CI_test: Combined Interaction Test

In combinIT: A Combined Interaction Test for Unreplicated Two-Way Tables

Combined Interaction Test

Description

This function reports the p-values of the tests for non-additivity developed by Boik (1993), Piepho (1994), Kharrati-Kopaei and Sadooghi-Alvandi (2007), Franck et al. (2013), Malik et al. (2016) and Kharrati-Kopaei and Miller (2016). In addition, it combines the p-values of these six tests (and some other available p-values) into a single p-value as a test statistic for testing interaction. There are four combination methods: Bonferroni, Sidak, Jacobi expansion, and Gaussian Copula. The results of these four combined tests are also reported. If there is a significant interaction, the type of interaction is also provided.

Usage

CI_test(
  x,
  nsim = 10000,
  nc0 = 10000,
  opvalue = NULL,
  alpha = 0.05,
  report = TRUE,
  Elapsed_time = TRUE
)

Arguments

x	numeric matrix, a \times b data matrix where the number of row and column is corresponding to the number of factor levels.
nsim	a numeric value, the number of Monte Carlo samples for computing an exact Monte Carlo p-value. The default value is 10000.
nc0	a numeric value, the number of Monte Carlo samples for computing the unbiasing constant c_0 in KKM.test. The default value is 10000.
opvalue	a numeric vector, other p-values (in addition to the six considered p-values) that are going to be combined.
alpha	a numeric value, the level of the test. The default value is 0.05.
report	logical: if TRUE the result of the test is reported at the alpha level.
Elapsed_time	logical: if TRUE the progress will be printed in the console.

Details

The data matrix is divided based on the row of the data matrix for KKSA_test and Franck_test. Note that KKSA_test is not applicable when a is less than four. Franck_test and Piepho_test are not applicable when a is less than three. This function needs mvtnorm package.

Value

An object of the class combtest, which is a list inducing following components:

nsim	The number of Monte Carlo samples that are used to estimate p-value.
Piepho_pvalue	The p-value of Piepho's (1994) test.
Piepho_Stat	The value of Piepho's (1994) test statistic.
Boik_pvalue	The p-value of Boik's (1993) test.
Boik_Stat	The value of Boik's (1993) test statistic.
Malik_pvalue	The p-value of Malik's (2016) et al. test.
Malik_Stat	The value of Malik's (2016) et al. test statistic.
KKM_pvalue	The p-value of Kharrati-Kopaei and Miller's (2016) test.
KKM_Stat	The value of Kharrati-Kopaei and Miller's (2016) test statistic.
KKSA_pvalue	The p-value of Kharrati-Kopaei and Sadooghi-Alvandi's (2007) test.
KKSA_Stat	The value of Kharrati-Kopaei and Sadooghi-Alvandi's (2007) test statistic.
Franck_pvalue	The p-value of Franck's (2013) et al. test.
Franck_Stat	The value of Franck's (2013) et al. test statistic.
Bonferroni	The combined p-value by using the Bonferroni method.
Sidak	The combined p-value by using the Sidak method.
Jacobi	The combined p-value by using the Jacobi method.
GC	The combined p-value by using the Gaussian copula.
data_name	The name of the input dataset.
test	The name of the test.
Level	The level of test.
Result	The result of the combined test at the alpha level with some descriptions on the type of significant interaction.

References

Shenavari, Z., Kharrati-Kopaei, M. (2018). A Method for Testing Additivity in Unreplicated Two-Way Layouts Based on Combining Multiple Interaction Tests. International Statistical Review 86(3): 469-487.

Examples

data(CNV)
CI_test(CNV, nsim = 1000, Elapsed_time = FALSE)

combinIT documentation built on Oct. 21, 2022, 9:05 a.m.