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author: Piotr Sulewski, Pomeranian University
The goal of the package is to put into practice the modular and logarithmic minimum tests for independence in two-way, three-way and four-way contingency tables. Statistic value, cv value and p-value are calculated. This package also includes three table generation functions and six data sets. To read more about the package please see (and cite :)) papers:
Sulewski, P. (2016). Moc testów niezależności w tablicy dwudzielczej większej niż 2×2. Przegląd statystyczny 63(2), 190-210.
Sulewski, P. (2019). The LMS for Testing Independence in Two-way Contingency Tables. Biometrical Letters 56(1), 17-43.
Sulewski, P. (2018). Power Analysis Of Independence Testing for the Three-Way Con-tingency Tables of Small Sizes. Journal of Applied Statistics 45(13), 2481-2498.
Sulewski, P. (2021). Logarithmic Minimum Test for Independence in Three Way Con-tingency Table of Small Sizes. Journal of Statistical Computation and Simulation 91(13), 2780-2799.
You can install the released version of PSIndependenceTest from CRAN with:
install.packages("PSIndependenceTest")You can install the development version of PSIndependenceTest from GitHub with:
library("remotes")
remotes::install_github("PiotrSule/PSIndependenceTest")This package includes four data sets
The first one, table1, consist of 40 observations presented as two-way contingency table 2 x 2. See details: Sulewski, P. (2017). A new test for independence in 2x2 contingency tables. Acta Universitatis Lodziensis. Folia Oeconomica 4(330), 55–75.
The second one, table2, consist of 25 observations described the effect of a treatment for rheumatoid arthritis vs. a placebo presented as two-way contingency table 2 x 3. See details: Sulewski, P. (2019). The LMS for Testing Independence in Two-way Contingency Tables. Biometrical Letters 56 (1), 17-43.
The third one, table3, consist of 695 observations described the frequency of watching videos at home or at friends’ homes for young people between 7 and 15 years of age, cross-classified according to age and sex. Data are presented as three-way contingency table 3 x 3 x 2. See details: Sulewski, P. (2021). Logarithmic Minimum Test for Independence in Three Way Contingency Table of Small Sizes. Journal of Statistical Computation and Simulation 91(13), 2780-2799
The fourth one, table4, consist of 100 observations obtained using the Monte Carlo method when Ho is true, i.e. all probabilities pijt equal 1/24. Data is presented as three-way contingency table 2 x 3 x 4.
The fifth one, table5,provides information on the fate of passengers on the fatal maiden voyage of the ocean liner ‘Titanic’, summarized according to economic status (class), sex, age and survival. Data is presented as four-way contingency table 4 x 2 x 2 x 2. The sample size equals 2201.
The sixth one, table6, consist of 100 observations obtained using the Monte Carlo method when Ho is true, i.e. all probabilities pijtu equal 1/16. Data is presented as four-way contingency table 2 x 2 x 2 x 2.
library(PSIndependenceTest)
dim(table1)
#> [1] 2 2
length(table2)
#> [1] 6GenTab2
This function generating the two-way contingency table with the Monte Carlo method
GenTab2(matrix(1/8, nrow = 2, ncol = 4), 50)
#> [,1] [,2] [,3] [,4]
#> [1,] 5 4 5 5
#> [2,] 6 6 8 11
GenTab2(matrix(1/12, nrow = 4, ncol = 3), 60)
#> [,1] [,2] [,3]
#> [1,] 6 8 7
#> [2,] 1 2 5
#> [3,] 4 9 3
#> [4,] 3 5 7Mod2.stat
This function returns the statistic value of the modular independence test in the two-way contingency table.
Mod2.stat(table1)
#> [1] 1.273572
Mod2.stat(GenTab2(matrix(1/9, nrow = 3, ncol = 3), 90))
#> [1] 1.149439Mod2.cv
This function returns the critical value of the modular independence test in the two-way contingency table.
Mod2.cv(2, 2, 40, 0.05, B = 1e3)
#> [1] 1.265177
Mod2.cv(2, 3, 60, 0.1)
#> [1] 1.542129Mod2.pvalue
This function returns the p-value of the modular independence test in the two-way contingency table.
Mod2.pvalue(Mod2.stat(table1), 2, 2, 40, B = 1e3)
#> [1] 0.04695305
Mod2.pvalue(Mod2.stat(table2), 2, 3, 60)
#> [1] 0.6931307Mod2.test
This function returns the test statistic and p-value of the logarithmic minimum independence test in the two-way contingency table.
Mod2.test(table1, B = 1e3)
#>
#> Modular test for independence in two-way contingency table
#>
#> data: table1
#> D = 1.2736, p-value = 0.0488
Mod2.test(table2)
#>
#> Modular test for independence in two-way contingency table
#>
#> data: table2
#> D = 0.61103, p-value = 0.7001Lms2.stat
This function returns the statistic value of the logarithmic minimum independence test in the two-way contingency table.
Lms2.stat(table1)
#> [1] 1.660665
Lms2.stat(GenTab2(matrix(1/9, nrow = 3, ncol = 3), 90))
#> [1] 1.759932Lms2.cv
This function returns the critical value of the logarithmic minimum independence test in the two-way contingency table.
Lms2.cv(2, 2, 40, 0.05, B = 1e3)
#> [1] 1.34987
Lms2.cv(2, 3, 60, 0.1)
#> [1] 1.605235Lms2.pvalue
This function returns the p-value of the logarithmic minimum independence test in the two-way contingency table.
Lms2.pvalue(Lms2.stat(table1), 2, 2, 40, B = 1e3)
#> [1] 0.008991009
Lms2.pvalue(Lms2.stat(table2), 2, 3, 60)
#> [1] 0.7009299Lms2.test
This function returns the test statistic and p-value of the logarithmic minimum independence test in the two-way contingency table.
Lms2.test(table1, B = 1e3)
#>
#> Modular test for independence in two-way contingency table
#>
#> data: table1
#> D = 1.6607, p-value = 0.0176
Lms2.test(table2)
#>
#> Modular test for independence in two-way contingency table
#>
#> data: table2
#> D = 0.61437, p-value = 0.7059GenTab3
This function generating the three-way contingency table with the Monte Carlo method
GenTab3(array(1/12, dim=c(2,2,3)), 60)
#> , , 1
#>
#> [,1] [,2]
#> [1,] 5 7
#> [2,] 5 5
#>
#> , , 2
#>
#> [,1] [,2]
#> [1,] 8 5
#> [2,] 6 5
#>
#> , , 3
#>
#> [,1] [,2]
#> [1,] 5 4
#> [2,] 0 5
GenTab3(array(1/18, dim=c(2,3,3)), 80)
#> , , 1
#>
#> [,1] [,2] [,3]
#> [1,] 5 8 0
#> [2,] 4 5 6
#>
#> , , 2
#>
#> [,1] [,2] [,3]
#> [1,] 3 3 6
#> [2,] 5 2 4
#>
#> , , 3
#>
#> [,1] [,2] [,3]
#> [1,] 10 3 6
#> [2,] 5 3 2Mod3.stat
This function returns the statistic value of the modular independence test in the three-way contingency table.
Mod3.stat(table3)
#> [1] 2.641208
Mod3.stat(GenTab3(array(1/12, dim=c(2,2,3)), 120))
#> [1] 1.890008Mod3.cv
This function returns the critical value of the modular independence test in the three-way contingency table.
Mod3.cv(2, 2, 2, 80, 0.05, B = 1e3)
#> [1] 2.380025
Mod3.cv(2, 2, 2, 80, 0.1)
#> [1] 2.181818Mod3.pvalue
This function returns the p-value of the modular independence test in the three-way contingency table.
Mod3.pvalue(Mod3.stat(table4), 2, 2, 2, 80, B = 1e3)
#> [1] 0.02397602
Mod3.pvalue(Mod3.stat(table4), 2, 2, 2, 80)
#> [1] 0.02409759Mod3.test
This function returns the test statistic and p-value of the modular independence test in the three-way contingency table.
Mod3.test(table4, B = 1e2)
#>
#> Modular test for independence in three-way contingency table
#>
#> data: table4
#> D = 2.5886, p-value = 0.0265
Mod3.test(table4, B = 1e3)
#>
#> Modular test for independence in three-way contingency table
#>
#> data: table4
#> D = 2.5886, p-value = 0.0283Lms3.stat
This function returns the statistic value of the logarithmic minimum independence test in the three-way contingency table.
Lms3.stat(table3)
#> [1] 2.712789
Lms3.stat(GenTab3(array(1/12, dim=c(2,2,3)), 120))
#> [1] 3.960989Lms3.cv
This function returns the critical value of the logarithmic minimum independence test in the three-way contingency table.
Lms3.cv(2, 2, 2, 80, 0.05, B = 1e2)
#> [1] 2.775388
Lms3.cv(2, 2, 2, 80, 0.1, B = 1e3)
#> [1] 2.313046Lms3.pvalue
This function returns the p-value of the logarithmic minimum independence test in the three-way contingency table.
Lms3.pvalue(Lms3.stat(table4), 2, 2, 2, 80, B = 1e3)
#> [1] 0.04095904
Lms3.pvalue(Lms3.stat(table4), 2, 2, 2, 80)
#> [1] 0.04019598Lms3.test
This function returns the test statistic and p-value of the logarithmic minimum independence test in the three-way contingency table.
Lms3.test(table4, B = 1e2)
#>
#> Logarithmic minimum test for independence in three-way contingency
#> table
#>
#> data: table4
#> D = 2.6637, p-value = 0.04
Lms3.test(table4, B = 1e3)
#>
#> Logarithmic minimum test for independence in three-way contingency
#> table
#>
#> data: table4
#> D = 2.6637, p-value = 0.0371GenTab4
This function generating the four-way contingency table with the Monte Carlo method.
GenTab4(array(1/16, dim=c(2,2,2,2)), 100)
#> , , 1, 1
#>
#> [,1] [,2]
#> [1,] 7 7
#> [2,] 9 9
#>
#> , , 2, 1
#>
#> [,1] [,2]
#> [1,] 10 8
#> [2,] 5 4
#>
#> , , 1, 2
#>
#> [,1] [,2]
#> [1,] 1 3
#> [2,] 5 5
#>
#> , , 2, 2
#>
#> [,1] [,2]
#> [1,] 1 11
#> [2,] 5 10
GenTab4(array(1/36, dim=c(2,3,2,3)), 150)
#> , , 1, 1
#>
#> [,1] [,2] [,3]
#> [1,] 2 3 4
#> [2,] 5 4 4
#>
#> , , 2, 1
#>
#> [,1] [,2] [,3]
#> [1,] 5 7 6
#> [2,] 9 3 6
#>
#> , , 1, 2
#>
#> [,1] [,2] [,3]
#> [1,] 1 4 5
#> [2,] 2 5 2
#>
#> , , 2, 2
#>
#> [,1] [,2] [,3]
#> [1,] 7 6 4
#> [2,] 4 7 1
#>
#> , , 1, 3
#>
#> [,1] [,2] [,3]
#> [1,] 6 1 2
#> [2,] 5 1 4
#>
#> , , 2, 3
#>
#> [,1] [,2] [,3]
#> [1,] 7 5 3
#> [2,] 3 4 3Mod4.stat
This function returns the statistic value of the modular independence test in the four-way contingency table.
Mod4.stat(table5)
#> [1] 46.70092
Mod4.stat(table6)
#> [1] 3.7301Mod4.cv
This function returns the critical value of the modular independence test in the four-way contingency table.
Mod4.cv(2, 2, 2, 2, 160, 0.05, B = 1e2)
#> [1] 4.395262
Mod4.cv(2, 2, 2, 2, 160, 0.1, B = 1e3)
#> [1] 4.425875Mod4.pvalue
This function returns the p-value of the modular independence test in the four-way contingency table.
Mod4.pvalue(Mod4.stat(table6), 2, 2, 2, 2, 160, B = 1e2)
#> [1] 0.3168317
Mod4.pvalue(Mod4.stat(table6), 2, 2, 2, 2, 160, B = 1e3)
#> [1] 0.3426573Mod4.test
This function returns the test statistic and p-value of the modular independence test in the -way contingency table.
Mod4.test(table6, B = 1e2)
#>
#> Modular test for independence in four-way contingency table
#>
#> data: table6
#> D = 3.7301, p-value = 0.3101
Mod4.test(table6, B = 1e3)
#>
#> Modular test for independence in four-way contingency table
#>
#> data: table6
#> D = 3.7301, p-value = 0.3111Lms4.stat
This function returns the statistic value of the logarithmic minimum independence test in the four-way contingency table.
Lms4.stat(table5)
#> [1] 116.0267
Lms4.stat(table6)
#> [1] 4.097161Lms4.cv
This function returns the critical value of the logarithmic minimum independence test in the four-way contingency table.
Lms4.cv(2, 2, 2, 2, 160, 0.05, B = 1e2)
#> [1] 5.321681
Lms4.cv(2, 2, 2, 2, 160, 0.1, B = 1e3)
#> [1] 4.764324Lms4.pvalue
This function returns the p-value of the logarithmic minimum independence test in the four-way contingency table.
Lms4.pvalue(Lms4.stat(table6), 2, 2, 2, 2, 160, B = 1e2)
#> [1] 0.2475248
Lms4.pvalue(Lms4.stat(table6), 2, 2, 2, 2, 160, B = 1e3)
#> [1] 0.2597403Lms4.test
This function returns the test statistic and p-value of the logarithmic minimum independence test in the four-way contingency table.
Lms4.test(table6, B = 1e2)
#>
#> Logarithmic minimum test for independence in four-way contingency table
#>
#> data: table6
#> D = 4.0972, p-value = 0.248
Lms4.test(table6, B = 1e3)
#>
#> Logarithmic minimum test for independence in four-way contingency table
#>
#> data: table6
#> D = 4.0972, p-value = 0.2513These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
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