp. 125-132.
22 Artero, A.O., Ferreira de Oliveira, M.C. and Levkowitz, H. (2004) Uncovering clusters in crowded parallel coordinates visualizations. Proceedings of the IEEE Symposium on Information Visualization (InfoVis'o5); Austin, TX, Washington, DC: IEEE Computer Society Press, pp. 81-88.
23 Graham, M. and Kennedy, J. (2003) Using curves to enhance parallel coordinate visualizations. Proceedings of the Seventh International Conference on Information Visualization (IV'03); London, UK, Washington, DC: IEEE Computer Society Press, pp. 10-16.
24 Lanzenberger, M., Miksch, S. and Pohl, M. (2005) Exploring highly structured data-A comparative study of stardinates and parallel coordinates. Proceedings of the Ninth International Conference on Information Visualization (IV'05); Greenwich, UK, London: IEEE Computer Society Press, pp. 3-9.
25 Kobsa, A. (2004) User experiment with tree visualization systems. Proceedings of the IEEE Symposium on Information Visualization (InfoVis'04); Austin, TX, Washington, DC: IEEE Computer Society Press, pp. 9-16.
26 Ghoniem, M., Fekete, J. and Castagliola, P. (2004) A comparison of the readability of graphs using node-link and matrix-based representations. (InfoVis'04). Proceedings of the IEEE Symposium on Information Visualization; Austin, TX, Washington, DC: IEEE Computer Society Press, pp. 17-24.
27 Irani, P., Slonowsky, D. and Shajahan, P. (2006) Human perception of structure in shaded space-filling visualizations. Information Visualization 5: 47-61.
28 North, C. (2006) Visualization viewpoints: Toward measuring visualization insight. IEEE Computer Graphics and Applications 26: 6-9.
29 Martens, J. (2003) Image Technology Design: A Perceptual Approach The International Series in Engineering and Computer Science. Dordrecht: Kluwer Academic Publisher, p. 193.
30 McGrath, R.E. (1996) Understanding Statistics -- A Research Perspective. Reading, MA: Addison-Wesley, p. 26.
31 Siegel, S. and Castellan, N.J. (1988) Nonparametric Statistics for the Behavioral Sciences. 2nd edn. New York: McGraw-Hill, p. 42.
32 Wilson, P., Tanner, X., Jr, and Theodore, G.B. (1964) Definitions of d and as psychophysical measures. In: J.A. Swets et al. (eds.) Signal Detection and Recognition by Human Observers Inc. New York: John Wiley & Sons, pp. 147-163.
33 Cowan, N. (2001) The magical number 4 in short-term memory: A reconsideration of mental storage capacity. Behavioral and Brain Sciences 24: 87-185.