Di Rienzo, Guzman and Casanoves test for multiple comparisons

Di Rienzo, Guzman and Casanoves (DGC) test for multiple comparisons. Implements a cluster-based method for identifying groups of nonhomogeneous means. Average linkage clustering is applied to a distance matrix obtained from the sample means. The distribution of \(Q\) (distance between the source and the root node of the tree) is used to build a test with a significance level of \(\alpha\). Groups whose means join above \(c\) (the \(\alpha\)-level cut-off criterion) are statistically different.

Usage

dgc_test(
  y,
  trt,
  alpha = 0.05,
  show_plot = TRUE,
  console = TRUE,
  abline_options,
  ...
)

Arguments

y: Either a model (created with lm() or aov()) or a numerical vector with the values of the response variable for each unit.
trt: If y is a model, a string with the name of the column containing the treatments. If y is a vector, a vector of the same length as y with the treatments for each unit.
alpha: Value equivalent to 0.05 or 0.01, corresponding to the significance level of the test. The default value is 0.05.
show_plot: Logical value indicating whether the constructed dendrogram should be plotted or not.
console: Logical value indicating whether the results should be printed on the console or not.
abline_options: list with optional arguments for the line in the dendrogram.
...: Optional arguments for the plot() function.

Value

A list with three data.frame and one hclust:

stats: data.frame containing summary statistics by treatment.
groups: data.frame indicating the group to which each treatment is assigned.
parameters: data.frame with the values used for the test. treatments is the total number of treatments, alpha is the significance level used, c is the cut-off criterion for the dendrogram (the height of the horizontal line on the dendrogram), q is the \(1 - \alpha\) quantile of the distribution of \(Q\) (distance from the root node) under the null hypothesis and SEM is an estimate of the standard error of the mean.
dendrogram_data: object of class hclust with data used to build the dendrogram.

References

Di Rienzo, J. A., Guzman, A. W., & Casanoves, F. (2002). A Multiple-Comparisons Method Based on the Distribution of the Root Node Distance of a Binary Tree. Journal of Agricultural, Biological, and Environmental Statistics, 7(2), 129-142. <jstor.org/stable/1400690>

Author

Santiago Garcia Sanchez

Examples

data("PlantGrowth")
# Using vectors -------------------------------------------------------
weights <- PlantGrowth$weight
treatments <- PlantGrowth$group
dgc_test(y = weights, trt = treatments, show_plot = FALSE)
#>      group
#> ctrl     1
#> trt1     1
#> trt2     2
#> Treatments within the same group are not significantly different
# Using a model -------------------------------------------------------
model <- lm(weights ~ treatments)
dgc_test(y = model, trt = "treatments", show_plot = FALSE)
#>      group
#> ctrl     1
#> trt1     1
#> trt2     2
#> Treatments within the same group are not significantly different