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Statistical procedures for agricultural research, page 143, Grain Yields of Three Rice Varieties Grown under Three Management practices and Five Nitrogen levels; in a split-split-plot design with nitrogen as main-plot, management practice as subplot, and variety as sub-subplot factores, with three replications.
library(agricolae)
library(xtable)
sspdata <- read.csv("/Volumes/Celine/RQMA/RWorkDir/sspdata.csv") # path of data on my computer
print(sspdata, type = "html") # attached data## block nitrogen management variety yield
## 1 1 0 m1 1 3.320
## 2 1 0 m2 1 3.766
## 3 1 0 m3 1 4.660
## 4 1 50 m1 1 3.188
## 5 1 50 m2 1 3.625
## 6 1 50 m3 1 5.232
## 7 1 80 m1 1 5.468
## 8 1 80 m2 1 5.759
## 9 1 80 m3 1 6.215
## 10 1 110 m1 1 4.246
## 11 1 110 m2 1 5.255
## 12 1 110 m3 1 6.829
## 13 1 140 m1 1 3.132
## 14 1 140 m2 1 5.389
## 15 1 140 m3 1 5.217
## 16 2 0 m1 1 3.864
## 17 2 0 m2 1 4.311
## 18 2 0 m3 1 5.915
## 19 2 50 m1 1 4.752
## 20 2 50 m2 1 4.809
## 21 2 50 m3 1 5.170
## 22 2 80 m1 1 5.788
## 23 2 80 m2 1 6.130
## 24 2 80 m3 1 7.106
## 25 2 110 m1 1 4.842
## 26 2 110 m2 1 5.742
## 27 2 110 m3 1 5.869
## 28 2 140 m1 1 4.375
## 29 2 140 m2 1 4.315
## 30 2 140 m3 1 5.389
## 31 3 0 m1 1 4.507
## 32 3 0 m2 1 4.875
## 33 3 0 m3 1 5.400
## 34 3 50 m1 1 4.756
## 35 3 50 m2 1 5.295
## 36 3 50 m3 1 6.046
## 37 3 80 m1 1 4.422
## 38 3 80 m2 1 5.308
## 39 3 80 m3 1 6.318
## 40 3 110 m1 1 4.863
## 41 3 110 m2 1 5.345
## 42 3 110 m3 1 6.011
## 43 3 140 m1 1 4.678
## 44 3 140 m2 1 5.896
## 45 3 140 m3 1 7.309
## 46 1 0 m1 2 6.101
## 47 1 0 m2 2 5.096
## 48 1 0 m3 2 6.573
## 49 1 50 m1 2 5.595
## 50 1 50 m2 2 6.357
## 51 1 50 m3 2 7.016
## 52 1 80 m1 2 5.442
## 53 1 80 m2 2 6.398
## 54 1 80 m3 2 6.953
## 55 1 110 m1 2 6.209
## 56 1 110 m2 2 6.992
## 57 1 110 m3 2 7.565
## 58 1 140 m1 2 6.860
## 59 1 140 m2 2 6.857
## 60 1 140 m3 2 7.254
## 61 2 0 m1 2 5.122
## 62 2 0 m2 2 4.873
## 63 2 0 m3 2 5.495
## 64 2 50 m1 2 6.780
## 65 2 50 m2 2 5.925
## 66 2 50 m3 2 7.442
## 67 2 80 m1 2 5.988
## 68 2 80 m2 2 6.533
## 69 2 80 m3 2 6.914
## 70 2 110 m1 2 6.768
## 71 2 110 m2 2 7.856
## 72 2 110 m3 2 7.626
## 73 2 140 m1 2 6.894
## 74 2 140 m2 2 6.974
## 75 2 140 m3 2 7.812
## 76 3 0 m1 2 4.815
## 77 3 0 m2 2 4.166
## 78 3 0 m3 2 4.225
## 79 3 50 m1 2 5.390
## 80 3 50 m2 2 5.163
## 81 3 50 m3 2 4.478
## 82 3 80 m1 2 6.509
## 83 3 80 m2 2 6.569
## 84 3 80 m3 2 7.991
## 85 3 110 m1 2 5.779
## 86 3 110 m2 2 6.164
## 87 3 110 m3 2 7.362
## 88 3 140 m1 2 6.573
## 89 3 140 m2 2 7.422
## 90 3 140 m3 2 8.950
## 91 1 0 m1 3 5.355
## 92 1 0 m2 3 7.442
## 93 1 0 m3 3 7.018
## 94 1 50 m1 3 6.706
## 95 1 50 m2 3 8.592
## 96 1 50 m3 3 8.480
## 97 1 80 m1 3 8.452
## 98 1 80 m2 3 8.662
## 99 1 80 m3 3 9.112
## 100 1 110 m1 3 8.042
## 101 1 110 m2 3 9.080
## 102 1 110 m3 3 9.660
## 103 1 140 m1 3 9.314
## 104 1 140 m2 3 9.224
## 105 1 140 m3 3 10.360
## 106 2 0 m1 3 5.536
## 107 2 0 m2 3 6.462
## 108 2 0 m3 3 8.020
## 109 2 50 m1 3 6.546
## 110 2 50 m2 3 7.646
## 111 2 50 m3 3 9.942
## 112 2 80 m1 3 6.698
## 113 2 80 m2 3 8.526
## 114 2 80 m3 3 9.140
## 115 2 110 m1 3 7.414
## 116 2 110 m2 3 9.016
## 117 2 110 m3 3 8.966
## 118 2 140 m1 3 8.508
## 119 2 140 m2 3 9.680
## 120 2 140 m3 3 9.896
## 121 3 0 m1 3 5.244
## 122 3 0 m2 3 5.584
## 123 3 0 m3 3 7.642
## 124 3 50 m1 3 7.092
## 125 3 50 m2 3 7.212
## 126 3 50 m3 3 8.714
## 127 3 80 m1 3 8.650
## 128 3 80 m2 3 8.514
## 129 3 80 m3 3 9.320
## 130 3 110 m1 3 6.902
## 131 3 110 m2 3 7.778
## 132 3 110 m3 3 9.128
## 133 3 140 m1 3 8.032
## 134 3 140 m2 3 9.294
## 135 3 140 m3 3 9.712attach(sspdata)
model <- ssp.plot(block,nitrogen,management,variety,yield)##
## ANALYSIS SPLIT-SPLIT PLOT: yield
## Class level information
##
## nitrogen : 0 50 80 110 140
## management : m1 m2 m3
## variety : 1 2 3
## block : 1 2 3
##
## Number of observations: 135
##
## Analysis of Variance Table
##
## Response: yield
## Df Sum Sq Mean Sq F value Pr(>F)
## block 2 0.732 0.366 0.6578 0.543910
## nitrogen 4 61.641 15.410 27.6953 9.734e-05 ***
## Ea 8 4.451 0.556
## management 2 42.936 21.468 81.9965 2.303e-10 ***
## nitrogen:management 8 1.103 0.138 0.5266 0.822648
## Eb 20 5.236 0.262
## variety 2 206.013 103.007 207.8667 < 2.2e-16 ***
## variety:nitrogen 8 14.145 1.768 3.5679 0.001916 **
## variety:management 4 3.852 0.963 1.9432 0.114899
## variety:nitrogen:management 16 3.699 0.231 0.4666 0.953759
## Ec 60 29.732 0.496
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## cv(a) = 11.4 %, cv(b) = 7.8 %, cv(c) = 10.7 %, Mean = 6.554415gla <- model$gl.a; glb <- model$gl.b; glc <- model$gl.c
Ea <- model$Ea; Eb <- model$Eb; Ec <- model$Ec
LSD.test(yield,nitrogen,gla,Ea,console = TRUE)##
## Study: yield ~ nitrogen
##
## LSD t Test for yield
##
## Mean Square Error: 0.5564188
##
## nitrogen, means and individual ( 95 %) CI
##
## yield std r LCL UCL Min Max
## 0 5.384704 1.206963 27 5.053665 5.715743 3.320 8.020
## 50 6.220333 1.615861 27 5.889294 6.551372 3.188 9.942
## 80 6.995741 1.371302 27 6.664702 7.326780 4.422 9.320
## 110 6.937370 1.474547 27 6.606331 7.268409 4.246 9.660
## 140 7.233926 1.968153 27 6.902887 7.564965 3.132 10.360
##
## alpha: 0.05 ; Df Error: 8
## Critical Value of t: 2.306004
##
## Least Significant Difference 0.4681598
## Means with the same letter are not significantly different.
##
## Groups, Treatments and means
## a 140 7.234
## a 80 6.996
## a 110 6.937
## b 50 6.22
## c 0 5.385LSD.test(yield,management,glb,Eb,console = TRUE)##
## Study: yield ~ management
##
## LSD t Test for yield
##
## Mean Square Error: 0.2618167
##
## management, means and individual ( 95 %) CI
##
## yield std r LCL UCL Min Max
## m1 5.900378 1.486531 45 5.741267 6.059488 3.132 9.314
## m2 6.486156 1.621936 45 6.327045 6.645266 3.625 9.680
## m3 7.276711 1.635020 45 7.117601 7.435822 4.225 10.360
##
## alpha: 0.05 ; Df Error: 20
## Critical Value of t: 2.085963
##
## Least Significant Difference 0.2250164
## Means with the same letter are not significantly different.
##
## Groups, Treatments and means
## a m3 7.277
## b m2 6.486
## c m1 5.9LSD.test(yield,variety,glc,Ec,console = TRUE)##
## Study: yield ~ variety
##
## LSD t Test for yield
##
## Mean Square Error: 0.4955415
##
## variety, means and individual ( 95 %) CI
##
## yield std r LCL UCL Min Max
## 1 5.126822 0.971530 45 4.916915 5.336730 3.132 7.309
## 2 6.396133 1.065752 45 6.186226 6.606041 4.166 8.950
## 3 8.140289 1.314438 45 7.930381 8.350197 5.244 10.360
##
## alpha: 0.05 ; Df Error: 60
## Critical Value of t: 2.000298
##
## Least Significant Difference 0.2968543
## Means with the same letter are not significantly different.
##
## Groups, Treatments and means
## a 3 8.14
## b 2 6.396
## c 1 5.127