Combined Analysis of Augmented Randomised Complete Block Design in Multiple Environments
Source:R/augmentedRCBD.menv.R
augmentedRCBD.menv.RdaugmentedRCBD.menv is an extension of
augmentedRCBD designed for the combined/pooled
analysis of data from augmented randomised complete block design across
multiple environments such as locations and/or seasons.
This function performs analysis under the following two scenarios.
- Scenario 1:
Replicated test treatments across environments.
- Scenario 2:
Non-replicated test treatments across environments.
Arguments
- block
Vector of blocks (as a factor).
- treatment
Vector of treatments/genotypes (as a factor).
- env
Vector of environments (as a factor).
- y
Numeric vector of response variable (Trait).
- checks
Character vector of the checks present in
treatmentlevels. If not specified, checks are inferred from the data on the basis of number of replications of treatments/genotypes.- method.comp
Method for comparison of treatments (
"lsd"for least significant difference or"tukey"for Tukey's honest significant difference). If"none", no comparisons will be made, the ANOVA output will be given as a data frame and the adjusted means will be computed directly from treatment and block effects instead of usingemmeans.- scenario
Either
1or2(see Details).- alpha
Type I error probability (Significance level) to be used for multiple comparisons.
- group
If
TRUE, genotypes will be grouped according to"method.comp". Default isTRUE.- console
If
TRUE, output will be printed to console. Default isTRUE. Default isTRUE.- simplify
If
TRUE, ANOVA output will be given as a data frame instead of asummary.aovobject. Default isTRUE.- truncate.means
If
TRUE, the negative adjusted means will be truncated to zero. Default isTRUE.
Value
A list of class augmentedRCBD.menv containing the following
components:
DetailsDetails of the augmented design used.
MeansA data frame with the "Means", "Block", "SE", "Mix", "Max" and "Adjusted Means" for each "Treatment".
ANOVA, Treatment AdjustedAn object of class
summary.aovfor ANOVA table with treatments adjusted.ANOVA, Block AdjustedAn object of class
summary.aovfor ANOVA table with block adjusted.Block effectsA vector of block effects.
Treatment effectsA vector of treatment effects.
Std. ErrorsA data frame of standard error of difference between various combinations along with critical difference and tukey's honest significant difference (when
method.comp = "tukey") atalpha.Overall adjusted meanOverall adjusted mean.
CVCoefficient of variation.
Comparison methodThe method for comparison of treatments.
ComparisonsA data frame of pairwise comparisons of treatments. This is computed only if argument
groupisTRUEGroupsA data frame with compact letter display of pairwise comparisons of treatments. Means with at least one letter common are not significantly different statistically. This is computed only if argument
groupisTRUEwarningA vector of warning messages (if any) captured during model fitting.
Details
The method of analysis is determined by whether the test treatments are
replicated across different environments as indicated by the scenario
argument. The design is balanced in terms of the checks being replicated
across all the blocks and environments.
- Scenario
1: The test treatments are replicated across all environments. Here the Treatment \u00D7 Environment interaction is fully estimable as it is balanced.
- Scenario
2: The test treatments are replicated across all environments. Here the Treatment \u00D7 Environment interaction is only partially estimable as it is unbalanced..
Note
Data should preferably be balanced i.e. all the check genotypes should be present in all the blocks. If not, a warning is issued.
There should not be any missing values.
The number of test genotypes can vary within a block.
When a large number of treatments or genotypes are involved, the analysis becomes memory intensive because calculating adjusted means necessitates the creation of a reference grid matrix by
emmeans, which can grow exponentially in size
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
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# 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
#> treatment1 - treatment10 -2.08 5.60 24 -0.372 0.713
#> treatment1 - treatment11 4.92 5.60 24 0.878 0.389
#> treatment1 - treatment12 7.17 5.60 24 1.280 0.213
#> treatment1 - treatment13 4.42 5.60 24 0.789 0.438
#> treatment1 - treatment14 3.42 5.60 24 0.610 0.547
#> treatment1 - treatment15 1.42 5.60 24 0.253 0.802
#> treatment1 - treatment16 -9.58 5.60 24 -1.712 0.100
#> treatment1 - treatment17 3.17 5.60 24 0.566 0.577
#> treatment1 - treatment18 6.42 5.60 24 1.146 0.263
#> treatment1 - treatment19 -0.58 5.60 24 -0.104 0.918
#> treatment1 - treatment20 6.17 5.60 24 1.102 0.282
#> treatment1 - treatment21 9.17 5.60 24 1.637 0.115
#> treatment1 - treatment22 -7.33 5.60 24 -1.310 0.203
#> treatment1 - treatment23 7.17 5.60 24 1.280 0.213
#> treatment1 - treatment24 10.92 5.60 24 1.950 0.063
#> treatment1 - treatment25 -0.33 5.60 24 -0.060 0.953
#> treatment1 - treatment26 9.92 5.60 24 1.771 0.089
#> treatment1 - treatment27 3.67 5.60 24 0.655 0.519
#> treatment1 - treatment28 14.92 5.60 24 2.665 0.014 *
#> treatment2 - treatment3 -1.89 2.29 24 -0.826 0.417
#> treatment2 - treatment4 -2.44 2.29 24 -1.070 0.295
#> treatment2 - treatment5 1.83 5.60 24 0.327 0.746
#> treatment2 - treatment6 1.83 5.60 24 0.327 0.746
#> treatment2 - treatment7 -13.42 5.60 24 -2.397 0.025 *
#> treatment2 - treatment8 6.83 5.60 24 1.221 0.234
#> treatment2 - treatment9 2.83 5.60 24 0.506 0.617
#> treatment2 - treatment10 -6.42 5.60 24 -1.146 0.263
#> treatment2 - treatment11 0.58 5.60 24 0.104 0.918
#> treatment2 - treatment12 2.83 5.60 24 0.506 0.617
#> treatment2 - treatment13 0.08 5.60 24 0.015 0.988
#> treatment2 - treatment14 -0.92 5.60 24 -0.164 0.871
#> treatment2 - treatment15 -2.92 5.60 24 -0.521 0.607
#> treatment2 - treatment16 -13.92 5.60 24 -2.486 0.020 *
#> treatment2 - treatment17 -1.17 5.60 24 -0.208 0.837
#> treatment2 - treatment18 2.08 5.60 24 0.372 0.713
#> treatment2 - treatment19 -4.92 5.60 24 -0.878 0.389
#> treatment2 - treatment20 1.83 5.60 24 0.327 0.746
#> treatment2 - treatment21 4.83 5.60 24 0.863 0.396
#> treatment2 - treatment22 -11.67 5.60 24 -2.084 0.048 *
#> treatment2 - treatment23 2.83 5.60 24 0.506 0.617
#> treatment2 - treatment24 6.58 5.60 24 1.176 0.251
#> treatment2 - treatment25 -4.67 5.60 24 -0.834 0.413
#> treatment2 - treatment26 5.58 5.60 24 0.997 0.329
#> treatment2 - treatment27 -0.67 5.60 24 -0.119 0.906
#> treatment2 - treatment28 10.58 5.60 24 1.890 0.071
#> treatment3 - treatment4 -0.56 2.29 24 -0.243 0.810
#> treatment3 - treatment5 3.72 5.60 24 0.665 0.512
#> treatment3 - treatment6 3.72 5.60 24 0.665 0.512
#> treatment3 - treatment7 -11.53 5.60 24 -2.059 0.050
#> treatment3 - treatment8 8.72 5.60 24 1.558 0.132
#> treatment3 - treatment9 4.72 5.60 24 0.844 0.407
#> treatment3 - treatment10 -4.53 5.60 24 -0.809 0.427
#> treatment3 - treatment11 2.47 5.60 24 0.442 0.663
#> treatment3 - treatment12 4.72 5.60 24 0.844 0.407
#> treatment3 - treatment13 1.97 5.60 24 0.352 0.728
#> treatment3 - treatment14 0.97 5.60 24 0.174 0.864
#> treatment3 - treatment15 -1.03 5.60 24 -0.184 0.856
#> treatment3 - treatment16 -12.03 5.60 24 -2.149 0.042 *
#> treatment3 - treatment17 0.72 5.60 24 0.129 0.898
#> treatment3 - treatment18 3.97 5.60 24 0.710 0.485
#> treatment3 - treatment19 -3.03 5.60 24 -0.541 0.594
#> treatment3 - treatment20 3.72 5.60 24 0.665 0.512
#> treatment3 - treatment21 6.72 5.60 24 1.201 0.242
#> treatment3 - treatment22 -9.78 5.60 24 -1.747 0.093
#> treatment3 - treatment23 4.72 5.60 24 0.844 0.407
#> treatment3 - treatment24 8.47 5.60 24 1.513 0.143
#> treatment3 - treatment25 -2.78 5.60 24 -0.496 0.624
#> treatment3 - treatment26 7.47 5.60 24 1.335 0.194
#> treatment3 - treatment27 1.22 5.60 24 0.218 0.829
#> treatment3 - treatment28 12.47 5.60 24 2.228 0.036 *
#> treatment4 - treatment5 4.28 5.60 24 0.764 0.452
#> treatment4 - treatment6 4.28 5.60 24 0.764 0.452
#> treatment4 - treatment7 -10.97 5.60 24 -1.960 0.062
#> treatment4 - treatment8 9.28 5.60 24 1.657 0.110
#> treatment4 - treatment9 5.28 5.60 24 0.943 0.355
#> treatment4 - treatment10 -3.97 5.60 24 -0.710 0.485
#> treatment4 - treatment11 3.03 5.60 24 0.541 0.594
#> treatment4 - treatment12 5.28 5.60 24 0.943 0.355
#> treatment4 - treatment13 2.53 5.60 24 0.452 0.656
#> treatment4 - treatment14 1.53 5.60 24 0.273 0.787
#> treatment4 - treatment15 -0.47 5.60 24 -0.084 0.933
#> treatment4 - treatment16 -11.47 5.60 24 -2.049 0.052
#> treatment4 - treatment17 1.28 5.60 24 0.228 0.821
#> treatment4 - treatment18 4.53 5.60 24 0.809 0.427
#> treatment4 - treatment19 -2.47 5.60 24 -0.442 0.663
#> treatment4 - treatment20 4.28 5.60 24 0.764 0.452
#> treatment4 - treatment21 7.28 5.60 24 1.300 0.206
#> treatment4 - treatment22 -9.22 5.60 24 -1.647 0.113
#> treatment4 - treatment23 5.28 5.60 24 0.943 0.355
#> treatment4 - treatment24 9.03 5.60 24 1.613 0.120
#> treatment4 - treatment25 -2.22 5.60 24 -0.397 0.695
#> treatment4 - treatment26 8.03 5.60 24 1.434 0.164
#> treatment4 - treatment27 1.78 5.60 24 0.318 0.754
#> treatment4 - treatment28 13.03 5.60 24 2.327 0.029 *
#> treatment5 - treatment6 -0.00 7.67 24 -0.000 1.000
#> treatment5 - treatment7 -15.25 7.67 24 -1.989 0.058
#> treatment5 - treatment8 5.00 7.67 24 0.652 0.520
#> treatment5 - treatment9 1.00 6.86 24 0.146 0.885
#> treatment5 - treatment10 -8.25 7.67 24 -1.076 0.293
#> treatment5 - treatment11 -1.25 7.67 24 -0.163 0.872
#> treatment5 - treatment12 1.00 7.67 24 0.130 0.897
#> treatment5 - treatment13 -1.75 7.67 24 -0.228 0.821
#> treatment5 - treatment14 -2.75 7.67 24 -0.359 0.723
#> treatment5 - treatment15 -4.75 7.67 24 -0.620 0.541
#> treatment5 - treatment16 -15.75 7.67 24 -2.055 0.051
#> treatment5 - treatment17 -3.00 7.67 24 -0.391 0.699
#> treatment5 - treatment18 0.25 7.67 24 0.033 0.974
#> treatment5 - treatment19 -6.75 7.67 24 -0.881 0.387
#> treatment5 - treatment20 -0.00 7.67 24 -0.000 1.000
#> treatment5 - treatment21 3.00 7.67 24 0.391 0.699
#> treatment5 - treatment22 -13.50 7.67 24 -1.761 0.091
#> treatment5 - treatment23 1.00 7.67 24 0.130 0.897
#> treatment5 - treatment24 4.75 7.67 24 0.620 0.541
#> treatment5 - treatment25 -6.50 7.67 24 -0.848 0.405
#> treatment5 - treatment26 3.75 7.67 24 0.489 0.629
#> treatment5 - treatment27 -2.50 7.67 24 -0.326 0.747
#> treatment5 - treatment28 8.75 7.67 24 1.141 0.265
#> treatment6 - treatment7 -15.25 7.67 24 -1.989 0.058
#> treatment6 - treatment8 5.00 6.86 24 0.729 0.473
#> treatment6 - treatment9 1.00 7.67 24 0.130 0.897
#> treatment6 - treatment10 -8.25 7.67 24 -1.076 0.293
#> treatment6 - treatment11 -1.25 7.67 24 -0.163 0.872
#> treatment6 - treatment12 1.00 6.86 24 0.146 0.885
#> treatment6 - treatment13 -1.75 7.67 24 -0.228 0.821
#> treatment6 - treatment14 -2.75 7.67 24 -0.359 0.723
#> treatment6 - treatment15 -4.75 7.67 24 -0.620 0.541
#> treatment6 - treatment16 -15.75 7.67 24 -2.055 0.051
#> treatment6 - treatment17 -3.00 7.67 24 -0.391 0.699
#> treatment6 - treatment18 0.25 7.67 24 0.033 0.974
#> treatment6 - treatment19 -6.75 7.67 24 -0.881 0.387
#> treatment6 - treatment20 -0.00 7.67 24 -0.000 1.000
#> treatment6 - treatment21 3.00 7.67 24 0.391 0.699
#> treatment6 - treatment22 -13.50 7.67 24 -1.761 0.091
#> treatment6 - treatment23 1.00 7.67 24 0.130 0.897
#> treatment6 - treatment24 4.75 7.67 24 0.620 0.541
#> treatment6 - treatment25 -6.50 7.67 24 -0.848 0.405
#> treatment6 - treatment26 3.75 7.67 24 0.489 0.629
#> treatment6 - treatment27 -2.50 7.67 24 -0.326 0.747
#> treatment6 - treatment28 8.75 7.67 24 1.141 0.265
#> treatment7 - treatment8 20.25 7.67 24 2.642 0.014 *
#> treatment7 - treatment9 16.25 7.67 24 2.120 0.045 *
#> treatment7 - treatment10 7.00 6.86 24 1.021 0.317
#> treatment7 - treatment11 14.00 6.86 24 2.042 0.052
#> treatment7 - treatment12 16.25 7.67 24 2.120 0.045 *
#> treatment7 - treatment13 13.50 7.67 24 1.761 0.091
#> treatment7 - treatment14 12.50 7.67 24 1.631 0.116
#> treatment7 - treatment15 10.50 7.67 24 1.370 0.183
#> treatment7 - treatment16 -0.50 7.67 24 -0.065 0.949
#> treatment7 - treatment17 12.25 7.67 24 1.598 0.123
#> treatment7 - treatment18 15.50 7.67 24 2.022 0.054
#> treatment7 - treatment19 8.50 7.67 24 1.109 0.278
#> treatment7 - treatment20 15.25 7.67 24 1.989 0.058
#> treatment7 - treatment21 18.25 7.67 24 2.381 0.026 *
#> treatment7 - treatment22 1.75 7.67 24 0.228 0.821
#> treatment7 - treatment23 16.25 7.67 24 2.120 0.045 *
#> treatment7 - treatment24 20.00 7.67 24 2.609 0.015 *
#> treatment7 - treatment25 8.75 7.67 24 1.141 0.265
#> treatment7 - treatment26 19.00 7.67 24 2.479 0.021 *
#> treatment7 - treatment27 12.75 7.67 24 1.663 0.109
#> treatment7 - treatment28 24.00 7.67 24 3.131 0.005 **
#> treatment8 - treatment9 -4.00 7.67 24 -0.522 0.607
#> treatment8 - treatment10 -13.25 7.67 24 -1.728 0.097
#> treatment8 - treatment11 -6.25 7.67 24 -0.815 0.423
#> treatment8 - treatment12 -4.00 6.86 24 -0.583 0.565
#> treatment8 - treatment13 -6.75 7.67 24 -0.881 0.387
#> treatment8 - treatment14 -7.75 7.67 24 -1.011 0.322
#> treatment8 - treatment15 -9.75 7.67 24 -1.272 0.216
#> treatment8 - treatment16 -20.75 7.67 24 -2.707 0.012 *
#> treatment8 - treatment17 -8.00 7.67 24 -1.044 0.307
#> treatment8 - treatment18 -4.75 7.67 24 -0.620 0.541
#> treatment8 - treatment19 -11.75 7.67 24 -1.533 0.138
#> treatment8 - treatment20 -5.00 7.67 24 -0.652 0.520
#> treatment8 - treatment21 -2.00 7.67 24 -0.261 0.796
#> treatment8 - treatment22 -18.50 7.67 24 -2.413 0.024 *
#> treatment8 - treatment23 -4.00 7.67 24 -0.522 0.607
#> treatment8 - treatment24 -0.25 7.67 24 -0.033 0.974
#> treatment8 - treatment25 -11.50 7.67 24 -1.500 0.147
#> treatment8 - treatment26 -1.25 7.67 24 -0.163 0.872
#> treatment8 - treatment27 -7.50 7.67 24 -0.978 0.338
#> treatment8 - treatment28 3.75 7.67 24 0.489 0.629
#> treatment9 - treatment10 -9.25 7.67 24 -1.207 0.239
#> treatment9 - treatment11 -2.25 7.67 24 -0.294 0.772
#> treatment9 - treatment12 -0.00 7.67 24 -0.000 1.000
#> treatment9 - treatment13 -2.75 7.67 24 -0.359 0.723
#> treatment9 - treatment14 -3.75 7.67 24 -0.489 0.629
#> treatment9 - treatment15 -5.75 7.67 24 -0.750 0.460
#> treatment9 - treatment16 -16.75 7.67 24 -2.185 0.039 *
#> treatment9 - treatment17 -4.00 7.67 24 -0.522 0.607
#> treatment9 - treatment18 -0.75 7.67 24 -0.098 0.923
#> treatment9 - treatment19 -7.75 7.67 24 -1.011 0.322
#> treatment9 - treatment20 -1.00 7.67 24 -0.130 0.897
#> treatment9 - treatment21 2.00 7.67 24 0.261 0.796
#> treatment9 - treatment22 -14.50 7.67 24 -1.892 0.071
#> treatment9 - treatment23 -0.00 7.67 24 -0.000 1.000
#> treatment9 - treatment24 3.75 7.67 24 0.489 0.629
#> treatment9 - treatment25 -7.50 7.67 24 -0.978 0.338
#> treatment9 - treatment26 2.75 7.67 24 0.359 0.723
#> treatment9 - treatment27 -3.50 7.67 24 -0.457 0.652
#> treatment9 - treatment28 7.75 7.67 24 1.011 0.322
#> treatment10 - treatment11 7.00 6.86 24 1.021 0.317
#> treatment10 - treatment12 9.25 7.67 24 1.207 0.239
#> treatment10 - treatment13 6.50 7.67 24 0.848 0.405
#> treatment10 - treatment14 5.50 7.67 24 0.717 0.480
#> treatment10 - treatment15 3.50 7.67 24 0.457 0.652
#> treatment10 - treatment16 -7.50 7.67 24 -0.978 0.338
#> treatment10 - treatment17 5.25 7.67 24 0.685 0.500
#> treatment10 - treatment18 8.50 7.67 24 1.109 0.278
#> treatment10 - treatment19 1.50 7.67 24 0.196 0.847
#> treatment10 - treatment20 8.25 7.67 24 1.076 0.293
#> treatment10 - treatment21 11.25 7.67 24 1.468 0.155
#> treatment10 - treatment22 -5.25 7.67 24 -0.685 0.500
#> treatment10 - treatment23 9.25 7.67 24 1.207 0.239
#> treatment10 - treatment24 13.00 7.67 24 1.696 0.103
#> treatment10 - treatment25 1.75 7.67 24 0.228 0.821
#> treatment10 - treatment26 12.00 7.67 24 1.565 0.131
#> treatment10 - treatment27 5.75 7.67 24 0.750 0.460
#> treatment10 - treatment28 17.00 7.67 24 2.218 0.036 *
#> treatment11 - treatment12 2.25 7.67 24 0.294 0.772
#> treatment11 - treatment13 -0.50 7.67 24 -0.065 0.949
#> treatment11 - treatment14 -1.50 7.67 24 -0.196 0.847
#> treatment11 - treatment15 -3.50 7.67 24 -0.457 0.652
#> treatment11 - treatment16 -14.50 7.67 24 -1.892 0.071
#> treatment11 - treatment17 -1.75 7.67 24 -0.228 0.821
#> treatment11 - treatment18 1.50 7.67 24 0.196 0.847
#> treatment11 - treatment19 -5.50 7.67 24 -0.717 0.480
#> treatment11 - treatment20 1.25 7.67 24 0.163 0.872
#> treatment11 - treatment21 4.25 7.67 24 0.554 0.584
#> treatment11 - treatment22 -12.25 7.67 24 -1.598 0.123
#> treatment11 - treatment23 2.25 7.67 24 0.294 0.772
#> treatment11 - treatment24 6.00 7.67 24 0.783 0.441
#> treatment11 - treatment25 -5.25 7.67 24 -0.685 0.500
#> treatment11 - treatment26 5.00 7.67 24 0.652 0.520
#> treatment11 - treatment27 -1.25 7.67 24 -0.163 0.872
#> treatment11 - treatment28 10.00 7.67 24 1.305 0.204
#> treatment12 - treatment13 -2.75 7.67 24 -0.359 0.723
#> treatment12 - treatment14 -3.75 7.67 24 -0.489 0.629
#> treatment12 - treatment15 -5.75 7.67 24 -0.750 0.460
#> treatment12 - treatment16 -16.75 7.67 24 -2.185 0.039 *
#> treatment12 - treatment17 -4.00 7.67 24 -0.522 0.607
#> treatment12 - treatment18 -0.75 7.67 24 -0.098 0.923
#> treatment12 - treatment19 -7.75 7.67 24 -1.011 0.322
#> treatment12 - treatment20 -1.00 7.67 24 -0.130 0.897
#> treatment12 - treatment21 2.00 7.67 24 0.261 0.796
#> treatment12 - treatment22 -14.50 7.67 24 -1.892 0.071
#> treatment12 - treatment23 -0.00 7.67 24 -0.000 1.000
#> treatment12 - treatment24 3.75 7.67 24 0.489 0.629
#> treatment12 - treatment25 -7.50 7.67 24 -0.978 0.338
#> treatment12 - treatment26 2.75 7.67 24 0.359 0.723
#> treatment12 - treatment27 -3.50 7.67 24 -0.457 0.652
#> treatment12 - treatment28 7.75 7.67 24 1.011 0.322
#> treatment13 - treatment14 -1.00 7.67 24 -0.130 0.897
#> treatment13 - treatment15 -3.00 7.67 24 -0.391 0.699
#> treatment13 - treatment16 -14.00 6.86 24 -2.042 0.052
#> treatment13 - treatment17 -1.25 7.67 24 -0.163 0.872
#> treatment13 - treatment18 2.00 7.67 24 0.261 0.796
#> treatment13 - treatment19 -5.00 6.86 24 -0.729 0.473
#> treatment13 - treatment20 1.75 7.67 24 0.228 0.821
#> treatment13 - treatment21 4.75 7.67 24 0.620 0.541
#> treatment13 - treatment22 -11.75 7.67 24 -1.533 0.138
#> treatment13 - treatment23 2.75 7.67 24 0.359 0.723
#> treatment13 - treatment24 6.50 7.67 24 0.848 0.405
#> treatment13 - treatment25 -4.75 7.67 24 -0.620 0.541
#> treatment13 - treatment26 5.50 7.67 24 0.717 0.480
#> treatment13 - treatment27 -0.75 7.67 24 -0.098 0.923
#> treatment13 - treatment28 10.50 7.67 24 1.370 0.183
#> treatment14 - treatment15 -2.00 6.86 24 -0.292 0.773
#> treatment14 - treatment16 -13.00 7.67 24 -1.696 0.103
#> treatment14 - treatment17 -0.25 7.67 24 -0.033 0.974
#> treatment14 - treatment18 3.00 6.86 24 0.438 0.666
#> treatment14 - treatment19 -4.00 7.67 24 -0.522 0.607
#> treatment14 - treatment20 2.75 7.67 24 0.359 0.723
#> treatment14 - treatment21 5.75 7.67 24 0.750 0.460
#> treatment14 - treatment22 -10.75 7.67 24 -1.402 0.174
#> treatment14 - treatment23 3.75 7.67 24 0.489 0.629
#> treatment14 - treatment24 7.50 7.67 24 0.978 0.338
#> treatment14 - treatment25 -3.75 7.67 24 -0.489 0.629
#> treatment14 - treatment26 6.50 7.67 24 0.848 0.405
#> treatment14 - treatment27 0.25 7.67 24 0.033 0.974
#> treatment14 - treatment28 11.50 7.67 24 1.500 0.147
#> treatment15 - treatment16 -11.00 7.67 24 -1.435 0.164
#> treatment15 - treatment17 1.75 7.67 24 0.228 0.821
#> treatment15 - treatment18 5.00 6.86 24 0.729 0.473
#> treatment15 - treatment19 -2.00 7.67 24 -0.261 0.796
#> treatment15 - treatment20 4.75 7.67 24 0.620 0.541
#> treatment15 - treatment21 7.75 7.67 24 1.011 0.322
#> treatment15 - treatment22 -8.75 7.67 24 -1.141 0.265
#> treatment15 - treatment23 5.75 7.67 24 0.750 0.460
#> treatment15 - treatment24 9.50 7.67 24 1.239 0.227
#> treatment15 - treatment25 -1.75 7.67 24 -0.228 0.821
#> treatment15 - treatment26 8.50 7.67 24 1.109 0.278
#> treatment15 - treatment27 2.25 7.67 24 0.294 0.772
#> treatment15 - treatment28 13.50 7.67 24 1.761 0.091
#> treatment16 - treatment17 12.75 7.67 24 1.663 0.109
#> treatment16 - treatment18 16.00 7.67 24 2.087 0.048 *
#> treatment16 - treatment19 9.00 6.86 24 1.313 0.202
#> treatment16 - treatment20 15.75 7.67 24 2.055 0.051
#> treatment16 - treatment21 18.75 7.67 24 2.446 0.022 *
#> treatment16 - treatment22 2.25 7.67 24 0.294 0.772
#> treatment16 - treatment23 16.75 7.67 24 2.185 0.039 *
#> treatment16 - treatment24 20.50 7.67 24 2.674 0.013 *
#> treatment16 - treatment25 9.25 7.67 24 1.207 0.239
#> treatment16 - treatment26 19.50 7.67 24 2.544 0.018 *
#> treatment16 - treatment27 13.25 7.67 24 1.728 0.097
#> treatment16 - treatment28 24.50 7.67 24 3.196 0.004 **
#> treatment17 - treatment18 3.25 7.67 24 0.424 0.675
#> treatment17 - treatment19 -3.75 7.67 24 -0.489 0.629
#> treatment17 - treatment20 3.00 6.86 24 0.438 0.666
#> treatment17 - treatment21 6.00 7.67 24 0.783 0.441
#> treatment17 - treatment22 -10.50 7.67 24 -1.370 0.183
#> treatment17 - treatment23 4.00 7.67 24 0.522 0.607
#> treatment17 - treatment24 7.75 7.67 24 1.011 0.322
#> treatment17 - treatment25 -3.50 7.67 24 -0.457 0.652
#> treatment17 - treatment26 6.75 7.67 24 0.881 0.387
#> treatment17 - treatment27 0.50 7.67 24 0.065 0.949
#> treatment17 - treatment28 11.75 7.67 24 1.533 0.138
#> treatment18 - treatment19 -7.00 7.67 24 -0.913 0.370
#> treatment18 - treatment20 -0.25 7.67 24 -0.033 0.974
#> treatment18 - treatment21 2.75 7.67 24 0.359 0.723
#> treatment18 - treatment22 -13.75 7.67 24 -1.794 0.085
#> treatment18 - treatment23 0.75 7.67 24 0.098 0.923
#> treatment18 - treatment24 4.50 7.67 24 0.587 0.563
#> treatment18 - treatment25 -6.75 7.67 24 -0.881 0.387
#> treatment18 - treatment26 3.50 7.67 24 0.457 0.652
#> treatment18 - treatment27 -2.75 7.67 24 -0.359 0.723
#> treatment18 - treatment28 8.50 7.67 24 1.109 0.278
#> treatment19 - treatment20 6.75 7.67 24 0.881 0.387
#> treatment19 - treatment21 9.75 7.67 24 1.272 0.216
#> treatment19 - treatment22 -6.75 7.67 24 -0.881 0.387
#> treatment19 - treatment23 7.75 7.67 24 1.011 0.322
#> treatment19 - treatment24 11.50 7.67 24 1.500 0.147
#> treatment19 - treatment25 0.25 7.67 24 0.033 0.974
#> treatment19 - treatment26 10.50 7.67 24 1.370 0.183
#> treatment19 - treatment27 4.25 7.67 24 0.554 0.584
#> treatment19 - treatment28 15.50 7.67 24 2.022 0.054
#> treatment20 - treatment21 3.00 7.67 24 0.391 0.699
#> treatment20 - treatment22 -13.50 7.67 24 -1.761 0.091
#> treatment20 - treatment23 1.00 7.67 24 0.130 0.897
#> treatment20 - treatment24 4.75 7.67 24 0.620 0.541
#> treatment20 - treatment25 -6.50 7.67 24 -0.848 0.405
#> treatment20 - treatment26 3.75 7.67 24 0.489 0.629
#> treatment20 - treatment27 -2.50 7.67 24 -0.326 0.747
#> treatment20 - treatment28 8.75 7.67 24 1.141 0.265
#> treatment21 - treatment22 -16.50 7.67 24 -2.152 0.042 *
#> treatment21 - treatment23 -2.00 6.86 24 -0.292 0.773
#> treatment21 - treatment24 1.75 7.67 24 0.228 0.821
#> treatment21 - treatment25 -9.50 7.67 24 -1.239 0.227
#> treatment21 - treatment26 0.75 7.67 24 0.098 0.923
#> treatment21 - treatment27 -5.50 7.67 24 -0.717 0.480
#> treatment21 - treatment28 5.75 7.67 24 0.750 0.460
#> 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
#> 12 76.50 5.36 24 65.44 87.56 123
#> 23 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