This task view collects information on R packages for experimental design and analysis of data from experiments. Please feel free to suggest enhancements, and please send information on new packages or major package updates if you think they belong here. Contact details are given on my Web page .

Experimental design is applied in many areas, and methods have been tailored to the needs of various fields. This task view starts out with a section on the most general packages, continues with specific sections on agricultural and industrial experimentation and closes with a section on the various special experimental design packages that have been developed for specific purposes. Of course, the division into fields is not always clear-cut, and some packages from the more specialized sections can also be applied in general contexts.

Experimental designs for general purposes

There are a few packages for creating and analyzing experimental designs for general purposes: First of all, the standard (generalized) linear model functions in the base package stats are of course very important for analyzing data from designed experiments (especially functions lm(), aov() and the methods and functions for the resulting linear model objects). These are concisely explained in Kuhnert and Venables (2005, p. 109 ff.); Vikneswaran (2005) points out specific usages for experimental design (using function contrasts(), multiple comparison functions and some convenience functions like model.tables(), replications() and plot.design()). granova offers some interesting non-standard graphical representations for results of simply-structured experiments (one-way and two-way layouts, paired data). AlgDesign creates full factorial designs with or without additional quantitative variables, creates mixture designs (i.e., designs where the levels of factors sum to 1=100%) and creates D-, A-, or I-optimal designs exactly or approximately. NOTE: Bob Wheeler, the author and maintainer of AlgDesign, would like to retire from this job and is looking for an "heir" whom he can entrust with continuing the package. Please contact Bob, if you are interested. Package conf.design allows to create a design with certain interaction effects confounded with blocks (function conf.design()) and allows to combine existing designs in several ways (e.g., useful for Taguchi's inner and outer array designs in industrial experimentation). Package dae provides various utility functions around experimental design and R factors, e.g. a randomization routine that can handle various nested structures (according to Bailey 1981) and functions for combining several factors into one or dividing one factor into several factors. Furthermore, the package provides features for post-processing objects returned by the aov() function, e.g. extraction of Yates effects for 2-level experiments. blockTools assigns units to blocks in order to end up with homogeneous sets of blocks in case of too small block sizes.

Experimental designs for agricultural and plant breeding experiments

agricolae offers extensive functionality on experimental design especially for agricultural and plant breeding experiments, which can also be useful for other purposes. It supports planning of lattice designs, factorial designs, randomized complete block designs, completely randomized designs, (Graeco-)Latin square designs, balanced incomplete block designs and alpha designs. There are also various analysis facilities for experimental data, e.g. treatment comparison procedures and several non-parametric tests, but also some quite specialized possibilities for specific types of experiments.

Experimental designs for industrial experiments

Some further packages especially handle designs for industrial experiments that are often highly fractionated, intentionally confounded and have few extra degrees of freedom for error.

A suite of related packages (cf. Groemping 2009), DoE.base, FrF2 and DoE.wrapper, works with the same principal syntax and output structure, for which a central feature is the class design for experimental design objects. A fourth package, RcmdrPlugin.DoE (beta version!), integrates the functionality from these three packages into the R-Commander (package Rcmdr, Fox 2005) for the benefit of those R users who cannot or do not want to do command line programming.

DoE.base provides full factorial designs and orthogonal arrays for main effects experiments (those listed by Kuhfeld 2009 up to 144 runs, plus a few additional ones) The package also provides the infrastructure for the other two packages of the suite, including the class design for experimental design data frames, and various methods for this class. There is also some experimental functionality for assessing the quality of orthogonal arrays. FrF2 generates regular Fractional Factorial designs for factors with 2 levels as well as Plackett-Burman type screening designs. Regular fractional factorials default to maximum resolution minimum aberration designs and can be customized in various ways, supported by an incorporated catalogue of designs (including the designs catalogued by Chen, Sun and Wu 1993, and further larger designs catalogued in Block and Mee 2005 and Xu 2009; the additional package FrF2.catlg128 provides a very large complete catalogue for resolution IV 128 run designs with up to 23 factors for special purposes). Analysis-wise, FrF2 provides simple graphical analysis tools (normal and half-normal effects plots (modified from BsMD, cf. below), main effects plots and interaction plot matrices similar to those in Minitab software, and a cube plot for the combinations of three factors). It can also show the alias structure for regular fractional factorials of 2-level factors. DoE.wrapper brings some functionality from packages rsm, lhs, DiceDesign (cf. also below) and AlgDesign into the context of the other two packages and adds convenience features and other possibilities. In particular, the package allows to automatically choose the cube portion of central composite designs (CCDs) or to augment an existing cube into a CCD.

BHH2 accompanies the 2nd edition of the book by Box, Hunter and Hunter and provides various of its data sets. It can generate full and fractional factorial two-level-designs from a number of factors and a list of defining relations (function ffDesMatrix(), less comfortable than package FrF2). It also provides several functions for analyzing data from 2-level factorial experiments: The function anovaPlot assesses effect sizes relative to residuals, and the function lambdaPlot() assesses the effect of Box-Cox transformations on statistical significance of effects. BsMD provides Bayesian charts as proposed by Box and Meyer (1986) as well as effects plots (normal, half-normal and Lenth) for assessing which effects are active in a fractional factorial experiment with 2-level factors. Apart from tools for planning and analysing factorial designs, R also offers support for response surface optimization via package rsm. This package supports sequential optimization with first order and second order response surface models, offering optimization approaches like steepest ascent and visualization of the response function for linear model objects. Also, coding for response surface investigations is facilitated.

Experimental designs for computer experiments

Computer experiments with quantitative factors require special types of experimental designs: it is often possible to include many different levels of the factors, and replication will usually not be beneficial. Also, the experimental region is often too large to assume that a linear or quadratic model adequately represents the phenomenon under investigation. Consequently, it is desirable to fill the experimental space with points as well as possible (space-filling designs) in such a way that each run provides additional information even if some factors turn out to be irrelevant. The lhs package provides latin hypercube designs for this purpose. Furthermore, the package provides ways to analyse such computer experiments with emphasis on what follow-up experiments to conduct. Another package with similar orientation is the DiceDesign package, which adds further ways to construct space-filling designs and some measures to assess the quality of designs for computer experiments. The package DiceKriging provides the kriging methodology which is often used for creating meta models from computer experiments.

Experimental designs for special purposes

Various further packages handle special situations in experimental design: desirability provides ways to combine several target criteria into a desirability function in order to simplify multi-criteria analysis. experiment contains tools for clinical experiments, e.g., a randomization tool, and it provides a few special analysis options for clinical trials. The DoseFinding package provides functions for the design and analysis of dose-finding experiments (for example pharmaceutical Phase II clinical trials); it combines the facilities of the MCPMod package (maintenance discontinued; described in Bornkamp, Pinheiro and Bretz 2009) with a special type of optimal designs for dose finding situations (MED-optimal designs, or D-optimal designs, or a mixture of both; cf., Dette et al. 2008). ldDesign suggests appropriate designs for linkage equilibrium studies, crossdes creates and analyses cross-over designs of various types (including latin squares, mutually orthogonal latin squares and Youden squares) that can for example be used in sensometrics. Package SensoMineR contains special designs for sensometric studies, e.g., for the triangle test.

Key references for packages in this task view

• Atkinson, A.C. and Donev, A.N. (1992). Optimum Experimental Designs . Oxford: Clarendon Press.
• Bailey, R.A. (1981). A unified approach to design of experiments. Journal of the Royal Statistical Society, Series A 144 , 214-223.
• Ball, R.D. (2005). Experimental Designs for Reliable Detection of Linkage Disequilibrium in Unstructured Random Population Association Studies. Genetics 170 , 859-873.
• Block, R. and Mee, R. (2005). Resolution IV Designs with 128 Runs. Journal of Quality Technology 37 , 282-293.
• Bornkamp B., Pinheiro J. C., and Bretz, F. (2009). MCPMod: An R Package for the Design and Analysis of Dose-Finding Studies . Journal of Statistical Software 29 (7), 1-23.
• Box G. E. P, Hunter, W. C. and Hunter, J. S. (2005). Statistics for Experimenters (2nd edition). New York: Wiley.
• Box, G. E. P and R. D. Meyer (1986). An Analysis for Unreplicated Fractional Factorials. Technometrics 28 , 11-18.
• Box, G. E. P and R. D. Meyer (1993). Finding the Active Factors in Fractionated Screening Experiments. Journal of Quality Technology 25 , 94-105.
• Chen, J., Sun, D.X. and Wu, C.F.J. (1993). A catalogue of 2-level and 3-level orthogonal arrays. International Statistical Review 61 , 131-145.
• Collings, B. J. (1989). Quick Confounding. Technometrics 31 , 107-110.
• Daniel, C. (1959). Use of Half Normal Plots in Interpreting Two Level Experiments. Technometrics 1 , 311-340.
• Derringer, G. and Suich, R. (1980). Simultaneous Optimization of Several Response Variables. Journal of Quality Technology 12 , 214-219.
• Dette, H., Bretz, F., Pepelyshev, A. and Pinheiro, J. C. (2008). Optimal Designs for Dose Finding Studies. Journal of the American Statisical Association 103 , 1225-1237.
• Federov, V.V. (1972). Theory of Optimal Experiments . Academic Press, New York.
• Fox, J. (2005). The R Commander: A Basic-Statistics Graphical User Interface to R . Journal of Statistical Software 14 (9), 1-42.
• Groemping, U. (2009). Design of Experiments in R . Presentation at UseR! 2009 in Rennes, France.
• Hoaglin D., Mosteller F. and Tukey J. (eds., 1991). Fundamentals of Exploratory Analysis of Variance . Wiley, New York.
• Jones, B. and Kenward, M.G. (1989). Design and Analysis of Cross-Over Trials . Chapman and Hall, London.
• Johnson, M.E., Moore L.M. and Ylvisaker D. (1990). Minimax and maximin distance designs. Journal of Statistical Planning and Inference , 26 , 131-148.
• Kuhfeld, W. (2009). Orthogonal arrays. Website courtesy of SAS Institute Inc., accessed August 4th 2010. URL http://support.sas.com/techsup/technote/ts723.html .
• Kuhnert, P. and Venables, B. (2005) An Introduction to R: Software for Statistical Modelling & Computing . URL http://CRAN.R-project.org/doc/contrib/Kuhnert+Venables-R_Course_Notes.zip . (PDF document (about 360 pages) of lecture notes in combination with the data sets and R scripts)
• Kunert, J. (1998). Sensory Experiments as Crossover Studies. Food Quality and Preference 9 , 243-253.
• Lenth, R.V. (1989). Quick and Easy Analysis of Unreplicated Factorials. Technometrics 31 , 469-473.
• Lenth, R.V. (2009). Response-Surface Methods in R, Using rsm . Journal of Statistical Software 32 (7), 1-17.
• Mee, R. (2009). A Comprehensive Guide to Factorial Two-Level Experimentation . New York: Springer.
• Myers, R. H. and Montgomery, C. M. (1995). Response Surface Methodology: Process and Product Optimization Using Designed Experiments . New York: Wiley.
• Plackett, R.L. and Burman, J.P. (1946). The design of optimum multifactorial experiments. Biometrika 33 , 305-325.
• Rosenbaum, P. (1989). Exploratory Plots for Paired Data. The American Statistician 43 , 108-109.
• Sacks, J., Welch, W.J., Mitchell, T.J. and Wynn, H.P. (1989). Design and analysis of computer experiments. Statistical Science 4 , 409-435.
• Santner T.J., Williams B.J. and Notz W.I. (2003). The Design and Analysis of Computer Experiments . Springer, New York.
• Sen S, Satagopan JM and Churchill GA (2005). Quantitative Trait Locus Study Design from an Information Perspective. Genetics 170 , 447-464.
• Stein, M. (1987). Large Sample Properties of Simulations Using Latin Hypercube Sampling. Technometrics 29 , 143-151.
• Stocki, R. (2005). A Method to Improve Design Reliability Using Optimal Latin Hypercube Sampling. Computer Assisted Mechanics and Engineering Sciences 12 , 87-105.
• Vikneswaran (2005). An R companion to "Experimental Design". URL http://CRAN.R-project.org/doc/contrib/Vikneswaran-ED_companion.pdf . (The file accompanies the book "Experimental Design with Applications in Management, Engineering and the Sciences" by Berger and Maurer, 2002.)
• Xu, H. (2009). Algorithmic Construction of Efficient Fractional Factorial Designs With Large Run Sizes. Technometrics 51 , 262-277.