{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "options(repr.plot.width=10, repr.plot.height=6.5)   # this command just formats the size of the figures. Adapt to view them nicely\n",
    "                                                    # in your browser."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAABLAAAAMMCAIAAADM7MkYAAAACXBIWXMAABJ0AAASdAHeZh94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\nrkJggg==",
      "text/plain": [
       "Plot with title “Histogram of X1^2”"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 390,
       "width": 600
      },
      "text/plain": {
       "height": 390,
       "width": 600
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAABLAAAAMMCAIAAADM7MkYAAAACXBIWXMAABJ0AAASdAHeZh94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\nAACAQhEIAQAAAECh/j+WlqjAjHBVEAAAAABJRU5ErkJggg==",
      "text/plain": [
       "Plot with title “Histogram of X1^2 + X2^2 + X3^2”"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 390,
       "width": 600
      },
      "text/plain": {
       "height": 390,
       "width": 600
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# The chi^2 test\n",
    "\n",
    "# Visualized chi^2 distributions\n",
    "\n",
    "# chi_df^2 = sum(i=1..df) X_i^2. Sum the squares of df N(0,1) i.i.d. standard normal RVs. \n",
    "\n",
    "# work from the definition.\n",
    "\n",
    "X1 <- rnorm(10000,mean = 0,sd = 1) #generate 1000 random N(0,1) datapoints.\n",
    "hist1=hist(X1^2,breaks = seq(0,30,by=0.1),plot = FALSE) #chi^2_1\n",
    "plot( hist1, col=rgb(0,0,1,1/4),xlim=c(0,10), xlab = \"chi^2\")\n",
    "\n",
    "X2 <- rnorm(10000,mean = 0,sd = 1) #generate 1000 random N(0,1) datapoints.\n",
    "hist2 <- hist(X1^2+X2^2,breaks = seq(0,30,by=0.1),plot = FALSE) #chi^2_2\n",
    "plot( hist2, col=rgb(1,0,0,1/4),  add=T) \n",
    "\n",
    "X3 <- rnorm(10000,mean = 0,sd = 1) #generate 1000 random N(0,1) datapoints.\n",
    "hist3 <- hist(X1^2+X2^2+X3^2,breaks = seq(0,30,by=0.1),plot = FALSE) #chi^2_3\n",
    "plot( hist3, col=rgb(0,1,0,1/4),  add=T)  \n",
    "\n",
    "\n",
    "# Use the numerical computation of chi^2 in R\n",
    "df=3 #degree of freedom = number of RV to square and sum\n",
    "\n",
    "x=seq(0,40,by=0.05)\n",
    "y=1000*dchisq(x,df)  #pdf of chi^2\n",
    "\n",
    "plot( hist3, col=rgb(0,1,0,1/4),xlim=c(0,15))  \n",
    "lines(x,y, xlab = \"chi^2\", ylab = \"probability density\", col='red')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<span style=white-space:pre-wrap>'measured chi^2:  12.8        critical chi^2:  11.0704976935164'</span>"
      ],
      "text/latex": [
       "'measured chi\\textasciicircum{}2:  12.8        critical chi\\textasciicircum{}2:  11.0704976935164'"
      ],
      "text/markdown": [
       "<span style=white-space:pre-wrap>'measured chi^2:  12.8        critical chi^2:  11.0704976935164'</span>"
      ],
      "text/plain": [
       "[1] \"measured chi^2:  12.8        critical chi^2:  11.0704976935164\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAABLAAAAMMCAMAAAB0UK59AAADAFBMVEUAAAABAQECAgIDAwME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\nQbAAWINgAbAGwQJgDYIFwBoEC4A1/g+VntJOtE3iCQAAAABJRU5ErkJggg==",
      "text/plain": [
       "Plot with title “Histogram of sample(1:6, n, replace = T, prob = probabilities)”"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 390,
       "width": 600
      },
      "text/plain": {
       "height": 390,
       "width": 600
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# chi^2 testing\n",
    "\n",
    "# Example: The unfair dice\n",
    "\n",
    "# Generate some data for testing:\n",
    "n = 10  # number of dice throw\n",
    "\n",
    "# Probabilities : Vector of p_i. i-th number: probability to find i on dice\n",
    "#probabilities <- c(1/6,1/6,1/6,1/6,1/6,1/6)         # a fair die\n",
    "probabilities <- c(1/10,1/10,1/10,1/10,3/10,3/10)   # an unfair die, lots of 5 and 6\n",
    "\n",
    "\n",
    "\n",
    "mydata=hist(sample(1:6,n,replace=T,prob=probabilities), breaks = seq(0.5,6.5,by=1)) # role die n times, count observations.\n",
    "# 1) Hypothesis\n",
    "\n",
    "#H_1: This dice is unfair! H_0: the dice is fair. Under H_0, all p_i = 1/6.\n",
    "# Is there significant evidence that the observed numbers deviate from what we expect if H_0 was valid?\n",
    "\n",
    "# 2) Significance\n",
    "alpha=0.05\n",
    "\n",
    "# 3) Compute test statistic\n",
    "\n",
    "chisquare = 0\n",
    "\n",
    "for (i in seq(1,6,by=1)) { chisquare = chisquare +  (mydata$counts[i]-n*1/6)^2/(n*1/6)  }\n",
    "\n",
    "# 4) Critical region\n",
    "# Reject H_0 if chisquare > chi_5(1-alpha)\n",
    "\n",
    "K= qchisq(1-alpha,5)\n",
    "\n",
    "# 5) decide\n",
    "\n",
    "paste('measured chi^2: ',chisquare, '       critical chi^2: ',K )\n",
    "\n",
    "\n",
    "# Repeat in R\n",
    "\n",
    "#chisq.test(x=mydata$counts,p = c(1/6,1/6,1/6,1/6,1/6,1/6))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "\tChi-squared test for given probabilities\n",
       "\n",
       "data:  mydata$counts\n",
       "X-squared = 51.44, df = 5, p-value = 7.027e-10\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Repeat in R\n",
    "\n",
    "chisq.test(x=mydata$counts,p = c(1/6,1/6,1/6,1/6,1/6,1/6))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}