CH4/templates/10_stat.non_parametric_tests_rel.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Непараметрические криетрии"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "  Критерий | Одновыборочный | Двухвыборочный | Двухвыборочный (связанные выборки)  \n",
    "  ------------- | -------------|\n",
    "  **Знаков**  | $\\times$ | | $\\times$ \n",
    "  **Ранговый** | $\\times$  | $\\times$ | $\\times$  \n",
    "  **Перестановочный** | $\\times$  | $\\times$ | $\\times$ "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Терапия при анорексии"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "В исследовании оценивается эффективность поведенческой терапии для лечения анорексии. Для 50 пациентов известен вес до начала терапии и по её окончании. Была ли терапия эффективной?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import itertools\n",
    "\n",
    "from scipy import stats\n",
    "from statsmodels.stats.descriptivestats import sign_test\n",
    "from statsmodels.stats.weightstats import zconfint"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Загрузка данных"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "weight_data = pd.read_csv('weight.txt', sep = '\\t', header = 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Before</th>\n",
       "      <th>After</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>80.5</td>\n",
       "      <td>82.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>84.9</td>\n",
       "      <td>85.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>81.5</td>\n",
       "      <td>81.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>82.6</td>\n",
       "      <td>81.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>79.9</td>\n",
       "      <td>76.4</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Before  After\n",
       "0    80.5   82.2\n",
       "1    84.9   85.6\n",
       "2    81.5   81.4\n",
       "3    82.6   81.9\n",
       "4    79.9   76.4"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "weight_data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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vY3p+0aYUPb/tz6L0GaM5defsSje5MLPflfQOPvCWJ4rfFrdN8dsqil+0ieIXqIebXCSS\nU29MznI8zjnuM7ot2jkZK2+ROkAlkcY2UlYpXt461uz5Xc7dr5V0bUNZAAAAgEZVanuY+kS8hdZ7\ntD20uG3aHlpF2wPaRNsDUA9tDwAAAEBJFL8zyqk3Jmc5Hucc9xndFu2cjJW3SB2gkkhjGymrFC9v\nHRS/AAAAyAY9vyiNnt8Wt03Pb6vo+UWb6PkF6qHnFwAAACiJ4ndGOfXG5CzH45zjPqPbop2TsfIW\nqQNUEmlsI2WV4uWtg+IXAAAA2aDnF6XR89vitun5bRU9v2gTPb9APfT8AgAAACVR/M4op96YnOV4\nnHPcZ3RbtHMyVt4idYBKIo1tpKxSvLx1UPwCAAAgG/T8ojR6flvcNj2/raLnF22i5xeoh55fAMCv\nMLODzGyHmV2ZOgsAdAnF74xy6o3JWY7HOcd97qnzJN2aOsQ8RDsnY+UtUgeoJNLYRsoqxctbB8Uv\nAPSMmR0n6UWSPpI6CwB0DT2/KI2e3xa3Tc9vq/rW82tml0v6H5KOkvQOdz/rAOswZydCzy9QDz2/\nAIB9zOz3Je1x96FGVU9vinoAmId1qQNEVRSFBoNB6hhoWI7HOcd97pnnSjrLzF4k6VBJjzGzS9z9\n9StX3Lx5sxYXFyVJCwsLWlpa2nfsJ/1/XVhe3ovYhTzzyPtIr23q5clj837+/eeSeY3v5LEuHe/V\nlofDoc4///zO5Imcd+vWrRoOh/vmq7rWbHsws0MkfUnSozQqlj/h7lsOsF5Wb6HlWCDk2Pawffv2\nJMc55Vin2ueU+tb2MGFmv6setD1Em2/XytuttodCywvWeW6zifMr0rkQKasUK2/dObtUz6+ZHebu\n95vZwZK+LOlcd//ainXCTKSYTY7FLz2/eaD4RZu6Vfw2t03OLzSl7pxdqu3B3e8f/3jI+O9wRgNA\nx7n7tZKuTZ0DALqk1Afexl+WvlPSXZKudvevNxur+5b3H6G/cjzOOe4zui3aORkrb5E6QCWRxjZS\nVile3jrKXvn9paRnmNmRkv7WzJ7q7r/y5elRPjwxj+WXnnmm9t5338ohaMWmjRv1sW3b9svT1v5P\nTJYGPV5eL+nUU09VKoXSfPRFSv/6ivbhCQBAHJW/59fM/qukX7j7+1c8nlX/WKqeTCldX2aWPb8J\ntpty2/T85iO3ObtL6PkF6mn8e37N7LFmdtT450MlvUDSt2bdIAAAAJBKmZ7fX5O03cyGkm6Q9AV3\n/2yzsYBuKFIHSCCnvi/EEO2cjJW3SB2gkkhjGymrFC9vHWv2/Lr7LZJOaiELAAAA0KjKPb+rPlFm\n/WP0/La4XdHz2+p2M3odT9DzizbR8wvU03jPLwAAANAXFL/AFEXqAAnk1PeFGKKdk7HyFqkDVBJp\nbCNlleLlrYPiFwAAANmg53dG9Py2uF3R89vqdjN6HU/Q84s20fML1EPPLwAAAFASxS8wRZE6QAI5\n9X0hhmjnZKy8ReoAlUQa20hZpXh566D4BQAAQDbo+Z0RPb8tblf0/La63YxexxP0/KJN9PwC9dDz\nCwAAAJRE8QtMUaQOkEBOfV+IIdo5GStvkTpAJZHGNlJWKV7eOtalDgAA6K7bb79d5533J3r44fbe\nwn71q1+q173uFa1tD0Be6PmdET2/LW5X9Py2ut2MXscT9Pyu7sILL9Rb3nKJHnjgzS2kkqRv6JRT\nbtV1132mpe21j57f+I45ZlF79nyvte1t3LhJd921u7XtdV3dOZsrvwCAqdatO0EPPNDWldjDJd3a\n0raA2YwK3/aK+z17svq3eePo+QWmKFIHSCCnvi/EEO2cjJW3SB2gEsa2ObHGth6KXwAAAGSD4heY\nYpA6QAKDwSB1BGA/0c7JWHkHqQNUwtg2J9bY1kPxCwAAgGxQ/AJTFKkDJJBT3xdiiHZOxspbpA5Q\nCWPbnFhjW8+axa+ZHWdmXzSzvzezW8zs3DaCAQAAAPNW5qvOHpL0x+4+NLMjJH3DzK5y9281nA1I\nbpA6QAI59X0hhmjnZKy8g9QBKmFsmxNrbOtZ88qvu9/l7sPxz/dJ2iXpCU0HAwAAAOatUs+vmS1K\nWpJ0QxNhgK4pUgdIIKe+L8QQ7ZyMlbdIHaASxrY5sca2ntJ3eBu3PHxC0nnjK8C/YvPmzVpcXJQk\nLSwsaGlpad9l9Mmg9mVZGp3Wg2U/q6XlQzS5PWY6xfi/g54va43fN7U8eayt7U2W9227Y6+3eS9v\n3bpVw+Fw33wFAMiHlbn3tpmtk/QZSZ9z9w+ssk6p+8T3hZm1fqf0fdtW+3dpZ7t5bNsk5fQ6nqh7\nn/iIys7ZF154oc4993r94hcXtpBKkj6jU075S1133Wda2l77Rhcv2nydpZhRrNdzSYpj2OfxrKru\nnF227eFCSbeuVvgCAAAAEZT5qrPnSnqNpN8zs51mtsPMzmg+GpBekTpAAjn1fSGGaOdkrLxF6gCV\nMLbNiTW29azZ8+vuX5Z0cAtZAAAAgEZxhzdgikHqAAnk9F2PiCHaORkr7yB1gEoY2+bEGtt6KH4B\nAACQDYpfYIoidYAEcur76qM+3pI+2jkZK2+ROkAljG1zYo1tPaW/5xcAEAK3pAeAKbjyC0wxSB0g\ngZz6vvqoj7ekj3ZOxso7SB2gEsa2ObHGth6KXwDoKW5JDwC/irYHYIpC0f7tXl9RFFldAeired2S\n/hGT5UHDy9INN1zX6i3cN27cpG3bPjZKM4dbaC8fu9XW79ZN3AcNPP/+c8m8blE+eWzl748++hjt\n3btH7So0fTyGks6f8vsqy82M5/Ll4XCo888f5W17PDds2KgrrtjW2i3pS93euNQTcXvj9ratvG73\nm3K725Wm+E26z9u3Z1f89u32xvO8JX2K2xtLZ2r/V0ChZl+J87117Fr/gOzW7Y0LNTO2zdyOd7Wx\n7daYThSa39g2f3vj5WPb9ds3152zKX5nRPHLdvu4bZOyvH98D4vfSyTd7e5/PGWdQMVv05ovLPbb\nWicLtflvkzGd7/b6Pp5tFr/0/AJAj3BLegCYjuIXmKJIHSCBnL7rsY/c/cvufrC7L7n7M9z9JHf/\nfOpc9RSpA1QS6zVUpA5QCWPbnFhjWw/FLwAAALJBz++M6Pllu33cNj2/+aDnd7n+91PS8zv3Lba+\nvb6PJz2/AAAAQAMofoEpitQBEsip7wtRFKkDVBLrNVSkDlAJY9ucWGNbD8UvAAAAskHP74zo+WW7\nfdw2Pb/5oOd3uf73U9LzO/cttr69vo8nPb8AAABAAyh+gSmK1AESyKnvC1EUqQNUEus1VKQOUAlj\n25xYY1vPmsWvmX3UzPaY2c1tBAIAAACasmbPr5mdIuk+SZe4+9OnrEfPb1vbVl49sLltN+W26fnN\nBz2/y/W/n5Ke37lvsfXt9X08O9Xz6+7XS9o76wYAAACArlg3zyf7o9e+dp5PtyY76CD9yZ/+qZ74\nxCe2ul3ko5A0SJyhbUVRaDAYpI4BLFMo0isx1muoEGPblEKMbTfNtfi95dJL9djxz4dK+nVJvzFe\nvm3833kuX7Vuna76nd/ROeecs69Re3Lgml6W9j+ti/F/+76sNX7ft2Wt8fumliePtbW9yfK+bbf8\nejrm6KO1Z2+aN5iOOvzwJNsFAKRR6nt+zWyTpE+v2fM7z2QlnHPYYTr5Ax/QOeec0/KW6fllu/3c\ndqqe39SvJ0n0/K6Cnt8Gttb7/tTRNhnT+W6v7+PZqZ7fyXb0yP8jAAAAgJDKfNXZZZK+IulEM7vD\nzN7QfCygG4rUARLI6bseEUWROkAlsV5DReoAlTC2zYk1tvWs2fPr7q9uIwgAAADQtLl+4A3om0Hq\nAAnk8mlfRDJIHaCSWK+hQUPPe8i4bzRngzk+F+M5TxS/AABgzh5Q+x9A6zPGc57KfuANyFKROkAC\nOfV9IYoidYBKYr2GitQBKipSB6igSB2goiJ1gNZQ/AIAACAbFL/AFIPUARKI1a+IPAxSB6gk1mto\nkDpARYPUASoYpA5Q0SB1gNZQ/AIAACAbFL/AFEXqAAnE6ldEHorUASqJ9RoqUgeoqEgdoIIidYCK\nitQBWkPxCwAAgGxQ/AJTDFIHSCBWvyLyMEgdoJJYr6FB6gAVDVIHqGCQOkBFg9QBWkPxCwAAgGxQ\n/AJTFKkDJBCrXxF5KFIHqCTWa6hIHaCiInWACorUASoqUgdoDcUvAAAAskHxC0wxSB0ggVj9isjD\nIHWASmK9hgapA1Q0SB2ggkHqABUNUgdoDcUvAAAAskHxC0xRpA6QQKx+ReShSB2gklivoSJ1gIqK\n1AEqKFIHqKhIHaA1FL8AAADIBsUvMMUgdYAEYvUrIg+D1AEqifUaGqQOUNEgdYAKBqkDVDRIHaA1\nFL8AAADIRqni18zOMLNvmdm3zeydTYcCuqJIHSCBWP2KOJD+zdlF6gCVxHoNFakDVFSkDlBBkTpA\nRUXqAK1Zs/g1s4Mk/V9JL5T0m5JeZWZPbjoY0AXD1AESGA5z3Ov+6OecHeucjPUaipRVipU3UlYp\nXt7Zlbny+yxJ33H377n7P0vaJunFzcYCuuGe1AESuOeeHPe6V3o4Z8c6J2O9hiJllWLljZRVipd3\ndmWK3ydI+v6y5R+MHwMAdA9zNgBMsW6eT3bmkUfO8+nWdNODD+p569e3uk3kZXfqAAns3r07dQR0\nyPr16/Xww1fryCPPbGV7Dz20R/ffv/LR3a1se15ivYZ2pw5Q0e7UASrYnTpARbtTB2iNufv0FcxO\nlvTf3f2M8fK7JLm7v2fFetOfCAA6zN0tdYZ5YM4GkIM6c3aZ4vdgSbdJOk3SjyR9TdKr3H3XrBsF\nADSDORsApluz7cHdHzazt0q6SqMe4Y8yiQJANzFnA8B0a175BQAAAPqi8h3ezOxEM9tpZjvG/73X\nzM41sw1mdpWZ3WZmXzCzo5oInMKUfb7AzH4wfnyHmZ2ROus8mdnbzeybZnazmV1qZo/q+XFeub+H\nZHCMzzOzW8Z/zh0/1ttjLK26z709ztHm7GjzbbR5MtI8F2l+6vq8YmYfNbM9ZnbzssdWHUsze7eZ\nfcfMdpnZ6V3Oa2abzOz+ZeP8F2s+f50rvzb6MvUfSHq2pLdK+id3f6+N7ii0wd3fNfOTd9SKfX6j\npJ+7+/vTppo/MztW0vWSnuzuD5rZX0v6rKSnqofHecr+Lqq/x/g3JX1c0m9LekjS5yS9WdIfqYfH\nWJq6z69VT4/zctHm7K7Pt9HmyUjzXKT5KcK8YmanSLpP0iXu/vTxY+/RAcbSzJ4q6VKN9uc4SddI\nepK32CpQMe8mSZ+erFdG5Su/Kzxf0u3u/n2NvkT94vHjF0t6Sc3n7qrl+yxJvfiE+CoOlnS4ma2T\ndKikH6rfx3n5/h6m0f5K/T3GT5F0g7s/4O4PS/qSpJdKOkv9Pcar7bPU3+O8XLQ5O8J8G22ejDLP\nRZqfOj+vuPv1kvaueHi18/QsSdvc/SF33y3pOxrdPKc1FfNKFce5bvH7CkmXjX/e6O57JMnd75L0\n+JrP3VWv0OhfeBNvNbOhmX2kK2+/zIO73ynpfZLu0GhyvNfdr1FPj/MB9vee8f5KPT3Gkr4p6Xnj\nt5IOk/QiSb+unh7jsQPt83GSXP09zstFm7M7Pd9GmyeDzXOR5qeo88rjVxnLlTfK+aG6caOc1fJK\n0uK45WH7+KrxVDMXv2a2XqN/HVw+fmjl5fDefZLuAPv8F5JOcPclSXdJSv7WxryY2YJG/8raJOlY\nja4UvEY9Pc4H2N8jzOzV6vExdvdvSXqPpKs1eutzp6SHD7Rqm7maNGWfP6ieHueJaHN2hPk22jwZ\naZ6LND/1aF5JPpYVTfL+SNIT3f0kSe+QdJmZHTHtL9a58vtvJX3D3e8eL+8xs42SZGbHSPpxjefu\nqsk+/0SS3P0ny3pgPqxRf0xfPF/Sd939p+O3cf5G0nPU3+O8cn+vkPScnh9juftF7v6v3X2g0Y3d\nb1N/j7GkA+7zt/t+nMeizdkR5tto82SoeS7S/BR0XlltLH+o0VX2ieP0SHtMSgfM6+4Puvve8c87\nJN0u6cRpT1Sn+H2V9n876kpJm8c/ny3pUzWeu6v22+fx4E+8VKO3PvriDkknm9mjzcw0+sL8W9Xf\n43yg/d1Tiu74AAAEjklEQVTV82MsM3vc+L9PlPQHGr0l3tdjLOnA+9z34zwWbc6OMN9GmydDzXOR\n5qcg84pp/97Y1cbySkmvtNE3lxwv6V9qdLOctpXKa2aPHX84VmZ2gkZ5vzv1md298h+NmuR/Iukx\nyx47WqNPBN6m0ZerL8zy3F39s8o+XyLpZklDSX+rUS9S8qxz3OcLJO0a7+PFktb3+Tiv2N+Pjfe3\n78f4SxpNyDslDcaP9fYYT9nnvh/nUHN2pPk22jwZaZ6LND91fV7R6B8Od0p6QKN/BL1B0obVxlLS\nuyX9w/hcOb3LefXIPyx2SLpR0ovWen5ucgEAAIBs1P22BwAAACAMil8AAABkg+IXAAAA2aD4BQAA\nQDYofgEAAJANil8AAABkg+IXrTCzh8f33R6a2Y1mdnKJv3Oumd1qZn/VRkYAwHRm9hIz+6WZnbjs\nsf9lZreY2XvM7MVm9uSUGYG18D2/aIWZ/czdjxz/fLqk/+yj20BO+zu7JJ3m7neW3MbBPrplJwCg\nAWa2TdKvSfqiu28ZP3aPpA3u7mZ2kaTPuPsnKzwnczdaxZVftGX5LQqPkvTTfb8w+w9m9rXxVeEL\nxo99UNIJkj5nZueZ2QYz+xszu8nMvmJmTxuvd4GZXWJm10u6xMwOMrP3mtkN4+d7U4v7CAC9ZWaH\nS3qupD/U6PbTMrNPSTpC0jfM7L9JOkvSe8fv9B1vZieY2efM7Otmdu3kirGZXWRmHzSzr0p6T5o9\nQq7WpQ6AbBxqZjskHSrpGEm/J0lm9gJJT3L3Z43vNX+lmZ3i7m82szM0uk3kXjP7P5J2uPsfmNmp\nkv5K0jPGz/0USc919wfHxe497v5sM3uUpC+b2VXu/r2W9xcA+ubFkj7v7v9gZneb2TPc/cXjd/ZO\nkiQzO17Sp939ivHyNZL+nbvfbmbPkvRBSaeNn+8J7r5mCxwwbxS/aMv9yybHkzUqXp8m6XRJLxgX\nxibpcElPknT9+O9NrhifotH9u+Xu283saDM7Yvy7K939wfHPp0v6V2b28vHykePno/gFgHpeJWnr\n+Oe/Hi/v1P7v7O0zvlL8HEmXjy9uSNL6Zatc3lBOYCqKX7TO3b9qZo81s8dqNGn+T3f/8Fp/bcrv\nfrHsZ5P0Nne/um5OAMCImW3Q6B27p5mZSzpYo3n5P035awdJ2ju58HEAv1jlcaBR9PyiLfuuDIw/\nCXyQpH+S9AVJbxxfIZCZHTsuile6TtJrx+sMJN3t7vcdYL0vSHqLma0br/skMzt0njsCABl6uaRL\n3P14dz/B3TdJ+kcze96K9X6u0Ttucvefj9d52eSXZvb01hIDq+DKL9ry6GWtDZL0eh991cjV42L4\n78bviv1coyL3bu1/tXeLpAvN7CaNrha8fpXtfETSoqQd47fZfizpJXPeFwDIzSv0qx9M+6RGrQ+/\nXPbYNkkfNrO3SXqZpNdI+ksz+y8a1RzbJN2s6e/mAY3iq84AAACQDdoeAAAAkA2KXwAAAGSD4hcA\nAADZoPgFAABANih+AQAAkA2KXwAAAGSD4hcAAADZoPgFAABANv4/diLzqmBPkjMAAAAASUVORK5C\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8fdcf47750>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pylab.figure(figsize=(12,4))\n",
    "\n",
    "pylab.subplot(1,2,1)\n",
    "pylab.grid()\n",
    "pylab.hist(weight_data.Before, color = 'r')\n",
    "pylab.xlabel('Before')\n",
    "\n",
    "pylab.subplot(1,2,2)\n",
    "pylab.grid()\n",
    "pylab.hist(weight_data.After, color = 'b')\n",
    "pylab.xlabel('After')\n",
    "\n",
    "pylab.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Before</th>\n",
       "      <th>After</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>29.000000</td>\n",
       "      <td>29.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>82.689655</td>\n",
       "      <td>85.696552</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>4.845495</td>\n",
       "      <td>8.351924</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>70.000000</td>\n",
       "      <td>71.300000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>80.400000</td>\n",
       "      <td>81.900000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>82.600000</td>\n",
       "      <td>83.900000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>85.000000</td>\n",
       "      <td>90.900000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>94.900000</td>\n",
       "      <td>103.600000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          Before       After\n",
       "count  29.000000   29.000000\n",
       "mean   82.689655   85.696552\n",
       "std     4.845495    8.351924\n",
       "min    70.000000   71.300000\n",
       "25%    80.400000   81.900000\n",
       "50%    82.600000   83.900000\n",
       "75%    85.000000   90.900000\n",
       "max    94.900000  103.600000"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "weight_data.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Двухвыборочные критерии для связных выборок"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$H_0\\colon$ медианы веса до и после терапии совпадает\n",
    "\n",
    "$H_1\\colon$ медианы веса до и после тепрапии отличаются"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "95% confidence interval for median weight before therapy: [80.926107, 84.453203]\n"
     ]
    }
   ],
   "source": [
    "print '95%% confidence interval for median weight before therapy: [%f, %f]' % zconfint(weight_data.Before)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "95% confidence interval for median weight after therapy: [82.656817, 88.736286]\n"
     ]
    }
   ],
   "source": [
    "print '95%% confidence interval for median weight after therapy: [%f, %f]' % zconfint(weight_data.After)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXQAAAEACAYAAACj0I2EAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nEgQ6ACRBoANAEv8Bj9Bsj29skdAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8fae3c5b10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pylab.hist(weight_data.After - weight_data.Before)\n",
    "pylab.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Критерий знаков"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$H_0\\colon$ медианы равны\n",
    "\n",
    "$H_1\\colon$ медианы не равны"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "M: 3, p-value: 0.264931\n"
     ]
    }
   ],
   "source": [
    "print \"M: %d, p-value: %f\" % sign_test(weight_data.After - weight_data.Before)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Критерий знаковых рангов Вилкоксона"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "WilcoxonResult(statistic=131.5, pvalue=0.062919722626026672)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.wilcoxon(weight_data.After, weight_data.Before)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "WilcoxonResult(statistic=131.5, pvalue=0.062919722626026672)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.wilcoxon(weight_data.After - weight_data.Before)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Перестановочный критерий"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "$H_0\\colon E(X_1 - X_2) = 0$\n",
    "\n",
    "$H_1\\colon E(X_1 - X_2) ≠ 0$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def permutation_t_stat_1sample(sample, mean):\n",
    "    t_stat = sum(map(lambda x: x - mean, sample))\n",
    "    return t_stat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def permutation_zero_distr_1sample(sample, mean, max_permutations = None):\n",
    "    centered_sample = map(lambda x: x - mean, sample)\n",
    "    if max_permutations:\n",
    "        signs_array = set([tuple(x) for x in 2 * np.random.randint(2, size = (max_permutations, \n",
    "                                                                              len(sample))) - 1 ])\n",
    "    else:\n",
    "        signs_array =  itertools.product([-1, 1], repeat = len(sample))\n",
    "    distr = [sum(centered_sample * np.array(signs)) for signs in signs_array]\n",
    "    return distr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8fabf35710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pylab.hist(permutation_zero_distr_1sample(weight_data.After - weight_data.Before, 0., \n",
    "                               max_permutations = 10000))\n",
    "pylab.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def permutation_test(sample, mean, max_permutations = None, alternative = 'two-sided'):\n",
    "    if alternative not in ('two-sided', 'less', 'greater'):\n",
    "        raise ValueError(\"alternative not recognized\\n\"\n",
    "                         \"should be 'two-sided', 'less' or 'greater'\")\n",
    "    \n",
    "    t_stat = permutation_t_stat_1sample(sample, mean)\n",
    "    \n",
    "    zero_distr = permutation_zero_distr_1sample(sample, mean, max_permutations)\n",
    "    \n",
    "    if alternative == 'two-sided':\n",
    "        return sum([1. if abs(x) >= abs(t_stat) else 0. for x in zero_distr]) / len(zero_distr)\n",
    "    \n",
    "    if alternative == 'less':\n",
    "        return sum([1. if x <= t_stat else 0. for x in zero_distr]) / len(zero_distr)\n",
    "\n",
    "    if alternative == 'greater':\n",
    "        return sum([1. if x >= t_stat else 0. for x in zero_distr]) / len(zero_distr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p-value: 0.034000\n"
     ]
    }
   ],
   "source": [
    "print \"p-value: %f\" % permutation_test(weight_data.After - weight_data.Before, 0., \n",
    "                               max_permutations = 1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p-value: 0.034821\n"
     ]
    }
   ],
   "source": [
    "print \"p-value: %f\" % permutation_test(weight_data.After - weight_data.Before, 0., \n",
    "                               max_permutations = 50000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "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": 0
}