KKSA_test {combinIT}

Kharrati-Kopaei and Sadooghi-Alvandi's (2007) test for interaction

Description

This function calculates Kharrati-Kopaei and Sadooghi-Alvandi's test statistic and corresponding p-value for testing interaction.

Usage

KKSA_test(
  x,
  nsim = 10000,
  alpha = 0.05,
  report = TRUE,
  plot = FALSE,
  vecolor = c("blue", "red"),
  linetype = c(1, 2),
  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.

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.

plot

logical: if TRUE an interaction plot will be plotted.

vecolor

character vector with length two, for visualizing the colors of lines in interaction plot. The default colors are blue and red.

linetype

numeric vector with length two, for visualizing the line types in interaction plot. The default line types are 1 and 2.

Elapsed_time

logical: if TRUE the progress will be printed in the console.

Details

Suppose that a \ge b and b \ge 4. Consider the l-th division of the data table into two sub-tables, obtained by putting a_1 (2 \le a_1 \le a-2) rows in the first sub-table and the remaining a_2 rows in the second sub-table (a_1+a_2=a). Let RSS1 and RSS2 denote the residual sum of squares for these two sub-tables, respectively. For a particular division l, let F_l=max\{F_l,1/F_l\} where F_l=(a_2-1)RSS1/((a_1-1)RSS2) and let P_l denote the corresponding p-value. Kharrati-Kopaei and Sadooghi-Alvandi (2007) proposed their test statistic as the minimum value of P_l over l=1,…,2^{(a-1)}-a-1 all possible divisions of the table. If plot is TRUE an interaction plot will be plotted by displaying levels of column factor on the horizontal axis, levels of row factor using lines that are visually distinguished by line type and color, and the observed values on the vertical axis. Color and line type are used to display which levels of row factor are assigned to which sub-tables based on the minimum p-values among all possible configurations. Note that the grouping colors and line types appear whether or not the KKSA.test detects a significant non-additivity. The default colors are blue and red, and the default line types are one and two for the two sub-tables. They can be customized by supplying arguments called vecolor and linetype. Note that this method of testing requires that the data matrix has more than three rows. This test procedure is powerful for detecting interaction when the magnitude of interaction effects is heteroscedastic across the sub-tables of observations.

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 Bonferroni-adjusted p-value is calculated.

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

Kharrati-Kopaei, M., Sadooghi-Alvandi, S.M. (2007). A New Method for Testing Interaction in Unreplicated Two-Way Analysis of Variance. Communications in Statistics-Theory and Methods 36:2787–2803.

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(IDCP)
KKSA_test(IDCP, nsim = 1000, Elapsed_time = FALSE)