Analysis of Augmented Randomised Complete Block Design

augmentedRCBD is a function for analysis of variance of an augmented randomised block design (Federer, 1956; Federer, 1961; Searle, 1965) and the generation as well as comparison of the adjusted means of the treatments/genotypes.

augmentedRCBD(
  block,
  treatment,
  y,
  checks = NULL,
  method.comp = c("lsd", "tukey", "none"),
  alpha = 0.05,
  group = TRUE,
  console = TRUE,
  simplify = FALSE,
  truncate.means = TRUE
)

Arguments

block: Vector of blocks (as a factor).
treatment: Vector of treatments/genotypes (as a factor).
y: Numeric vector of response variable (Trait).
checks: Character vector of the checks present in treatment levels. 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 using emmeans.
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 is TRUE.
console: If TRUE, output will be printed to console. Default is TRUE. Default is TRUE.
simplify: If TRUE, ANOVA output will be given as a data frame instead of a summary.aov object. Default is TRUE.
truncate.means: If TRUE, the negative adjusted means will be truncated to zero. Default is TRUE.

Value

A list of class augmentedRCBD containing the following components:

Details: Details of the augmented design used.
Means: A data frame with the "Means", "Block", "SE", "Mix", "Max" and "Adjusted Means" for each "Treatment".
ANOVA, Treatment Adjusted: An object of class summary.aov for ANOVA table with treatments adjusted.
ANOVA, Block Adjusted: An object of class summary.aov for ANOVA table with block adjusted.
Block effects: A vector of block effects.
Treatment effects: A vector of treatment effects.
Std. Errors: A data frame of standard error of difference between various combinations along with critical difference and tukey's honest significant difference (when method.comp = "tukey") at alpha.
Overall adjusted mean: Overall adjusted mean.
CV: Coefficient of variation.
Comparisons: A data frame of pairwise comparisons of treatments. This is computed only if argument group is TRUE
Groups: A 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 group is TRUE
warning: A vector of warning messages (if any) captured during model fitting.

Details

This function borrows code from DAU.test function of agricolae package (de Mendiburu et al., 2016) as well as from Appendix VIII of Mathur et al., (2008).

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.

In case the large number of treatments or genotypes, it is advisable to avoid comparisons with the group = FALSE argument as it will be memory and processor intensive. Further it is advised to simplify output with simplify = TRUE in order to reduce output object size.

References

Federer WT (1956). “Augmented (or Hoonuiaku) designs.” The Hawaiian Planters' Record, LV(2), 191--208.

Federer WT (1956). “Augmented (or Hoonuiaku) Designs.” Technical Report BU-74-M, Cornell University, New York.

Federer WT (1961). “Augmented designs with one-way elimination of heterogeneity.” Biometrics, 17(3), 447--473.

Searle SR (1965). “Computing Formulae for Analyzing Augmented Randomized Complete Block Designs.” Technical Report BU-207-M, Cornell University, New York.

Mathur PN, Muralidharan K, Parthasarathy VA, Batugal P, Bonnot F (2008). Data Analysis Manual for Coconut Researchers-Bioversity Technical Bulletin No. 14. Bioversity International. ISBN 978-92-9043-736-9.

de Mendiburu F (2015). agricolae: Statistical Procedures for Agricultural Research. R package version 1.2-8.

Examples

# 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 (checks inferred)
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 (checks inferred)
out2 <- 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 y1 (checks specified)
out1 <- augmentedRCBD(data$blk, data$trt, data$y1, method.comp = "lsd",
                      alpha = 0.05, group = TRUE, console = TRUE,
                      checks = c("1", "2", "3", "4"))
#> 
#> 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 (checks specified)
out2 <- augmentedRCBD(data$blk, data$trt, data$y1, method.comp = "lsd",
                      alpha = 0.05, group = TRUE, console = TRUE,
                      checks = c("1", "2", "3", "4"))
#> 
#> 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

if (FALSE) {
# Error in case checks not replicated across all blocks
# Check 1 and 4 not replicated in all 3 blocks
trt <- c(1, 2, 3, 14, 7, 11, 12, 1, 2, 3, 4, 5, 9, 13, 2, 3, 4, 8, 6, 10)
data$trt <- as.factor(trt)
table(data$trt, data$blk)
# Results for variable y1 (checks specified)
out1 <- augmentedRCBD(data$blk, data$trt, data$y1, method.comp = "lsd",
                      alpha = 0.05, group = TRUE, console = TRUE,
                      checks = c("1", "2", "3", "4"))
}

# Warning in case test treatments are replicated
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
out1 <- augmentedRCBD(data$blk, data$trt, data$y1, method.comp = "lsd",
                      alpha = 0.05, group = TRUE, console = TRUE,
                      checks = c("2", "3"))
#> Warning: Test treatments are replicated.
#> 
#> Augmented Design Details
#> ========================
#>                                  
#> Number of blocks           "3"   
#> Number of treatments       "12"  
#> Number of check treatments "2"   
#> Number of test treatments  "10"  
#> Check treatments           "2, 3"
#> 
#> Warning: Following test treatments are replicated.
#>  Treatment Block
#>          1     1
#>          1     2
#>          1     3
#>          4     2
#>          4     3
#>          4     1
#> 
#> 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                    1   13.5   13.50   0.501 0.5058  
#>   Treatment: Test and Test vs. Check 10  271.6   27.16   1.007 0.5210  
#> 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              1   13.5   13.50   0.501  0.506
#>   Treatment: Test               9  560.7   62.31   2.310  0.160
#>   Treatment: Test vs. Check     1    1.4    1.42   0.053  0.826
#> 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)              8.995369 22.01088
#> A Test Treatment and a Control Treatment            7.344688 17.97180
#> 
#> Treatment Means
#> ===============
#>  Treatment Block Means   SE r   Min   Max Adjusted Means
#>          1     1 84.67 3.84 3 79.00 92.00          84.67
#>          1     2 84.67 3.84 3 79.00 92.00          84.67
#>          1     3 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     2 83.33 3.93 3 78.00 91.00          83.33
#>          4     3 83.33 3.93 3 78.00 91.00          83.33
#>          4     1 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
#>    treatment2 - treatment3    -3.00 4.24  6  -0.707   0.506    
#>    treatment2 - treatment1    -5.67 4.24  6  -1.336   0.230    
#>    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 - treatment1    -2.67 4.24  6  -0.629   0.553    
#>    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    
#>    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    
#>    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