---
title: "PSIndependenceTest"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{PSIndependenceTest}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
```
# PSIndependenceTest: Independence Tests for Two-Way, Three-Way and Four-Way Contingency Tables
**author: Piotr Sulewski, Pomeranian University**
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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.

## Installation

You can install the released version of **PSIndependenceTest** from CRAN with:

``` r
install.packages("PSIndependenceTest")
```

You can install the development version of **PSIndependenceTest** from [GitHub](https://github.com/) with:

```r
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. 
  
  
```{r}
library(PSIndependenceTest)
dim(table1)
length(table2)
```

### Functions
  
**GenTab2**
  
This function generating the two-way contingency table with the Monte Carlo method

```{r}
GenTab2(matrix(1/8, nrow = 2, ncol = 4), 50)
GenTab2(matrix(1/12, nrow = 4, ncol = 3), 60)
``` 
  
  
**Mod2.stat**
  
This function returns the statistic value of the modular independence test in the two-way contingency table.

```{r}
Mod2.stat(table1)
Mod2.stat(GenTab2(matrix(1/9, nrow = 3, ncol = 3), 90))
```

**Mod2.cv**
  
This function returns the critical value of the modular independence test in the two-way contingency table.

```{r}
Mod2.cv(2, 2, 40, 0.05, B = 1e3) 
Mod2.cv(2, 3, 60, 0.1) 
```

**Mod2.pvalue**

This function returns the p-value of the modular independence test in the two-way contingency table.

```{r}
Mod2.pvalue(Mod2.stat(table1), 2, 2, 40, B = 1e3)
Mod2.pvalue(Mod2.stat(table2), 2, 3, 60)
```

**Mod2.test**

This function returns the test statistic and p-value of the logarithmic minimum independence test in the two-way contingency table.

```{r}
Mod2.test(table1, B = 1e3)
Mod2.test(table2)
```

**Lms2.stat**
  
This function returns the statistic value of the logarithmic minimum independence test in the two-way contingency table.

```{r}
Lms2.stat(table1)
Lms2.stat(GenTab2(matrix(1/9, nrow = 3, ncol = 3), 90))
```

**Lms2.cv**
  
This function returns the critical value of the logarithmic minimum independence test in the two-way contingency table.

```{r}
Lms2.cv(2, 2, 40, 0.05, B = 1e3) 
Lms2.cv(2, 3, 60, 0.1)  
```

**Lms2.pvalue**

This function returns the p-value of the logarithmic minimum independence test in the two-way contingency table.

```{r}
Lms2.pvalue(Lms2.stat(table1), 2, 2, 40, B = 1e3)
Lms2.pvalue(Lms2.stat(table2), 2, 3, 60)
```

**Lms2.test**

This function returns the test statistic and p-value of the logarithmic minimum independence test in the two-way contingency table.

```{r}
Lms2.test(table1, B = 1e3)
Lms2.test(table2)
```

**GenTab3**
  
This function generating the three-way contingency table with the Monte Carlo method

```{r}
GenTab3(array(1/12, dim=c(2,2,3)), 60)
GenTab3(array(1/18, dim=c(2,3,3)), 80)
``` 

**Mod3.stat**
  
This function returns the statistic value of the modular independence test in the three-way contingency table.

```{r}
Mod3.stat(table3)
Mod3.stat(GenTab3(array(1/12, dim=c(2,2,3)), 120))
```

**Mod3.cv**
  
This function returns the critical value of the modular independence test in the three-way contingency table.

```{r}
Mod3.cv(2, 2, 2, 80, 0.05, B = 1e3) 
Mod3.cv(2, 2, 2, 80, 0.1) 
```

**Mod3.pvalue**

This function returns the p-value of the modular independence test in the three-way contingency table.

```{r}
Mod3.pvalue(Mod3.stat(table4), 2, 2, 2, 80, B = 1e3)
Mod3.pvalue(Mod3.stat(table4), 2, 2, 2, 80)
```

**Mod3.test**

This function returns the test statistic and p-value of the modular independence test in the three-way contingency table.

```{r}
Mod3.test(table4, B = 1e2)
Mod3.test(table4, B = 1e3)
```

**Lms3.stat**
  
This function returns the statistic value of the logarithmic minimum independence test in the three-way contingency table.


```{r}
Lms3.stat(table3)
Lms3.stat(GenTab3(array(1/12, dim=c(2,2,3)), 120))
```

**Lms3.cv**
  
This function returns the critical value of the logarithmic minimum independence test in the three-way contingency table.

```{r}
Lms3.cv(2, 2, 2, 80, 0.05, B = 1e2) 
Lms3.cv(2, 2, 2, 80, 0.1, B = 1e3) 
```

**Lms3.pvalue**

This function returns the p-value of the logarithmic minimum independence test in the three-way contingency table.


```{r}
Lms3.pvalue(Lms3.stat(table4), 2, 2, 2, 80, B = 1e3)
Lms3.pvalue(Lms3.stat(table4), 2, 2, 2, 80)
```

**Lms3.test**

This function returns the test statistic and p-value of the logarithmic minimum independence test in the three-way contingency table.

```{r}
Lms3.test(table4, B = 1e2)
Lms3.test(table4, B = 1e3)
```

**GenTab4**
  
This function generating the four-way contingency table with the Monte Carlo method.

```{r}
GenTab4(array(1/16, dim=c(2,2,2,2)), 100)
GenTab4(array(1/36, dim=c(2,3,2,3)), 150)
``` 

**Mod4.stat**
  
This function returns the statistic value of the modular independence test in the four-way contingency table.

```{r}
Mod4.stat(table5)
Mod4.stat(table6)
```

**Mod4.cv**
  
This function returns the critical value of the modular independence test in the four-way contingency table.

```{r}
Mod4.cv(2, 2, 2, 2, 160, 0.05, B = 1e2)
Mod4.cv(2, 2, 2, 2, 160, 0.1, B = 1e3)
```

**Mod4.pvalue**

This function returns the p-value of the modular independence test in the four-way contingency table.

```{r}
Mod4.pvalue(Mod4.stat(table6), 2, 2, 2, 2, 160, B = 1e2)
Mod4.pvalue(Mod4.stat(table6), 2, 2, 2, 2, 160, B = 1e3)
```

**Mod4.test**

This function returns the test statistic and p-value of the modular independence test in the -way contingency table.

```{r}
Mod4.test(table6, B = 1e2)
Mod4.test(table6, B = 1e3)
```

**Lms4.stat**
  
This function returns the statistic value of the logarithmic minimum independence test in the four-way contingency table.

```{r}
Lms4.stat(table5)
Lms4.stat(table6)
```

**Lms4.cv**
  
This function returns the critical value of the logarithmic minimum independence test in the four-way contingency table.

```{r}
Lms4.cv(2, 2, 2, 2, 160, 0.05, B = 1e2)
Lms4.cv(2, 2, 2, 2, 160, 0.1, B = 1e3)
```

**Lms4.pvalue**

This function returns the p-value of the logarithmic minimum independence test in the four-way contingency table.

```{r}
Lms4.pvalue(Lms4.stat(table6), 2, 2, 2, 2, 160, B = 1e2)
Lms4.pvalue(Lms4.stat(table6), 2, 2, 2, 2, 160, B = 1e3)
```

**Lms4.test**

This function returns the test statistic and p-value of the logarithmic minimum independence test in the four-way contingency table.

```{r}
Lms4.test(table6, B = 1e2)
Lms4.test(table6, B = 1e3)
```
