{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "from scipy import stats\n",
    "from statsmodels.stats import proportion\n",
    "sns.set_style('ticks')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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op6dHklRdXa3S0lJt3bpVlmWpsbHRrqUBAEPEtkjcfPPN8nq9wdutra3KyMiQJGVnZ6u5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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b339208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p = 0.45 # probability for head\n",
    "n = 100\n",
    "heads = (np.random.random(n) < p).sum()\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.bar([0, 1], [heads, n-heads])\n",
    "ax.set_xticks((0,1))\n",
    "ax.set_xticklabels(('Heads', 'Tails'))\n",
    "ax.set_ylabel('Frequency')\n",
    "sns.despine()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "http://statsmodels.sourceforge.net/devel/stats.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "P-value for two-sided biomial test for a fair coin: 0.0035\n"
     ]
    }
   ],
   "source": [
    "print(\"P-value for two-sided biomial test for a fair coin: {:.2g}\".format(\n",
    "    proportion.binom_test(heads, n, prop=0.5)\n",
    "))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(39.0, 61.0, 35)"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "min_heads, max_heads = proportion.binom_test_reject_interval(0.5, n, alpha=0.05)\n",
    "min_heads, max_heads, heads"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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JTU0lLS2Nbdu2tWvbvXs3N9100yXeihDqqfWBlVlunnNFZHJd+IBOJZHa2lru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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b523400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rv = stats.binom(n, 0.5)\n",
    "max_freq = rv.pmf(n//2)\n",
    "fig, ax = plt.subplots()\n",
    "ax.fill_between([min_heads, max_heads], [max_freq*1.1]*2, alpha=0.2)\n",
    "ax.plot(rv.pmf(np.arange(0, n+1)))\n",
    "ax.axvline(heads, color='k', ls='--')\n",
    "ax.annotate('rejection region', (0.4, 1.01), xycoords='axes fraction')\n",
    "ax.annotate('observed', \n",
    "            (heads, 0.05), xytext=(-60, 0), \n",
    "            xycoords='data', textcoords='offset points',\n",
    "            arrowprops=dict(arrowstyle='->')\n",
    ")\n",
    "ax.set(\n",
    "    ylim=(0, max_freq*1.1),\n",
    "    xlabel='Heads',\n",
    "    ylabel='Probability'\n",
    ")\n",
    "sns.despine()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [conda env:simarba]",
   "language": "python",
   "name": "conda-env-simarba-py"
  },
  "language_info": {
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