gpTwoWay: Two-Way ANOVA under Heteroscedasticity

In twowaytests: Two-Way Tests in Independent Groups Designs

Two-Way ANOVA under Heteroscedasticity

Description

gpTwoWay computes a two-way ANOVA for main effects and interaction effect under heteroscedasticity.

Usage

gpTwoWay(formula, data, method = c("gPB","gPQ"), seed = 123, alpha = 0.05, 
  na.rm = TRUE, verbose = TRUE)

Arguments

formula	a formula of the form lhs ~ rhs where lhs gives the sample values and rhs gives the two factors.
data	a data frame containing the variables in formula.
method	a character string to select the method. "gPB": Parametric Bootstrap based Generalized Test, "gPQ": Generalized Pivotal Quantity based Generalized Test.
seed	a seed number for the reproducibility of results. Default is set to 123.
alpha	the level of significance to assess the statistical difference. Default is set to alpha = 0.05.
na.rm	a logical value indicating whether NA values should be stripped before the computation proceeds.
verbose	a logical for printing output to R console.

Value

A list containing the following components:

output	a data frame of output.
alpha	the level of significance to assess the statistical difference.
method	the selected method used in generalized test.
data	a data frame containing the variables in which NA values (if exist) are removed.
formula	a formula of the form lhs ~ rhs where lhs gives the sample values and rhs gives the two factors.

Note

These tests available from this R library are based on two Generalized P-value approaches, for Two-Way ANOVA under unequal variances and cell frequencies. The first test, the gPQ, is an extension Li et al. (2011), and the second test, gPB, is a generalized test that is numerically equivalent to the Parametric Bootstrap test derived by Xu et al. (2013). The gPQ test tends to assure the intended size of the test, but somewhat conservative, especially when the sample sizes are small.

The gPB test tends to exceed the intended size of the test. Hence, the gPB is recommended for situations of small sample sizes, and gPQ otherwise.

Author(s)

Sam Weerahandi, Osman Dag, Malwane Ananda

References

Dag, O., Kasikci, M., Yilmaz, M.A., Weerahandi, S., Ananda, M.M.A. (2024). twowaytests: An R Package for Two-Way Tests in Independent Groups Designs. SoftwareX, 27, 1-8.

Ananda, M.M., Dag, O., Weerahandi, S. (2023). Heteroscedastic two-way ANOVA under constraints. Communications in Statistics-Theory and Methods, 52:22, 8207-8222.

Li, X., Wang J., Liang H. (2011). Comparison of several means: a fiducial based approach. Computational Statistics and Data Analysis, 55:5, 1993-2002.

Xu L., Yang F., Abula A., Qin, S. (2013). A parametric bootstrap approach for two-way ANOVA in presence of possible interactions with unequal variances. Journal of Multivariate Analysis, 115, 172-180.

Examples

library(twowaytests)
data(alveolar)



# to use Parametric Bootstrap based Generalized Test
gpTwoWay(cell ~ ovalbumin*treatment, data = alveolar, method = "gPB")

# to use Generalized Pivotal Quantity based Generalized Test
gpTwoWay(cell ~ ovalbumin*treatment, data = alveolar, method = "gPQ")

out <- gpTwoWay(cell ~ ovalbumin*treatment, data = alveolar, method = "gPB")
paircompTwoWay(out)

out <- gpTwoWay(cell ~ treatment*ovalbumin, data = alveolar, method = "gPB")
paircompTwoWay(out)

twowaytests documentation built on April 3, 2025, 7:51 p.m.