augmentedRCBD OutputR/describe.augmentedRCBD.R
describe.augmentedRCBD.Rddescribe.augmentedRCBD computes descriptive statistics from the
adjusted means in an object of class augmentedRCBD.
describe.augmentedRCBD(aug)A list with the following descriptive statistics:
The number of treatments/genotypes.
The mean value.
The standard error.
The standard deviation.
The minimum value
The maximum value
The skewness estimator.
The p-value from D'Agostino test of skewness.
The kurtosis estimator.
The p-value from Anscombe-Glynn test of kurtosis.
describe.augmentedRCBD computes the following descriptive statistics
from the adjusted means in an object of class augmentedRCBD.
Count
Mean
Standard deviation
Standard error
Minimum
Maximum
Skewness statistic along with p-value from D'Agostino test of skewness (D'Agostino, 1970).
Kurtosis statistic along with p-value from Anscombe-Glynn test of kurtosis (Anscombe and Glynn, 1983).
D'Agostino RB (1970). “Transformation to normality of the null distribution of g1.” Biometrika, 57(3), 679–681.
Anscombe FJ, Glynn WJ (1983). “Distribution of the kurtosis statistic b2 for normal samples.” Biometrika, 70(1), 227–234.
# Example data
blk <- c(rep(1,7),rep(2,6),rep(3,7))
trt <- c(1, 2, 3, 4, 7, 11, 12, 1, 2, 3, 4, 5, 9, 1, 2, 3, 4, 8, 6, 10)
y1 <- c(92, 79, 87, 81, 96, 89, 82, 79, 81, 81, 91, 79, 78, 83, 77, 78, 78,
70, 75, 74)
y2 <- c(258, 224, 238, 278, 347, 300, 289, 260, 220, 237, 227, 281, 311, 250,
240, 268, 287, 226, 395, 450)
data <- data.frame(blk, trt, y1, y2)
# Convert block and treatment to factors
data$blk <- as.factor(data$blk)
data$trt <- as.factor(data$trt)
# Results for variable y1
out1 <- augmentedRCBD(data$blk, data$trt, data$y1, method.comp = "lsd",
alpha = 0.05, group = TRUE, console = TRUE)
#>
#> Augmented Design Details
#> ========================
#>
#> Number of blocks "3"
#> Number of treatments "12"
#> Number of check treatments "4"
#> Number of test treatments "8"
#> Check treatments "1, 2, 3, 4"
#>
#>
#> ANOVA, Treatment Adjusted
#> =========================
#> Df Sum Sq Mean Sq F value Pr(>F)
#> Block (ignoring Treatments) 2 360.1 180.04 6.675 0.0298 *
#> Treatment (eliminating Blocks) 11 285.1 25.92 0.961 0.5499
#> Treatment: Check 3 52.9 17.64 0.654 0.6092
#> Treatment: Test and Test vs. Check 8 232.2 29.02 1.076 0.4779
#> Residuals 6 161.8 26.97
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> ANOVA, Block Adjusted
#> =====================
#> Df Sum Sq Mean Sq F value Pr(>F)
#> Treatment (ignoring Blocks) 11 575.7 52.33 1.940 0.215
#> Treatment: Check 3 52.9 17.64 0.654 0.609
#> Treatment: Test 7 505.9 72.27 2.679 0.125
#> Treatment: Test vs. Check 1 16.9 16.87 0.626 0.459
#> Block (eliminating Treatments) 2 69.5 34.75 1.288 0.342
#> Residuals 6 161.8 26.97
#>
#> Coefficient of Variation
#> ========================
#> 6.372367
#>
#> Overall Adjusted Mean
#> =====================
#> 81.0625
#>
#> Standard Errors
#> ===============
#> Std. Error of Diff. CD (5%)
#> Control Treatment Means 4.240458 10.37603
#> Two Test Treatments (Same Block) 7.344688 17.97180
#> Two Test Treatments (Different Blocks) 8.211611 20.09309
#> A Test Treatment and a Control Treatment 6.704752 16.40594
#>
#> Treatment Means
#> ===============
#> Treatment Block Means SE r Min Max Adjusted Means
#> 1 84.67 3.84 3 79.00 92.00 84.67
#> 10 3 74.00 <NA> 1 74.00 74.00 77.25
#> 11 1 89.00 <NA> 1 89.00 89.00 86.50
#> 12 1 82.00 <NA> 1 82.00 82.00 79.50
#> 2 79.00 1.15 3 77.00 81.00 79.00
#> 3 82.00 2.65 3 78.00 87.00 82.00
#> 4 83.33 3.93 3 78.00 91.00 83.33
#> 5 2 79.00 <NA> 1 79.00 79.00 78.25
#> 6 3 75.00 <NA> 1 75.00 75.00 78.25
#> 7 1 96.00 <NA> 1 96.00 96.00 93.50
#> 8 3 70.00 <NA> 1 70.00 70.00 73.25
#> 9 2 78.00 <NA> 1 78.00 78.00 77.25
#>
#>
#> Comparisons
#> ===========
#>
#> Method : lsd
#>
#> contrast estimate SE df t.ratio p.value sig
#> treatment1 - treatment2 5.67 4.24 6 1.336 0.230
#> treatment1 - treatment3 2.67 4.24 6 0.629 0.553
#> treatment1 - treatment4 1.33 4.24 6 0.314 0.764
#> treatment1 - treatment5 6.42 6.36 6 1.009 0.352
#> treatment1 - treatment6 6.42 6.36 6 1.009 0.352
#> treatment1 - treatment7 -8.83 6.36 6 -1.389 0.214
#> treatment1 - treatment8 11.42 6.36 6 1.795 0.123
#> treatment1 - treatment9 7.42 6.36 6 1.166 0.288
#> treatment1 - treatment10 7.42 6.36 6 1.166 0.288
#> treatment1 - treatment11 -1.83 6.36 6 -0.288 0.783
#> treatment1 - treatment12 5.17 6.36 6 0.812 0.448
#> treatment2 - treatment3 -3.00 4.24 6 -0.707 0.506
#> treatment2 - treatment4 -4.33 4.24 6 -1.022 0.346
#> treatment2 - treatment5 0.75 6.36 6 0.118 0.910
#> treatment2 - treatment6 0.75 6.36 6 0.118 0.910
#> treatment2 - treatment7 -14.50 6.36 6 -2.280 0.063
#> treatment2 - treatment8 5.75 6.36 6 0.904 0.401
#> treatment2 - treatment9 1.75 6.36 6 0.275 0.792
#> treatment2 - treatment10 1.75 6.36 6 0.275 0.792
#> treatment2 - treatment11 -7.50 6.36 6 -1.179 0.283
#> treatment2 - treatment12 -0.50 6.36 6 -0.079 0.940
#> treatment3 - treatment4 -1.33 4.24 6 -0.314 0.764
#> treatment3 - treatment5 3.75 6.36 6 0.590 0.577
#> treatment3 - treatment6 3.75 6.36 6 0.590 0.577
#> treatment3 - treatment7 -11.50 6.36 6 -1.808 0.121
#> treatment3 - treatment8 8.75 6.36 6 1.376 0.218
#> treatment3 - treatment9 4.75 6.36 6 0.747 0.483
#> treatment3 - treatment10 4.75 6.36 6 0.747 0.483
#> treatment3 - treatment11 -4.50 6.36 6 -0.707 0.506
#> treatment3 - treatment12 2.50 6.36 6 0.393 0.708
#> treatment4 - treatment5 5.08 6.36 6 0.799 0.455
#> treatment4 - treatment6 5.08 6.36 6 0.799 0.455
#> treatment4 - treatment7 -10.17 6.36 6 -1.598 0.161
#> treatment4 - treatment8 10.08 6.36 6 1.585 0.164
#> treatment4 - treatment9 6.08 6.36 6 0.956 0.376
#> treatment4 - treatment10 6.08 6.36 6 0.956 0.376
#> treatment4 - treatment11 -3.17 6.36 6 -0.498 0.636
#> treatment4 - treatment12 3.83 6.36 6 0.603 0.569
#> treatment5 - treatment6 0.00 8.21 6 0.000 1.000
#> treatment5 - treatment7 -15.25 8.21 6 -1.857 0.113
#> treatment5 - treatment8 5.00 8.21 6 0.609 0.565
#> treatment5 - treatment9 1.00 7.34 6 0.136 0.896
#> treatment5 - treatment10 1.00 8.21 6 0.122 0.907
#> treatment5 - treatment11 -8.25 8.21 6 -1.005 0.354
#> treatment5 - treatment12 -1.25 8.21 6 -0.152 0.884
#> treatment6 - treatment7 -15.25 8.21 6 -1.857 0.113
#> treatment6 - treatment8 5.00 7.34 6 0.681 0.521
#> treatment6 - treatment9 1.00 8.21 6 0.122 0.907
#> treatment6 - treatment10 1.00 7.34 6 0.136 0.896
#> treatment6 - treatment11 -8.25 8.21 6 -1.005 0.354
#> treatment6 - treatment12 -1.25 8.21 6 -0.152 0.884
#> treatment7 - treatment8 20.25 8.21 6 2.466 0.049 *
#> treatment7 - treatment9 16.25 8.21 6 1.979 0.095
#> treatment7 - treatment10 16.25 8.21 6 1.979 0.095
#> treatment7 - treatment11 7.00 7.34 6 0.953 0.377
#> treatment7 - treatment12 14.00 7.34 6 1.906 0.105
#> treatment8 - treatment9 -4.00 8.21 6 -0.487 0.643
#> treatment8 - treatment10 -4.00 7.34 6 -0.545 0.606
#> treatment8 - treatment11 -13.25 8.21 6 -1.614 0.158
#> treatment8 - treatment12 -6.25 8.21 6 -0.761 0.475
#> treatment9 - treatment10 -0.00 8.21 6 -0.000 1.000
#> treatment9 - treatment11 -9.25 8.21 6 -1.126 0.303
#> treatment9 - treatment12 -2.25 8.21 6 -0.274 0.793
#> treatment10 - treatment11 -9.25 8.21 6 -1.126 0.303
#> treatment10 - treatment12 -2.25 8.21 6 -0.274 0.793
#> treatment11 - treatment12 7.00 7.34 6 0.953 0.377
#>
#> Treatment Groups
#> ================
#>
#> Method : lsd
#>
#> Treatment Adjusted Means SE df lower.CL upper.CL Group
#> 8 73.25 5.61 6 59.52 86.98 1
#> 9 77.25 5.61 6 63.52 90.98 12
#> 10 77.25 5.61 6 63.52 90.98 12
#> 5 78.25 5.61 6 64.52 91.98 12
#> 6 78.25 5.61 6 64.52 91.98 12
#> 2 79.00 3.00 6 71.66 86.34 12
#> 12 79.50 5.61 6 65.77 93.23 12
#> 3 82.00 3.00 6 74.66 89.34 12
#> 4 83.33 3.00 6 76.00 90.67 12
#> 1 84.67 3.00 6 77.33 92.00 12
#> 11 86.50 5.61 6 72.77 100.23 12
#> 7 93.50 5.61 6 79.77 107.23 2
# Results for variable y2
out2 <- augmentedRCBD(data$blk, data$trt, data$y2, method.comp = "lsd",
alpha = 0.05, group = TRUE, console = TRUE)
#>
#> Augmented Design Details
#> ========================
#>
#> Number of blocks "3"
#> Number of treatments "12"
#> Number of check treatments "4"
#> Number of test treatments "8"
#> Check treatments "1, 2, 3, 4"
#>
#>
#> ANOVA, Treatment Adjusted
#> =========================
#> Df Sum Sq Mean Sq F value Pr(>F)
#> Block (ignoring Treatments) 2 7019 3510 12.261 0.007597 **
#> Treatment (eliminating Blocks) 11 58965 5360 18.727 0.000920 ***
#> Treatment: Check 3 2150 717 2.504 0.156116
#> Treatment: Test and Test vs. Check 8 56815 7102 24.810 0.000473 ***
#> Residuals 6 1718 286
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> ANOVA, Block Adjusted
#> =====================
#> Df Sum Sq Mean Sq F value Pr(>F)
#> Treatment (ignoring Blocks) 11 64708 5883 20.550 0.000707 ***
#> Treatment: Check 3 2150 717 2.504 0.156116
#> Treatment: Test 7 34863 4980 17.399 0.001366 **
#> Treatment: Test vs. Check 1 27694 27694 96.749 6.36e-05 ***
#> Block (eliminating Treatments) 2 1277 639 2.231 0.188645
#> Residuals 6 1717 286
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Coefficient of Variation
#> ========================
#> 6.057617
#>
#> Overall Adjusted Mean
#> =====================
#> 298.4792
#>
#> Standard Errors
#> ===============
#> Std. Error of Diff. CD (5%)
#> Control Treatment Means 13.81424 33.80224
#> Two Test Treatments (Same Block) 23.92697 58.54719
#> Two Test Treatments (Different Blocks) 26.75117 65.45775
#> A Test Treatment and a Control Treatment 21.84224 53.44603
#>
#> Treatment Means
#> ===============
#> Treatment Block Means SE r Min Max Adjusted Means
#> 1 256.00 3.06 3 250.00 260.00 256.00
#> 10 3 450.00 <NA> 1 450.00 450.00 437.67
#> 11 1 300.00 <NA> 1 300.00 300.00 299.42
#> 12 1 289.00 <NA> 1 289.00 289.00 288.42
#> 2 228.00 6.11 3 220.00 240.00 228.00
#> 3 247.67 10.17 3 237.00 268.00 247.67
#> 4 264.00 18.68 3 227.00 287.00 264.00
#> 5 2 281.00 <NA> 1 281.00 281.00 293.92
#> 6 3 395.00 <NA> 1 395.00 395.00 382.67
#> 7 1 347.00 <NA> 1 347.00 347.00 346.42
#> 8 3 226.00 <NA> 1 226.00 226.00 213.67
#> 9 2 311.00 <NA> 1 311.00 311.00 323.92
#>
#>
#> Comparisons
#> ===========
#>
#> Method : lsd
#>
#> contrast estimate SE df t.ratio p.value sig
#> treatment1 - treatment2 28.00 13.81 6 2.027 0.089
#> treatment1 - treatment3 8.33 13.81 6 0.603 0.568
#> treatment1 - treatment4 -8.00 13.81 6 -0.579 0.584
#> treatment1 - treatment5 -37.92 20.72 6 -1.830 0.117
#> treatment1 - treatment6 -126.67 20.72 6 -6.113 0.001 ***
#> treatment1 - treatment7 -90.42 20.72 6 -4.363 0.005 **
#> treatment1 - treatment8 42.33 20.72 6 2.043 0.087
#> treatment1 - treatment9 -67.92 20.72 6 -3.278 0.017 *
#> treatment1 - treatment10 -181.67 20.72 6 -8.767 0.000 ***
#> treatment1 - treatment11 -43.42 20.72 6 -2.095 0.081
#> treatment1 - treatment12 -32.42 20.72 6 -1.564 0.169
#> treatment2 - treatment3 -19.67 13.81 6 -1.424 0.204
#> treatment2 - treatment4 -36.00 13.81 6 -2.606 0.040 *
#> treatment2 - treatment5 -65.92 20.72 6 -3.181 0.019 *
#> treatment2 - treatment6 -154.67 20.72 6 -7.464 0.000 ***
#> treatment2 - treatment7 -118.42 20.72 6 -5.715 0.001 **
#> treatment2 - treatment8 14.33 20.72 6 0.692 0.515
#> treatment2 - treatment9 -95.92 20.72 6 -4.629 0.004 **
#> treatment2 - treatment10 -209.67 20.72 6 -10.118 0.000 ***
#> treatment2 - treatment11 -71.42 20.72 6 -3.447 0.014 *
#> treatment2 - treatment12 -60.42 20.72 6 -2.916 0.027 *
#> treatment3 - treatment4 -16.33 13.81 6 -1.182 0.282
#> treatment3 - treatment5 -46.25 20.72 6 -2.232 0.067
#> treatment3 - treatment6 -135.00 20.72 6 -6.515 0.001 ***
#> treatment3 - treatment7 -98.75 20.72 6 -4.766 0.003 **
#> treatment3 - treatment8 34.00 20.72 6 1.641 0.152
#> treatment3 - treatment9 -76.25 20.72 6 -3.680 0.010 *
#> treatment3 - treatment10 -190.00 20.72 6 -9.169 0.000 ***
#> treatment3 - treatment11 -51.75 20.72 6 -2.497 0.047 *
#> treatment3 - treatment12 -40.75 20.72 6 -1.967 0.097
#> treatment4 - treatment5 -29.92 20.72 6 -1.444 0.199
#> treatment4 - treatment6 -118.67 20.72 6 -5.727 0.001 **
#> treatment4 - treatment7 -82.42 20.72 6 -3.977 0.007 **
#> treatment4 - treatment8 50.33 20.72 6 2.429 0.051
#> treatment4 - treatment9 -59.92 20.72 6 -2.892 0.028 *
#> treatment4 - treatment10 -173.67 20.72 6 -8.381 0.000 ***
#> treatment4 - treatment11 -35.42 20.72 6 -1.709 0.138
#> treatment4 - treatment12 -24.42 20.72 6 -1.178 0.283
#> treatment5 - treatment6 -88.75 26.75 6 -3.318 0.016 *
#> treatment5 - treatment7 -52.50 26.75 6 -1.963 0.097
#> treatment5 - treatment8 80.25 26.75 6 3.000 0.024 *
#> treatment5 - treatment9 -30.00 23.93 6 -1.254 0.257
#> treatment5 - treatment10 -143.75 26.75 6 -5.374 0.002 **
#> treatment5 - treatment11 -5.50 26.75 6 -0.206 0.844
#> treatment5 - treatment12 5.50 26.75 6 0.206 0.844
#> treatment6 - treatment7 36.25 26.75 6 1.355 0.224
#> treatment6 - treatment8 169.00 23.93 6 7.063 0.000 ***
#> treatment6 - treatment9 58.75 26.75 6 2.196 0.070
#> treatment6 - treatment10 -55.00 23.93 6 -2.299 0.061
#> treatment6 - treatment11 83.25 26.75 6 3.112 0.021 *
#> treatment6 - treatment12 94.25 26.75 6 3.523 0.012 *
#> treatment7 - treatment8 132.75 26.75 6 4.962 0.003 **
#> treatment7 - treatment9 22.50 26.75 6 0.841 0.433
#> treatment7 - treatment10 -91.25 26.75 6 -3.411 0.014 *
#> treatment7 - treatment11 47.00 23.93 6 1.964 0.097
#> treatment7 - treatment12 58.00 23.93 6 2.424 0.052
#> treatment8 - treatment9 -110.25 26.75 6 -4.121 0.006 **
#> treatment8 - treatment10 -224.00 23.93 6 -9.362 0.000 ***
#> treatment8 - treatment11 -85.75 26.75 6 -3.205 0.018 *
#> treatment8 - treatment12 -74.75 26.75 6 -2.794 0.031 *
#> treatment9 - treatment10 -113.75 26.75 6 -4.252 0.005 **
#> treatment9 - treatment11 24.50 26.75 6 0.916 0.395
#> treatment9 - treatment12 35.50 26.75 6 1.327 0.233
#> treatment10 - treatment11 138.25 26.75 6 5.168 0.002 **
#> treatment10 - treatment12 149.25 26.75 6 5.579 0.001 **
#> treatment11 - treatment12 11.00 23.93 6 0.460 0.662
#>
#> Treatment Groups
#> ================
#>
#> Method : lsd
#>
#> Treatment Adjusted Means SE df lower.CL upper.CL Group
#> 8 213.67 18.27 6 168.95 258.38 12
#> 2 228.00 9.77 6 204.10 251.90 1
#> 3 247.67 9.77 6 223.76 271.57 123
#> 1 256.00 9.77 6 232.10 279.90 1234
#> 4 264.00 9.77 6 240.10 287.90 234
#> 12 288.42 18.27 6 243.70 333.13 345
#> 5 293.92 18.27 6 249.20 338.63 345
#> 11 299.42 18.27 6 254.70 344.13 45
#> 9 323.92 18.27 6 279.20 368.63 56
#> 7 346.42 18.27 6 301.70 391.13 56
#> 6 382.67 18.27 6 337.95 427.38 67
#> 10 437.67 18.27 6 392.95 482.38 7
# Descriptive statistics
describe.augmentedRCBD(out1)
#> $Count
#> [1] 12
#>
#> $Mean
#> [1] 81.0625
#>
#> $Std.Error
#> [1] 1.547002
#>
#> $Std.Deviation
#> [1] 5.358973
#>
#> $Min
#> [1] 73.25
#>
#> $Max
#> [1] 93.5
#>
#> $`Skewness(statistic)`
#> skew z
#> 0.9250344 1.6745760
#>
#> $`Skewness(p.value)`
#> [1] 0.09401746
#>
#> $`Kurtosis(statistic)`
#> kurt z
#> 3.522807 1.282305
#>
#> $`Kurtosis(p.value)`
#> [1] 0.1997357
#>
describe.augmentedRCBD(out2)
#> $Count
#> [1] 12
#>
#> $Mean
#> [1] 298.4792
#>
#> $Std.Error
#> [1] 18.92257
#>
#> $Std.Deviation
#> [1] 65.5497
#>
#> $Min
#> [1] 213.6667
#>
#> $Max
#> [1] 437.6667
#>
#> $`Skewness(statistic)`
#> skew z
#> 0.7449405 1.3680211
#>
#> $`Skewness(p.value)`
#> [1] 0.1713055
#>
#> $`Kurtosis(statistic)`
#> kurt z
#> 2.787997 0.536812
#>
#> $`Kurtosis(p.value)`
#> [1] 0.5913975
#>