CI_test {combinIT}

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)