math2_hw8.ipynb

{
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   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "### Задача 1\n",
    "\n",
    "Провести дисперсионный анализ для определения того, есть ли различия среднего роста среди взрослых футболистов, хоккеистов и штангистов. Даны значения роста в трех группах случайно выбранных спортсменов:\n",
    "\n",
    "football_players = [173, 175, 180, 178, 177, 185, 183, 182]\n",
    "\n",
    "hockey_players = [177, 179, 180, 188, 177, 172, 171, 184, 180]\n",
    "\n",
    "lifters = [172, 173, 169, 177, 166, 180, 178, 177, 172, 166, 170]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(8, 9, 11)"
      ]
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     "execution_count": 16,
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   ],
   "source": [
    "y1 = np.array([173, 175, 180, 178, 177, 185, 183, 182], dtype=np.float64)\n",
    "y2 = np.array([177, 179, 180, 188, 177, 172, 171, 184, 180], dtype=np.float64)\n",
    "y3 = np.array([172, 173, 169, 177, 166, 180, 178, 177, 172, 166, 170], dtype=np.float64)\n",
    "\n",
    "n1 = y1.shape[0]\n",
    "n2 = y2.shape[0]\n",
    "n3 = y3.shape[0]\n",
    "n1,n2,n3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(179.125, 178.66666666666666, 172.72727272727272)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Выборочные средние по каждой группе:\n",
    "y1_mean = y1.mean()\n",
    "y2_mean = y2.mean()\n",
    "y3_mean = y3.mean()\n",
    "\n",
    "y1_mean, y2_mean, y3_mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(176.46428571428572, 28)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = np.concatenate([y1, y2, y3])\n",
    "y_mean = y.mean()\n",
    "n = y.shape[0]\n",
    "y_mean, n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(253.9074675324678, 577.0568181818182, 830.9642857142854, 830.964285714286)"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "S2_F = n1 * (y1_mean - y_mean) ** 2 + n2 * (y2_mean - y_mean) ** 2 + n3 * (y3_mean - y_mean) ** 2\n",
    "\n",
    "S2_res = ((y1 - y1_mean) ** 2).sum() + ((y2 - y2_mean) ** 2).sum() + ((y3 - y3_mean) ** 2).sum()\n",
    "\n",
    "S2_F, S2_res, ((y - y_mean) ** 2).sum(), S2_F + S2_res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(126.9537337662339, 23.08227272727273)"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k = 3\n",
    "n = n1 + n2 + n3\n",
    "\n",
    "k1 = k - 1\n",
    "k2 = n - k\n",
    "\n",
    "sigma2_F = S2_F / k1\n",
    "sigma2_res = S2_res / k2\n",
    "\n",
    "sigma2_F, sigma2_res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.500053450812598"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T = sigma2_F / sigma2_res\n",
    "T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.3851899614491687"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy import stats\n",
    "alpha = 0.05\n",
    "\n",
    "F_crit = stats.f.ppf(1 - alpha, k1, k2)\n",
    "F_crit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Различие среднего роста спортсмена в зависимости от вида спорта является статистически значимым.\n"
     ]
    }
   ],
   "source": [
    "if T > F_crit:\n",
    "    print('Различие среднего роста спортсмена в зависимости от вида спорта является статистически значимым.')\n",
    "else:\n",
    "    print('Статистически значимого различия не выявлно')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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