| Title: | Independence Tests for Two-Way, Three-Way and Four-Way Contingency Tables |
| Version: | 0.0.1 |
| Description: | Presentation two independence tests for two-way, three-way and four-way contingency tables. These tests are: the modular test and the logarithmic minimum test. For details on this method see: Sulewski (2017) <doi:10.18778/0208-6018.330.04>, Sulewski (2018) <doi:10.1080/02664763.2018.1424122>, Sulewski (2019) <doi:10.2478/bile-2019-0003>, Sulewski (2021) <doi:10.1080/00949655.2021.1908286>. |
| Depends: | R (≥ 3.5.0) |
| License: | GPL-3 |
| Language: | en-US |
| Encoding: | UTF-8 |
| RoxygenNote: | 7.2.3 |
| Suggests: | testthat, knitr, rmarkdown |
| VignetteBuilder: | knitr |
| LazyData: | true |
| NeedsCompilation: | no |
| Packaged: | 2023-09-14 13:41:07 UTC; piotr |
| Author: | Piotr Sulewski 
[aut, cre] |
| Maintainer: | Piotr Sulewski <piotr.sulewski@apsl.edu.pl> |
| Repository: | CRAN |
| Date/Publication: | 2023-09-14 19:10:06 UTC |
The list of package functions and their demonstration
Description
The PSIndependenceTest package puts 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. The list of package functions is as follows:
Data sets in the package and generating two-way, three-way and four-way contingemcy tables
Functions for the modular independence test and two-way contingency table
Functions for the modular independence test and three-way contingency table
Functions for the modular independence test and four-way contingency table
Functions for the logarithmic minimum independence test and two-way contingency table
Functions for the logarithmic minimum independence test and three-way contingency table
Functions for the logarithmic minimum independence test and four-way contingency table
Two-way contingency table r x c - generation
Description
Generating a two-way contingency table r x c
Usage
GenTab2(pij, n)
Arguments
pij |
a numeric matrix with non-negative probability values of the two-way contingency table |
n |
a sample size |
Details
Generating a two-way contingency table r x c using the probability matrix pij. If Ho is true then pij equals 1 / r / c.
Value
The function returns the two-way contingency table r x c
Author(s)
Piotr Sulewski, piotr.sulewski@apsl.edu.pl, Pomeranian University in Slupsk.
References
Sulewski, P. (2016). Moc testów niezależności w tablicy dwudzielczej większej niż 2×2, Przegląd statystyczny 63(2), 190-210
Examples
r = 6; c = 2
GenTab2(array(1 / r / c, dim = c(r, c)), 93)
GenTab2(matrix(c(0.125,0.25,0.25,0.375), nrow=2), 100)
Three-way contingency table r x c x t - generation
Description
Generating a three-way contingency table r x c x t.
Usage
GenTab3(pijt, n)
Arguments
pijt |
a numeric matrix with non-negative probability values of the three-way contingency table |
n |
a sample size |
Details
Generating a three-way contingency table r x c x t using the probability matrix pijt. If Ho is true then pijt equals 1 / r / c / t.
Value
The function returns the three-way contingency table r x c x t
Author(s)
Piotr Sulewski, piotr.sulewski@apsl.edu.pl, Pomeranian University in Slupsk.
References
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
Examples
r = 2; c = 3; t = 4
GenTab3(array(1 / (r * c * t), dim = c(r, c, t)),250)
table = GenTab3(array(0.125, dim = c(2, 2, 2)), 100)
GenTab3(prop.table(table),100)
Four-way contingency table r x c x t x u - generation
Description
Generating a four-way contingency table r x c x t x u.
Usage
GenTab4(pijtu, n)
Arguments
pijtu |
a numeric matrix with non-negative probability values of the four-way contingency table |
n |
a sample size |
Details
Generating a four-way contingency table r x c x t x u using the probability matrix pijtu. If Ho is true then pijtu equals 1 / r / c / t / u.
Value
The function returns the four-way contingency table r x c x t x u
Author(s)
Piotr Sulewski, piotr.sulewski@apsl.edu.pl, Pomeranian University in Slupsk.
References
Extension of the information contained in 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
Examples
r = 2; c = 2; t = 2; u = 3
GenTab4(array(1 / (r * c * t * u), dim = c(r, c, t, u)),150)
table = GenTab4(array(1/16, dim = c(2, 2, 2, 2)), 200)
GenTab4(prop.table(table),200)
Logarithmic Minimum Test for Independence in Two-Way Contingency Table
Description
Calculates the critical values of the logarithmic minimum test.
Usage
Lms2.cv(nr, nc, n, alfa, B = 10000)
Arguments
nr |
a number of rows |
nc |
a number of columns |
n |
a sample size |
alfa |
a significance level |
B |
an integer specifying the number of replicates used in the Monte Carlo test (optional) |
Details
The Critical value of the logarithmic minimum test for independence in r x c contingency table,
Value
The function returns the critical value of the logarithmic minimum test.
Author(s)
Piotr Sulewski, piotr.sulewski@apsl.edu.pl, Pomeranian University in Slupsk.
References
Sulewski, P. (2019). The LMS for Testing Independence in Two-way Contingency Tables. Biometrical Letters 56(1), 17-43 #'
Examples
Lms2.cv(2, 2, 40, 0.05, B = 1e3)
Lms2.cv(2, 3, 60, 0.1, B = 1e2)
Logarithmic Minimum Test for Independence in Two-Way Contingency Table
Description
Calculates the p-value of the logarithmic minimum test.
Usage
Lms2.pvalue(stat, nr, nc, n, B = 10000)
Arguments
stat |
a logarithmic minimum statistic value |
nr |
a number of rows |
nc |
a number of columns |
n |
a sample size |
B |
an integer specifying the number of replicates used in the Monte Carlo test (optional) |
Details
The p-value of the logarithmic minimum test for independence in r x c contingency table, data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABIAAAASCAYAAABWzo5XAAAAWElEQVR42mNgGPTAxsZmJsVqQApgmGw1yApwKcQiT7phRBuCzzCSDSHGMKINIeDNmWQlA2IigKJwIssQkHdINgxfmBBtGDEBS3KCxBc7pMQgMYE5c/AXPwAwSX4lV3pTWwAAAABJRU5ErkJggg==
Value
The function returns the p-value of the logarithmic minimum test.
Author(s)
Piotr Sulewski, piotr.sulewski@apsl.edu.pl, Pomeranian University in Slupsk.
References
Sulewski, P. (2019). The LMS for Testing Independence in Two-way Contingency Tables. Biometrical Letters 56(1), 17-43
Examples
Lms2.pvalue(Lms2.stat(table1), 2, 2, 40, B = 1e3)
Lms2.pvalue(Lms2.stat(table2), 2, 3, 60, B = 1e2)
Logarithmic Minimum Test for Independence in Two-Way Contingency Table
Description
Calculates the logarithmic minimum statistics (see Sulewski P. (2019)).
Usage
Lms2.stat(nij)
Arguments
nij |
a numeric matrix with non-negative values of the two-way contingency table cells |
Details
The statistic of the logarithmic minimum test for independence in r x c contingency table, see formula (4) and example 3 in the article.
Value
The function returns the value of the logarithmic minimum test statistic
Author(s)
Piotr Sulewski, piotr.sulewski@apsl.edu.pl, Pomeranian University in Slupsk.
References
Sulewski, P. (2019). The LMS for Testing Independence in Two-way Contingency Tables. Biometrical Letters 56(1), 17-43
Examples
Lms2.stat(table1)
Lms2.stat(table2)
Logarithmic Minimum Test for Independence in Two-Way Contingency Table
Description
Calculates the test statistic and p-value of the logarithmic minimum test.
Usage
Lms2.test(nij, B = 10000)
Arguments
nij |
a numeric matrix with non-negative values of the two-way contingency table cells |
B |
an integer specifying the number of replicates used in the Monte Carlo test (optional) |
Details
The test statistic and p-value of he logarithmic minimum test for independence in r x c contingency table,
Value
The function returns values of the test statistic and p-value of the logarithmic minimum test.
Author(s)
Piotr Sulewski, piotr.sulewski@apsl.edu.pl, Pomeranian University in Slupsk.
References
Sulewski, P. (2019). The LMS for Testing Independence in Two-way Contingency Tables. Biometrical Letters 56(1), 17-43
Examples
Lms2.test(GenTab2(matrix(1/6, nrow = 2, ncol = 3), 50), B = 1e2)
Lms2.test(table2, B = 1e3)
Logarithmic minimum test for independence in three-way contingency table
Description
Calculates the critical value of the Logarithmic minimum test for independence in three-way contingency table (see Sulewski P. (2018)).
Usage
Lms3.cv(nr, nc, nt, n, alfa, B = 10000)
Arguments
nr |
a number of rows |
nc |
a number of columns |
nt |
a number of tubes |
n |
a sample size |
alfa |
a significance level |
B |
an integer specifying the number of replicates used in the Monte Carlo test (optional) |
Details
The Critical value of the Logarithmic minimum test for independence in r x c x t contingency table,
Value
The function returns the critical value of the logarithmic minimum test.
Author(s)
Piotr Sulewski, piotr.sulewski@apsl.edu.pl, Pomeranian University in Slupsk.
References
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
Examples
Lms3.cv(2, 2, 2, 80, 0.05, B = 1e2)
Lms3.cv(2, 2, 2, 80, 0.1, B = 1e3)
Logarithmic minimum test for independence in three-way contingency table
Description
Calculates the p-value of the Logarithmic minimum test for independence in three-way contingency table
Usage
Lms3.pvalue(stat, nr, nc, nt, n, B = 10000)
Arguments
stat |
a Logarithmic minimum statistic value |
nr |
a number of rows |
nc |
a number of columns |
nt |
a number of tubes |
n |
a sample size |
B |
an integer specifying the number of replicates used in the Monte Carlo test (optional) |
Details
The Critical value of the modular test for independence in r x c x t contingency table,
Value
The function returns the p-value of the logarithmic minimum test.
Author(s)
Piotr Sulewski, piotr.sulewski@apsl.edu.pl, Pomeranian University in Slupsk.
References
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
Examples
tab1 = GenTab3(array(0.125, dim = c(2, 2, 2)), 100)
Lms3.pvalue(Lms3.stat(tab1), 2, 2, 2, 100, B=1e2)
Lms3.pvalue(Lms3.stat(table4), 2, 2, 2, 80, B = 1e3)
Logarithmic minimum test for independence in three-way contingency table
Description
Calculates the statistic of the Logarithmic minimum test for independence in three-way contingency table (see Sulewski P. (2018)).
Usage
Lms3.stat(nijt)
Arguments
nijt |
a numeric matrix with non-negative values of the three-way contingency table cells |
Details
The statistic of Logarithmic minimum test for independence in r x c x t contingency table, see formula (6) in the article.
Value
The function returns the value of the logarithmic minimum test statistic.
Author(s)
Piotr Sulewski, piotr.sulewski@apsl.edu.pl, Pomeranian University in Slupsk.
References
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
Examples
Lms3.stat(table3)
Lms3.stat(GenTab3(array(1/12, dim=c(2,2,3)), 120))
Logarithmic minimum test for independence in three-way contingency table
Description
Calculates the test statistic and p-value of the Logarithmic minimum test for independence in three-way contingency table
Usage
Lms3.test(nijt, B = 10000)
Arguments
nijt |
a numeric matrix with non-negative values of the three-way contingency table cells |
B |
an integer specifying the number of replicates used in the Monte Carlo test (optional) |
Details
The test statistic and p-value of the Logarithmic minimum test for independence in r x c x t contingency table,
Value
The function returns values of the test statistic and p-value of the logarithmic minimum test.
Author(s)
Piotr Sulewski, piotr.sulewski@apsl.edu.pl, Pomeranian University in Slupsk.
References
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
Examples
Lms3.test(GenTab3(array(0.125, dim = c(2, 2, 2)), 80), B = 1e2)
Lms3.test(table4, B = 1e3)
Logarithmic minimum test for independence in four-way contingency table
Description
Calculates the critical value of the Logarithmic minimum test for independence in four-way contingency table
Usage
Lms4.cv(nr, nc, nt, nu, n, alfa, B = 10000)
Arguments
nr |
a number of rows |
nc |
a number of columns |
nt |
a number of tubes |
nu |
a number of tubes |
n |
a sample size |
alfa |
a significance level |
B |
an integer specifying the number of replicates used in the Monte Carlo test (optional) |
Details
The Critical value of the Logarithmic minimum test for independence in r x c x t contingency table,
Value
The function returns the critical value of the logarithmic minimum test.
Author(s)
Piotr Sulewski, piotr.sulewski@apsl.edu.pl, Pomeranian University in Slupsk.
References
Extension of the information contained in 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
Examples
Lms4.cv(2, 2, 2, 2, 160, 0.05, B = 1e2)
Lms4.cv(2, 2, 2, 2, 160, 0.1, B = 1e3)
Logarithmic minimum test for independence in four-way contingency table
Description
Calculates the p-value of the Logarithmic minimum test for independence in four-way contingency table
Usage
Lms4.pvalue(stat, nr, nc, nt, nu, n, B = 10000)
Arguments
stat |
a Logarithmic minimum statistic value |
nr |
a number of rows |
nc |
a number of columns |
nt |
a number of tubes |
nu |
a number of |
n |
a sample size |
B |
an integer specifying the number of replicates used in the Monte Carlo test (optional) |
Details
The Critical value of the modular test for independence in r x c x t x u contingency table,
Value
The function returns the p-value of the logarithmic minimum test.
Author(s)
Piotr Sulewski, piotr.sulewski@apsl.edu.pl, Pomeranian University in Slupsk.
References
Extension of the information contained in 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
Examples
data = GenTab4(array(1/16, dim = c(2, 2, 2, 2)), 160)
Lms4.pvalue(Lms4.stat(data), 2, 2, 2, 2, 160, B=1e3)
Lms4.pvalue(Lms4.stat(table6), 2, 2, 2, 2, 160, B = 1e2)
Logarithmic minimum test for independence in four-way contingency table
Description
Calculates the statistic of the Logarithmic minimum test for independence in four-way contingency table
Usage
Lms4.stat(nijtu)
Arguments
nijtu |
a numeric matrix with non-negative values of the four-way contingency table cells |
Details
The statistic of Logarithmic minimum test for independence in r x c x t x u contingency table,
Value
The function returns the value of the logarithmic minimum test statistic.
Author(s)
Piotr Sulewski, piotr.sulewski@apsl.edu.pl, Pomeranian University in Slupsk.
References
Extension of the information contained in 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
Examples
Lms4.stat(GenTab4(array(1/16, dim = c(2, 2, 2, 2)), 160))
Lms4.stat(table5)
Logarithmic minimum test for independence in four-way contingency table
Description
Calculates the test statistic and p-value of the Logarithmic minimum test for independence in four-way contingency table
Usage
Lms4.test(nijtu, B = 10000)
Arguments
nijtu |
a numeric matrix with non-negative values of the four-way contingency table cells |
B |
an integer specifying the number of replicates used in the Monte Carlo test (optional) |
Details
The test statistic and p-value of the Logarithmic minimum test for independence in r x c x t x u contingency table,
Value
The function returns values of the test statistic and p-value of the logarithmic minimum test.
Author(s)
Piotr Sulewski, piotr.sulewski@apsl.edu.pl, Pomeranian University in Slupsk.
References
Extension of the information contained in 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
Examples
Lms4.test(GenTab4(array(1/16, dim = c(2, 2, 2, 2)), 160), B = 1e2)
Lms4.test(table6, B = 1e3)
Modular test for independence in two-way contingency table
Description
Calculates the critical value of the modular test for independence in two-way contingency table see formula (9) in the article.
Usage
Mod2.cv(nr, nc, n, alfa, B = 10000)
Arguments
nr |
a number of rows |
nc |
a number of columns |
n |
a sample size |
alfa |
a significance level |
B |
an integer specifying the number of replicates used in the Monte Carlo test (optional) |
Details
The Critical value of the modular test for independence in r x c contingency table, see formula (2) in the article.
Value
The function returns the critical value of the modular test.
Author(s)
Piotr Sulewski, piotr.sulewski@apsl.edu.pl, Pomeranian University in Slupsk.
References
Sulewski, P. (2016). Moc testów niezależności w tablicy dwudzielczej większej niż 2×2, Przegląd statystyczny 63(2), 190-210
Examples
Mod2.cv(2, 2, 40, 0.05, B = 1e2)
Mod2.cv(2, 3, 60, 0.1)
Modular test for independence in two-way contingency table
Description
Calculates the p-value of the modular test for independence in two-way contingency table
Usage
Mod2.pvalue(stat, nr, nc, n, B = 10000)
Arguments
stat |
a modular statistic value |
nr |
a number of rows |
nc |
a number of columns |
n |
a sample size |
B |
an integer specifying the number of replicates used in the Monte Carlo test (optional) |
Details
The p-value of the modular test for independence in r x c contingency table,
Value
The function returns the p-value of the modular test.
Author(s)
Piotr Sulewski, piotr.sulewski@apsl.edu.pl, Pomeranian University in Slupsk.
References
Sulewski, P. (2016). Moc testów niezależności w tablicy dwudzielczej większej niż 2×2, Przegląd statystyczny 63(2), 190-210
Examples
pij=matrix(1/4, nrow = 2, ncol = 2)
tab4=GenTab2(pij, 30)
Mod2.pvalue(Mod2.stat(tab4), 2, 2, 30, B=1e3)
Mod2.pvalue(2.5, 3, 2, 60)
Modular test for independence in two-way contingency table
Description
Calculates the statistic of the modular test for independence in two-way contingency table (see Sulewski P. (2016)).
Usage
Mod2.stat(nij)
Arguments
nij |
a numeric matrix with non-negative values of the two-way contingency table cells |
Details
The statistic of the modular test for independence in r x c contingency table, see formula (2) in the article.
Value
The function returns the value of the modular test statistic.
Author(s)
Piotr Sulewski, piotr.sulewski@apsl.edu.pl, Pomeranian University in Slupsk.
References
Sulewski, P. (2016). Moc testów niezależności w tablicy dwudzielczej większej niż 2×2, Przegląd statystyczny 63(2), 190-210
Examples
tab5=GenTab2(matrix(1/12, nrow = 3, ncol = 4), 60)
Mod2.stat(tab5)
Mod2.stat(table1)
Modular test for independence in two-way contingency table
Description
Calculates the test statistic and p-value of the modular test for independence in two-way contingency table
Usage
Mod2.test(nij, B = 10000)
Arguments
nij |
a numeric matrix with non-negative values of the two-way contingency table cells |
B |
an integer specifying the number of replicates used in the Monte Carlo test (optional) |
Details
The test statistic and p-value of the modular test for independence in r x c contingency table,
Value
The function returns values of the test statistic and p-value of the modular test.
Author(s)
Piotr Sulewski, piotr.sulewski@apsl.edu.pl, Pomeranian University in Slupsk.
References
Sulewski, P. (2016). Moc testów niezależności w tablicy dwudzielczej większej niż 2×2, Przegląd statystyczny 63(2), 190-210
Examples
pij=matrix(1/4, nrow = 2, ncol = 2)
Mod2.test(GenTab2(pij, 50), B = 1e3)
Mod2.test(table1, B = 1e2)
Modular test for independence in three-way contingency table
Description
Calculates the critical value of the modular test for independence in three-way contingency table (see Sulewski P. (2018)).
Usage
Mod3.cv(nr, nc, nt, n, alfa, B = 10000)
Arguments
nr |
a number of rows |
nc |
a number of columns |
nt |
a number of tubes |
n |
a sample size |
alfa |
a significance level |
B |
an integer specifying the number of replicates used in the Monte Carlo test (optional) |
Details
The Critical value of the modular test for independence in r x c x t contingency table,
Value
The function returns the critical value of the modular test.
Author(s)
Piotr Sulewski, piotr.sulewski@apsl.edu.pl, Pomeranian University in Slupsk.
References
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
Examples
Mod3.cv(2, 2, 2, 80, 0.05, B = 1e2)
Mod3.cv(2, 2, 2, 80, 0.1, B = 1e3)
Modular test for independence in three-way contingency table
Description
Calculates the p-value of the modular test for independence in three-way contingency table
Usage
Mod3.pvalue(stat, nr, nc, nt, n, B = 10000)
Arguments
stat |
a modular statistic value |
nr |
a number of rows |
nc |
a number of columns |
nt |
a number of tubes |
n |
a sample size |
B |
an integer specifying the number of replicates used in the Monte Carlo test (optional) |
Details
The Critical value of the modular test for independence in r x c x t contingency table,
Value
The function returns the p-value of the modular test.
Author(s)
Piotr Sulewski, piotr.sulewski@apsl.edu.pl, Pomeranian University in Slupsk.
References
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
Examples
data = GenTab3(array(0.125, dim = c(2, 2, 2)), 80)
Mod3.pvalue(Mod3.stat(data), 2, 2, 2, 80, B = 1e2)
Mod3.pvalue(Mod3.stat(table4), 2, 2, 2, 80, B = 1e3)
Modular test for independence in three-way contingency table
Description
Calculates the statistic of the modular test for independence in three-way contingency table (see Sulewski P. (2018)).
Usage
Mod3.stat(nijt)
Arguments
nijt |
a numeric matrix with non-negative values of the three-way contingency table cells |
Details
The statistic of the modular test for independence in r x c x t contingency table, see formula (6) in the article.
Value
The function returns the value of the modular test statistic.
Author(s)
Piotr Sulewski, piotr.sulewski@apsl.edu.pl, Pomeranian University in Slupsk.
References
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
Examples
Mod3.stat(GenTab3(array(0.125, dim = c(2, 2, 2)), 100))
Mod3.stat(table4)
Modular test for independence in three-way contingency table
Description
Calculates the test statistic and p-value of the modular test for independence in three-way contingency table
Usage
Mod3.test(nijt, B = 10000)
Arguments
nijt |
a numeric matrix with non-negative values of the three-way contingency table cells |
B |
an integer specifying the number of replicates used in the Monte Carlo test (optional) |
Details
The test statistic and p-value of the modular test for independence in r x c x t contingency table,
Value
The function returns values of the test statistic and p-value of the modular test.
Author(s)
Piotr Sulewski, piotr.sulewski@apsl.edu.pl, Pomeranian University in Slupsk.
References
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
Examples
Mod3.test(GenTab3(array(0.125, dim = c(2, 2, 2)), 80), B = 1e3)
Mod3.test(table4, B = 1e3)
Modular test for independence in four-way contingency table
Description
Calculates the critical value of the modular test for independence in four-way contingency table
Usage
Mod4.cv(nr, nc, nt, nu, n, alfa, B = 10000)
Arguments
nr |
a number of rows |
nc |
a number of columns |
nt |
a number of tubes |
nu |
a number of tubes |
n |
a sample size |
alfa |
a significance level |
B |
an integer specifying the number of replicates used in the Monte Carlo test (optional) |
Details
The Critical value of the Logarithmic minimum test for independence in r x c x t contingency table,
Value
The function returns the critical value of the modular test.
Author(s)
Piotr Sulewski, piotr.sulewski@apsl.edu.pl, Pomeranian University in Slupsk.
References
Extension of the information contained in 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
Examples
Mod4.cv(2, 2, 2, 2, 160, 0.05, B = 1e2)
Mod4.cv(2, 2, 2, 2, 160, 0.1, B = 1e3)
MOdular test for independence in four-way contingency table
Description
Calculates the p-value of the modular test for independence in four-way contingency table
Usage
Mod4.pvalue(stat, nr, nc, nt, nu, n, B = 10000)
Arguments
stat |
a Logarithmic minimum statistic value |
nr |
a number of rows |
nc |
a number of columns |
nt |
a number of tubes |
nu |
a number of |
n |
a sample size |
B |
an integer specifying the number of replicates used in the Monte Carlo test (optional) |
Details
The Critical value of the modular test for independence in r x c x t x u contingency table,
Value
The function returns the p-value of the modular test.
Author(s)
Piotr Sulewski, piotr.sulewski@apsl.edu.pl, Pomeranian University in Slupsk.
References
Extension of the information contained in 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
Examples
Mod4.pvalue(Mod4.stat(table6), 2, 2, 2, 2, 160, B = 1e2)
Mod4.pvalue(Mod4.stat(table6), 2, 2, 2, 2, 160, B = 1e3)
Modular test for independence in four-way contingency table
Description
Calculates the statistic of the modular test for independence in four-way contingency table
Usage
Mod4.stat(nijtu)
Arguments
nijtu |
a numeric matrix with non-negative values of the four-way contingency table cells |
Details
The statistic of Logarithmic minimum test for independence in r x c x t x u contingency table,
Value
The function returns the value of the modular test statistic.
Author(s)
Piotr Sulewski, piotr.sulewski@apsl.edu.pl, Pomeranian University in Slupsk.
References
Extension of the information contained in 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
Examples
Mod4.stat(GenTab4(array(1/16, dim = c(2, 2, 2, 2)), 100))
Mod4.stat(table6)
Modular test for independence in four-way contingency table
Description
Calculates the test statistic and p-value of the modular test for independence in four-way contingency table
Usage
Mod4.test(nijtu, B = 10000)
Arguments
nijtu |
a numeric matrix with non-negative values of the four-way contingency table cells |
B |
an integer specifying the number of replicates used in the Monte Carlo test (optional) |
Details
The test statistic and p-value of the modular test for independence in r x c x t x u contingency table,
Value
The function returns values of the test statistic and p-value of the modular test.
Author(s)
Piotr Sulewski, piotr.sulewski@apsl.edu.pl, Pomeranian University in Slupsk.
References
Extension of the information contained in 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
Examples
Mod4.test(GenTab4(array(1/16, dim = c(2, 2, 2, 2)), 160), B = 1e2)
Mod4.test(table6, B = 1e2)
First data set as two-way contingency table 2 x 2
Description
The first data set from Sulewski, P. (2017) A new test for independence in 2x2 contingency tables, Acta Universitatis Lodziensis. Folia Oeconomica, 4(330), 55–75 consist of 40 observations described the effect of a treatment for rheumatoid arthritis vs. a placebo. See Table 17 in the paper.
Usage
table1
Format
two-way contingency table 2 x 2
Second data set as two-way contingency table 2 x 3
Description
The second data set obtained using the Monte Carlo method consist of 60 observations when Ho is true, i.e. all probabilities equal 1/6
Usage
table2
Format
two-way contingency table 2 x 3
Third data set: three-way contingency table 3 x 3 x 2
Description
The third data set from 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 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. See Table 10 in the paper.
Usage
table3
Format
three-way contingency table 3 x 3 x 2
Fourth data set: three-way contingency table 2 x 2 x 2
Description
The fourth data set obtained using the Monte Carlo method consist of 80 observations when Ho is true, i.e. all probabilities equal 1/8.
Usage
table4
Format
three-way contingency table 2 x 2 x 2
Fifth data set: four-way contingency table 4 x 2 x 2 x 2
Description
The fifth data set provides information on the fate of 2201 passengers on the fatal maiden voyage of the ocean liner ‘Titanic’, summarized according to economic status (class), sex, age and survival.
Usage
table5
Format
four-way contingency table 4 x 2 x 2 x 2
Sixth data set: four-way contingency table 2 x 2 x 2 x 2
Description
The sixth data set obtained using the Monte Carlo method consist of 160 observations when Ho is true, i.e. all probabilities equal 1/16.
Usage
table6
Format
four-way contingency table 2 x 2 x 2 x 2