{
  "_id": "6a197bfeacfb0bcc41df60ea",
  "Package": "dae",
  "Version": "3.2.33",
  "Date": "2025-10-31",
  "Title": "Functions Useful in the Design and ANOVA of Experiments",
  "Authors@R": "person(\"Chris\",\"Brien\", role = c(\"aut\",\"cre\"),\ncomment = c(ORCID = \"0000-0003-0581-1817\"),\nemail = \"chris.brien@adelaide.edu.au\")",
  "VignetteBuilder": "R.rsp",
  "Description": "The content falls into the following groupings: (i) Data,\n(ii) Factor manipulation functions, (iii) Design functions,\n(iv) ANOVA functions, (v) Matrix functions, (vi) Projector and\ncanonical efficiency functions, and (vii) Miscellaneous\nfunctions. There is a vignette describing how to use the design\nfunctions for randomizing and assessing designs available as a\nvignette called 'DesignNotes'. The ANOVA functions facilitate\nthe extraction of information when the 'Error' function has\nbeen used in the call to 'aov'. The package 'dae' can also be\ninstalled from <http://chris.brien.name/rpackages/>.",
  "License": "GPL (>=2)",
  "URL": "http://chris.brien.name",
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  "RoxygenNote": "5.0.1",
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  "Repository": "https://briencj.r-universe.dev",
  "Date/Publication": "2025-10-31 07:05:52 UTC",
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  "Author": "Chris Brien [aut, cre] (ORCID: <https://orcid.org/0000-0003-0581-1817>)",
  "Maintainer": "Chris Brien <chris.brien@adelaide.edu.au>",
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    "decomp.relate",
    "degfree",
    "degfree<-",
    "design.plot",
    "designAmeasures",
    "designAnatomy",
    "designBlocksGGPlot",
    "designGGPlot",
    "designLatinSqrSys",
    "designPlot",
    "designPlotlabels",
    "designRandomize",
    "designTwophaseAnatomies",
    "detect.diff",
    "efficiencies",
    "efficiencies.p2canon",
    "efficiencies.pcanon",
    "efficiency.criteria",
    "elements",
    "extab",
    "fac.ar1mat",
    "fac.combine",
    "fac.divide",
    "fac.gen",
    "fac.genfactors",
    "fac.match",
    "fac.meanop",
    "fac.multinested",
    "fac.nested",
    "fac.recast",
    "fac.recode",
    "fac.split",
    "fac.sumop",
    "fac.uncombine",
    "fac.uselogical",
    "fac.vcmat",
    "fitted.aovlist",
    "fitted.errors",
    "get.daeRNGkind",
    "get.daeTolerance",
    "harmonic.mean",
    "interaction.ABC.plot",
    "is.allzero",
    "is.projector",
    "makeLevsPadNums",
    "marginality",
    "marginality.pcanon",
    "marginality.pstructure",
    "mat.ar1",
    "mat.ar2",
    "mat.ar3",
    "mat.arma",
    "mat.banded",
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    "porthogonalize",
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    "power.exp",
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    "pstructure",
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    "strength",
    "summary.p2canon",
    "summary.pcanon",
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      "title": "Randomly generated set of values indexed by three factors",
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        "Yield"
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      "table": true,
      "tojson": true
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        "Harvest.Order",
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        "Mainplots",
        "Subplots",
        "BMainplots",
        "Border",
        "Lines",
        "Lines.named",
        "Groups",
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        "Combinations",
        "Lines.short"
      ],
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      "table": true,
      "tojson": true
    },
    {
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      "title": "Data for an experiment with rows and columns from Williams (2002)",
      "object": "Casuarina.dat",
      "file": "Casuarina.dat.rda",
      "class": [
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      ],
      "fields": [
        "Reps",
        "Rows",
        "Columns",
        "InocTime",
        "Provenances",
        "Countries",
        "Dbh"
      ],
      "rows": 240,
      "table": true,
      "tojson": true
    },
    {
      "name": "Exp249.munit.des",
      "title": "Systematic, main-unit design for an experiment to be run in a greenhouse",
      "object": "Exp249.munit.des",
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      "class": [
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      ],
      "fields": [
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        "Cols",
        "Lines",
        "Blocks"
      ],
      "rows": 264,
      "table": true,
      "tojson": true
    },
    {
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      "title": "Data for a 2^4 factorial experiment",
      "object": "Fac4Proc.dat",
      "file": "Fac4Proc.dat.rda",
      "class": [
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      "fields": [
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        "Catal",
        "Temp",
        "Press",
        "Conc",
        "Conv"
      ],
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      "table": true,
      "tojson": true
    },
    {
      "name": "LatticeSquare_t49.des",
      "title": "A Lattice square design for 49 treatments",
      "object": "LatticeSquare_t49.des",
      "file": "LatticeSquare_t49.des.rda",
      "class": [
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      ],
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        "Runs",
        "Times",
        "Lines"
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      "table": true,
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      "title": "The design and data from McIntyre's (1955) two-phase experiment",
      "object": "McIntyreTMV.dat",
      "file": "McIntyreTMV.dat.rda",
      "class": [
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        "NicPlant",
        "Posn",
        "Lot",
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        "AssPosn",
        "Treat",
        "SqrtCount"
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      "rows": 128,
      "table": true,
      "tojson": true
    },
    {
      "name": "Oats.dat",
      "title": "Data for an experiment to investigate nitrogen response of 3 oats varieties",
      "object": "Oats.dat",
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      "class": [
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    },
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      "name": "Sensory3Phase.dat",
      "title": "Data for the three-phase sensory evaluation experiment in Brien, C.J. and Payne, R.W. (1999)",
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      "file": "Sensory3Phase.dat.rda",
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        "Trellis",
        "Method",
        "Score"
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      "name": "Sensory3PhaseShort.dat",
      "title": "Data for the three-phase sensory evaluation experiment in Brien, C.J. and Payne, R.W. (1999)",
      "object": "Sensory3PhaseShort.dat",
      "file": "Sensory3PhaseShort.dat.rda",
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      "name": "SPLGrass.dat",
      "title": "Data for an experiment to investigate the effects of grazing patterns on pasture composition",
      "object": "SPLGrass.dat",
      "file": "SPLGrass.dat.rda",
      "class": [
        "data.frame"
      ],
      "fields": [
        "Rows",
        "Columns",
        "SubRows",
        "SubColumns",
        "Period",
        "Spring",
        "Summer",
        "Main.Grass"
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      "rows": 36,
      "table": true,
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  "_help": [
    {
      "page": "dae-package",
      "title": "Functions Useful in the Design and ANOVA of Experiments",
      "topics": [
        "dae-package",
        "dae"
      ]
    },
    {
      "page": "ABC.Interact.dat",
      "title": "Randomly generated set of values indexed by three factors",
      "topics": [
        "ABC.Interact.dat"
      ]
    },
    {
      "page": "as.data.frame.pstructure",
      "title": "Coerces a pstructure.object to a data.frame.",
      "topics": [
        "as.data.frame.pstructure"
      ]
    },
    {
      "page": "as.numfac",
      "title": "Convert a factor to a numeric vector, possibly centering or scaling the values",
      "topics": [
        "as.numfac"
      ]
    },
    {
      "page": "BIBDWheat.dat",
      "title": "Data for a balanced incomplete block experiment",
      "topics": [
        "BIBDWheat.dat"
      ]
    },
    {
      "page": "blockboundaryPlot",
      "title": "This function plots a block boundary on a plot produced by 'designPlot'.",
      "topics": [
        "blockboundaryPlot"
      ]
    },
    {
      "page": "Cabinet1.des",
      "title": "A design for one of the growth cabinets in an experiment with 50 lines and 4 harvests",
      "topics": [
        "Cabinet1.des"
      ]
    },
    {
      "page": "Casuarina.dat",
      "title": "Data for an experiment with rows and columns from Williams (2002)",
      "topics": [
        "Casuarina.dat"
      ]
    },
    {
      "page": "correct.degfree",
      "title": "Check the degrees of freedom in an object of class projector",
      "topics": [
        "correct.degfree"
      ]
    },
    {
      "page": "dae-deprecated",
      "title": "Deprecated Functions in Package dae",
      "topics": [
        "Ameasures",
        "blockboundary.plot",
        "dae-deprecated",
        "design.plot",
        "proj2.decomp",
        "proj2.ops",
        "projs.canon",
        "projs.structure"
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    {
      "page": "daeTips",
      "title": "The intermittent, randomly-presented, startup tips.",
      "topics": [
        "daeTips"
      ]
    },
    {
      "page": "decomp.relate",
      "title": "Examines the relationship between the eigenvectors for two decompositions",
      "topics": [
        "decomp.relate"
      ]
    },
    {
      "page": "degfree",
      "title": "Degrees of freedom extraction and replacement",
      "topics": [
        "degfree",
        "degfree<-"
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    },
    {
      "page": "designAmeasures",
      "title": "Calculates the average variance of pairwise differences from the variance matrix for predictions",
      "topics": [
        "designAmeasures"
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    },
    {
      "page": "designAnatomy",
      "title": "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.",
      "topics": [
        "designAnatomy"
      ]
    },
    {
      "page": "designBlocksGGPlot",
      "title": "Adds block boundaries to a plot produced by 'designGGPlot'.",
      "topics": [
        "designBlocksGGPlot"
      ]
    },
    {
      "page": "designGGPlot",
      "title": "Plots labels on two-way grids of coloured cells using 'ggplot2' to represent an experimental design",
      "topics": [
        "designGGPlot"
      ]
    },
    {
      "page": "designLatinSqrSys",
      "title": "Generate a systematic plan for a Latin Square design",
      "topics": [
        "designLatinSqrSys"
      ]
    },
    {
      "page": "designPlot",
      "title": "A graphical representation of an experimental design using labels stored in a matrix.",
      "topics": [
        "designPlot"
      ]
    },
    {
      "page": "designPlotlabels",
      "title": "Plots labels on a two-way grid using 'ggplot2'",
      "topics": [
        "designPlotlabels"
      ]
    },
    {
      "page": "designRandomize",
      "title": "Randomize allocated to recipient factors to produce a layout for an experiment",
      "topics": [
        "designRandomize"
      ]
    },
    {
      "page": "designTwophaseAnatomies",
      "title": "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.",
      "topics": [
        "designTwophaseAnatomies"
      ]
    },
    {
      "page": "detect.diff",
      "title": "Computes the detectable difference for an experiment",
      "topics": [
        "detect.diff"
      ]
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      "page": "efficiencies",
      "title": "Extracts the canonical efficiency factors from a 'pcanon.object' or a 'p2canon.object'.",
      "topics": [
        "efficiencies",
        "efficiencies.p2canon",
        "efficiencies.pcanon"
      ]
    },
    {
      "page": "efficiency.criteria",
      "title": "Computes efficiency criteria from a set of efficiency factors",
      "topics": [
        "efficiency.criteria"
      ]
    },
    {
      "page": "elements",
      "title": "Extract the elements of an array specified by the subscripts",
      "topics": [
        "elements"
      ]
    },
    {
      "page": "Exp249.munit.des",
      "title": "Systematic, main-unit design for an experiment to be run in a greenhouse",
      "topics": [
        "Exp249.munit.des"
      ]
    },
    {
      "page": "extab",
      "title": "Expands the values in table to a vector",
      "topics": [
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      ]
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    {
      "page": "fac.ar1mat",
      "title": "forms the ar1 correlation matrix for a (generalized) factor",
      "topics": [
        "fac.ar1mat"
      ]
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    {
      "page": "fac.combine",
      "title": "Combines several factors into one",
      "topics": [
        "fac.combine"
      ]
    },
    {
      "page": "fac.divide",
      "title": "Divides a factor into several separate factors",
      "topics": [
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      ]
    },
    {
      "page": "fac.gen",
      "title": "Generate all combinations of several factors and, optionally, replicate them",
      "topics": [
        "fac.gen"
      ]
    },
    {
      "page": "fac.genfactors",
      "title": "Generate all combinations of the levels of the supplied factors, without replication",
      "topics": [
        "fac.genfactors"
      ]
    },
    {
      "page": "fac.match",
      "title": "Match, for each combination of a set of columns in 'x', the row that has the same combination in 'table'",
      "topics": [
        "fac.match"
      ]
    },
    {
      "page": "fac.meanop",
      "title": "computes the projection matrix that produces means",
      "topics": [
        "fac.meanop"
      ]
    },
    {
      "page": "fac.multinested",
      "title": "Creates several factors, one for each level of the nesting factor and each of whose values are either generated within those of a level of the nesting factor or using the values of the nested factor within the levels of the nesting factor.",
      "topics": [
        "fac.multinested"
      ]
    },
    {
      "page": "fac.nested",
      "title": "creates a factor, the nested factor, whose values are generated within those of the factor nesting.fac",
      "topics": [
        "fac.nested"
      ]
    },
    {
      "page": "fac.recast",
      "title": "Recasts a factor by modifying the values in the factor vector and/or the levels attribute, possibly combining some levels into a single level.",
      "topics": [
        "fac.recast"
      ]
    },
    {
      "page": "fac.recode",
      "title": "Recodes factor 'levels' using values in a vector. The values in the vector do not have to be unique.",
      "topics": [
        "fac.recode"
      ]
    },
    {
      "page": "fac.split",
      "title": "Splits a factor whose levels consist of several delimited strings into several factors",
      "topics": [
        "fac.split"
      ]
    },
    {
      "page": "fac.sumop",
      "title": "computes the summation matrix that produces sums corresponding to a (generalized) factor",
      "topics": [
        "fac.sumop"
      ]
    },
    {
      "page": "fac.uncombine",
      "title": "Cleaves a single factor, each of whose levels has delimited strings, into several factors using the separated strings.",
      "topics": [
        "fac.uncombine"
      ]
    },
    {
      "page": "fac.uselogical",
      "title": "Forms a two-level 'factor' from a 'logical' object.",
      "topics": [
        "fac.uselogical"
      ]
    },
    {
      "page": "fac.vcmat",
      "title": "forms the variance matrix for the variance component of a (generalized) factor",
      "topics": [
        "fac.vcmat"
      ]
    },
    {
      "page": "Fac4Proc.dat",
      "title": "Data for a 2^4 factorial experiment",
      "topics": [
        "Fac4Proc.dat"
      ]
    },
    {
      "page": "fitted.aovlist",
      "title": "Extract the fitted values for a fitted model from an aovlist object",
      "topics": [
        "fitted",
        "fitted.aovlist"
      ]
    },
    {
      "page": "fitted.errors",
      "title": "Extract the fitted values for a fitted model",
      "topics": [
        "fitted.errors"
      ]
    },
    {
      "page": "get.daeRNGkind",
      "title": "Gets the value of daeRNGkind for the package dae from the daeEnv environment",
      "topics": [
        "get.daeRNGkind"
      ]
    },
    {
      "page": "get.daeTolerance",
      "title": "Gets the value of daeTolerance for the package dae",
      "topics": [
        "get.daeTolerance"
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    {
      "page": "harmonic.mean",
      "title": "Calcuates the harmonic mean.",
      "topics": [
        "harmonic.mean"
      ]
    },
    {
      "page": "interaction.ABC.plot",
      "title": "Plots an interaction plot for three factors",
      "topics": [
        "interaction.ABC.plot"
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    },
    {
      "page": "is.allzero",
      "title": "Tests whether all elements are approximately zero",
      "topics": [
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    {
      "page": "is.projector",
      "title": "Tests whether an object is a valid object of class projector",
      "topics": [
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    {
      "page": "LatticeSquare_t49.des",
      "title": "A Lattice square design for 49 treatments",
      "topics": [
        "LatticeSquare_t49.des"
      ]
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    {
      "page": "makeLevsPadNums",
      "title": "make a set of levels that consist of a prefix combined with padded numeric values",
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      "page": "marginality",
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        "marginality.pcanon",
        "marginality.pstructure"
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      "page": "mat.ar1",
      "title": "Forms an ar1 correlation matrix",
      "topics": [
        "mat.ar1"
      ]
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    {
      "page": "mat.ar2",
      "title": "Forms an ar2 correlation matrix",
      "topics": [
        "mat.ar2"
      ]
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    {
      "page": "mat.ar3",
      "title": "Forms an ar3 correlation matrix",
      "topics": [
        "mat.ar3"
      ]
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    {
      "page": "mat.arma",
      "title": "Forms an arma correlation matrix",
      "topics": [
        "mat.arma"
      ]
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    {
      "page": "mat.banded",
      "title": "Form a banded matrix from a vector of values",
      "topics": [
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      "page": "mat.cor",
      "title": "Forms a correlation matrix in which all correlations have the same value.",
      "topics": [
        "mat.cor"
      ]
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    {
      "page": "mat.corg",
      "title": "Forms a general correlation matrix",
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        "mat.corg"
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      "page": "mat.dirprod",
      "title": "Forms the direct product of two matrices",
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      "page": "mat.dirsum",
      "title": "Forms the direct sum of a list of matrices",
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      "page": "mat.exp",
      "title": "Forms an exponential correlation matrix",
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    {
      "page": "mat.gau",
      "title": "Forms an exponential correlation matrix",
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      "page": "mat.ginv",
      "title": "Computes the generalized inverse of a matrix",
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      "page": "mat.I",
      "title": "Forms a unit matrix",
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      "page": "mat.J",
      "title": "Forms a square matrix of ones",
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      "page": "mat.ma1",
      "title": "Forms an ma1 correlation matrix",
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      "page": "mat.ma2",
      "title": "Forms an ma2 correlation matrix",
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      "page": "mat.ncssvar",
      "title": "Calculates the variance matrix of the random effects for a natural cubic smoothing spline",
      "topics": [
        "mat.ncssvar"
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    {
      "page": "mat.random",
      "title": "Calculates the variance matrix for the random effects from a mixed model, based on a supplied formula or a matrix.",
      "topics": [
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      "page": "mat.sar",
      "title": "Forms an sar correlation matrix",
      "topics": [
        "mat.sar"
      ]
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    {
      "page": "mat.sar2",
      "title": "Forms an sar2 correlation matrix",
      "topics": [
        "mat.sar2"
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    },
    {
      "page": "mat.Vpred",
      "title": "Calculates the variances of a set of predicted effects from a mixed model",
      "topics": [
        "mat.Vpred"
      ]
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    {
      "page": "mat.Vpredicts",
      "title": "Calculates the variances of a set of predicted effects from a mixed model, based on supplied matrices or formulae.",
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        "mat.Vpredicts"
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      "page": "McIntyreTMV.dat",
      "title": "The design and data from McIntyre's (1955) two-phase experiment",
      "topics": [
        "McIntyreTMV.dat"
      ]
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      "page": "meanop",
      "title": "computes the projection matrix that produces means",
      "topics": [
        "meanop"
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      "page": "mpone",
      "title": "Converts the first two levels of a factor into the numeric values -1 and +1",
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      "page": "no.reps",
      "title": "Computes the number of replicates for an experiment",
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    {
      "page": "Oats.dat",
      "title": "Data for an experiment to investigate nitrogen response of 3 oats varieties",
      "topics": [
        "Oats.dat"
      ]
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      "page": "p2canon.object",
      "title": "Description of a p2canon object",
      "topics": [
        "p2canon.object"
      ]
    },
    {
      "page": "pcanon.object",
      "title": "Description of a pcanon object",
      "topics": [
        "pcanon.object"
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      "page": "porthogonalize.list",
      "title": "Takes a list of 'projectors' and constructs a 'pstructure.object' that includes projectors, each of which has been orthogonalized to all projectors preceding it in the list.",
      "topics": [
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        "porthogonalize.list"
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      "title": "Computes the power for an experiment",
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      "page": "print.aliasing",
      "title": "Print an aliasing data.frame",
      "topics": [
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      "page": "print.projector",
      "title": "Print projectors",
      "topics": [
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        "print.projector"
      ]
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      "page": "print.pstructure",
      "title": "Prints a pstructure.object",
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      "page": "print.summary.p2canon",
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      "page": "proj2.combine",
      "title": "Compute the projection and Residual operators for two, possibly nonorthogonal, projectors",
      "topics": [
        "proj2.combine"
      ]
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      "page": "proj2.efficiency",
      "title": "Computes the canonical efficiency factors for the joint decomposition of two projectors",
      "topics": [
        "proj2.efficiency"
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      "page": "proj2.eigen",
      "title": "Canonical efficiency factors and eigenvectors in joint decomposition of two projectors",
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        "proj2.eigen"
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      "page": "projector",
      "title": "Create projectors",
      "topics": [
        "projector"
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      "page": "projector-class",
      "title": "Class projector",
      "topics": [
        "coerce,projector,matrix-method",
        "coerce<-,projector,matrix-method",
        "projector-class"
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      "page": "projs.2canon",
      "title": "A canonical analysis of the relationships between two sets of projectors",
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        "projs.2canon"
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      "page": "projs.combine.p2canon",
      "title": "Extract, from a p2canon object, the projectors that give the combined canonical decomposition",
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      "page": "pstructure.formula",
      "title": "Takes a formula and constructs a 'pstructure.object' that includes the orthogonalized projectors for the terms in a formula",
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        "pstructure",
        "pstructure.formula"
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      "page": "pstructure.object",
      "title": "Description of a pstructure object",
      "topics": [
        "pstructure.object"
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      "page": "qqyeffects",
      "title": "Half or full normal plot of Yates effects",
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        "qqyeffects"
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      "page": "rep.data.frame",
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        "residuals.aovlist"
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      "title": "Data for the three-phase sensory evaluation experiment in Brien, C.J. and Payne, R.W. (1999)",
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        "Sensory3Phase.dat",
        "Sensory3PhaseShort.dat"
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        "set.daeRNGkind"
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      "page": "summary.pcanon",
      "title": "Summarizes the anatomy of a design, being the decomposition of the sample space based on its canonical analysis, as produced by designAnatomy",
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        "summary,pcanon-method",
        "summary.pcanon"
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      "page": "Zncsspline",
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