Piepho_test {combinIT}

Piepho's (1994) Test for Interaction

Description

This function tests the interaction based on a statistic proposed by Piepho (1994). This function reports Piepho's test statistic, an asymptotic p-value, and a Monte Carlo p-value.

Usage

Piepho_test(x, nsim = 10000, alpha = 0.05, report = 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.

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.

Details

Piepho (1994) proposed three test statistics. The third one is based on Grubbs’ (1948) type estimator of variance for the level of the row factor. This type of estimator is used in this function. Piepho (1994) proposed an asymptotic distribution of test statistic; however, a Monte Carlo method is used to calculate the p-value. The Piepho test is not applicable when the row number of the data matrix is less than three. Note that Piepho’s test is powerful for detecting interactions when the Grubbs’ type estimators of variances are heterogeneous across the levels of one factor.

Value

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

pvalue_exact

The calculated exact Monte Carlo p-value.

pvalue_appro

The asymptotic p-value.

statistic

The value of the 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

Piepho, H. P. (1994). On Tests for Interaction in a Nonreplicated Two-Way Layout. Australian Journal of Statistics 36:363-369.

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.

Grubbs, F.E. (1948). On Estimating Precision of Measuring Instruments and Product Variability. Journal of the American Statistical Association 43(242): 243-264.

Examples

data(MVGH)
Piepho_test(MVGH, nsim = 1000)