2017-08-02_D8_Analysis.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from scipy import stats\n",
    "from matplotlib import pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "raw_data = pd.Series([7, 2, 6, 6, 2, 2, 8, 1, 3, 7, 8, 8, 8, 4, 5, 3, 4, 7,\n",
    "                      1, 1, 3, 3, 8, 7, 6, 2, 1, 1, 5, 7, 4, 5, 8, 3, 2, 1,\n",
    "                      4, 3, 8, 7, 8, 5, 3, 4, 2, 2, 6, 7, 6, 4, 6, 6, 3, 3,\n",
    "                      6, 2, 5, 2, 4, 6, 4, 6, 8, 6, 2, 4, 5, 7])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "68"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n = len(raw_data) # Número de experimentos\n",
    "n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1     6\n",
       "2    10\n",
       "3     9\n",
       "4     9\n",
       "5     6\n",
       "6    11\n",
       "7     8\n",
       "8     9\n",
       "dtype: int64"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "freqs = raw_data.value_counts().sort_index()\n",
    "freqs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f29e4727250>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "freqs.plot.bar();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k = len(freqs.index) # Número de lados do dado\n",
    "k"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1    8.5\n",
       "2    8.5\n",
       "3    8.5\n",
       "4    8.5\n",
       "5    8.5\n",
       "6    8.5\n",
       "7    8.5\n",
       "8    8.5\n",
       "dtype: float64"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "expected = pd.Series([float(n) / k] * k, index=freqs.index)\n",
    "expected"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.5882352941176472"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "chi_squared = ((freqs - expected) ** 2 / expected).sum()\n",
    "chi_squared"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = k - 1\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.92030761806367933"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p = stats.chi2.sf(chi_squared, df=df)\n",
    "p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Retain the null! Can't tell anything about any possible dice bias...\n"
     ]
    }
   ],
   "source": [
    "alpha = .05\n",
    "print([\"Retain the null! Can't tell anything about any possible dice bias...\",\n",
    "       \"Reject the null! Dice is biased!!\"][p <= alpha])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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sWLCAxMRE+vfvz1dffWU7klLnTUvf5XTpt27d2nIS5cuio6NZsmQJderU4YYb\nbiArK8t2JKXOi5a+S0ZGBnFxccTExNiOonxczZo1Wb58OZUrV6ZHjx5nrrSmlD/Q0nfJyMjQoR3l\ntvr165OSkkJERATdu3fX4ld+Q0sfOHDgANnZ2bRr1852FOVHGjduTEpKCmFhYXTv3p0tW7bYjqRU\nmbT0gdTUVADat29vOYnyN02aNOGLL744U/w6xq98nZY+sH79ekSENm3a2I6i/FCTJk1ISUkhPDyc\nq6++mq+//tp2JKXOSksfZ+k3a9aMKlWq2I6i/FTTpk356quviI2NpWfPnixZssR2JKVK5Vbpi0hv\nEdkuItki8nApz0eKyAeu59eJSJxr+jUiki4im1z/dvds/PIzxrBu3Todz1flVr9+fb788kuaNm1K\nnz59mDNnju1ISv1BmaUvIqHAdOA6IAG4RUQSSsx2J5BvjGkETAOecU3fD/QxxiQCg4FZngruKbt2\n7SIvL0/H85VH1KxZky+++IKrrrqKW265hWeeeUZP0qZ8ijtr+u2AbGNMjjGmEJgD9CsxTz/gHdf9\neUAPERFjzAZjzI+u6VuAKBGJ9ERwT1m/fj2Arukrj4mOjmbp0qUMGjSIhx9+mLvuuouTJ0/ajqUU\n4N4J12oDe4o93guUXC0+M48x5pSIHAKq41zTP60/kGGMOXHhcT1v/fr1REZGkpiYaDuKCiCVKlVi\n9uzZNGrUiCeeeIKdO3cyb948qlatajuaCnIVsiFXRJrjHPL5x1meHyoiaSKSlpeXVxGRzli/fj1X\nXHGFXhNXeVxISAiTJ0/m7bffZvXq1bRt25ZNmzbZjqWCnDulnwvULfa4jmtaqfOISBgQDfzqelwH\n+AT4P2PMjtI+wBjzhjEmyRiTFBsbe35LUA6nTp0iPT1dx/OVVw0ePJiUlBSOHj1K+/btef/9921H\nUkHMndJPBRqLSAMRiQAGAQtLzLMQ54ZagAHASmOMEZGqwGfAw8YYnzsl4ZYtWygoKNDxfOV1HTt2\nJCMjg7Zt2/K3v/2NESNGUFhYaDuWCkJllr4x5hQwHFgKbAPmGmO2iMgkEenrmm0mUF1EsoGRwOnd\nOocDjYDxIrLRdavp8aW4QKdPjduhQwfLSVQw+POf/8yKFSsYOXIkr7zyCld36kROTo7tWCrIiK/t\nTpaUlGTS0tIq5LNuvfVWVq9ezZ49exCRCvlMpQA+/PBD7kpOxhEWxqvTp/N/d92l/x9U5SIi6caY\npLLmC9pmN7M9AAALhklEQVQjco0xrFmzhk6dOul/bKrCDRw4kCygjcPB7f/4Bzf36sWBAwdsx1JB\nIGhLf9euXezdu5fOnTvbjqKCVL1KlfjcGJ4CPlmxgpZxcSyaP992LBXggrb0v/zySwAtfWVVKM4N\nYGuBmCNH6HPTTQy67jr27dtnOZkKVEFb+mvWrCE6OprmzZvbjqIUbYB0Y5gMfLJkCc3i4vj3G2/o\nKRyUxwV16Xfs2JHQ0FDbUZQCIAJ4DMgEWhQWMuQf/6BTixZU1I4NKjgEZenn5eWxbds2OnXqZDuK\nUn9wGfBFUREzgR1bt9K2bVvuGDiQn376yXY0FQCCsvQ///xzAHr06GE5iVKlCwGGAN8BY0SYPW8e\nTerX54lx4/jtt98sp1P+LChLf9myZcTExOiVspTPqwI8YwxbgZ4OB+OeeIL4Sy/lhWef5dixY7bj\nKT8UdKVvjGHZsmX07NlTx/OV32gEfFJUxDrg8mPHGPXQQzSqVYvpL7+s5a/OS9CV/rZt28jNzaVX\nr162oyh13toBy4qK+AJocPgww++7j/qXXMKUSZPIz8+3nE75g6Ar/eXLlwNwzTXXWE6i1IW7Gljj\nKv+kggIemzCBen/+MyOHD9fz+ahzCrrSX7ZsGU2aNKF+/fq2oyhVLoKz/P/rcLAR6Odw8PL06TRq\n2JC/dO3KokWLcDgcllMqXxNUpV9QUEBKSooO7aiA0wp4z+FgFzA+JISNq1bRp08fGtaqxZNPPMGe\nPXvKegsVJIKq9JctW8axY8e48cYbbUdRyitqAxOLitgFfAjE//orj44bR/169ehx1VW8/fbbustn\nkAuq0v/444+JiYmhS5cutqMo5VXhuK5m5HCQDUwIDWXX2rXccccdXFK9OoNuuokPP/yQI0eOWE6q\nKlrQlP7Jkyf59NNP6dOnj14PVwWVhsAEh4PvjeErYLAxfD5/PsnJydSIiaHPtdfy73//m/3799uO\nqipAmO0AFWXZsmUcPHiQv/71r7ajKGWFAFcBV506xavAV8DHwCfLlrFo2TJCROjQujW9+vWjV69e\ntG3blrCwoKmIoBE0V85KTk4mJSWF3NxcIiIiPP7+Sp23qCg4ftx2CgywAZgfGsqyoiLWG4MBoitX\npnu3bvS87jo6depE8+bN9YBGH+bulbOC4mf8wIEDLFiwgGHDhmnhK1WCAFcAVzgcTAIOAJ8DywoL\nWbpoEZ8sWgQ4fwSuuuoqOnXtSseOHWnXrh1RUVH2gqsLEhSlP2vWLAoLC7n99tttR1HK51UDBgID\nT57EAD8AX4nwZWEhXy5fzmLXAY6hISE0b9yYKzp04Io2bWjTpg2tWrWicuXKFtOrsgT88M6pU6do\n3LgxderUYc2aNR57X6XKzUeGd87Xr8A3wDfh4WQUFZHucJDnei5EhCZxcTRv3ZqEFi1ISEggISGB\npk2bEhkZaTF14NPhHZePPvqInTt38uKLL9qOolRAqA7cANxw8iTg3CbwI5ABpIeFsXH3brJ++IFP\nPvmEItdrQkJCaFi3Lk2bN6dh48Y0bNiQ+Ph44uPjadCgAZUqVbKyLMEooNf0T5w4QYsWLQgPD2fz\n5s2EhATNHqrKH/jpmr67juO8HsBWEbaGh7PF4eB7h4McEY6W6J3aNWvSID6eOnFx1K5dmzp16lC7\ndu0zt0svvVS3x5XBo2v6ItIbeAnndZz/nzHm6RLPRwLv4rzU56/AzcaYna7nHgHuBBzACGPM0vNY\njnKZOnUq2dnZLF26VAtfqQpWCWgJtDQGCgvPTDfGkAfsAHJCQ8kJC2NHfj4/rFtH6tq1zBfheIkf\nBRGhZrVq/PmSS4i99FJia9YkNja21Fv16tWJjo7WH4mzKLP0RSQUmA5cA+wFUkVkoTFma7HZ7gTy\njTGNRGQQ8Axws4gkAIOA5kAtYIWINDHGeP0sUCtXrmTChAn0799fz7WjlA8RoKbrdqXDASVOCmeM\n4QCQ67rtjYhw/nv4MPvy88nbupUcEfKA384xUhEVGUnVKlWIjo6marVqRMfEULVqVedj179VqlTh\noosuonLlyr+7lZwWFRUVMCuO7qzptwOyjTE5ACIyB+gHFC/9fsBE1/15wKsiIq7pc4wxJ4AfRCTb\n9X7feCb+HxUVFTF//nyGDBlCkyZNmDlzprc+SinlBYJzu0F1nH8pFP8r4QxX2Z8A9gN5p2+hofwa\nGsohEQ4Zw8GDBzl04AAHs7PJB34QOfNcyb8myhIVGUnliy6iUmQkkZGRRFaq9PtbZCQRERHO585y\ni4iIICIigvDwcMLCwggPD//drWbNml6/jKs7pV8bKH6Kvr1A+7PNY4w5JSKHcH5ntYG1JV5b+4LT\nnsO+ffvo2bMne/fu5eDBg7Rq1YqFCxcSHR3tjY9TqvxcG0LVhYvEWShnSqWUvxx+x5jf/WD8Bhwt\ncSsICeFoSAhHRf433RiOOhwcPXSI48ZQaAwnXO9x+nao2P1C4ITI/553zV+W9jVr0uPnn0HkfP5n\nOC8+sfeOiAwFhgLUq1fvgt4jOjqa+Ph4unTpwpVXXsnNN9+s59hRvq12bfjlF9BTHVgR6brV8MSb\nORxw6pTzdvoviBJ/SRjgZLHbqRKPTwIRv/zifC8v/n/CnXfOBeoWe1zHNa20efaKSBgQjXODrjuv\nxRjzBvAGOPfecTd8cZUqVWLBggUX8lKl7Ni1y3YCVYEEiHDdbHJny0Qq0FhEGohIBM4NswtLzLMQ\nGOy6PwBYaZz7gi4EBolIpIg0ABoD6z0TXSml1Pkqc03fNUY/HFiKc5fNt4wxW0RkEpBmjFkIzARm\nuTbUHsD5w4Brvrk4N/qeAu6piD13lFJKlS6gD85SSqlg4e7BWYGx46lSSim3aOkrpVQQ0dJXSqkg\noqWvlFJBREtfKaWCiM/tvSMieUB5jlqpgfN0HMEk2JY52JYXdJmDRXmWub4xJrasmXyu9MtLRNLc\n2W0pkATbMgfb8oIuc7CoiGXW4R2llAoiWvpKKRVEArH037AdwIJgW+ZgW17QZQ4WXl/mgBvTV0op\ndXaBuKavlFLqLAKm9EWkt4hsF5FsEXnYdp6KICI7RWSTiGwUkYA8S52IvCUiv4jI5mLTqonIchH5\n3vVvjM2MnnaWZZ4oIrmu73qjiPzFZkZPE5G6IpIiIltFZIuI3OeaHpDf9TmW1+vfc0AM77gu3v4d\nxS7eDtxS4uLtAUdEdgJJxpiA3ZdZRLoAR4B3jTEtXNOeBQ4YY552/cDHGGMespnTk86yzBOBI8aY\n521m8xYRuRS41BiTISIXA+nAjcDtBOB3fY7lTcbL33OgrOmfuXi7MaYQOH3xduXnjDGrcV6jobh+\nwDuu++/g/I8lYJxlmQOaMeYnY0yG6/5vwDacl74NyO/6HMvrdYFS+qVdvL1C/ge0zADLRCTddZ3h\nYHGJMeYn1/2fgUtshqlAw0UkyzX8ExDDHKURkTjgcmAdQfBdl1he8PL3HCilH6w6GWOuAK4D7nEN\nCwQV12U5/X+Msmz/AhoCrYGfgKl243iHiPwJ+Ai43xhzuPhzgfhdl7K8Xv+eA6X03boAe6AxxuS6\n/v0F+ATnMFcw2OcaEz09NvqL5TxeZ4zZZ4xxGGOKgDcJwO9aRMJxFuBsY8zHrskB+12XtrwV8T0H\nSum7c/H2gCIilV0bgBCRykAvYPO5XxUwFgKDXfcHAwssZqkQp4vP5SYC7LsWEcF5re1txpgXij0V\nkN/12Za3Ir7ngNh7B8C1a9OL/O/i7VMsR/IqEYnHuXYPzgvcvx+Iyywi/wG64jz74D5gAjAfmAvU\nw3lG1mRjTMBs+DzLMnfF+Se/AXYC/yg21u33RKQTsAbYBBS5Jo/FOc4dcN/1OZb3Frz8PQdM6Sul\nlCpboAzvKKWUcoOWvlJKBREtfaWUCiJa+kopFUS09JVSKoho6SulVBDR0ldKqSCipa+UUkHk/wdv\nP++m2taKOQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f29a5f41a50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(0, 25, 500)\n",
    "chi_squared_y = stats.chi2.pdf(x, df=df)\n",
    "filt_alpha = x > stats.chi2.isf(alpha, df=df)\n",
    "plt.plot(x, chi_squared_y, color=\"black\")\n",
    "plt.fill_between(x[filt_alpha], chi_squared_y[filt_alpha], 0, color=\"red\")\n",
    "plt.plot([chi_squared], [stats.chi2.pdf(chi_squared, df=df)], \"bx\");"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}