Boik_test {combinIT} | R Documentation |
Boik's (1993) Locally Best Invariant (LBI) Test
Description
This function calculates the LBI test statistic for testing the null hypothesis There is no interaction.
It returns an exact p-value when
where
. It returns an exact Monte Carlo p-value when
. It also provides an asymptotic chi-squared p-value. Note that the p-value of the Boik.test is always one when
.
Usage
Boik_test(x, nsim = 10000, alpha = 0.05, report = TRUE)
Arguments
x |
a numeric matrix, |
nsim |
a numeric value, the number of Monte Carlo samples for calculating an exact Monte Carlo p-value. The default value is 10000. |
alpha |
a numeric value, the level of the test. The default value is 0.05. |
report |
logical: if |
Details
The LBI test statistic is where
and
is the residual
matrix of the input data matrix,
, under the null hypothesis
There is no interaction. This test rejects the null hypothesis of no interaction when
is small.
Boik (1993) provided the exact distribution of
when
under
. In addition, he provided an asymptotic distribution of
under
when
tends to infinity where
.
Note that the LBI test is powerful when the
matrix of interaction terms has small rank and one singular value dominates the remaining singular values or
in practice, if the largest eigenvalue of
is expected to dominate the remaining eigenvalues.
Value
An object of the class ITtest
, which is a list inducing following components:
pvalue_exact |
An exact Monte Carlo p-value when |
pvalue_appro |
An chi-squared asymptotic p-value. |
statistic |
The value of test statistic. |
Nsim |
The number of Monte Carlo samples that are used to estimate p-value. |
data_name |
The name of the input dataset. |
test |
The name of the test. |
Level |
The level of test. |
Result |
The result of the test at the alpha level with some descriptions on the type of significant interaction. |
References
Boik, R.J. (1993). Testing additivity in two-way classifications with no replications: the locally best invariant test. Journal of Applied Statistics 20(1): 41-55.
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(MVGH)
Boik_test(MVGH, nsim = 1000)