Analysis of Augmented Randomised Complete Block Design for Multiple Traits/Characters

augmentedRCBD.bulk is a wrapper around the functions augmentedRCBD, describe.augmentedRCBD, freqdist.augmentedRCBD and gva.augmentedRCBD. It will carry out these analyses for multiple traits/characters from the input data as a data frame object.

Usage

augmentedRCBD.bulk(
  data,
  block,
  treatment,
  traits,
  checks = NULL,
  check.inference = c("overall", "traitwise"),
  alpha = 0.05,
  describe = TRUE,
  freqdist = TRUE,
  gva = TRUE,
  k = 2.063,
  check.col = "red",
  console = TRUE
)

Arguments

data: The data as a data frame object. The data frame should possess columns specifying the block, treatment and multiple traits/characters.
block: Name of column specifying the blocks in the design as a character string.
treatment: Name of column specifying the treatments as a character string.
traits: Name of columns specifying the multiple traits/characters as a character vector.
checks: Character vector of the checks present in treatment levels. It can also be a named list with the character vector of checks for each trait in traits column. The list names should be same as trait names. If not specified, checks are inferred from the data on the basis of number of replications of treatments/genotypes.
check.inference: The method for inference of checks if checks is not specified. Either "overall" to infer checks on the basis of all the trait data or "traitwise" to infer checks on the basis of each trait separately.
alpha: Type I error probability (Significance level) to be used for multiple comparisons.
describe: If TRUE, descriptive statistics will be computed. Default is TRUE.
freqdist: If TRUE, frequency distributions be plotted. Default is TRUE.
gva: If TRUE, genetic variability analysis will be done. Default is TRUE.
k: The standardized selection differential or selection intensity required for computation of Genetic advance. Default is 2.063 for 5% selection proportion (see Details in gva.augmentedRCBD). Ignored if gva = FALSE.
check.col: The colour(s) to be used to highlight check values in the plot as a character vector. Must be valid colour values in R (named colours, hexadecimal representation, index of colours [1:8] in default R palette() etc.).
console: If TRUE, output will be printed to console. Default is TRUE.

Value

A list of class augmentedRCBD.bulk containing the following components:

Details: Details of the augmented design used and the traits/characters.
ANOVA, Treatment Adjusted: A data frame of mean sum of squares, p value and stastical significance of the specified traits from treatment adjusted ANOVA.
ANOVA, Block Adjusted: A data frame of mean sum of squares, p value and stastical significance of the specified traits from block adjusted ANOVA
Means: A data frame of the adjusted means of the treatments for the specified traits.
Check statistics: A list of data frames with check statistics such as number of replications, standard error, minimum and maximum value
alpha: Type I error probability (Significance level) used.
Std. Errors: A data frame of standard error of difference between various combinations for the specified traits.
CD: A data frame of critical difference (at the specified alpha) between various combinations for the specified traits.
Overall adjusted mean: A data frame of the overall adjusted mean for the specified traits.
CV: A data frame of the coefficient of variance for the specified traits.
Descriptive statistics: A data frame of descriptive statistics for the specified traits.
Frequency distribution: A list of ggplot2 plot grobs of the frequency distribution plots.
k: The standardized selection differential or selection intensity used for computaton of Genetic advance.
Genetic variability analysis: A data frame of genetic variability statistics for the specified traits.
GVA plots: A list of three ggplot2 objects with the plots for (a) Phenotypic and Genotypic CV, (b) Broad sense heritability and (c) Genetic advance over mean
warnings: A list of warning messages (if any) captured during model fitting, frequency distribution plotting and genetic variability analysis.

Note

In this case treatment comparisons/grouping by least significant difference or Tukey's honest significant difference method is not computed. Also the output object size is reduced using the simplify = TRUE argument in the augmentedRCBD function.

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)
dataf <- data.frame(blk, trt, y1, y2)

bout <- augmentedRCBD.bulk(data = dataf, block = "blk",
                           treatment = "trt", traits = c("y1", "y2"),
                           checks = NULL, alpha = 0.05, describe = TRUE,
                           freqdist = TRUE, gva = TRUE,
                           check.col = c("brown", "darkcyan",
                                         "forestgreen", "purple"),
                           console = TRUE)
#> 
#> ANOVA for y1 computed (1/2)
#> 
#> ANOVA for y2 computed (2/2)
#> 
#> Augmented Design Details
#> ========================
#>   Trait Number of blocks Number of treatments Number of check treatments
#> 1    y1                3                   12                          4
#> 2    y2                3                   12                          4
#>   Number of test treatments Check treatments
#> 1                         8       1, 2, 3, 4
#> 2                         8       1, 2, 3, 4
#> 
#> 
#> ANOVA, Treatment Adjusted
#> =========================
#>                                           Mean.Sq
#>                              Source Df     y1    Df      y2   
#>         Block (ignoring Treatments)  2 180.04  *  2 3509.67 **
#>      Treatment (eliminating Blocks) 11  25.92 ⁿˢ 11 5360.49 **
#>                    Treatment: Check  3  17.64 ⁿˢ  3  716.75 ⁿˢ
#>  Treatment: Test and Test vs. Check  8  29.02 ⁿˢ  8 7101.89 **
#>                           Residuals  6  26.97     6  286.25   
#> ⁿˢ P > 0.05; * P <= 0.05; ** P <= 0.01
#> 
#> ANOVA, Block Adjusted
#> =====================
#>                                       Mean.Sq
#>                          Source Df    y1    Df       y2   
#>     Treatment (ignoring Blocks) 11 52.33 ⁿˢ 11  5882.50 **
#>                Treatment: Check  3 17.64 ⁿˢ  3   716.75 ⁿˢ
#>                 Treatment: Test  7 72.27 ⁿˢ  7  4980.41 **
#>       Treatment: Test vs. Check  1 16.87 ⁿˢ  1 27694.41 **
#>  Block (eliminating Treatments)  2 34.75 ⁿˢ  2   638.58 ⁿˢ
#>                       Residuals  6 26.97     6   286.25   
#> ⁿˢ P > 0.05; * P <= 0.05; ** P <= 0.01
#> 
#> Coefficient of Variation
#> ========================
#>  Trait   CV
#>     y1 6.37
#>     y2 6.06
#> 
#> 
#> Overall Adjusted Mean
#> =====================
#>  Trait Overall.adjusted.mean
#>     y1                 81.06
#>     y2                298.48
#> 
#> 
#> Standard Errors
#> ===============
#>                                Comparison   y1    y2
#>  A Test Treatment and a Control Treatment 6.70 21.84
#>                   Control Treatment Means 4.24 13.81
#>    Two Test Treatments (Different Blocks) 8.21 26.75
#>          Two Test Treatments (Same Block) 7.34 23.93
#> 
#> 
#> Critical Difference
#> ===================
#> alpha = 0.05 
#>                                Comparison    y1    y2
#>  A Test Treatment and a Control Treatment 16.41 53.45
#>                   Control Treatment Means 10.38 33.80
#>    Two Test Treatments (Different Blocks) 20.09 65.46
#>          Two Test Treatments (Same Block) 17.97 58.55
#> 
#> 
#> Descriptive Statistics
#> ======================
#>  Trait Count   Mean Std.Error Std.Deviation    Min    Max Skewness Skewness_sig
#>     y1    12  81.06      1.55          5.36  73.25  93.50     0.93           ⁿˢ
#>     y2    12 298.48     18.92         65.55 213.67 437.67     0.74           ⁿˢ
#>  Kurtosis Kurtosis_sig
#>      3.52           ⁿˢ
#>      2.79           ⁿˢ
#> ⁿˢ P > 0.05; * P <= 0.05; ** P <= 0.01
#> 
#> 
#> Genetic Variability Analysis
#> ============================
#> k = 2.063 
#>  Trait   Mean      PV      GV     EV   GCV GCV.category   PCV PCV.category  ECV
#>   y1 †  81.06   72.27   45.30  26.97  8.30          Low 10.49       Medium 6.41
#>   y2   298.48 4980.41 4694.16 286.25 22.95         High 23.64         High 5.67
#>    hBS hBS.category     GA   GAM GAM.category
#>  62.68         High  10.99 13.56       Medium
#>  94.25         High 137.22 45.97         High
#> 
#> Warning: 
#> † P-value for "Treatment: Test" is > 0.05. Genetic variability analysis may not be appropriate for this trait.
#> Warning: 
#> ‡ Negative GV detected.
#>  GCV, GCV category, hBS, hBS category, GA, GAM and
#>  GAM category could not be computed.
#> 
#> 
#> Warning Messages
#> ================
#> 
#> 
#> [Frequency Distribution]
#> <y1>
#> Removed 2 rows containing missing values or values outside the scale range
#> (`geom_bar()`).
#> 
#> <y2>
#> Removed 2 rows containing missing values or values outside the scale range
#> (`geom_bar()`).
#> 
#> 
#> 
#> [GVA]
#> <y1>
#> P-value for "Treatment: Test" is > 0.05. Genetic variability analysis may not be appropriate for this trait.
#> 
#> 
#> Treatment Means
#> ===============
#>  Treatment Block    y1     y2
#>          1       84.67 256.00
#>         10     3 77.25 437.67
#>         11     1 86.50 299.42
#>         12     1 79.50 288.42
#>          2       79.00 228.00
#>          3       82.00 247.67
#>          4       83.33 264.00
#>          5     2 78.25 293.92
#>          6     3 78.25 382.67
#>          7     1 93.50 346.42
#>          8     3 73.25 213.67
#>          9     2 77.25 323.92

# Frequency distribution plots
lapply(bout$`Frequency distribution`, plot)


#> $y1
#> NULL
#> 
#> $y2
#> NULL
#> 

# GVA plots
bout$`GVA plots`
#> $`Phenotypic and Genotypic CV`

#> 
#> $`Broad sense heritability`

#> 
#> $`Genetic advance over mean`

#>