Compute Descriptive Statistics from augmentedRCBD.menv Output
Source: R/describe.augmentedRCBD.menv.R
describe.augmentedRCBD.menv.Rddescribe.augmentedRCBD.menv computes descriptive statistics from the
adjusted means in an object of class augmentedRCBD.menv.
Usage
# S3 method for class 'augmentedRCBD.menv'
describe(aug, ...)Value
A list with the following descriptive statistics:
- Count
The number of treatments/genotypes.
- Mean
The mean value.
- Std.Error
The standard error.
- Std.Deviation
The standard deviation.
- Min
The minimum value
- Max
The maximum value
- Skewness(statistic)
The skewness estimator.
- Skewness(p.value)
The p-value from D'Agostino test of skewness.
- Kurtosis(statistic)
The kurtosis estimator.
- Kurtosis(p.value)
The p-value from Anscombe-Glynn test of kurtosis.
Details
describe.augmentedRCBD.menv computes the following descriptive
statistics from the adjusted means (averaged across environments) in an
object of class augmentedRCBD.menv.
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).
References
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.
Examples
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Scenario 1: Test treatments are replicated across all environments
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Example data
blk1 <- c(1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3,
4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6,
7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9)
trt1 <- c(1, 2, 3, 4, 7, 11, 12, 1, 2, 3, 4, 5, 9, 1, 2, 3, 4, 8, 6, 10,
1, 2, 3, 4, 8, 11, 5, 1, 2, 3, 4, 12, 9, 1, 2, 3, 4, 7, 6, 10,
1, 2, 3, 4, 7, 9, 12, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 8, 11, 10)
y1 <- c(92, 79, 87, 81, 96, 89, 82, 79, 81, 81, 91, 79, 78, 83, 77,
78, 78, 70, 75, 74, 90, 80, 85, 78, 95, 86, 81, 78, 78, 76, 88,
76, 79, 80, 76, 75, 74, 77, 75, 72, 91, 81, 86, 80, 94, 87, 83,
78, 79, 77, 90, 74, 76, 82, 83, 86, 76, 73, 74, 69)
env1 <- c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3,
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3)
data1 <- data.frame(env1, blk1, trt1, y1)
chks1 <- c(1, 2, 3, 4)
# Convert block, treatment and environment to factors
data1$blk1 <- as.factor(data1$blk1)
data1$trt1 <- as.factor(data1$trt1)
data1$env1 <- as.factor(data1$env1)
# Contingency tables of factors
table(data1$env1, data1$trt1)
#>
#> 1 2 3 4 5 6 7 8 9 10 11 12
#> 1 3 3 3 3 1 1 1 1 1 1 1 1
#> 2 3 3 3 3 1 1 1 1 1 1 1 1
#> 3 3 3 3 3 1 1 1 1 1 1 1 1
table(data1$env1, data1$blk1)
#>
#> 1 2 3 4 5 6 7 8 9
#> 1 7 6 7 0 0 0 0 0 0
#> 2 0 0 0 7 6 7 0 0 0
#> 3 0 0 0 0 0 0 7 6 7
table(data1$blk1, data1$trt1)
#>
#> 1 2 3 4 5 6 7 8 9 10 11 12
#> 1 1 1 1 1 0 0 1 0 0 0 1 1
#> 2 1 1 1 1 1 0 0 0 1 0 0 0
#> 3 1 1 1 1 0 1 0 1 0 1 0 0
#> 4 1 1 1 1 1 0 0 1 0 0 1 0
#> 5 1 1 1 1 0 0 0 0 1 0 0 1
#> 6 1 1 1 1 0 1 1 0 0 1 0 0
#> 7 1 1 1 1 0 0 1 0 1 0 0 1
#> 8 1 1 1 1 1 1 0 0 0 0 0 0
#> 9 1 1 1 1 0 0 0 1 0 1 1 0
# Results
out1 <- augmentedRCBD.menv(block = data1$blk1, treatment = data1$trt1,
env = data1$env1, y = data1$y1, checks = chks1,
scenario = 1, method.comp = "lsd", alpha = 0.05,
group = TRUE, console = TRUE)
#> NOTE: Results may be misleading due to involvement in interactions
#>
#> Augmented Design Details
#> ========================
#>
#> Number of blocks "9"
#> Number of treatments "12"
#> Number of environments "3"
#> Number of check treatments "4"
#> Number of test treatments "8"
#> Check treatments "1, 2, 3, 4"
#>
#>
#> ANOVA, Treatment Adjusted
#> =========================
#> Df Sum Sq Mean Sq
#> Environment 2 24.7 12.35
#> Treatment (eliminating Blocks) 11 691.2 62.83
#> Treatment: Check 3 85.9 28.63
#> Treatment: Test and Test vs. Check 8 605.3 75.66
#> Block (within Environment, ignoring Treatments) 6 672.5 112.08
#> Environment × Treatment interaction 22 398.7 18.12
#> Interaction: Check × Environment 6 17.6 2.94
#> Interaction: Test and Test vs. Check × Environment 16 381.1 23.82
#> Residuals 18 546.5 30.36
#> F value Pr(>F)
#> Environment 0.407 0.6718
#> Treatment (eliminating Blocks) 2.070 0.0824 .
#> Treatment: Check 0.943 0.4406
#> Treatment: Test and Test vs. Check 2.492 0.0513 .
#> Block (within Environment, ignoring Treatments) 3.692 0.0144 *
#> Environment × Treatment interaction 0.597 0.8753
#> Interaction: Check × Environment 0.097 0.9958
#> Interaction: Test and Test vs. Check × Environment 0.785 0.6846
#> Residuals
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> ANOVA, Block Adjusted
#> =====================
#> Df Sum Sq Mean Sq
#> Environment 2 24.7 12.35
#> Treatment (ignoring Blocks) 11 691.2 62.83
#> Treatment: Check 3 85.9 28.63
#> Treatment: Test 7 561.2 80.17
#> Treatment: Test vs. Check 1 44.1 44.10
#> Block (within Environment, eliminating Treatments) 6 672.5 112.08
#> Environment × Treatment interaction 22 398.7 18.12
#> Interaction: Check × Environment 6 17.6 2.94
#> Interaction: Test × Environment 14 340.2 24.30
#> Interaction: Test vs. Check × Environment 2 40.9 20.47
#> Residuals 18 546.5 30.36
#> F value Pr(>F)
#> Environment 0.407 0.6718
#> Treatment (ignoring Blocks) 2.070 0.0824 .
#> Treatment: Check 0.943 0.4406
#> Treatment: Test 2.640 0.0459 *
#> Treatment: Test vs. Check 1.453 0.2437
#> Block (within Environment, eliminating Treatments) 3.692 0.0144 *
#> Environment × Treatment interaction 0.597 0.8753
#> Interaction: Check × Environment 0.097 0.9958
#> Interaction: Test × Environment 0.800 0.6596
#> Interaction: Test vs. Check × Environment 0.674 0.5219
#> Residuals
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Coefficient of Variation
#> ========================
#> 6.81942
#>
#> Overall Adjusted Mean
#> =====================
#> 80.31944
#>
#> Standard Errors
#> ===============
#> Std. Error of Diff. CD (5%)
#> Control Treatment Means 1.499657 3.150662
#> Two Test Treatments (Same Block) 4.498971 9.451987
#> Two Test Treatments (Different Blocks) 5.030003 10.567643
#> A Test Treatment and a Control Treatment 3.749143 7.876656
#>
#> Treatment Means
#> ===============
#> Treatment Means SE r Min Max Adjusted Means
#> 1 83.67 1.92 9 78.00 92.00 83.67
#> 10 71.67 1.45 3 69.00 74.00 74.17
#> 11 83.00 4.58 3 74.00 89.00 81.25
#> 12 80.33 2.19 3 76.00 83.00 78.75
#> 2 79.33 0.73 9 76.00 83.00 79.33
#> 3 81.22 1.61 9 75.00 87.00 81.22
#> 4 81.78 2.10 9 74.00 91.00 81.78
#> 5 78.00 2.08 3 74.00 81.00 77.08
#> 6 75.33 0.33 3 75.00 76.00 78.08
#> 7 89.00 6.03 3 77.00 96.00 88.67
#> 8 79.33 7.88 3 70.00 95.00 79.50
#> 9 81.33 2.85 3 78.00 87.00 80.33
#>
#>
#> Comparisons
#> ===========
#>
#> Method : lsd
#>
#> contrast estimate SE df t.ratio p.value sig
#> treatment1 - treatment2 4.33 2.60 18 1.668 0.113
#> treatment1 - treatment3 2.44 2.60 18 0.941 0.359
#> treatment1 - treatment4 1.89 2.60 18 0.727 0.476
#> treatment1 - treatment5 6.58 3.90 18 1.690 0.108
#> treatment1 - treatment6 5.58 3.90 18 1.433 0.169
#> treatment1 - treatment7 -5.00 3.90 18 -1.283 0.216
#> treatment1 - treatment8 4.17 3.90 18 1.069 0.299
#> treatment1 - treatment9 3.33 3.90 18 0.856 0.404
#> treatment1 - treatment10 9.50 3.90 18 2.438 0.025 *
#> treatment1 - treatment11 2.42 3.90 18 0.620 0.543
#> treatment1 - treatment12 4.92 3.90 18 1.262 0.223
#> treatment2 - treatment3 -1.89 2.60 18 -0.727 0.476
#> treatment2 - treatment4 -2.44 2.60 18 -0.941 0.359
#> treatment2 - treatment5 2.25 3.90 18 0.577 0.571
#> treatment2 - treatment6 1.25 3.90 18 0.321 0.752
#> treatment2 - treatment7 -9.33 3.90 18 -2.395 0.028 *
#> treatment2 - treatment8 -0.17 3.90 18 -0.043 0.966
#> treatment2 - treatment9 -1.00 3.90 18 -0.257 0.800
#> treatment2 - treatment10 5.17 3.90 18 1.326 0.201
#> treatment2 - treatment11 -1.92 3.90 18 -0.492 0.629
#> treatment2 - treatment12 0.58 3.90 18 0.150 0.883
#> treatment3 - treatment4 -0.56 2.60 18 -0.214 0.833
#> treatment3 - treatment5 4.14 3.90 18 1.062 0.302
#> treatment3 - treatment6 3.14 3.90 18 0.806 0.431
#> treatment3 - treatment7 -7.44 3.90 18 -1.911 0.072
#> treatment3 - treatment8 1.72 3.90 18 0.442 0.664
#> treatment3 - treatment9 0.89 3.90 18 0.228 0.822
#> treatment3 - treatment10 7.06 3.90 18 1.811 0.087
#> treatment3 - treatment11 -0.03 3.90 18 -0.007 0.994
#> treatment3 - treatment12 2.47 3.90 18 0.635 0.534
#> treatment4 - treatment5 4.69 3.90 18 1.205 0.244
#> treatment4 - treatment6 3.69 3.90 18 0.948 0.356
#> treatment4 - treatment7 -6.89 3.90 18 -1.768 0.094
#> treatment4 - treatment8 2.28 3.90 18 0.585 0.566
#> treatment4 - treatment9 1.44 3.90 18 0.371 0.715
#> treatment4 - treatment10 7.61 3.90 18 1.953 0.066
#> treatment4 - treatment11 0.53 3.90 18 0.135 0.894
#> treatment4 - treatment12 3.03 3.90 18 0.777 0.447
#> treatment5 - treatment6 -1.00 4.86 18 -0.206 0.839
#> treatment5 - treatment7 -11.58 5.03 18 -2.303 0.033 *
#> treatment5 - treatment8 -2.42 4.86 18 -0.497 0.625
#> treatment5 - treatment9 -3.25 4.86 18 -0.669 0.512
#> treatment5 - treatment10 2.92 5.03 18 0.580 0.569
#> treatment5 - treatment11 -4.17 4.86 18 -0.857 0.402
#> treatment5 - treatment12 -1.67 5.03 18 -0.331 0.744
#> treatment6 - treatment7 -10.58 4.86 18 -2.178 0.043 *
#> treatment6 - treatment8 -1.42 4.86 18 -0.292 0.774
#> treatment6 - treatment9 -2.25 5.03 18 -0.447 0.660
#> treatment6 - treatment10 3.92 4.68 18 0.836 0.414
#> treatment6 - treatment11 -3.17 5.03 18 -0.630 0.537
#> treatment6 - treatment12 -0.67 5.03 18 -0.133 0.896
#> treatment7 - treatment8 9.17 5.03 18 1.822 0.085
#> treatment7 - treatment9 8.33 4.86 18 1.715 0.104
#> treatment7 - treatment10 14.50 4.86 18 2.984 0.008 **
#> treatment7 - treatment11 7.42 4.86 18 1.526 0.144
#> treatment7 - treatment12 9.92 4.68 18 2.118 0.048 *
#> treatment8 - treatment9 -0.83 5.03 18 -0.166 0.870
#> treatment8 - treatment10 5.33 4.68 18 1.139 0.270
#> treatment8 - treatment11 -1.75 4.68 18 -0.374 0.713
#> treatment8 - treatment12 0.75 5.03 18 0.149 0.883
#> treatment9 - treatment10 6.17 5.03 18 1.226 0.236
#> treatment9 - treatment11 -0.92 5.03 18 -0.182 0.857
#> treatment9 - treatment12 1.58 4.68 18 0.338 0.739
#> treatment10 - treatment11 -7.08 4.86 18 -1.458 0.162
#> treatment10 - treatment12 -4.58 5.03 18 -0.911 0.374
#> treatment11 - treatment12 2.50 4.86 18 0.514 0.613
#>
#> Treatment Groups
#> ================
#>
#> Method : lsd
#>
#> Treatment Adjusted Means SE df lower.CL upper.CL Group
#> 10 74.17 3.44 18 66.95 81.39 1
#> 5 77.08 3.44 18 69.86 84.30 12
#> 6 78.08 3.44 18 70.86 85.30 12
#> 12 78.75 3.44 18 71.53 85.97 12
#> 2 79.33 1.84 18 75.47 83.19 12
#> 8 79.50 3.44 18 72.28 86.72 123
#> 9 80.33 3.44 18 73.11 87.55 123
#> 3 81.22 1.84 18 77.36 85.08 123
#> 11 81.25 3.44 18 74.03 88.47 123
#> 4 81.78 1.84 18 77.92 85.64 123
#> 1 83.67 1.84 18 79.81 87.53 23
#> 7 88.67 3.44 18 81.45 95.89 3
# Descriptive statistics
describe(out1)
#> $Count
#> [1] 12
#>
#> $Mean
#> [1] 80.31944
#>
#> $Std.Error
#> [1] 1.037641
#>
#> $Std.Deviation
#> [1] 3.594494
#>
#> $Min
#> [1] 74.16667
#>
#> $Max
#> [1] 88.66667
#>
#> $`Skewness(statistic)`
#> skew z
#> 0.6959039 1.2824470
#>
#> $`Skewness(p.value)`
#> [1] 0.1996859
#>
#> $`Kurtosis(statistic)`
#> kurt z
#> 3.898051 1.581580
#>
#> $`Kurtosis(p.value)`
#> [1] 0.1137455
#>
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Test treatments are not replicated across all environments
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Example data
blk2 <- c(1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3,
4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6,
7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9)
trt2 <- c(1, 2, 3, 4, 7, 10, 11, 1, 2, 3, 4, 5, 9, 1, 2, 3, 4, 8, 6, 12,
1, 2, 3, 4, 16, 19, 13, 1, 2, 3, 4, 20, 17, 1, 2, 3, 4, 15, 14, 18,
1, 2, 3, 4, 22, 25, 27, 1, 2, 3, 4, 21, 23, 1, 2, 3, 4, 24, 26, 28)
y2 <- c(92, 79, 87, 81, 96, 89, 82, 79, 81, 81, 91, 79, 78, 83, 77,
78, 78, 70, 75, 74, 90, 80, 85, 78, 95, 86, 81, 78, 78, 76, 88,
76, 79, 80, 76, 75, 74, 77, 75, 72, 91, 81, 86, 80, 94, 87, 83,
78, 79, 77, 90, 74, 76, 82, 83, 86, 76, 73, 74, 69)
env2 <- c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3,
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3)
data2 <- data.frame(env2, blk2, trt2, y2)
chks2 <- c(1, 2, 3, 4)
# Convert block, treatment and environment to factors
data2$blk2 <- as.factor(data2$blk2)
data2$trt2 <- as.factor(data2$trt2)
data2$env2 <- as.factor(data2$env2)
# Contingency tables of factors
table(data2$env2, data2$trt2)
#>
#> 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
#> 1 3 3 3 3 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
#> 2 3 3 3 3 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0
#> 3 3 3 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1
table(data2$env2, data2$blk2)
#>
#> 1 2 3 4 5 6 7 8 9
#> 1 7 6 7 0 0 0 0 0 0
#> 2 0 0 0 7 6 7 0 0 0
#> 3 0 0 0 0 0 0 7 6 7
table(data2$blk2, data2$trt2)
#>
#> 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
#> 1 1 1 1 1 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
#> 2 1 1 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
#> 3 1 1 1 1 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
#> 4 1 1 1 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0
#> 5 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0
#> 6 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0
#> 7 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0
#> 8 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0
#> 9 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1
# Results
out2 <- augmentedRCBD.menv(block = data2$blk2, treatment = data2$trt2,
env = data2$env2, y = data2$y2, checks = chks2,
scenario = 2, method.comp = "lsd", alpha = 0.05,
group = TRUE, console = TRUE)
#>
#> Augmented Design Details
#> ========================
#>
#> Number of blocks "9"
#> Number of treatments "28"
#> Number of environments "3"
#> Number of check treatments "4"
#> Number of test treatments "24"
#> Check treatments "1, 2, 3, 4"
#>
#>
#> ANOVA, Treatment Adjusted
#> =========================
#> Df Sum Sq Mean Sq
#> Environment 2 24.7 12.35
#> Treatment (eliminating Blocks) 27 1550.0 57.41
#> Treatment: Check 3 85.9 28.63
#> Treatment: Test and Test vs. Check 24 1464.1 61.00
#> Block (within Environment, ignoring Treatments) 6 194.8 32.47
#> Environment × Treatment interaction 6 17.6 2.94
#> Residuals 18 546.5 30.36
#> F value Pr(>F)
#> Environment 0.407 0.6718
#> Treatment (eliminating Blocks) 1.891 0.0817 .
#> Treatment: Check 0.943 0.4406
#> Treatment: Test and Test vs. Check 2.009 0.0664 .
#> Block (within Environment, ignoring Treatments) 1.070 0.4162
#> Environment × Treatment interaction 0.097 0.9958
#> Residuals
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> ANOVA, Block Adjusted
#> =====================
#> Df Sum Sq Mean Sq
#> Environment 2 24.7 12.35
#> Treatment (ignoring Blocks) 27 1550.0 57.41
#> Treatment: Check 3 85.9 28.63
#> Treatment: Test 23 1420.0 61.74
#> Treatment: Test vs. Check 1 44.1 44.10
#> Block (within Environment, eliminating Treatments) 6 194.8 32.47
#> Environment × Treatment interaction 6 17.6 2.94
#> Residuals 18 546.5 30.36
#> F value Pr(>F)
#> Environment 0.407 0.6718
#> Treatment (ignoring Blocks) 1.891 0.0817 .
#> Treatment: Check 0.943 0.4406
#> Treatment: Test 2.033 0.0643 .
#> Treatment: Test vs. Check 1.453 0.2437
#> Block (within Environment, eliminating Treatments) 1.070 0.4162
#> Environment × Treatment interaction 0.097 0.9958
#> Residuals
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Coefficient of Variation
#> ========================
#> NA
#>
#> Overall Adjusted Mean
#> =====================
#> 79.98214
#>
#> Standard Errors
#> ===============
#> Std. Error of Diff. CD (5%)
#> Control Treatment Means NA NA
#> Two Test Treatments (Same Block) NA NA
#> Two Test Treatments (Different Blocks) NA NA
#> A Test Treatment and a Control Treatment NA NA
#>
#> Treatment Means
#> ===============
#> Treatment Means SE r Min Max Adjusted Means
#> 1 83.67 1.92 9 78.00 92.00 83.67
#> 10 89.00 <NA> 1 89.00 89.00 85.75
#> 11 82.00 <NA> 1 82.00 82.00 78.75
#> 12 74.00 <NA> 1 74.00 74.00 76.50
#> 13 81.00 <NA> 1 81.00 81.00 79.25
#> 14 75.00 <NA> 1 75.00 75.00 80.25
#> 15 77.00 <NA> 1 77.00 77.00 82.25
#> 16 95.00 <NA> 1 95.00 95.00 93.25
#> 17 79.00 <NA> 1 79.00 79.00 80.50
#> 18 72.00 <NA> 1 72.00 72.00 77.25
#> 19 86.00 <NA> 1 86.00 86.00 84.25
#> 2 79.33 0.73 9 76.00 83.00 79.33
#> 20 76.00 <NA> 1 76.00 76.00 77.50
#> 21 74.00 <NA> 1 74.00 74.00 74.50
#> 22 94.00 <NA> 1 94.00 94.00 91.00
#> 23 76.00 <NA> 1 76.00 76.00 76.50
#> 24 73.00 <NA> 1 73.00 73.00 72.75
#> 25 87.00 <NA> 1 87.00 87.00 84.00
#> 26 74.00 <NA> 1 74.00 74.00 73.75
#> 27 83.00 <NA> 1 83.00 83.00 80.00
#> 28 69.00 <NA> 1 69.00 69.00 68.75
#> 3 81.22 1.61 9 75.00 87.00 81.22
#> 4 81.78 2.10 9 74.00 91.00 81.78
#> 5 79.00 <NA> 1 79.00 79.00 77.50
#> 6 75.00 <NA> 1 75.00 75.00 77.50
#> 7 96.00 <NA> 1 96.00 96.00 92.75
#> 8 70.00 <NA> 1 70.00 70.00 72.50
#> 9 78.00 <NA> 1 78.00 78.00 76.50
#>
#>
#> Comparisons
#> ===========
#>
#> Method : lsd
#>
#> contrast estimate SE df t.ratio p.value sig
#> treatment1 - treatment2 4.33 2.29 24 1.896 0.070
#> treatment1 - treatment3 2.44 2.29 24 1.070 0.295
#> treatment1 - treatment4 1.89 2.29 24 0.826 0.417
#> treatment1 - treatment5 6.17 5.60 24 1.102 0.282
#> treatment1 - treatment6 6.17 5.60 24 1.102 0.282
#> treatment1 - treatment7 -9.08 5.60 24 -1.623 0.118
#> treatment1 - treatment8 11.17 5.60 24 1.995 0.058
#> treatment1 - treatment9 7.17 5.60 24 1.280 0.213
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#> treatment7 - treatment12 16.25 7.67 24 2.120 0.045 *
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#> treatment7 - treatment21 18.25 7.67 24 2.381 0.026 *
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#> treatment22 - treatment23 14.50 7.67 24 1.892 0.071
#> treatment22 - treatment24 18.25 7.67 24 2.381 0.026 *
#> treatment22 - treatment25 7.00 6.86 24 1.021 0.317
#> treatment22 - treatment26 17.25 7.67 24 2.250 0.034 *
#> treatment22 - treatment27 11.00 6.86 24 1.604 0.122
#> treatment22 - treatment28 22.25 7.67 24 2.903 0.008 **
#> treatment23 - treatment24 3.75 7.67 24 0.489 0.629
#> treatment23 - treatment25 -7.50 7.67 24 -0.978 0.338
#> treatment23 - treatment26 2.75 7.67 24 0.359 0.723
#> treatment23 - treatment27 -3.50 7.67 24 -0.457 0.652
#> treatment23 - treatment28 7.75 7.67 24 1.011 0.322
#> treatment24 - treatment25 -11.25 7.67 24 -1.468 0.155
#> treatment24 - treatment26 -1.00 6.86 24 -0.146 0.885
#> treatment24 - treatment27 -7.25 7.67 24 -0.946 0.354
#> treatment24 - treatment28 4.00 6.86 24 0.583 0.565
#> treatment25 - treatment26 10.25 7.67 24 1.337 0.194
#> treatment25 - treatment27 4.00 6.86 24 0.583 0.565
#> treatment25 - treatment28 15.25 7.67 24 1.989 0.058
#> treatment26 - treatment27 -6.25 7.67 24 -0.815 0.423
#> treatment26 - treatment28 5.00 6.86 24 0.729 0.473
#> treatment27 - treatment28 11.25 7.67 24 1.468 0.155
#>
#> Treatment Groups
#> ================
#>
#> Method : lsd
#>
#> Treatment Adjusted Means SE df lower.CL upper.CL Group
#> 28 68.75 5.36 24 57.69 79.81 1
#> 8 72.50 5.36 24 61.44 83.56 12
#> 24 72.75 5.36 24 61.69 83.81 12
#> 26 73.75 5.36 24 62.69 84.81 12
#> 21 74.50 5.36 24 63.44 85.56 12
#> 9 76.50 5.36 24 65.44 87.56 123
#> 23 76.50 5.36 24 65.44 87.56 123
#> 12 76.50 5.36 24 65.44 87.56 123
#> 18 77.25 5.36 24 66.19 88.31 1234
#> 5 77.50 5.36 24 66.44 88.56 12345
#> 6 77.50 5.36 24 66.44 88.56 12345
#> 20 77.50 5.36 24 66.44 88.56 12345
#> 11 78.75 5.36 24 67.69 89.81 12345
#> 13 79.25 5.36 24 68.19 90.31 12345
#> 2 79.33 1.62 24 76.00 82.67 12
#> 27 80.00 5.36 24 68.94 91.06 12345
#> 14 80.25 5.36 24 69.19 91.31 12345
#> 17 80.50 5.36 24 69.44 91.56 12345
#> 3 81.22 1.62 24 77.89 84.56 234
#> 4 81.78 1.62 24 78.44 85.11 2345
#> 15 82.25 5.36 24 71.19 93.31 12345
#> 1 83.67 1.62 24 80.33 87.00 2345
#> 25 84.00 5.36 24 72.94 95.06 12345
#> 19 84.25 5.36 24 73.19 95.31 12345
#> 10 85.75 5.36 24 74.69 96.81 2345
#> 22 91.00 5.36 24 79.94 102.06 345
#> 7 92.75 5.36 24 81.69 103.81 45
#> 16 93.25 5.36 24 82.19 104.31 5
# Descriptive statistics
describe(out2)
#> $Count
#> [1] 28
#>
#> $Mean
#> [1] 79.98214
#>
#> $Std.Error
#> [1] 1.103167
#>
#> $Std.Deviation
#> [1] 5.837409
#>
#> $Min
#> [1] 68.75
#>
#> $Max
#> [1] 93.25
#>
#> $`Skewness(statistic)`
#> skew z
#> 0.6337023 1.5424127
#>
#> $`Skewness(p.value)`
#> [1] 0.1229733
#>
#> $`Kurtosis(statistic)`
#> kurt z
#> 3.2759337 0.8663834
#>
#> $`Kurtosis(p.value)`
#> [1] 0.38628
#>