# dae v3.1-23

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## Functions Useful in the Design and ANOVA of Experiments

The content falls into the following groupings: (i) Data, (ii) Factor manipulation functions, (iii) Design functions, (iv) ANOVA functions, (v) Matrix functions, (vi) Projector and canonical efficiency functions, and (vii) Miscellaneous functions. There is a vignette describing how to use the design functions for randomizing and assessing designs available as a vignette called 'DesignNotes'. The ANOVA functions facilitate the extraction of information when the 'Error' function has been used in the call to 'aov'. The package 'dae' can also be installed from <http://chris.brien.name/rpackages/>.

## Functions in dae

 Name Description LatticeSquare_t49.des A Lattice square design for 49 treatments Oats.dat Data for an experiment to investigate nitrogen response of 3 oats varieties McIntyreTMV.dat The design and data from McIntyre's (1955) two-phase experiment Exp249.munit.des Systematic, main-unit design for an experiment to be run in a greenhouse dae-deprecated Deprecated Functions in Package dae BIBDWheat.dat Data for a balanced incomplete block experiment Fac4Proc.dat Data for a 2^4 factorial experiment dae-package dae as.numfac Convert a factor to a numeric vector Zncsspline Calculates the design matrix for fitting the random component of a natural cubic smoothing spline designPlot A graphical representation of an experimental design using labels stored in a matrix. Sensory3Phase.dat Data for the three-phase sensory evaluation experiment in Brien, C.J. and Payne, R.W. (1999) as.data.frame.pstructure Coerces a pstructure.object to a data.frame. designRandomize Randomize allocated to recipient factors to produce a layout for an experiment designPlotlabels Plots labels on a two-way grid using ggplot2 designTwophaseAnatomies Given the layout for a design and three structure formulae, obtain the anatomies for the (i) two-phase, (ii) first-phase, (iii) cross-phase, treatments, and (iv) combined-units designs. fac.combine Combines several factors into one fac.divide Divides a factor into several individual factors designAnatomy Given the layout for a design, obtain its anatomy via the canonical analysis of its projectors to show the confounding and aliasing inherent in the design. blockboundaryPlot This function plots a block boundary on a plot produced by designPlot. Casuarina.dat Data for an experiment with rows and columns from Williams (2002) SPLGrass.dat Data for an experiment to investigate the effects of grazing patterns on pasture composition designBlocksGGPlot Adds block boundaries to a plot produced by designGGPlot. fac.vcmat forms the variance matrix for the variance component of a (generalized) factor extab Expands the values in table to a vector daeTips The intermittent, randomly-presented, startup tips. designGGPlot Plots labels on two-way grids of coloured cells using ggplot2 fitted.aovlist Extract the fitted values for a fitted model from an aovlist object degfree Degrees of freedom extraction and replacement decomp.relate Examines the relationship between the eigenvectors for two decompositions mat.ar1 Forms an ar1 correlation matrix designLatinSqrSys Generate a systematic plan for a Latin Square design detect.diff Computes the detectable difference for an experiment correct.degfree Check the degrees of freedom in an object of class projector designAmeasures Calculates the average variance of pairwise differences from the variance matrix for predictions that can be obtained using mat.Vpredicts fac.match Match, for each combination of a set of columns in x, the row that has the same combination in table mat.Vpredicts Calculates the variances of a set of predicted effects from a mixed model, based on supplied matrices or formulae. efficiencies Extracts the canonical efficiency factors from a pcanon.object or a p2canon.object. mat.J Forms a square matrix of ones efficiency.criteria Computes efficiency criteria from a set of efficiency factors fac.nested creates a factor, the nested factor, whose values are generated within those of the factor nesting.fac fac.gen Generate all combinations of several factors and, optionally, replicate them elements Extract the elements of an array specified by the subscripts fitted.errors Extract the fitted values for a fitted model is.allzero Tests whether all elements are approximately zero fac.meanop computes the projection matrix that produces means interaction.ABC.plot Plots an interaction plot for three factors fac.sumop computes the summation matrix that produces sums corresponding to a (generalized) factor harmonic.mean Calcuates the harmonic mean. mat.exp Forms an exponential correlation matrix fac.uselogical Forms a two-level factor from a logical object. fac.ar1mat forms the ar1 correlation matrix for a (generalized) factor fac.multinested Creates several factors, one for each level of nesting.fac and each of whose values are either generated within those of a level of nesting.fac or using the values of nested.fac within a levels of nesting.fac. fac.recode Recodes factor levels using values in a vector. The values in the vector do not have to be unique. get.daeTolerance Gets the value of daeTolerance for the package dae mat.arma Forms an arma correlation matrix mat.dirprod Forms the direct product of two matrices mat.Vpred Calculates the variances of a set of predicted effects from a mixed model mat.dirsum Forms the direct sum of a list of matrices is.projector Tests whether an object is a valid object of class projector mat.ma1 Forms an ma1 correlation matrix p2canon.object Description of a p2canon object mat.banded Form a banded matrix from a vector of values marginality Extracts the marginality matrix (matrices) from a pstructure.object or a pcanon.object. mat.I Forms a unit matrix pcanon.object Description of a pcanon object mat.ncssvar Calculates the variance matrix of the random effects for a natural cubic smoothing spline print.summary.p2canon Prints the values in an summary.p2canon object mat.gau Forms an exponential correlation matrix mat.ar2 Forms an ar2 correlation matrix mat.sar Forms an sar correlation matrix power.exp Computes the power for an experiment pstructure.object Description of a pstructure object print.summary.pcanon Prints the values in an summary.pcanon object mat.ma2 Forms an ma2 correlation matrix proj2.eigen Canonical efficiency factors and eigenvectors in joint decomposition of two projectors mat.ar3 Forms an ar3 correlation matrix mpone Converts the first two levels of a factor into the numeric values -1 and +1 meanop computes the projection matrix that produces means no.reps Computes the number of replicates for an experiment projector Create projectors projector-class Class projector qqyeffects Half or full normal plot of Yates effects proj2.efficiency Computes the canonical efficiency factors for the joint decomposition of two projectors rep.data.frame Replicate the rows of a data.frame by repeating each row consecutively and/or repeating all rows as a group resid.errors Extract the residuals for a fitted model mat.sar2 Forms an sar2 correlation matrix residuals.aovlist Extract the residuals from an aovlist object yates.effects Extract Yates effects print.projector Print projectors print.pstructure Prints a pstructure.object print.aliasing Print an aliasing data.frame projs.2canon A canonical analysis of the relationships between two sets of projectors projs.combine.p2canon Extract, from a p2canon object, the projectors that give the combined canonical decomposition set.daeTolerance Sets the values of daeTolerance for the package dae show-methods Methods for Function show in Package dae rmvnorm generates a vector of random values from a multivariate normal distribution summary.p2canon Summarize a canonical analysis of the relationships between two sets of projectors proj2.combine Compute the projection and Residual operators for two, possibly nonorthogonal, projectors summary.pcanon Summarizes the anatomy of a design, being the decomposition of the sample space based on its canonical analysis, as produced by designAnatomy pstructure.formula Takes a formula and constructs a pstructure.object that includes the orthogonalized projectors for the terms in a formula strength Generate paper strength values tukey.1df Performs Tukey's one-degree-of-freedom-test-for-nonadditivity ABC.Interact.dat Randomly generated set of values indexed by three factors Cabinet1.des A design for one of the growth cabinets in an experiment with 50 lines and 4 harvests No Results!