CH4/templates/11_stat.non_parametric_tests_ind.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": [
    "## Недвижимость в Сиэттле"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Имеются данные о продажной стоимости недвижимости в Сиэтле для 50 сделок в 2001 году и 50 в 2002. Изменились ли в среднем цены?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true,
    "scrolled": 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\n",
    "from statsmodels.stats.weightstats import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "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,
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "seattle_data = pd.read_csv('seattle.txt', sep = '\\t', header = 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100, 2)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "seattle_data.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Price</th>\n",
       "      <th>Year</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>142.0</td>\n",
       "      <td>2002</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>232.0</td>\n",
       "      <td>2002</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>132.5</td>\n",
       "      <td>2002</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>200.0</td>\n",
       "      <td>2002</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>362.0</td>\n",
       "      <td>2002</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Price  Year\n",
       "0  142.0  2002\n",
       "1  232.0  2002\n",
       "2  132.5  2002\n",
       "3  200.0  2002\n",
       "4  362.0  2002"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "seattle_data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true,
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "price2001 = seattle_data[seattle_data['Year']  == 2001].Price\n",
    "price2002 = seattle_data[seattle_data['Year']  == 2002].Price"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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k0JMcgJ7k8tCTjJXQk7wcPckASkdPMgAAADBGnZ0kl9rnU0cHSKijAyTwOuYptl6F5gJG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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f04704ce750>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pylab.figure(figsize=(12,4))\n",
    "\n",
    "pylab.subplot(1,2,1)\n",
    "pylab.grid()\n",
    "pylab.hist(price2001, color = 'r')\n",
    "pylab.xlabel('2001')\n",
    "\n",
    "pylab.subplot(1,2,2)\n",
    "pylab.grid()\n",
    "pylab.hist(price2002, color = 'b')\n",
    "pylab.xlabel('2002')\n",
    "\n",
    "pylab.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Двухвыборочные критерии для независимых выборок"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$H_0\\colon$ медианы стоимости недвижимости в 2001 и 2002 годах совпадают\n",
    "\n",
    "$H_1\\colon$ медианы стоимости недвижимости в 2001 и 2002 годах не совпадают"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "95% confidence interval for the mean: [245.193581, 332.659499]\n"
     ]
    }
   ],
   "source": [
    "print '95%% confidence interval for the mean: [%f, %f]' % zconfint(price2001)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "95% confidence interval for the mean: [241.437946, 417.076334]\n"
     ]
    }
   ],
   "source": [
    "print '95%% confidence interval for the mean: [%f, %f]' % zconfint(price2002)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Ранговый критерий Манна-Уитни"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$H_0\\colon P(X > Y) = \\frac1{2}$ \n",
    "\n",
    "$H_1\\colon  P(X > Y) ≠ \\frac1{2}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MannwhitneyuResult(statistic=1295.5, pvalue=0.75638726757017483)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.mannwhitneyu(price2001, price2002)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Перестановочный критерий"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "$H_0\\colon F_{X_1}(x) = F_{X_2}(x)$\n",
    "\n",
    "$H_1\\colon F_{X_1}(x) = F_{X_2}(x + \\Delta), \\Delta\\neq 0$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true,
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "def permutation_t_stat_ind(sample1, sample2):\n",
    "    return np.mean(sample1) - np.mean(sample2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "def get_random_combinations(n1, n2, max_combinations):\n",
    "    index = range(n1 + n2)\n",
    "    indices = set([tuple(index)])\n",
    "    for i in range(max_combinations - 1):\n",
    "        np.random.shuffle(index)\n",
    "        indices.add(tuple(index))\n",
    "    return [(index[:n1], index[n1:]) for index in indices]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "def permutation_zero_dist_ind(sample1, sample2, max_combinations = None):\n",
    "    joined_sample = np.hstack((sample1, sample2))\n",
    "    n1 = len(sample1)\n",
    "    n = len(joined_sample)\n",
    "    \n",
    "    if max_combinations:\n",
    "        indices = get_random_combinations(n1, len(sample2), max_combinations)\n",
    "    else:\n",
    "        indices = [(list(index), filter(lambda i: i not in index, range(n))) \\\n",
    "                    for index in itertools.combinations(range(n), n1)]\n",
    "    \n",
    "    distr = [joined_sample[list(i[0])].mean() - joined_sample[list(i[1])].mean() \\\n",
    "             for i in indices]\n",
    "    return distr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Nm8j0TlU9n+TtwHG+/ZFNA1+SZmxml0uUJE3fVL6Rm+RXknw2yfNJrh9q35vk60ke6X7u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\nEENfkhry//aZ9kfI5IsDAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0460e0fed0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pylab.hist(permutation_zero_dist_ind(price2001, price2002, max_combinations = 1000))\n",
    "pylab.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "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_ind(sample, mean)\n",
    "    \n",
    "    zero_distr = permutation_zero_dist_ind(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": 16,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p-value: 0.435700\n"
     ]
    }
   ],
   "source": [
    "print \"p-value: %f\" % permutation_test(price2001, price2002, max_permutations = 10000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p-value: 0.442080\n"
     ]
    }
   ],
   "source": [
    "print \"p-value: %f\" % permutation_test(price2001, price2002, 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,
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}