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# Design And Analysis Of Experiments With R

Concepts and application of analysis of variance to experimental data, including blocked, nested, factorial and split plot designs, and repeated measures. Covers the concepts of fixed and random effects, multiple comparisons, analysis of covariance. Participants learn how to design and evaluate complex field and laboratory experiments with open-source software packages. Prerequisite: knowledge equivalent to REN R 581 and REN R 582 is required.

## Design and Analysis of Experiments with R

It never hurts to go back to basics before tackling more complex things. The purpose of this post is to give a brief overview of the basics of design of experiments, their analysis and how to present results using R and packages like ggplot2 and agricolae. Included are one- and two-factor experiments.

The design of experiments (DOE) deals with the planning and performance of tests with the objective of generating data. Statistical analysis of these data will provide objective evidence that will allow the researcher to resolve questions about a given situation, process or phenomenon.

The different values assigned to each factor studied in an experimental design are called levels. A combination of levels of all the factors studied is called a treatment or design point. In the case of experimenting with a single factor, each level is a treatment.

The aov function is used for the analysis of factorial designs. Previously, it is recommended to convert the factor values into the factor class and then perform the analysis. Here I going to analyze our first design (one_fct_dgn):

To visualize the results of this type of experiments, bar graphs are usually used, whose height represents the magnitude of each mean, together with error bars representing the standard deviation and letters showing the significant differences established by the multiple comparisons test:

For a blocked design we want the \(t\) experimental units within each block should be as homogeneous as possible (as similar as possible, so that there is unlikely to be unwanted variation coming into the experiment this way). The variation between blocks (the groups of experimental units) should be large enough (i.e., blocking factors different enough) so that conclusions can be drawn. Allocation of treatments to experimental units is done randomly (i.e., treatments are randomly assigned to units) within each block.

This task view collects information on R packages for experimental design and analysis of data from experiments. With a strong increase in the number of relevant packages, packages that focus on analysis only and do not make relevant contributions for design creation are no longer added to this task view. 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, computer experiments, and experimentation in the clinical trials contexts, and closes with a section on various special experimental design packages that have been developed for other 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. You may also notice that my own experience is mainly from industrial experimentation (in a broad sense), which may explain a somewhat biased view on things.

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 functionslm(),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 functioncontrasts(), multiple comparison functions and some convenience functions likemodel.tables(),replications() andplot.design()). Lawson (2014) is a good introductory textbook on experimental design in R, which gives many example applications. Lalanne (2012) provides an R companion to the well-known book by Montgomery (2005); he so far covers approximately the first ten chapters; he does not include R's design generation facilities, but mainly discusses the analysis of existing designs. PackageGAD handles general balanced analysis of variance models with fixed and/or random effects and also nested effects (the latter can only be random); they quote Underwood 1997 for this work. The package is quite valuable, as many users have difficulties with using the R packages for handling random or mixed effects. Packagegranova offers some interesting non-standard graphical representations for results of simply-structured experiments (one-way and two-way layouts, paired data).

Packageagricolae 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. The packageagridat offers a large repository of useful agricultural data sets.

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. Thelhs 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 theDiceDesign package, which adds further ways to construct space-filling designs and some measures to assess the quality of designs for computer experiments. The packageDiceKriging provides the kriging methodology which is often used for creating meta models from computer experiments, the packageDiceEval creates and evaluates meta models (among others Kriging ones), and the packageDiceView provides facilities for viewing sections of multidimensional meta models.

PackageMaxPro provides maximum projection designs as introduced by Joseph, Gul and Ba(2015). Packagesimrel allows creation of designs for computer experiments according to the Multi-level binary replacement (MBR) strategy by Martens et al. (2010).

Packagetgp is another package dedicated to planning and analysing computer experiments. Here, emphasis is on Bayesian methods. The package can for example be used with various kinds of (surrogate) models for sequential optimization, e.g. with an expected improvement criterion for optimizing a noisy blackbox target function. Packageplgp enhances the functionality offered bytgp with particle learning facilities and learning for dynamic regression trees.

PackageBatchExperiments is also designed for computer experiments, in this case specifically for experiments with algorithms to be run under different scenarios. The package is described in a technical report by Bischl et al. (2012).

The advent of single cell RNA sequencing (scRNA-seq) enabled researchers to study transcriptomic activity within individual cells and identify inherent cell types in the sample. Although numerous computational tools have been developed to analyze single cell transcriptomes, there are no published studies and analytical packages available to guide experimental design and to devise suitable analysis procedure for cell type identification.

We have developed an empirical methodology to address this important gap in single cell experimental design and analysis into an easy-to-use tool called SCEED (Single Cell Empirical Experimental Design and analysis). With SCEED, user can choose a variety of combinations of tools for analysis, conduct performance analysis of analytical procedures and choose the best procedure, and estimate sample size (number of cells to be profiled) required for a given analytical procedure at varying levels of cell type rarity and other experimental parameters. Using SCEED, we examined 3 single cell algorithms using 48 simulated single cell datasets that were generated for varying number of cell types and their proportions, number of genes expressed per cell, number of marker genes and their fold change, and number of single cells successfully profiled in the experiment.

Based on our study, we found that when marker genes are expressed at fold change of 4 or more, either Seurat or SIMLR algorithm can be used to analyze single cell dataset for any number of single cells isolated (minimum 1000 single cells were tested). However, when marker genes are expected to be only up to fold change of 2, choice of the single cell algorithm is dependent on the number of single cells isolated and rarity of cell types to be identified. In conclusion, our work allows the assessment of various single cell methods and also aids in the design of single cell experiments. 041b061a72

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