6. k-sample Tests.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import typing as tp\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.patches as mpatches\n",
    "import seaborn as sns\n",
    "import scipy.stats as stats\n",
    "from statsmodels.distributions.empirical_distribution import ECDF"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "%load_ext pycodestyle_magic\n",
    "%pycodestyle_on\n",
    "\n",
    "%load_ext mypy_ipython"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# №1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Условие:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Сравнить на выборках $\\mathcal{N} (1, 1)$ и $\\mathcal{N} (2, 4)$ размера а) 20 б) 100 критерии Манна-Уитни,\n",
    "Смирнова, Баумгартнера-Вейсса-Шиндлера. У последнего критерия в Python нет реализации, поэтому используйте permutation подход для вычисления уровня значимости."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Решение:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Для начала напишем необходимые функции, вычисляющие p-value критерия Баумгартнера-Вейсса-Шиндлера. Для этого реализуем метод перестановок."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "def permutation_method(first_data: np.ndarray, second_data: np.ndarray,\n",
    "                       statistic: tp.Callable[[np.ndarray, np.ndarray], float],\n",
    "                       permutations_number: int) -> float:\n",
    "    true_statistic_value = statistic(first_data, second_data)\n",
    "    united_data = np.concatenate([first_data, second_data])\n",
    "    p_value = 0\n",
    "    for _ in range(permutations_number):\n",
    "        data_permutation = np.random.permutation(united_data)\n",
    "        stat_value = statistic(data_permutation[:first_data.size],\n",
    "                               data_permutation[first_data.size:])\n",
    "        p_value += stat_value > true_statistic_value\n",
    "    return p_value / permutations_number\n",
    "\n",
    "\n",
    "def BWStest_statistic(first_data: np.ndarray,\n",
    "                      second_data: np.ndarray) -> float:\n",
    "    if not first_data.size or not second_data.size:\n",
    "        raise Exception(\"Data is empty!\")\n",
    "\n",
    "    united_data = np.concatenate([first_data, second_data])\n",
    "    united_ranks = stats.rankdata(united_data, method='ordinal')\n",
    "    first_data_ranks = united_ranks[:first_data.size]\n",
    "    second_data_ranks = united_ranks[first_data.size:]\n",
    "\n",
    "    first_data_ranks.sort()\n",
    "    second_data_ranks.sort()\n",
    "    n = first_data.size\n",
    "    m = second_data.size\n",
    "\n",
    "    B_X = sum((rank - (i+1)*(n+m)/n)**2 / ((i+1) * (1 - (i+1)/(n+1)))\n",
    "              for i, rank in enumerate(first_data_ranks))\n",
    "    B_X *= (n+1) / (m*(n+m))\n",
    "\n",
    "    B_Y = sum((rank - (i+1)*(n+m)/m)**2 / ((i+1) * (1 - (i+1)/(m+1)))\n",
    "              for i, rank in enumerate(second_data_ranks))\n",
    "    B_Y *= (m+1) / (n*(n+m))\n",
    "\n",
    "    return (B_X+B_Y) / 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Теперь сравним критерии. Для этого построим графики ЭФР p-value для каждого из критериев."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_mannwhitneyu_pvalues(number_of_samples: int,\n",
    "                             sample_size: int) -> tp.List[float]:\n",
    "    return [stats.mannwhitneyu(stats.norm.rvs(1, 1, sample_size),\n",
    "                               stats.norm.rvs(2, 2, sample_size)).pvalue\n",
    "            for _ in range(number_of_samples)]\n",
    "\n",
    "\n",
    "def get_ks_2samp_pvalues(number_of_samples: int,\n",
    "                         sample_size: int) -> tp.List[float]:\n",
    "    return [stats.ks_2samp(stats.norm.rvs(1, 1, sample_size),\n",
    "                           stats.norm.rvs(2, 2, sample_size)).pvalue\n",
    "            for _ in range(number_of_samples)]\n",
    "\n",
    "\n",
    "def get_BWStest_pvalues(number_of_samples: int,\n",
    "                        sample_size: int,\n",
    "                        number_of_permutations: int = 500) -> tp.List[float]:\n",
    "    return [permutation_method(stats.norm.rvs(1, 1, sample_size),\n",
    "                               stats.norm.rvs(2, 2, sample_size),\n",
    "                               BWStest_statistic,\n",
    "                               number_of_permutations)\n",
    "            for _ in range(number_of_samples)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def build_pvalue_plots(number_of_samples: int, sample_size: int) -> None:\n",
    "    x = np.arange(0, 1, 0.01)\n",
    "\n",
    "    plt.figure(figsize=(15, 10))\n",
    "    red_patch = mpatches.Patch(color='red', label='Smirnov')\n",
    "    blue_patch = mpatches.Patch(color='blue', label='Mann-Whitney')\n",
    "    green_patch = mpatches.Patch(color='green', label='BWS')\n",
    "\n",
    "    plt.title(label='ECDFs of p-values')\n",
    "    plt.legend(handles=[red_patch, blue_patch, green_patch], loc='upper right')\n",
    "    plt.plot(x, ECDF(get_ks_2samp_pvalues(number_of_samples,\n",
    "                                          sample_size))(x), 'r')\n",
    "    plt.plot(x, ECDF(get_mannwhitneyu_pvalues(number_of_samples,\n",
    "                                              sample_size))(x), 'b')\n",
    "    plt.plot(x, ECDF(get_BWStest_pvalues(number_of_samples,\n",
    "                                         sample_size))(x), 'g')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1080x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "build_pvalue_plots(number_of_samples=200, sample_size=20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "build_pvalue_plots(number_of_samples=200, sample_size=100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# №2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Условие:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "В файле Pulse.csv указаны данные о замере пульса дважды через небольшое время.\n",
    "\n",
    "Студенты с показателем ran = 1 между замерами должны были бежать, студенты с показателем ran = 2 сидеть.\n",
    "\n",
    "Показатели Smokes, Alcohol принимают 1, если студент употребляет сигареты и алкоголь\n",
    "и 2 иначе.\n",
    "\n",
    "Exercise — как часто студент занимается физическими нагрузками (1 — часто, 3 — редко).\n",
    "\n",
    "Как пульс зависит от образа жизни? Изменение пульса у бежавших студентов? Если ли значимая разница между изменением пульса в разные годы?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Решение:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Height</th>\n",
       "      <th>Weight</th>\n",
       "      <th>Age</th>\n",
       "      <th>Gender</th>\n",
       "      <th>Smokes</th>\n",
       "      <th>Alcohol</th>\n",
       "      <th>Exercise</th>\n",
       "      <th>Ran</th>\n",
       "      <th>Pulse1</th>\n",
       "      <th>Pulse2</th>\n",
       "      <th>Year</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>173</td>\n",
       "      <td>57.0</td>\n",
       "      <td>18</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>86.0</td>\n",
       "      <td>88.0</td>\n",
       "      <td>93</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>179</td>\n",
       "      <td>58.0</td>\n",
       "      <td>19</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>82.0</td>\n",
       "      <td>150.0</td>\n",
       "      <td>93</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>167</td>\n",
       "      <td>62.0</td>\n",
       "      <td>18</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>96.0</td>\n",
       "      <td>176.0</td>\n",
       "      <td>93</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>195</td>\n",
       "      <td>84.0</td>\n",
       "      <td>18</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>71.0</td>\n",
       "      <td>73.0</td>\n",
       "      <td>93</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>173</td>\n",
       "      <td>64.0</td>\n",
       "      <td>18</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>90.0</td>\n",
       "      <td>88.0</td>\n",
       "      <td>93</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Height  Weight  Age  Gender  Smokes  Alcohol  Exercise  Ran  Pulse1  \\\n",
       "0     173    57.0   18       2       2        1         2    2    86.0   \n",
       "1     179    58.0   19       2       2        1         2    1    82.0   \n",
       "2     167    62.0   18       2       2        1         1    1    96.0   \n",
       "3     195    84.0   18       1       2        1         1    2    71.0   \n",
       "4     173    64.0   18       2       2        1         3    2    90.0   \n",
       "\n",
       "   Pulse2  Year  \n",
       "0    88.0    93  \n",
       "1   150.0    93  \n",
       "2   176.0    93  \n",
       "3    73.0    93  \n",
       "4    88.0    93  "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pulse_df = pd.read_csv(\"Pulse.csv\", sep='\\t')\n",
    "pulse_df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Как пульс и изменение пульса у бежавших студентов зависит от образа жизни?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "pulse_df['Pulse diff'] = pulse_df['Pulse2'] - pulse_df['Pulse1']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Для начала посмотрим, как пульс и его изменение зависят от того, насколько человек интенсивно занимается спортом. В качестве первого шага проверим однородность данных с помощью k-sample Anderson-Darling."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "first_exercise_data = pulse_df.loc[pulse_df[\"Exercise\"] == 1]\n",
    "second_exercise_data = pulse_df.loc[pulse_df[\"Exercise\"] == 2]\n",
    "third_exercise_data = pulse_df.loc[pulse_df[\"Exercise\"] == 3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "14"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "first_exercise_data[\"Pulse1\"].size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "59"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "second_exercise_data[\"Pulse1\"].size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "37"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "third_exercise_data[\"Pulse1\"].size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Anderson_ksampResult(statistic=2.397433117349596, critical_values=array([0.44925884, 1.3052767 , 1.9434184 , 2.57696569, 3.41634856,\n",
       "       4.07210043, 5.56419101]), significance_level=0.03040937125519201)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.anderson_ksamp([first_exercise_data[\"Pulse1\"],\n",
    "                      second_exercise_data[\"Pulse1\"],\n",
    "                      third_exercise_data[\"Pulse1\"]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Видим, что данные неоднородны. Выясним, какие из выборок однородны с помощью критериев Манна-Уитни и BWS."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.054"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "permutation_method(first_exercise_data[\"Pulse1\"],\n",
    "                   second_exercise_data[\"Pulse1\"],\n",
    "                   BWStest_statistic, 500)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.104"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "permutation_method(second_exercise_data[\"Pulse1\"],\n",
    "                   third_exercise_data[\"Pulse1\"],\n",
    "                   BWStest_statistic, 500)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.008"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "permutation_method(first_exercise_data[\"Pulse1\"],\n",
    "                   third_exercise_data[\"Pulse1\"],\n",
    "                   BWStest_statistic, 500)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Видим, что третья и первая выборки неоднородны, а p-value в остальном случае хоть и больше 0.05, но все еще довольно мал.\n",
    "\n",
    "Теперь применим для тех же выборок критерий Манна-Уитни с альтернативой доминирования."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MannwhitneyuResult(statistic=286.0, pvalue=0.9631441661296231)"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.mannwhitneyu(first_exercise_data[\"Pulse1\"],\n",
    "                   second_exercise_data[\"Pulse1\"],\n",
    "                   alternative='less')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MannwhitneyuResult(statistic=888.5, pvalue=0.9374964936087348)"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.mannwhitneyu(second_exercise_data[\"Pulse1\"],\n",
    "                   third_exercise_data[\"Pulse1\"],\n",
    "                   alternative='less')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MannwhitneyuResult(statistic=136.0, pvalue=0.9954722213124471)"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.mannwhitneyu(first_exercise_data[\"Pulse1\"],\n",
    "                   third_exercise_data[\"Pulse1\"],\n",
    "                   alternative='less')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Видим, что во всех случаях p-value близок к единице, а значит, согласно критерию Манна-Уитни, чем реже человек занимается спортом, тем больше у него пульс до физических нагрузок.\n",
    "\n",
    "Теперь рассмотрим, насколько однородно изменение пульса для тех, кто бегал относительно того, насколько интенсивно человек занимается спортом."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "first_exercise_pulse_diff = \\\n",
    "    first_exercise_data.loc[first_exercise_data[\"Ran\"] == 1][\"Pulse diff\"]\n",
    "second_exercise_pulse_diff = \\\n",
    "    second_exercise_data.loc[second_exercise_data[\"Ran\"] == 1][\"Pulse diff\"]\n",
    "third_exercise_pulse_diff = \\\n",
    "    third_exercise_data.loc[third_exercise_data[\"Ran\"] == 1][\"Pulse diff\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "first_exercise_pulse_diff.size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "25"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "second_exercise_pulse_diff.size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "14"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "third_exercise_pulse_diff.size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/dmitrii/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:3: UserWarning: p-value capped: true value larger than 0.25\n",
      "  This is separate from the ipykernel package so we can avoid doing imports until\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Anderson_ksampResult(statistic=-1.1223952617603856, critical_values=array([0.44925884, 1.3052767 , 1.9434184 , 2.57696569, 3.41634856,\n",
       "       4.07210043, 5.56419101]), significance_level=0.25)"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.anderson_ksamp([first_exercise_pulse_diff,\n",
    "                      second_exercise_pulse_diff,\n",
    "                      third_exercise_pulse_diff])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "По результатам k-sample Anderson-Darling выборки однородны. Убедимся в их попарной однородности с помощью критерия BWS."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.968"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "permutation_method(first_exercise_pulse_diff, second_exercise_pulse_diff,\n",
    "                   BWStest_statistic, 500)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.604"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "permutation_method(second_exercise_pulse_diff, third_exercise_pulse_diff,\n",
    "                   BWStest_statistic, 500)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.906"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "permutation_method(first_exercise_pulse_diff, third_exercise_pulse_diff,\n",
    "                   BWStest_statistic, 500)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Как видим, во всех трех случаях BWS критерий демонстрирует большой p-value, поэтому можно принять гипотезу однородности данных изменения пульса у бежавших студентов относительно их любви к спорту."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Проведем аналогичное исследование относильно курения и употребления алкоголя. Сначала рассмотрим курение."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "smoking_people_data = pulse_df.loc[pulse_df[\"Smokes\"] == 1]\n",
    "not_smoking_people_data = pulse_df.loc[pulse_df[\"Smokes\"] == 2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "11"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "smoking_people_data[\"Pulse1\"].size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "99"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "not_smoking_people_data[\"Pulse1\"].size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.89"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "permutation_method(smoking_people_data[\"Pulse1\"],\n",
    "                   not_smoking_people_data[\"Pulse1\"],\n",
    "                   BWStest_statistic, 500)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MannwhitneyuResult(statistic=473.0, pvalue=0.23939523427493187)"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.mannwhitneyu(smoking_people_data[\"Pulse1\"],\n",
    "                   not_smoking_people_data[\"Pulse1\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "И критерий Манна-Уитни, и BWS принимают гипотезу однородности данных, а значит пульс незначимо зависит от того, курит ли человек. Здесь, правда, возможна ошибка в выводах, так как выборка курящих людей слишком мала, что может быть фатально для асимптотических критериев.\n",
    "\n",
    "Посмотрим на подвыборки тех студентов, которым пришлось бежать."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "4:80: E501 line too long (82 > 79 characters)\n"
     ]
    }
   ],
   "source": [
    "smoking_people_pulse_diff = \\\n",
    "    smoking_people_data.loc[smoking_people_data[\"Ran\"] == 1][\"Pulse diff\"]\n",
    "not_smoking_pulse_diff = \\\n",
    "    not_smoking_people_data.loc[not_smoking_people_data[\"Ran\"] == 1][\"Pulse diff\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "smoking_people_pulse_diff.size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "43"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "not_smoking_pulse_diff.size"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Видим, что выборка курящих и бежавших людей крайне мала - всего 3 человека, поэтому пропустим их сравнение.\n",
    "\n",
    "Теперь проделаем аналогичные действия относительно употребления алкоголя."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "drinking_people_data = pulse_df.loc[pulse_df[\"Alcohol\"] == 1]\n",
    "not_drinking_people_data = pulse_df.loc[pulse_df[\"Alcohol\"] == 2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "68"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "drinking_people_data[\"Pulse1\"].size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "42"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "not_drinking_people_data[\"Pulse1\"].size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.66"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "permutation_method(drinking_people_data[\"Pulse1\"],\n",
    "                   not_drinking_people_data[\"Pulse1\"],\n",
    "                   BWStest_statistic, 500)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MannwhitneyuResult(statistic=1418.0, pvalue=0.4766681863495431)"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.mannwhitneyu(drinking_people_data[\"Pulse1\"],\n",
    "                   not_drinking_people_data[\"Pulse1\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Опять же и критерий Манна-Уитни, и BWS принимают гипотезу однородности данных, а значит пульс незначимо зависит от того, выпивает ли человек.\n",
    "\n",
    "Теперь проведем анализ разницы пульса для бежавших студентов."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "4:80: E501 line too long (84 > 79 characters)\n"
     ]
    }
   ],
   "source": [
    "drinking_people_pulse_diff = \\\n",
    "    drinking_people_data.loc[drinking_people_data[\"Ran\"] == 1][\"Pulse diff\"]\n",
    "not_drinking_people_pulse_diff = \\\n",
    "    not_drinking_people_data.loc[not_drinking_people_data[\"Ran\"] == 1][\"Pulse diff\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "31"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "drinking_people_pulse_diff.size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "15"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "not_drinking_people_pulse_diff.size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.828"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "permutation_method(drinking_people_pulse_diff,\n",
    "                   not_drinking_people_pulse_diff,\n",
    "                   BWStest_statistic, 500)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MannwhitneyuResult(statistic=227.0, pvalue=0.45334021875640623)"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.mannwhitneyu(drinking_people_pulse_diff,\n",
    "                   not_drinking_people_pulse_diff)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Как видим, критерии BWS и Манна-Уитни демонстрирует большой p-value, поэтому можно принять гипотезу однородности данных изменения пульса у бежавших студентов относительно их любви к алкоголю.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Вывод**: алкоголь и курение незначительно влияют на пульс человека в отличие от того, насколько интенсивно человек занимается спортом. При этом изменение пульса после бега в целом не зависит от того, какой образ жизни человек ведет."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Если ли значимая разница между изменением пульса в разные годы?**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "year_to_pulse_diff = {}\n",
    "for year, df_slice in pulse_df.groupby('Year'):\n",
    "    year_to_pulse_diff[year] = df_slice[\"Pulse diff\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/dmitrii/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:1: UserWarning: p-value capped: true value larger than 0.25\n",
      "  \"\"\"Entry point for launching an IPython kernel.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Anderson_ksampResult(statistic=-1.2929933692305589, critical_values=array([0.52625, 1.32975, 1.8935 , 2.43675, 3.138  , 3.66875, 4.854  ]), significance_level=0.25)"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.anderson_ksamp(year_to_pulse_diff.values())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Как видим, ее нет."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# №3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Условие:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "В файле taylor.txt содержится информация о результатах австралийского игрока в крикет Марка Тэйлора. Посчитано, сколько очков он набирал в первом и во втором раундах игры (* означает, что во втором раунде он не появлялся). Можно ли утверждать, что удачный первый раунд помогает набирать очки во втором?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Решение:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>First</th>\n",
       "      <th>Second</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>136</td>\n",
       "      <td>60</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>62</td>\n",
       "      <td>27</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>85</td>\n",
       "      <td>37</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>71</td>\n",
       "      <td>48</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>9</td>\n",
       "      <td>164</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   First  Second\n",
       "0    136      60\n",
       "1     62      27\n",
       "2     85      37\n",
       "4     71      48\n",
       "6      9     164"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "taylor_df = pd.read_csv(\"taylor.txt\", sep='\\t')\n",
    "taylor_df = taylor_df.drop(columns=\"Unnamed: 2\")\n",
    "taylor_df = taylor_df.loc[taylor_df['Second'] != \"*\"]\n",
    "taylor_df[\"Second\"] = pd.to_numeric(taylor_df[\"Second\"])\n",
    "taylor_df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Разделим наш dataframe на 2 половины: в первую попадут те строки, которые меньше медианы значений очков за первый раунд, а во второй - все остальные. Соответственно так мы поделим все игры на успешные и неуспешные по первому раунду."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "first_round_median = taylor_df[\"First\"].median()\n",
    "less_points_df = taylor_df.loc[taylor_df[\"First\"] < first_round_median]\n",
    "greater_points_df = taylor_df.loc[taylor_df[\"First\"] >= first_round_median]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Для ответа на вопрос, влияет ли успешность первого раунда на успешность второго, нужно выполняется ли гипотеза доминирования для очков во втором раунде для двух полученных датафреймов. Проверим это с помощью критерия Манна-Уитни. Заодно и проверим однородность с помощью критерия BWS."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.244"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "permutation_method(less_points_df[\"Second\"],\n",
    "                   greater_points_df[\"Second\"],\n",
    "                   BWStest_statistic, 500)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MannwhitneyuResult(statistic=231.5, pvalue=0.08683809411856896)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.mannwhitneyu(less_points_df[\"Second\"], greater_points_df[\"Second\"], alternative=\"less\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Видим, что критерии BWS и Манна-Уитни не отвергают гипотезу однородности, а значит можно сказать, что успешный первый раунд не влияет на успешность второго."
   ]
  }
 ],
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