---
title: "Plot for distribution of common statistics and p-value"
author: "Keon-Woong Moon"
date: "`r Sys.Date()`"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{plot.htest}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE,comment = NA,fig.width=6,fig.height = 5, fig.align='center',out.width="90%")
```

To understand the concept of p value is very important. To teach the the distribution of common statistic( $\chi^2$ for chisq.test() , t for Student's t-test , F for F-test) and concept of the p-value, plot.htest() function can be used.

## Package Installation

You can install this package form the github. Currently, package `webr` is under construction and consists of only one function - plot.htest().   

```{r,eval=FALSE}
#install.packages("devtools")
devtools::install_github("cardiomoon/webr")
```

## Coverage of plot.htest() 

The plot.htest() function is a S3 method for class "htest". Currently, this function covers Welch Two Sample t-test, Pearson's Chi-squared test, Two Sample t-test, One Sample t-test, Paired t-test and F test to compare two variances.
 

## For Chi-squared Test

You can show the distribution of chi-squre statistic and p-value. 

```{r,message=FALSE}
 require(moonBook)
 require(webr)
 
 # chi-squared test
 x=chisq.test(table(acs$sex,acs$DM))
 x
 plot(x)
```

## For one sample t-test

You can show the distribution of t-statistic and p-value in one sample t-test.

```{r}
t.test(acs$age,mu=63)

plot(t.test(acs$age,mu=63))
```
 
## Student t-test to compare means for two independent samples

Before performing a t-test, you have to compare two variances.

### F test to compare two variances


```{r}
x=var.test(age~DM,data=acs)
x
plot(x)
``` 

### Use for Two Sample t-test for independence samples 

Based on the result of var.test(), you can perform t.test with default option(var.equal=FALSE).
```{r}
x=t.test(age~DM,data=acs)
x
plot(x)
```

## Student t-test using pooled variance

To compare means of body-mass index between male and female patients, perform F test first.
 
```{r}
var.test(BMI~sex,data=acs)
plot(var.test(BMI~sex,data=acs))
```
Based on the result of F test, you can perform t-test using pooled variance.

```{r}
x=t.test(BMI~sex,data=acs,var.equal=TRUE)
x
plot(x)
```


## Paired t-test

You can show the distribution of t-statistic and p-value in paired t-test.

```{r}
x=t.test(iris$Sepal.Width,iris$Petal.Width,paired=TRUE)
plot(x)
```
 

## Options for t-test

You can change the options of t.test. 

```{r}
x=t.test(BMI~sex, data=acs,conf.level=0.99,alternative="greater",var.equal=TRUE)
plot(x)
```