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.
CI_test(
x,
nsim = 10000,
nc0 = 10000,
opvalue = NULL,
alpha = 0.05,
report = TRUE,
Elapsed_time = TRUE
)An object of the class combtest, which is a list inducing following components:
The number of Monte Carlo samples that are used to estimate p-value.
The p-value of Piepho's (1994) test.
The value of Piepho's (1994) test statistic.
The p-value of Boik's (1993) test.
The value of Boik's (1993) test statistic.
The p-value of Malik's (2016) et al. test.
The value of Malik's (2016) et al. test statistic.
The p-value of Kharrati-Kopaei and Miller's (2016) test.
The value of Kharrati-Kopaei and Miller's (2016) test statistic.
The p-value of Kharrati-Kopaei and Sadooghi-Alvandi's (2007) test.
The value of Kharrati-Kopaei and Sadooghi-Alvandi's (2007) test statistic.
The p-value of Franck's (2013) et al. test.
The value of Franck's (2013) et al. test statistic.
The combined p-value by using the Bonferroni method.
The combined p-value by using the Sidak method.
The combined p-value by using the Jacobi method.
The combined p-value by using the Gaussian copula.
The name of the input dataset.
The name of the test.
The level of test.
The result of the combined test at the alpha level with some descriptions on the type of significant interaction.
numeric matrix, \(a \times b\) data matrix where the number of row and column is corresponding to the number of factor levels.
a numeric value, the number of Monte Carlo samples for computing an exact Monte Carlo p-value. The default value is 10000.
a numeric value, the number of Monte Carlo samples for computing the unbiasing constant \(c_0\) in KKM.test. The default value is 10000.
a numeric vector, other p-values (in addition to the six considered p-values) that are going to be combined.
a numeric value, the level of the test. The default value is 0.05.
logical: if TRUE the result of the test is reported at the alpha level.
logical: if TRUE the progress will be printed in the console.
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.
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.
data(CNV)
CI_test(CNV, nsim = 1000, Elapsed_time = FALSE)
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