gginference

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Visualise the Results of Inferential Statistics using 'ggplot2'

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README
================

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# Overview

Visualise the results of F test to compare two variances, Student’s
t-test, test of equal or given proportions, Pearson’s chi-squared test
for count data and test for association/correlation between paired
samples.

# Installation

``` r
# CRAN installation:
install.packages("gginference")

# Or the development version from GitHub:
# install.packages("devtools")
devtools::install_github("okgreece/gginference")
```

# Usage

## One sample

### One sample t-test with normal population and σ2 unknown

The rejection regions for one sample t-test with normal population and
σ2 unknown are calculated using `ggttest` function. The
following table shows the rejection regions which is calculated with
**gginference** depending the specified parameters in `t.test`.

<table>
<colgroup>
<col style="width: 10%" />
<col style="width: 13%" />
<col style="width: 30%" />
<col style="width: 45%" />
</colgroup>
<thead>
<tr class="header">
<th>H0</th>
<th>H1</th>
<th>Rejection Region of gginference</th>
<th>Parameters of <code>t.test</code></th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td>μ = μ0</td>
<td>μ &lt; μ0</td>
<td>R = {z &lt;  − za}</td>
<td><ul>
<li>x = vector of sample data,</li>
<li>mu = μ0,</li>
<li>alternative = “less”</li>
</ul></td>
</tr>
<tr class="even">
<td></td>
<td>μ &gt; μ0</td>
<td>R = {z &gt; za}</td>
<td><ul>
<li>x = vector of sample data,</li>
<li>mu = μ0,</li>
<li>alternative = “greater”</li>
</ul></td>
</tr>
<tr class="odd">
<td></td>
<td>μ ≠ μ0</td>
<td>R = {|z| &gt; za/2}</td>
<td><ul>
<li>x = vector of sample data,</li>
<li>mu = μ0,</li>
<li>alternative = “two.sided”</li>
</ul></td>
</tr>
</tbody>
</table>

where

![](https://raw.githubusercontent.com/okgreece/gginference/master/readme_formula/1_One_sample_t-test_large.png)

### One sample t-test with normal population and n \< 30 and σ2 unknown

`ggttest` is also used to calculate rejection region for one sample
t-test with normal population and n \< 30 and σ2 unknown.

<table>
<colgroup>
<col style="width: 10%" />
<col style="width: 13%" />
<col style="width: 30%" />
<col style="width: 45%" />
</colgroup>
<thead>
<tr class="header">
<th>H0</th>
<th>H1</th>
<th>Rejection Region of gginference</th>
<th>Parameters of <code>t.test</code></th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td>μ = μ0</td>
<td>μ &lt; μ0</td>
<td>R = {t &lt;  − tn − 1, a}</td>
<td><ul>
<li>x = vector of sample data,</li>
<li>mu = μ0,</li>
<li>alternative = “less”</li>
</ul></td>
</tr>
<tr class="even">
<td></td>
<td>μ &gt; μ0</td>
<td>R = {t &gt; tn − 1, a}</td>
<td><ul>
<li>x = vector of sample data,</li>
<li>mu = μ0,</li>
<li>alternative = “greater”</li>
</ul></td>
</tr>
<tr class="odd">
<td></td>
<td>μ ≠ μ0</td>
<td>R = {|t| &gt; tn − 1, a/2}</td>
<td><ul>
<li>x = vector of sample data,</li>
<li>mu = μ0,</li>
<li>alternative = “two.sided”</li>
</ul></td>
</tr>
</tbody>
</table>

where

![](https://raw.githubusercontent.com/okgreece/gginference/master/readme_formula/2_One_sample_t-test_small.png)

## Two samples

### Two independent samples t-test with normal populations and σ12 = σ22 unknown

Next table shows the rejection regions of two independent samples t-test
with normal populations and σ12 =
σ22. `ggttest` is also used to visualize this
test.

<table>
<colgroup>
<col style="width: 15%" />
<col style="width: 17%" />
<col style="width: 26%" />
<col style="width: 40%" />
</colgroup>
<thead>
<tr class="header">
<th>H0</th>
<th>H1</th>
<th>Rejection Region of gginference</th>
<th>Parameters of <code>t.test</code></th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td>μ1 − μ2 = d0</td>
<td>μ1 − μ2 &lt; d0</td>
<td>R = {t &lt;  − tn1 + n2 − 2, a}</td>
<td><ul>
<li>x = vector of sample 1 data,</li>
<li>y = vector of sample 2 data,</li>
<li>paired = FALSE,</li>
<li>var.equal = TRUE,</li>
<li>alternative = “less”</li>
</ul></td>
</tr>
<tr class="even">
<td></td>
<td>μ1 − μ2 &gt; d0</td>
<td>R = {t &gt; tn1 + n2 − 2, a}</td>
<td><ul>
<li>x = vector of sample 1 data,</li>
<li>y = vector of sample 2 data,</li>
<li>paired = FALSE,</li>
<li>var.equal = TRUE,</li>
<li>alternative = “greater”</li>
</ul></td>
</tr>
<tr class="odd">
<td></td>
<td>μ1 − μ2 ≠ d0</td>
<td>R = {|t| &gt; tn1 + n2 − 2, a/2}</td>
<td><ul>
<li>x = vector of sample 1 data,</li>
<li>y = vector of sample 2 data,</li>
<li>paired = FALSE,</li>
<li>var.equal = TRUE,</li>
<li>alternative = “two.sided”</li>
</ul></td>
</tr>
</tbody>
</table>

where

![](https://raw.githubusercontent.com/okgreece/gginference/master/readme_formula/3_Two_samples_t-test_equal_var.png)

### Two independent samples t-test with normal populations and σ12 ![](https://raw.githubusercontent.com/okgreece/gginference/master/readme_formula/uneq.png) σ22

`ggttest` is used to visualize two independent samples t-test with
normal populations and σ12
![](https://raw.githubusercontent.com/okgreece/gginference/master/readme_formula/uneq.png) σ22. The following
table shows the rejection regions of this test.

<table>
<colgroup>
<col style="width: 15%" />
<col style="width: 17%" />
<col style="width: 26%" />
<col style="width: 40%" />
</colgroup>
<thead>
<tr class="header">
<th>H0</th>
<th>H1</th>
<th>Rejection Region of gginference</th>
<th>Parameters of <code>t.test</code></th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td>μ1 − μ2 = d0</td>
<td>μ1 − μ2 &lt; d0</td>
<td>R = {t &lt;  − tν, a}</td>
<td><ul>
<li>x = vector of sample 1 data,</li>
<li>y = vector of sample 2 data,</li>
<li>paired = FALSE,</li>
<li>var.equal = FALSE,</li>
<li>alternative = “less”</li>
</ul></td>
</tr>
<tr class="even">
<td></td>
<td>μ1 − μ2 &gt; d0</td>
<td>R = {t &gt; tν, a}</td>
<td><ul>
<li>x = vector of sample 1 data,</li>
<li>y = vector of sample 2 data,</li>
<li>paired = FALSE,</li>
<li>var.equal = FALSE,</li>
<li>alternative = “greater”</li>
</ul></td>
</tr>
<tr class="odd">
<td></td>
<td>μ1 − μ2 ≠ d0</td>
<td>R = {|t| &gt; tν, a/2}</td>
<td><ul>
<li>x = vector of sample 1 data,</li>
<li>y = vector of sample 2 data,</li>
<li>paired = FALSE,</li>
<li>var.equal = FALSE,</li>
<li>alternative = “two.sided”</li>
</ul></td>
</tr>
</tbody>
</table>

where

![](https://raw.githubusercontent.com/okgreece/gginference/master/readme_formula/4_Two_samples_t-test_unequal_var.png)

and ν degrees of freedom with

![](https://raw.githubusercontent.com/okgreece/gginference/master/readme_formula/4b_Two_samples_t-test_unequal_var_deg_freed.png)

## Paired samples with normal population

`ggttest` is used also to visualize the results of the paired sample
Student’s t-test. Next table shows th rejection region of this test.

<table>
<colgroup>
<col style="width: 14%" />
<col style="width: 17%" />
<col style="width: 27%" />
<col style="width: 40%" />
</colgroup>
<thead>
<tr class="header">
<th>H0</th>
<th>H1</th>
<th>Rejection Region of gginference</th>
<th>Parameters of <code>t.test</code></th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td>μ1 − μ2 = d0</td>
<td>μ1 − μ2 &lt; d0</td>
<td>R = {t &lt;  − tn − 1, a}</td>
<td><ul>
<li>x = vector of sample 1 data,</li>
<li>y = vector of sample 2 data,</li>
<li>paired = FALSE,</li>
<li>var.equal = FALSE,</li>
<li>alternative = “less”</li>
</ul></td>
</tr>
<tr class="even">
<td></td>
<td>μ1 − μ2 &gt; d0</td>
<td>R = {t &gt; tn − 1, a}</td>
<td><ul>
<li>x = vector of sample 1 data,</li>
<li>y = vector of sample 2 data,</li>
<li>paired = FALSE,</li>
<li>var.equal = FALSE,</li>
<li>alternative = “greater”</li>
</ul></td>
</tr>
<tr class="odd">
<td></td>
<td>μ1 − μ2 ≠ d0</td>
<td>R = {|t| &gt; tn − 1, a/2}</td>
<td><ul>
<li>x = vector of sample 1 data,</li>
<li>y = vector of sample 2 data,</li>
<li>paired = FALSE,</li>
<li>var.equal = FALSE,</li>
<li>alternative = “two.sided”</li>
</ul></td>
</tr>
</tbody>
</table>

where

![](https://raw.githubusercontent.com/okgreece/gginference/master/readme_formula/5a_Paired%20samples.png)

![](https://raw.githubusercontent.com/okgreece/gginference/master/readme_formula/5b_Paired%20samples.png)

![](https://raw.githubusercontent.com/okgreece/gginference/master/readme_formula/5c_Paired%20samples.png)

## Proportion test

### One-proportion z-test

`ggproptest()` is used to visualize one-proportion z-test. The rejection
regions are shown below.

<table>
<colgroup>
<col style="width: 10%" />
<col style="width: 13%" />
<col style="width: 30%" />
<col style="width: 45%" />
</colgroup>
<thead>
<tr class="header">
<th>H0</th>
<th>H1</th>
<th>Rejection Region of gginference</th>
<th>Parameters of <code>prop.test()</code></th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td>p = p0</td>
<td>p &lt; p0</td>
<td>R = {z &lt;  − za}</td>
<td><ul>
<li>x = vector of sample data,</li>
<li>mu = μ0,</li>
<li>alternative = “less”</li>
</ul></td>
</tr>
<tr class="even">
<td></td>
<td>p &gt; p0</td>
<td>R = {z &gt; za}</td>
<td><ul>
<li>x = vector of sample data,</li>
<li>mu = μ0,</li>
<li>alternative = “greater”</li>
</ul></td>
</tr>
<tr class="odd">
<td></td>
<td>p ≠ p0</td>
<td>R = {|z| &gt; za/2}</td>
<td><ul>
<li>x = vector of sample data,</li>
<li>mu = μ0,</li>
<li>alternative = “two.sided”</li>
</ul></td>
</tr>
</tbody>
</table>

where

![](https://raw.githubusercontent.com/okgreece/gginference/master/readme_formula/6a_one_proportion.png)

![](https://raw.githubusercontent.com/okgreece/gginference/master/readme_formula/6b_one_proportion.png)

### Two-proportion z-test

The results of two-proportion z-test are visualized using `ggproptest()`
and next table shows the rejection regions.

<table>
<colgroup>
<col style="width: 14%" />
<col style="width: 17%" />
<col style="width: 27%" />
<col style="width: 41%" />
</colgroup>
<thead>
<tr class="header">
<th>H0</th>
<th>H1</th>
<th>Rejection Region of gginference</th>
<th>Parameters of <code>prop.test()</code></th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td>p1 − p2 = d0</td>
<td>p1 − p2 &lt; d0</td>
<td>R = {z &lt;  − za}</td>
<td><ul>
<li>x = vector of sample 1 data,</li>
<li>y = vector of sample 2 data,</li>
<li>paired = FALSE,</li>
<li>var.equal = FALSE,</li>
<li>alternative = “less”</li>
</ul></td>
</tr>
<tr class="even">
<td></td>
<td>p1 − p2 &gt; d0</td>
<td>R = {z &gt; za}</td>
<td><ul>
<li>x = vector of sample 1 data,</li>
<li>y = vector of sample 2 data,</li>
<li>paired = FALSE,</li>
<li>var.equal = FALSE,</li>
<li>alternative = “greater”</li>
</ul></td>
</tr>
<tr class="odd">
<td></td>
<td>p1 − p2 ≠ d0</td>
<td>R = {|z| &gt; za/2}</td>
<td><ul>
<li>x = vector of sample 1 data,</li>
<li>y = vector of sample 2 data,</li>
<li>paired = FALSE,</li>
<li>var.equal = FALSE,</li>
<li>alternative = “two.sided”</li>
</ul></td>
</tr>
</tbody>
</table>

where

![](https://raw.githubusercontent.com/okgreece/gginference/master/readme_formula/7a_two_proportions.png)

![](https://raw.githubusercontent.com/okgreece/gginference/master/readme_formula/7b_two_proportions.png)

![](https://raw.githubusercontent.com/okgreece/gginference/master/readme_formula/7c_two_proportions.png)

![](https://raw.githubusercontent.com/okgreece/gginference/master/readme_formula/7d_two_proportions.png)

## Two-sample F test for equality of variances

`ggvartest` is used to visualize the results of the paired sample
Student’s t-test. The rejection region that is used in this test is
shown below.

<table>
<colgroup>
<col style="width: 21%" />
<col style="width: 23%" />
<col style="width: 22%" />
<col style="width: 32%" />
</colgroup>
<thead>
<tr class="header">
<th>H0</th>
<th>H1</th>
<th>Rejection Region of gginference</th>
<th>Parameters of <code>var.test</code></th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td>σ12 / σ22 = 1</td>
<td>σ12 / σ22 &lt; 1</td>
<td>R = {F &gt; Fn1 − 1, n2 − 1, 1 − a}</td>
<td><ul>
<li>x = vector of sample 1 data,</li>
<li>y = vector of sample 2 data,</li>
<li>ratio = 1</li>
<li>alternative = “less”</li>
</ul></td>
</tr>
<tr class="even">
<td></td>
<td>σ12 / σ22 &gt; 1</td>
<td>R = {F &gt; Fn1 − 1, n2 − 1, a}</td>
<td><ul>
<li>x = vector of sample data,</li>
<li>mu = μ0,</li>
<li>ratio = 1</li>
<li>alternative = “greater”</li>
</ul></td>
</tr>
<tr class="odd">
<td></td>
<td>σ12 / σ22 ≠ 1</td>
<td>R = {F &gt; Fn1 − 1, n2 − 1, a/2}</td>
<td><ul>
<li>x = vector of sample data,</li>
<li>mu = μ0,</li>
<li>ratio = 1</li>
<li>alternative = “two.sided”</li>
</ul></td>
</tr>
</tbody>
</table>

where

![](https://raw.githubusercontent.com/okgreece/gginference/master/readme_formula/8_test_cor.png)

## Test for Correlation Between Paired Samples

`ggcortest` is usesd to visualize the results of test for correlation
between paired samples. The following table shows the rejection region
of this test.

<table>
<colgroup>
<col style="width: 15%" />
<col style="width: 24%" />
<col style="width: 23%" />
<col style="width: 35%" />
</colgroup>
<thead>
<tr class="header">
<th>H0</th>
<th>H1</th>
<th>Rejection Region of gginference</th>
<th>Parameters of <code>cor.test</code></th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td>𝜚 = 0</td>
<td>𝜚 ≠ 0</td>
<td>R = {|t| &gt; tn − 2, a/2}</td>
<td><ul>
<li>x = vector of sample 1 data</li>
<li>y = vector of sample 2 data,</li>
<li>alternative = “two.sided”</li>
</ul></td>
</tr>
</tbody>
</table>

where

![](https://raw.githubusercontent.com/okgreece/gginference/master/readme_formula/8_test_cor.png)

## Chi-squared Test of Independence

The results of Pearson’s chi-squared test for count data are visulized
using `ggchisqtest`. Next table shows the rejection region of this test.

<table>
<colgroup>
<col style="width: 20%" />
<col style="width: 26%" />
<col style="width: 25%" />
<col style="width: 27%" />
</colgroup>
<thead>
<tr class="header">
<th>H0</th>
<th>H1</th>
<th>Rejection Region of gginference</th>
<th>Parameters of <code>chisq.test</code></th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td>Two variables are independent</td>
<td>Two variables are not independent</td>
<td>R = {X2 &gt; χa/22}</td>
<td><ul>
<li>x = 2-dimensional contingency table</li>
</ul></td>
</tr>
</tbody>
</table>

where

![](https://raw.githubusercontent.com/okgreece/gginference/master/readme_formula/9_chisq.png)

## ANOVA F-test

`ggaov` is used to visualize the results of ANOVA F-test. Table below
shows rejection region of Anova F-stest.

<table>
<colgroup>
<col style="width: 16%" />
<col style="width: 17%" />
<col style="width: 24%" />
<col style="width: 42%" />
</colgroup>
<thead>
<tr class="header">
<th>H0</th>
<th>H1</th>
<th>Rejection Region of gginference</th>
<th>Parameters of <code>aov</code></th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td>H0 : μ1 = μ2= ... = μk</td>
<td>Not all three population means are equal</td>
<td>R = {F &gt; Fk − 1, n − k, a}</td>
<td><ul>
<li>formula = formula specifying the model</li>
<li>data = data frame with the variables specified in the formula</li>
</ul></td>
</tr>
</tbody>
</table>

where

![](https://raw.githubusercontent.com/okgreece/gginference/master/readme_formula/10_anova.png)

# Getting help

If you encounter a bug, please feel free to open an
[issue](https://github.com/okgreece/gginference/issues) with a minimal
reproducible example.

gginference

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