×

zbMATH — the first resource for mathematics

Trellis display for modeling data from designed experiments. (English) Zbl 07260272
Summary: Visualizing data by graphing a response against certain factors, and conditioning on other factors, has arisen independently in many contexts. One is the interaction plots used in the analysis of data from designed experiments; these plots show conditional dependence based on the output of methods and models applied to the data. Trellis display, a framework for the visualization of multivariable data, allows conditioning to be readily carried out in a general way. It was developed initially in the context of data sets with a moderate or large number of observations to support the conditioning. This article demonstrates through examples that trellis display is also a highly useful visualization framework for designed experiments with a small number of runs. Trellis allows the visualization of conditional dependence, not only based on the output of models and methods, but also based on the raw data directly, which greatly aids the model building process. Trellis can even succeed for highly fractionated designs. The reason appears to be that for success, such designs require an engineering practice that keeps error variability small, which allows interpretable patterns to emerge on conditioning displays with a limited number of plotted points.
MSC:
62 Statistics
68 Computer science
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] R. A. Becker, W. S. Cleveland, and M. J. Shyu, The design and control of trellis display, J Comput Stat Graph 5 (1996), 123-155.
[2] P. Murrell, R Graphics, New York, Chapman & Hall, 2006.
[3] J. C. Pinheiro and D. M. Bates, Mixed Effects Models in S and S-Plus, New York, Springer-Verlag, 2000. · Zbl 0953.62065
[4] D. Sarkar, Lattice: Multivariate Data Visualization with R, New York, Springer, 2008. · Zbl 1166.62003
[5] A. Krause and M. Olson, The Basics of S and S-Plus, New York, Springer, 2000. · Zbl 0949.62002
[6] J. M. Chambers, Software for Data Analysis: Programming with R, New York, Springer, 2008. · Zbl 1180.62002
[7] S. McDaniel, Rapid Graphs with Tableau Software: Create Intuitive, Actionable Insights in Just 15 Days, United States, CreateSpace, 2009.
[8] G. E. P. Box, J. S. Hunter, and W. G. Hunter, Statistics for Experimenters: Design, Innovation, and Discovery, Chichester, Wiley, 2005. · Zbl 1082.62063
[9] R. A. Becker and W. S. Cleveland, Brushing scatterplots, Technometrics 29 (1987), 127-142 (reprinted in Dynamic Graphics for Data Analysis, W. S. Cleveland, and M. E. McGill, eds. New York, Chapman and Hall, 1988).
[10] W. S. Cleveland, Visualizing Data, Chicago, Hobart Press, 1993.
[11] O. L. Davies, The Design and Analysis of Industrial Experiments, (2nd ed.), New York, Hafner, 1967.
[12] S. Feiner and C. Beshers, Worlds within Worlds: Metaphors for Exploring n-Dimensional Worlds, In Proceedings of UIST’90 (ACM Symposium on User Interface Software), 1990. 76-83.
[13] A. E. Freeny and J. M. Landwehr, Graphical analysis for a large designed experiment, Technometrics 37 (1995), 1-14. · Zbl 0825.62659
[14] R. B. Gramacy and H. K. H. Lee, Adaptive design and analysis of supercomputer experiments, Technometrics 51 (2009), 130-145.
[15] W. A. Larsen and S. J. McCleary, The use of partial residual plots in regression analysis, Technometrics 14 (1972), 781-790.
[16] T. Mihalisin, J. Timlin, and J. Schwegler, Visualizing multivariate functions, data, and distributions, Comput Graph Appl 11 (1991), 28-35.
[17] R. D. Snee, Experimenting with a large number of variables, In Experiments in Industry, R. D. Snee, ed. Milwaukee, Wisconsin, American Society for Quality Control, 1985, 25-35.
[18] E. R. Tufte, The Visual Display of Quantitative Information, Cheshire, Connecticut, Graphics Press, 1983.
[19] P. A. Tukey and J. W. Tukey, Graphical display of data sets in 3 or more dimensions, In Interpreting Multivariate Data, V. Barnett, ed. Chichester, Wiley, 1981, 189-275.
[20] R. R. Barton, Graphical Methods for the Design of Experiments, New York, Springer, 1999. · Zbl 0928.62057
[21] J. A. Cornell and L. Ott, The use of gradients to aid in the interpretation of mixture response surfaces, Technometrics 17 (1975), 409-424. · Zbl 0331.62050
[22] C. Daniel, Applications of Statistics to Industrial Experimentation, New York, Wiley, 1976. · Zbl 0345.62058
[23] R. D. Snee, Graphical display of results of three-treatment randomized block experiments, J R Stat Soc C 34 (1985), 71-77.
[24] W. J. Youden, Graphical diagnosis of interlaboratory test results, Ind Qual Cont 15 (1959), 24-28.
[25] K. Hinkelmann and O. Kempthorne, Design and Analysis of Experiments: Introduction to Experimental Design, Chichester, Wiley, 1994. · Zbl 0805.62071
[26] Y. Hung, V. R. Joseph, and S. N. Melkote, Design and analysis of computer experiments with branching and nested factors, Technometrics 51 (2009), 366-376.
[27] A. C. Shoemaker, K.-L. Tsui, and C. F. J. Wu, Economical experimentation methods for robust design, Technometrics 33 (1991), 415-427.
[28] A. E. Vine, S. M. Lewis, A. M. Dean, and D. Brunson, A critical assessment of two-stage group screening through industrial experimentation, Technometrics 50 (2008), 15-25.
[29] NIST and SEMATECH. Engineering Statistics Handbook, www.itl.nist.gov/div898/handbook/eda/section1/eda15.htm. Verified 2010.
[30] W. F. Hunt Jr, Experimental design in air quality management, In Experiments in Industry, R. D. Snee, L. B. Hare, and J. R. Trout, eds. Milwaukee, American Society for Quality Control, 1985, 89-98.
[31] P. J. Rousseeuw and K. van Driessen, A fast algorithm for the minimum covariance determinant estimator, Technometrics 41 (1999), 212-223.
[32] O. Nalamasu, A. Freeny, E. Reichmanis, N. J. A. Sloane, and L. F. Thompson, Optimization of Resist Formulation and Processing with Disulfone Photo Acid Generators Using Design of Experiments, Technical Report, Bell Laboratories, Murray Hill, New Jersey, USA, 1993.
[33] J. W. Tukey, One degree of freedom for non-additivity, Biometrics 5 (1949), 232-242.
[34] J. W. Tukey, On the comparative anatomy of transformations, Ann Math Stat 28 (1957), 602-632. · Zbl 0083.14701
[35] J. W. Tukey, Exploratory Data Analysis, Reading, Massachusetts, Addison-Wesley, 1977. · Zbl 0409.62003
[36] G. E. P. Box and D. R. Cox, An analysis of transformations, J R Stat Soc B 26 (1964), 211-252. · Zbl 0156.40104
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.