ClustMC: Cluster-Based Multiple Comparisons

Description

Multiple comparison techniques are typically applied following an F test from an ANOVA to decide which means are significantly different from one another. As an alternative to traditional methods, cluster analysis can be performed to group the means of different treatments into non-overlapping clusters. Treatments in different groups are considered statistically different. Several approaches have been proposed, with varying clustering methods and cut-off criteria. This package implements cluster-based multiple comparisons tests and also provides a visual representation in the form of a dendrogram. Di Rienzo, J. A., Guzman, A. W., & Casanoves, F. (2002) <jstor.org/stable/1400690>. Bautista, M. G., Smith, D. W., & Steiner, R. L. (1997) doi:10.2307/1400402.

Author(s)

Maintainer: Santiago Garcia Sanchez santiagoesquel@gmail.com [copyright holder]

See Also

Useful links:

• https://github.com/SGS2000/ClustMC

• https://sgs2000.github.io/ClustMC/

• Report bugs at https://github.com/SGS2000/ClustMC/issues

Loaf volumes from a bread-baking experiment

Description

Includes the volumes (ml) of 85 loaves of bread made under controlled conditions from 100-gram batches of dough made with 17 different varieties of wheat flour and 5 levels of potassium bromate (mg).

Usage

bread

Format

A tibble with 85 rows and 3 columns:

variety

a factor indicating the variety of flour used.

bromate

a number denoting the amount of potassium bromate used (milligrams).

volume

a number denoting the volume of the loaf made under each condition (milliliters).

Details

Data from a bread-baking experiment by Larmour (1941). Later reproduced by Scheffe (1959) and then used by Duncan (1965) to contrast different multiple comparison methods. Jolliffe (1975) applies this dataset to illustrate his cluster-based test.

Source

Larmour, R. K. (1941). A comparison of hard red spring and hard red winter wheats. Cereal Chemistry, 18(6), 778-789. Available at: https://archive.org/details/sim_cereal-chemistry_1941-11_18_6

References

Duncan, D. B. (1965). A bayesian approach to multiple comparisons. Technometrics, 7(2), 171-222. doi:10.2307/1266670

Jolliffe, I. T. (1975). Cluster analysis as a multiple comparison method. Applied Statistics: Proceedings of Conference at Dalhousie University, Halifax, 159-168.

Scheffe, H. (1950).The analysis of variance. Wiley-Interscience Publication.

Examples

data(bread)
summary(bread)

Bautista, Smith and Steiner test for multiple comparisons

Description

Bautista, Smith and Steiner (BSS) test for multiple comparisons. Implements a procedure for grouping treatments following the determination of differences among them. First, a cluster analysis of the treatment means is performed and the two closest means are grouped. A nested analysis of variance from the original ANOVA is then constructed with the treatment source now partitioned into "groups" and "treatments within groups". This process is repeated until there are no differences among the group means or there are differences among the treatments within groups.

Usage

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

Arguments

Value

A list with three data.frame and one hclust:

Author(s)

Santiago Garcia Sanchez

References

Bautista, M. G., Smith, D. W., & Steiner, R. L. (1997). A Cluster-Based Approach to Means Separation. Journal of Agricultural, Biological, and Environmental Statistics, 2(2), 179-197. doi:10.2307/1400402

Examples

data("PlantGrowth")
# Using vectors -------------------------------------------------------
weights <- PlantGrowth$weight
treatments <- PlantGrowth$group
bss_test(y = weights, trt = treatments, show_plot = FALSE)
# Using a model -------------------------------------------------------
model <- lm(weights ~ treatments)
bss_test(y = model, trt = "treatments", show_plot = FALSE)

Nitrogen content of red clover plants

Description

Includes the nitrogen content (mg) of 30 red clover plants inoculated with one of four single-strain cultures of Rhizobium trifolii or a composite of five Rhizobium meliloti strains, resulting in six treatments in total.

Usage

clover

Format

A tibble with 30 rows and 2 columns:

treatment

a factor denoting the treatment applied to each plant.

nitrogen

a number denoting the nitrogen content of each plant (milligrams).

Details

Data originally from an experiment by Erdman (1946), conducted in a greenhouse using a completely random design. The current dataset was presented by Steel and Torrie (1980) and later used by Bautista et al. (1997) to illustrate their proposed procedure.

Source

Steel, R., & Torrie, J. (1980). Principles and procedures of statistics: A biometrical approach (2nd ed.). San Francisco: McGraw-Hill. Available at: https://archive.org/details/principlesproce00stee

References

Bautista, M. G., Smith, D. W., & Steiner, R. L. (1997). A Cluster-Based Approach to Means Separation. Journal of Agricultural, Biological, and Environmental Statistics, 2(2), 179-197. doi:10.2307/1400402

Erdman, L. W. (1946). Studies to determine if antibiosis occurs among rhizobia. Journal of the American Society of Agronomy, 38, 251-258. doi:10.2134/agronj1946.00021962003800030005x

Examples

data(clover)
summary(clover)

Di Rienzo, Guzman and Casanoves test for multiple comparisons

Description

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

Value

A list with three data.frame and one hclust:

Author(s)

Santiago Garcia Sanchez

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>

Examples

data("PlantGrowth")
# Using vectors -------------------------------------------------------
weights <- PlantGrowth$weight
treatments <- PlantGrowth$group
dgc_test(y = weights, trt = treatments, show_plot = FALSE)
# Using a model -------------------------------------------------------
model <- lm(weights ~ treatments)
dgc_test(y = model, trt = "treatments", show_plot = FALSE)

Jolliffe test for multiple comparisons

Description

I.T. Jolliffe test for multiple comparisons. Implements a cluster-based alternative closely linked to the Student-Newman-Keuls multiple comparison method. Single-linkage cluster analysis is applied, using the p-values obtained with the SNK test for pairwise mean comparison as a similarity measure. Groups whose means join beyond 1 - \alpha are statistically different. Alternatively, complete linkage cluster analysis can also be applied.

Usage

jolliffe_test(
  y,
  trt,
  alpha = 0.05,
  method = "single",
  show_plot = TRUE,
  console = TRUE,
  abline_options,
  ...
)

Arguments

Value

A list with three data.frame and one hclust:

Author(s)

Santiago Garcia Sanchez

References

Jolliffe, I. T. (1975). Cluster analysis as a multiple comparison method. Applied Statistics: Proceedings of Conference at Dalhousie University, Halifax, 159-168.

Examples

data("PlantGrowth")
# Using vectors -------------------------------------------------------
weights <- PlantGrowth$weight
treatments <- PlantGrowth$group
jolliffe_test(y = weights, trt = treatments, alpha = 0.1, show_plot = FALSE)
# Using a model -------------------------------------------------------
model <- lm(weights ~ treatments)
jolliffe_test(y = model, trt = "treatments", alpha = 0.1, show_plot = FALSE)