{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Statistical Inference"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\alpha = \\pi^2$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "“package ‘dplyr’ was built under R version 3.4.1”"
     ]
    }
   ],
   "source": [
    "suppressPackageStartupMessages(library(tidyverse))\n",
    "suppressPackageStartupMessages(library(pwr))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "options(repr.plot.width=4, repr.plot.height=3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Coin toss experiment"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "n <- 12\n",
    "outcomes <- c(\"H\", \"T\")\n",
    "tosses <- sample(outcomes, n, replace=TRUE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>'H'</li>\n",
       "\t<li>'T'</li>\n",
       "\t<li>'H'</li>\n",
       "\t<li>'T'</li>\n",
       "\t<li>'H'</li>\n",
       "\t<li>'H'</li>\n",
       "\t<li>'T'</li>\n",
       "\t<li>'T'</li>\n",
       "\t<li>'H'</li>\n",
       "\t<li>'T'</li>\n",
       "\t<li>'H'</li>\n",
       "\t<li>'T'</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 'H'\n",
       "\\item 'T'\n",
       "\\item 'H'\n",
       "\\item 'T'\n",
       "\\item 'H'\n",
       "\\item 'H'\n",
       "\\item 'T'\n",
       "\\item 'T'\n",
       "\\item 'H'\n",
       "\\item 'T'\n",
       "\\item 'H'\n",
       "\\item 'T'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 'H'\n",
       "2. 'T'\n",
       "3. 'H'\n",
       "4. 'T'\n",
       "5. 'H'\n",
       "6. 'H'\n",
       "7. 'T'\n",
       "8. 'T'\n",
       "9. 'H'\n",
       "10. 'T'\n",
       "11. 'H'\n",
       "12. 'T'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       " [1] \"H\" \"T\" \"H\" \"T\" \"H\" \"H\" \"T\" \"T\" \"H\" \"T\" \"H\" \"T\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "tosses"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tosses\n",
       "H T \n",
       "6 6 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "table(tosses)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "\tExact binomial test\n",
       "\n",
       "data:  table(tosses)\n",
       "number of successes = 6, number of trials = 12, p-value = 1\n",
       "alternative hypothesis: true probability of success is not equal to 0.5\n",
       "95 percent confidence interval:\n",
       " 0.2109446 0.7890554\n",
       "sample estimates:\n",
       "probability of success \n",
       "                   0.5 \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "binom.test(table(tosses))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Note on using `dylyr`\n",
    "\n",
    "Here, using `dplyr` is more complex because of the need to convert to and from a data.matrix. We will stick with basic R but an example is shown below using `dplyr` for those who are curious."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "\tExact binomial test\n",
       "\n",
       "data:  as.matrix(tbl)\n",
       "number of successes = 6, number of trials = 12, p-value = 1\n",
       "alternative hypothesis: true probability of success is not equal to 0.5\n",
       "95 percent confidence interval:\n",
       " 0.2109446 0.7890554\n",
       "sample estimates:\n",
       "probability of success \n",
       "                   0.5 \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "tbl <- data.frame(tosses) %>% count(tosses) %>% select(n)\n",
    "binom.test(as.matrix(tbl))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise 1** \n",
    "\n",
    "Repeat the coin toss experiment with 10 tosses and evaluate if the results are statistically significant."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise 2**\n",
    "\n",
    "Repeat the coin toss experiment with 12 tosses, but set the probability of HEADS to be 0.3 and evaluate if the results are statistically significant."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise 3**\n",
    "\n",
    "Create a data sample with 2 HEADS and 10 TAILS and evaluate if the results are statistically significant."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## A two-sample model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Simulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "mu1 <- 0\n",
    "mu2 <- 2\n",
    "sigma <- 5\n",
    "n <- 12"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x1 <- rnorm(n, mu1, sigma)\n",
    "x2 <- rnorm(n, mu2, sigma)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "\tWelch Two Sample t-test\n",
       "\n",
       "data:  x1 and x2\n",
       "t = -0.38018, df = 21.96, p-value = 0.7075\n",
       "alternative hypothesis: true difference in means is not equal to 0\n",
       "95 percent confidence interval:\n",
       " -5.320465  3.672143\n",
       "sample estimates:\n",
       "mean of x mean of y \n",
       " 1.036991  1.861152 \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t.test(x=x1, y=x2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sample size calculation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "d <- abs(mu1 - mu2)/sigma"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "alpha <- 0.05\n",
    "power <- 0.8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "     Two-sample t test power calculation \n",
       "\n",
       "              n = 99.08032\n",
       "              d = 0.4\n",
       "      sig.level = 0.05\n",
       "          power = 0.8\n",
       "    alternative = two.sided\n",
       "\n",
       "NOTE: n is number in *each* group\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pwr.t.test(d=d, sig.level=alpha, power=power)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise**\n",
    "\n",
    "- Suppose that company XYZ Dairies sells milk in glass bottles\n",
    "- The company claims that the net content of each bottle is 1 gallon\n",
    "- Mr. Smith, owner of the ABC Supermarket, suspects he, and ultimately his customers, are being swindled by XYZ\n",
    "- Let μ denote the mean net content (in gallons) of the population of XYZ Dairies milk bottles\n",
    "- The company claims μ = 1\n",
    "- Mr. Smith hypothesizes that μ < 1\n",
    "- Mr. Smith has to give benefit of the doubt to company XYZ’s claim (i.e., μ = 1)\n",
    "- The purpose of the experiment is to ascertain if there is sufficient evidence to the contrary (i.e., show μ $\\ne$ 1)\n",
    "- The null hypothesis is formulated as H0 : μ = 1\n",
    "- The alternative is formulated as H1 : μ$\\ne$ 1\n",
    "- Mr. Smith has no interest in gathering evidence for showing that XYZ overfills its bottles (i.e., μ > 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise 4**\n",
    "\n",
    "Suppose the true value of $\\mu$ is 0.9. Simulate 20 samples each from the null distribution and the true distribution. Evaluate if the samples are statistically significant using a one-sided two sample T test."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise 5**\n",
    "\n",
    "Suppose the true value of $\\mu$ is 0.9. How many samples would be needed in each group to have a power of 0.9 at an alpha of 0.1 with a one-sided t-test?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Distribution of p-values under null distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "mu1 <- 0\n",
    "mu2 <- 0\n",
    "sigma <- 5\n",
    "n <- 12\n",
    "r <- 1000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "ps <- numeric(r)\n",
    "for (rep in 1:r) {\n",
    "    x1 <- rnorm(n, mu1, sigma)\n",
    "    x2 <- rnorm(n, mu2, sigma)\n",
    "    ps[rep] <- t.test(x=x1, y=x2)$p.value\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAeAAAAFoCAYAAACPNyggAAAEDWlDQ1BJQ0MgUHJvZmlsZQAA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\nZalPAAAAAElFTkSuQmCC",
      "text/plain": [
       "Plot with title “Histogram of ps”"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hist(ps)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAeAAAAFoCAYAAACPNyggAAAEDWlDQ1BJQ0MgUHJvZmlsZQAA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\nNKABDWhAAxrQgAY00Gzg/wPR1lnOIbbkoAAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "par(pty=\"s\")\n",
    "qqplot(ps[1:100], runif(length(ps[1:100])), ylab=\"Uniform\", xlab=\"P-values\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise 6**\n",
    "\n",
    "Plot the histogram of p-values and the QQ-plot when mu2 = 2."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "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": "3.4.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}