R: Analysis of Augmented Randomised Complete Block Design

augmentedRCBD {augmentedRCBD}

R Documentation

Analysis of Augmented Randomised Complete Block Design

Description

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.

Usage

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`.

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).

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.

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$y1, method.comp = "lsd",
                      alpha = 0.05, group = TRUE, console = TRUE)
# Results for variable y2 (checks inferred)
out2 <- augmentedRCBD(data$blk, data$trt, data$y1, method.comp = "lsd",
                     alpha = 0.05, group = TRUE, console = TRUE)

# Results for variable y1 (checks specified)
out1 <- augmentedRCBD(data$blk, data$trt, data$y1, method.comp = "lsd",
                      alpha = 0.05, group = TRUE, console = TRUE,
                      checks = c("1", "2", "3", "4"))
# Results for variable y2 (checks specified)
out2 <- augmentedRCBD(data$blk, data$trt, data$y1, method.comp = "lsd",
                      alpha = 0.05, group = TRUE, console = TRUE,
                      checks = c("1", "2", "3", "4"))

## Not run: 
# 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"))

## End(Not run)

# Warning in case test treatments are replicated
out1 <- augmentedRCBD(data$blk, data$trt, data$y1, method.comp = "lsd",
                      alpha = 0.05, group = TRUE, console = TRUE)
out1 <- augmentedRCBD(data$blk, data$trt, data$y1, method.comp = "lsd",
                      alpha = 0.05, group = TRUE, console = TRUE,
                      checks = c("2", "3"))

[Package augmentedRCBD version 0.1.7 Index]