---
title: "Hypothesis Test"
description: 
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Hypothesis Test}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---
This vignette will introduce you to find the critical value for comparison of observed and expected obtained last step. 

```{r setup, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
```

```{r load package,include = FALSE}
library(mixIndependR)
library(ggplot2)
```

```{r preparation, include=FALSE}
x <- mixexample

p <- AlleleFreq(x)
h <-Heterozygous(x)
H <- RxpHetero(h,p,HWE=FALSE)
AS<-AlleleShare(x,replacement=FALSE)
e <-RealProAlleleShare(AS)
ObsDist_K<-FreqHetero(h)
ExpDist_K<- DistHetero(H)
ObsDist_X<-FreqAlleleShare(AS)
ExpDist_X<-DistAlleleShare(e)
```
`Simulate_DistK` and `Simulate_DistX` simulate bundles of expected distributions for number of heterozygous loci and number of shared alleles respectively. 
```{r Simulation}
Simu_K <- Simulate_DistK(H,100,500)
Simu_X <- Simulate_DistX(e,100,500)
```
`Dist_SimuChisq` generates a bundle of chi-square values which can be distributed. `ecdf` build the cumulative probability functions for the chi-square values.

```{r Chi-square}
x2_K<-Dist_SimuChisq(Simu_K,ExpDist_K$Density,200)
x2_X<-Dist_SimuChisq(Simu_X,ExpDist_X$Density,200)
P1<-ecdf(x2_K)
P2<-ecdf(x2_X)
```
```{r Last plot, echo=FALSE, fig.height=4, fig.show='hold', fig.width=3}
x <- c(0:200)
dfX2 <- data.frame(x=x,y=P1(x))
ggplot(dfX2,aes(x=x,y=P1(x)))+
  geom_line()+
  geom_hline(yintercept = 0.95,color="Red")+
  ggtitle("CPF No. of Heterozygous Loci")+
  xlab("Chi-square")+ylab("1-p-value")

dfX22 <- data.frame(x=x,y=P2(x))
ggplot(dfX22,aes(x=x,y=P2(x)))+
  geom_line()+
  geom_hline(yintercept = 0.95,color="Red")+
  ggtitle("CPF No. of Shared Alleles")+
  xlab("Chi-square")+ylab("1-p-value")
```