Generates an alpha designs starting from the alpha design fixing under the series formulated by Patterson and Williams. These designs are generated by the alpha arrangements. They are similar to the lattice designs, but the tables are rectangular s by k (with s blocks and k<s columns. The number of treatments should be equal to s*k and all the experimental units r*s*k (r replications).
design.alpha( trt, k, r, serie = 2, seed = 0, kinds = "Super-Duper", randomization = TRUE )
| trt | Treatments |
|---|---|
| k | size block |
| r | Replications |
| serie | number plot, 1: 11,12; 2: 101,102; 3: 1001,1002 |
| seed | seed |
| kinds | method for to randomize |
| randomization | TRUE or FALSE - randomize |
Design parameters
Design statistics
Design sketch
Fieldbook
Parameters for the alpha design: I. r=2, k <= s; II. r=3, s odd, k <= s; III.r=3, s even, k <= s-1; IV. r=4, s odd but not a multiple of 3, k<=s
r= replications s=number of blocks k=size of block Number of treatment is equal to k*s
H.D. Patterson and E.R. Williams. Biometrika (1976) A new class of resolvable incomplete block designs. printed in Great Britain. Online: http://biomet.oxfordjournals.org/cgi/content/abstract/63/1/83
design.ab,
design.split,design.bib, design.crd
, design.cyclic , design.dau ,
design.graeco, design.lattice,
design.lsd, design.rcbd,
design.strip
library(agricolae) #Example one trt<-1:30 t <- length(trt) # size block k k<-3 # Blocks s s<-t/k # replications r r <- 2 outdesign<- design.alpha(trt,k,r,serie=2)#> #> Alpha Design (0,1) - Serie I #> #> Parameters Alpha Design #> ======================= #> Treatmeans : 30 #> Block size : 3 #> Blocks : 10 #> Replication: 2 #> #> Efficiency factor #> (E ) 0.6170213 #> #> <<< Book >>>#> [,1] [,2] [,3] #> [1,] 101 102 103 #> [2,] 104 105 106 #> [3,] 107 108 109 #> [4,] 110 111 112 #> [5,] 113 114 115 #> [6,] 116 117 118 #> [7,] 119 120 121 #> [8,] 122 123 124 #> [9,] 125 126 127 #> [10,] 128 129 130 #> [,1] [,2] [,3] #> [1,] 201 202 203 #> [2,] 204 205 206 #> [3,] 207 208 209 #> [4,] 210 211 212 #> [5,] 213 214 215 #> [6,] 216 217 218 #> [7,] 219 220 221 #> [8,] 222 223 224 #> [9,] 225 226 227 #> [10,] 228 229 230outdesign$sketch#> $rep1 #> [,1] [,2] [,3] #> [1,] "17" "5" "24" #> [2,] "7" "11" "30" #> [3,] "4" "2" "20" #> [4,] "26" "25" "12" #> [5,] "22" "18" "21" #> [6,] "16" "19" "15" #> [7,] "1" "13" "28" #> [8,] "3" "14" "6" #> [9,] "8" "10" "27" #> [10,] "29" "9" "23" #> #> $rep2 #> [,1] [,2] [,3] #> [1,] "16" "3" "1" #> [2,] "8" "7" "17" #> [3,] "21" "30" "27" #> [4,] "23" "15" "28" #> [5,] "5" "20" "10" #> [6,] "11" "12" "18" #> [7,] "29" "2" "24" #> [8,] "26" "22" "14" #> [9,] "19" "6" "25" #> [10,] "13" "9" "4" #># Example two trt<-letters[1:12] t <- length(trt) k<-3 r<-3 s<-t/k outdesign<- design.alpha(trt,k,r,serie=2)#> #> Alpha Design (0,1) - Serie III #> #> Parameters Alpha Design #> ======================= #> Treatmeans : 12 #> Block size : 3 #> Blocks : 4 #> Replication: 3 #> #> Efficiency factor #> (E ) 0.7096774 #> #> <<< Book >>>#> [,1] [,2] [,3] #> [1,] 101 102 103 #> [2,] 104 105 106 #> [3,] 107 108 109 #> [4,] 110 111 112 #> [,1] [,2] [,3] #> [1,] 201 202 203 #> [2,] 204 205 206 #> [3,] 207 208 209 #> [4,] 210 211 212 #> [,1] [,2] [,3] #> [1,] 301 302 303 #> [2,] 304 305 306 #> [3,] 307 308 309 #> [4,] 310 311 312outdesign$sketch#> $rep1 #> [,1] [,2] [,3] #> [1,] "g" "c" "k" #> [2,] "j" "d" "l" #> [3,] "e" "a" "f" #> [4,] "b" "i" "h" #> #> $rep2 #> [,1] [,2] [,3] #> [1,] "f" "l" "g" #> [2,] "b" "a" "c" #> [3,] "d" "h" "k" #> [4,] "e" "j" "i" #> #> $rep3 #> [,1] [,2] [,3] #> [1,] "c" "e" "h" #> [2,] "b" "d" "g" #> [3,] "i" "l" "a" #> [4,] "j" "k" "f" #>