2-4. 가설 검정 - 모평균.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "cd0560fe",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "pandas 0.25.1\n",
      "numpy 1.18.5\n",
      "scipy 1.5.2\n",
      "matplotlib 3.5.3\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import scipy\n",
    "\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "for i in [pd, np, scipy, mpl]:\n",
    "    print(i.__name__, i.__version__)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f52bdfd5",
   "metadata": {},
   "source": [
    "# 2-4 가설 검정 -  모평균"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "dc3b3a4d",
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import norm, t"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "41fde07b",
   "metadata": {},
   "source": [
    "## 1. 단일 모집단의 평균\n",
    "\n",
    "모집단의 평균($\\mu_0$)에 대한 검정입니다.\n",
    "\n",
    "$H_0: \\mu = \\mu_0$\n",
    "\n",
    "$H_1: $\n",
    "\n",
    "|대립 가설|검정 종류|\n",
    "|---|---|\n",
    "|$$H_1: \\mu < \\mu_0$$|좌측 꼬리(left)|\n",
    "|$$H_1: \\mu > \\mu_0$$|우측 꼬리(right)|\n",
    "|$$H_1: \\mu \\ne \\mu_0$$|양쪽 꼬리(two-sided)|\n",
    "\n",
    "### Z 검정\n",
    "\n",
    "#### 가정\n",
    "\n",
    "- 모분산($\\sigma^2$)을 알고 있습니다.\n",
    "\n",
    "\n",
    "- 모집단이 정규 분포를 따르거나, 중심극한정리를 적용할  만큼의 충분한 표본의 수(보통 25개 이상)일 경우\n",
    "\n",
    "\n",
    "- 표본은 서로 독립입니다.\n",
    "\n",
    "#### 증거의 확률 분포 및 통계량\n",
    "\n",
    "$H_0$이 맞다면, \n",
    "\n",
    "> $\\mu_{\\bar{X}}=\\mu_0$, $\\sigma^2_{\\bar{X}}=\\frac{\\sigma^2}{n}$ \n",
    "\n",
    "확률 분포와 검정 통계량\n",
    "\n",
    "> $\\bar{X} \\sim N(\\mu_0, \\frac{\\sigma^2}{n})$\n",
    ">\n",
    "> $Z = \\frac{\\bar{X}-\\mu_0}{\\sigma/\\sqrt{n}}\\sim N(0, 1)$ \n",
    "\n",
    "------------------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0691a5ae",
   "metadata": {},
   "source": [
    "**[Ex.1]**\n",
    "\n",
    "<div style=\"border: 1px solid #ddd; padding: 12px; margin-top: 10px\">\n",
    "\n",
    "이마의 온도를 측정하여 체온을 구하는 온도계가 있습니다. 이 체온계는 동일한 센서로 16번의 측정을 하여 평균값을 온도로 출력합니다.\n",
    "\n",
    "이 온도계의 센서로 실제 체온이 36.5도를 잴 경우 0.4도의 표준편차가 있다고 합니다. 이를 바탕으로 0.4를 모표준편차라고 가정합니다.\n",
    "\n",
    "체온이 36.5보다 높을 경우 알람을 울리는 기능을 만든다고 합니다. 유의 수준을 0.05로 할 때, 다음 센서 출력이 왔을 때의 알람 여부를 구하세요.\n",
    "\n",
    "```\n",
    "    36.27, 37.10, 36.81, 36.10, 36.47, 37.36, 35.73, 36.53, \n",
    "    37.21, 36.35, 36.43, 36.66, 37.30, 36.44, 36.52, 36.53\n",
    "```\n",
    "    \n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e902ffd2",
   "metadata": {},
   "source": [
    "$H_0: \\mu = 36.5$\n",
    "\n",
    "$H_1: \\mu > 36.5$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "02c76be4",
   "metadata": {},
   "source": [
    "$Z = \\frac{\\bar{X}-36.5}{0.4/\\sqrt{n}}\\sim N(0, 1)$\n",
    "\n",
    "**우측 검정** 입니다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "939d06aa",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "검정통계량(Z): 1.131249999999966, pvalue: 0.12897494127716136\n"
     ]
    }
   ],
   "source": [
    "X = [36.27, 37.10, 36.81, 36.10, 36.47, 37.36, 35.73, 36.53,\n",
    "    37.21, 36.35, 36.43, 36.66, 37.30, 36.44, 36.52, 36.53]\n",
    "\n",
    "X_bar = np.mean(X) # 표본평균 \n",
    "mu_X_bar = 36.5 # 표본평균의 모평균\n",
    "n = len(X)\n",
    "sigma_X_bar = 0.4 / (n ** 0.5) # 표본평균의 모표준편차\n",
    "\n",
    "Z = (X_bar - mu_X_bar) / sigma_X_bar # 검정통계량\n",
    "\n",
    "print(\"검정통계량(Z): {}, pvalue: {}\".format(Z, norm.sf(Z))) # sf = 1 - cdf"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1c0f9d9e",
   "metadata": {},
   "source": [
    "$H_0$ not Rejected → 알람을 울리지 않습니다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "25791ed4",
   "metadata": {},
   "outputs": [
    {
     "data": {
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WKyZBnmlHQRlTX1xNcKCFz+ZcT1CgxeiSRLyKJ79DtfaEiJ9b8dVxHE4XF8SHeV1gABjRL4J+kUHU1DvI29d2fxcROX8KDSJ+7uPGjorfGB7fzp69k8lk4hvD4wDI3VXUzt6dUFcH99zj3s4xgVvEHyg0iPixBoeTFbuLAUi/KM7gajov/SJ34Pl453G6fMS1oQGWLnVvDd28zoVIL6fQIOLHNh08RVlNPdEhgVw2sO31Xnq78UP6EBRopqCslp3HKowuR8RnKTSI+LGmoYlrL4zDYjYZXE3nBQVamDC0LwC5O7thiEJEAIUGEb/2n8ZfsNdd5J3zGc7UNLzyn+5e9VLEjyk0iPipAyVV7C+uIsBsYuIFsUaXc96aJkN+friU4gpNWBTpDgoNIn6q6TR+WkoMEUGBBldz/uIighg5IBKAT3S2QaRbKDSI+Kncne5frNd56aWWrWl6Ld1y6aWIKDSI+KOymno25p8E4DovvtTy65pey6o9JdTWO7rmoCEhcPy4e1MbafFzCg0ifujTr4ppcLoYGhfGoD6hRpfTZS5OjCA+wka13cG6/V3UHdJkgr593ZvJe68wEekKCg0ifqhpPsN1w33nLAM0dYdsHKLYqXkNIl1NoUHEzzidLlZ+5e4C+Q0fCw1w+tLLptd43urq4P773ZvaSIufU2gQ8TM7Cso5VV1PmC2Aywd5bxfItlyR0odAi4lDJ6s5eKLq/A/Y0AC/+517Uxtp8XMKDSJ+5tM97r/Axw/pQ6DF9z4CQm0BjG4MQ5921dkGEQEUGkT8TtMv0quHeX9Dp7ZMHOZuKf3pnhKDKxHxLQoNIn6ksq6BLYdOAad/sfqiqxtfW96+E9Q7nAZXI+I7FBpE/Mj6/Seod7gYGBNCcqzvXGr5dRcnRhATaqWyroGth0uNLkfEZyg0iPiRVY2n6yf68NAEgNlsYsJQ92tcpXkNIl1GoUHEjzRNgvTloYkmTcFopeY1iHSZAKMLEJGeceRUNfuLq7CYTYwf0sfocrpdUzDadqSU0mo7USHWzh0oOBgOHDj9tYgf05kGET+xuvEv7tSkKCKDvX9Vy/YkRAZxQXwYLhes2XseLaXNZkhOdm9mfWSKf9P/ABE/0TQ0cbUfDE00aXqtq/ZoXoNIV1BoEPEDDqer+UzDxAt8exLkmSZe0BQaSnC5XJ07iN0Ojz7q3uz2LqxOxPt0KjQsXLiQ5ORkgoKCSEtLY8OGDW3u+/e//50xY8YQFRVFaGgoqampvPbaay32cblczJkzh379+hEcHEx6ejp79uzpTGki0optR0opr20gIiiAkf0jjS6nx4xLjsEaYOZoaQ37ijvZUrq+HubPd2/19V1boIiX8Tg0LFu2jKysLObOncuWLVsYNWoUGRkZHD/e+opyMTEx/PKXvyQvL49t27aRmZlJZmYmH374YfM+zz77LC+++CKLFi1i/fr1hIaGkpGRQW1tbedfmYg0a7rU8qqhsQT4YOvotgRbLYxLjgE0RCHSFTz+9Hj++eeZOXMmmZmZjBgxgkWLFhESEsKSJUta3X/SpEncfPPNXHTRRQwZMoQHH3yQkSNHsnr1asB9lmHBggU8/vjj3HTTTYwcOZJXX32VgoIC3n333VaPWVdXR3l5eYtNRNq2yo8utfy6pksvV+nSS5Hz5lFosNvtbN68mfT09NMHMJtJT08nLy+v3ce7XC5yc3PZvXs3V199NQAHDhygsLCwxTEjIyNJS0tr85jZ2dlERkY2b0lJSZ68DBG/UlFbz5ZDpYDvN3VqzdUXnG4pbW9QS2mR8+FRaCgpKcHhcBAfH9/i9vj4eAoLC9t8XFlZGWFhYVitVqZOncpLL73E9ddfD9D8OE+OOXv2bMrKypq3w4cPe/IyRPzKhgMncThdDOoTQlJMiNHl9LjhCeHEhlmpqXeopbTIeeqR5k7h4eFs3bqVyspKcnNzycrKIiUlhUmTJnXqeDabDZvN1rVFiviotfvcPQquHOJ/ZxkATCYTV6T04f1tx1i7r4Rxg2OMLknEa3l0piE2NhaLxUJRUVGL24uKikhISGj7Scxmhg4dSmpqKg8//DC33nor2dnZAM2P8/SYItIxa/Y2TYL0/S6QbbmqcR2KtefT5ElEPAsNVquV0aNHk5ub23yb0+kkNzeX8ePHd/g4TqeTuro6AAYPHkxCQkKLY5aXl7N+/XqPjikiZztRWceuwgoArkjx39BwZWPb7M8On6La3uDZg4OD4Ysv3JvaSIuf83h4Iisri7vvvpsxY8Ywbtw4FixYQFVVFZmZmQDMmDGD/v37N59JyM7OZsyYMQwZMoS6ujo++OADXnvtNV5++WXAferwoYce4umnn2bYsGEMHjyYJ554gsTERKZNm9Z1r1TED63bfxJoGtf33yG9gTEh9I8K5mhpDZvyTzVPjuwQsxkuvrj7ihPxIh6HhunTp1NcXMycOXMoLCwkNTWVnJyc5omMhw4dwnxGf/aqqiruu+8+jhw5QnBwMMOHD+cvf/kL06dPb97nscceo6qqih/96EeUlpYyYcIEcnJyCAoK6oKXKOK/1u5zD034wwJV52IyuRfpenvzEdbuO+FZaBCRZiZXp3ur9h7l5eVERkZSVlZGRESE0eWI9BrXzl/BgZIq/jhjDOkj4tt/gA9757Mj/Peyzxk5IJJ/PjCh4w+02+F//sf99S9+AdZOrpYp0kt58jvUf1rDifiZgtIaDpRUYTbBuBRdMTA+xT0Z8oujZZRVe9AOur4efvUr96Y20uLnFBpEfFRe46WWlw6IIiLI95fCbk9CZBApfUNxumD9AV1FIdIZCg0iPmpN43yGK/18PsOZmt6Lpt4VIuIZhQYRH+RyuZrPNFzlp02dWtP0XjRNEBURzyg0iPig/BPVHCurxWoxM3pQtNHl9BpNvSq+KqqkuKLO4GpEvI9Cg4gPavpL+rKBUQRbLQZX03tEh1oZ0c89Ozxvv4YoRDyl0CDig5raJfvrehPn0jyvYa+GKEQ8pdAg4mOcTlfzX9H+vN5EW5rXoejoZMigINiwwb2p4Zz4uR5Z5VJEes7uogpOVtkJsVoYOSDK6HJ6nbGDY7CYTRw6Wc3hk9XtLxduscDYsT1TnEgvpzMNIj6m6S/oMckxWAP0X/zrwmwBjBoQCWheg4in9Iki4mPW7W+az6ChibY0rcWxriOhwW6H3/zGvdnt3VyZSO+m0CDiQ5xOFxsOuFe29OelsNvT9N6s33+Sdpffqa+Hxx5zb2ojLX5OoUHEh+wsLKespp5Qq4VLErV4W1tGD4omwGziaGkNR07VGF2OiNdQaBDxIU1dIMcOjiHAov/ebQmxBjAqKQo4/Z6JSPv0qSLiQ9btdw9NjNfQRLua3qMOzWsQEUChQcRnOJwuNjSu3qj5DO274ozQ0O68BhEBFBpEfMbOY+WU1zYQZgvgYs1naNflg6IItJgoKKvl8EnNaxDpCIUGER/RdJp9bHK05jN0QIg1gFGNza80RCHSMfpkEfERTb/4xqs/Q4c1vVfnbPIUFASffOLe1EZa/JxCg4gPcDhdrFd/Bo91aF6DxQKTJrk3i1YMFf+m0CDiA3YeK6eitoFwW0Dz0s/SvssHRhNoMXGsrJZDJ6uNLkek11NoEPEBTUMT49SfwSPBVguXJUUD55jXUF8PCxe6N3WEFD+nTxcRH9DUoEhDE567IiUGOEeTJ7sdHnjAvWntCfFzCg0iXs6h9SbOy+l5DR1Yh0LEz3UqNCxcuJDk5GSCgoJIS0tjw4YNbe67ePFiJk6cSHR0NNHR0aSnp5+1/z333IPJZGqxTZkypTOlifidLwvKqahrIDwogBHqz+CxywdFY7WYKSyv5eAJzWsQORePQ8OyZcvIyspi7ty5bNmyhVGjRpGRkcHx48db3X/FihXceeedfPLJJ+Tl5ZGUlMTkyZM5evRoi/2mTJnCsWPHmre//vWvnXtFIn6maSw+bXAMFrPJ4Gq8T1CghdSBUYD6NYi0x+PQ8PzzzzNz5kwyMzMZMWIEixYtIiQkhCVLlrS6/+uvv859991Hamoqw4cP549//CNOp5Pc3NwW+9lsNhISEpq36Ojozr0iET9zOjRoaKKzmoYoztmvQUQ8Cw12u53NmzeTnp5++gBmM+np6eTl5XXoGNXV1dTX1xMTE9Pi9hUrVhAXF8eFF17IrFmzOHGi7f+8dXV1lJeXt9hE/NGZ8xnU1KnzmiZDrte8BpFz8ig0lJSU4HA4iI+Pb3F7fHw8hYWFHTrGz372MxITE1sEjylTpvDqq6+Sm5vLvHnzWLlyJTfccAMOh6PVY2RnZxMZGdm8JSUlefIyRHzGmfMZLlJ/hk67fKDmNYh0REBPPtkzzzzDm2++yYoVKwg6ox3rHXfc0fz1pZdeysiRIxkyZAgrVqzguuuuO+s4s2fPJisrq/n78vJyBQfxS+sbV7Ucl6z5DOcjKNBCalIUG/JPsv7ACZJjQ0/fabPB+++f/lrEj3l0piE2NhaLxUJRUVGL24uKikhISDjnY+fPn88zzzzDRx99xMiRI8+5b0pKCrGxsezdu7fV+202GxERES02EX/UNJ9Bl1qev6YhinX7T7a8IyAApk51bwE9+neWSK/jUWiwWq2MHj26xSTGpkmN48ePb/Nxzz77LE899RQ5OTmMGTOm3ec5cuQIJ06coF+/fp6UJ+JXzlxvIi0lpp29pT1pHVmHQsTPeXz1RFZWFosXL2bp0qXs3LmTWbNmUVVVRWZmJgAzZsxg9uzZzfvPmzePJ554giVLlpCcnExhYSGFhYVUVlYCUFlZyaOPPsq6devIz88nNzeXm266iaFDh5KRkdFFL1PE92i9ia515joUh0/WnL6jvh5eecW9qY20+DmPz7VNnz6d4uJi5syZQ2FhIampqeTk5DRPjjx06BBm8+ks8vLLL2O327n11ltbHGfu3Lk8+eSTWCwWtm3bxtKlSyktLSUxMZHJkyfz1FNPYdP4oUibmoYmxmq9iS4RbHXPa9iYf4p1+08wsE+I+w67HRr/KOK22yAw0LgiRQzWqQG6Bx54gAceeKDV+1asWNHi+/z8/HMeKzg4mA8//LAzZYj4taax97TBGproKmmD+zSHhtvHanK1yNfpzxMRL+Tuz6BJkF3tCs1rEDknhQYRL7SrsJzy2gbCbAFcrPUmuszlg6IItJgoKKvlyKma9h8g4mcUGkS8UNPQxNjkaM1n6EIh1gBGDYgC1FJapDX6tBHxQs3rTWhoosulNfdrUGgQ+TqFBhEv4zxjvQnNZ+h6Te/p+q83eRKRnm0jLSLnb1dhBWU19YRaLVyi+QxdbvSgaALMJo6W1nD4ZDVJETb429/cd+oycPFzOtMg4mWaTpuPSVZ/hu4QYg1g5IBIoPG9Dghw92e47Ta1kRa/p08cES+zXpdadrvmIYoDGqIQOZNCg4gXcWq9iR7RFBry9p2AhgZ46y331tBgcGUixtK5NhEvsquwgtJq93yGS/tHGl2OzzpzXsORY6cYcPvt7jsqKzVEIX5NZxpEvMiZ8xkCNZ+h24TaTs9r2JCvIQqRJvrUEfEiTQ2Hxg/RfIbu1vQeb9C8BpFmCg0iXkL9GXpW03u8UWcaRJopNIh4iS+PlVNWU0+YLUD9GXrA6EHR7nUoSmuNLkWk11BoEPESTfMZtN5EzzhzHQoRcdMnj4iXWKf5DD1Ow0AiLSk0iHgBxxn9GfSLrOeMH9KHeksAT93yKK4lS8BqNbokEUMpNIh4gS8LyqmobSDcFsDFierP0FMuHxiNyRrIn4Zew8Ebb4fAQKNLEjGUQoOIF2gamhg3OAaL2WRwNf4j2GrhsqRoQEtli4BCg4hXUH8G44wfFMG1+zZS9va7aiMtfk/9UEV6uQaHk42az2CY8QPC+O+3fwWA64lMTOHhBlckYhydaRDp5b48Vk5FXQMRQQFc1E/9GXpaauPwBMDBw18aWImI8RQaRHq5vH1N8xn6aD6DAYICLc1fr9+x3cBKRIyn0CDSy6k/Q++xMb/U6BJEDNWp0LBw4UKSk5MJCgoiLS2NDRs2tLnv4sWLmThxItHR0URHR5Oenn7W/i6Xizlz5tCvXz+Cg4NJT09nz549nSlNxKc0OJxszD8FwBUpMQZXI+tLonE5nUaXIWIYj0PDsmXLyMrKYu7cuWzZsoVRo0aRkZHB8ePHW91/xYoV3HnnnXzyySfk5eWRlJTE5MmTOXr0aPM+zz77LC+++CKLFi1i/fr1hIaGkpGRQW2ter6Lf9t+tIzKugYigwO5KEHzGYxWUh/Fvv2fG12GiGE8Dg3PP/88M2fOJDMzkxEjRrBo0SJCQkJYsmRJq/u//vrr3HfffaSmpjJ8+HD++Mc/4nQ6yc3NBdxnGRYsWMDjjz/OTTfdxMiRI3n11VcpKCjg3XffPa8XJ+Lt1jbOZxif0gez5jP0CnlfbDO6BBHDeBQa7HY7mzdvJj09/fQBzGbS09PJy8vr0DGqq6upr68nJsZ9qvXAgQMUFha2OGZkZCRpaWltHrOuro7y8vIWm4gvWruvBIArh2o+g2GsVphzByu/cxn1lgDWHKgwuiIRw3gUGkpKSnA4HMTHx7e4PT4+nsLCwg4d42c/+xmJiYnNIaHpcZ4cMzs7m8jIyOYtKSnJk5ch4hVq6x1sapzPcKUmQRonMBC+N4nwKdU0WALIK+mL0+EwuioRQ/To1RPPPPMMb775Ju+88w5BQUGdPs7s2bMpKytr3g4fPtyFVYr0DlsOnaKuwUlcuI0hfcOMLsfvjQzZQ5i5mjJHGF/u3mR0OSKG8Cg0xMbGYrFYKCoqanF7UVERCQkJ53zs/PnzeeaZZ/joo48YOXJk8+1Nj/PkmDabjYiIiBabiK9p6s9w5ZA+mEyaz2AYhwPW7yZgp5O0YPd8hrU71ORJ/JNHocFqtTJ69OjmSYxA86TG8ePHt/m4Z599lqeeeoqcnBzGjBnT4r7BgweTkJDQ4pjl5eWsX7/+nMcU8XVr9jbNZ4g1uBI/V1sL3/9f+DVMtH0GwJqDNQYXJWIMj9eeyMrK4u6772bMmDGMGzeOBQsWUFVVRWZmJgAzZsygf//+ZGdnAzBv3jzmzJnDG2+8QXJycvM8hbCwMMLCwjCZTDz00EM8/fTTDBs2jMGDB/PEE0+QmJjItGnTuu6ViniRyroGPj9SBmg+Q2+SFvYFnISNJ+Ox2+uwWm1GlyTSozwODdOnT6e4uJg5c+ZQWFhIamoqOTk5zRMZDx06hNl8+gTGyy+/jN1u59Zbb21xnLlz5/Lkk08C8Nhjj1FVVcWPfvQjSktLmTBhAjk5Oec170HEm204cAKH08XAmBAGRIcYXY40utB2kBhLGScdkXy+Yz1jL7va6JJEepTJ5XK5jC7ifJWXlxMZGUlZWZnmN4hPePr9L/nj6gPcOS6J7O+MbP8B0n2qqiCscSLqn+D+op/xr7KJ/PfIYzz43R8aW5tIF/Dkd6jWnhDphdY0NXUaovkMvc2VYe6OkGsO1RtciUjPU2gQ6WVOVtnZeczdsGx8iuYz9DZXhrmvoPisrB811Wr0JP5FoUGkl2la1fLC+HD6hmuiXW+TbC0gMfA49a5ANm1ba3Q5Ij1KoUGkl2m61FJLYfcSgYHw2HfgTiAATCYY33i2Yc3uA8bWJtLDFBpEepmmpk5XqT9D72C1wg8nw7dovt6saYgi74iabol/UWgQ6UWOldWwv6QKswnGDY4xuhxpw5Wh7smQ2yv6UVZWbHA1Ij1HoUGkF1m7132W4dL+kUQGBxpcjQDuNtLb8mEf4HTf1M96ghTrEZxYWLd1jZHVifQohQaRXmS1Wkf3PrW1cOszMAewn775qvCtAKzZfdSQskSMoNAg0ks4nS5W7XGHhonDFBp6uwlhWwFYVaCOneI/FBpEeoldhRWUVNYRHGhh9KBoo8uRdowP24YFBwdq4zh8dK/R5Yj0CIUGkV5i9V73hLorUmKwBVgMrkbaE2Gp5rKQXQCs3rrR4GpEeoZCg0gv0TQ0MWFYX4MrkY6a0DivYdXeU8YWItJDFBpEeoHaegfrD5wE4GrNZ/AaE8M+A2DN8T44HA6DqxHpfgoNIr3AxvyT2BucJEQEMTQuzOhypINGhXxFuLmSMkcY23dtNrockW6n0CDSC5wemojFZFKXwV4lMBAemArfobkjZJMAk7O5O+Sq7V/0fG0iPUyhQaQX+PQr9yRIXWrZC1mt8NMb4RbOCg0AE8PdQxSr8rVUtvg+hQYRgx2vqGVXoXuJZa034X2a5jVsKU2gskpLZYtvU2gQMVjTqpYXJ0YQG6alsHsdpxP2FMARmttIn2mQrZCB1mM0EMC6z1b3eHkiPUmhQcRgp7tA6lLLXqmmBqb+P/gZLdpIn6npbMPqXQd7ri4RAyg0iBjI5VLraF/QNK/h06NWgysR6V4KDSIG2l1UQXFFHUGBZrWO9mLjw7ZhxsH+mniOFuwzuhyRbqPQIGKg1Y1nGdIG9yEoUK2jvVWkpYrUkK8AWP3ZeoOrEek+Cg0iBlqpSy19xoTGeQ0r96iltPguhQYRg1TbG1i/3906etKFmgTp7SaFuztCriruS319GzMmRbxcp0LDwoULSU5OJigoiLS0NDZs2NDmvjt27OCWW24hOTkZk8nEggULztrnySefxGQytdiGDx/emdJEvMbavSewO5wMiA5mSF+1jvZ2o0L2EG0po8IRypYv8owuR6RbeBwali1bRlZWFnPnzmXLli2MGjWKjIwMjh8/3ur+1dXVpKSk8Mwzz5CQkNDmcS+++GKOHTvWvK1ereudxbd9stv9f+baC+PUOro3CwyEe6+HqbTaEbKJxeTkmvAtAHyy/aueqU2kh3kcGp5//nlmzpxJZmYmI0aMYNGiRYSEhLBkyZJW9x87diy/+c1vuOOOO7DZ2m5cExAQQEJCQvMWG6sxXvFdLpeLT3Y1hobhGpro1axW+Nkt8F3OGRoArg3fBMCKgxr5Fd/k0U+23W5n8+bNpKennz6A2Ux6ejp5eed3Om7Pnj0kJiaSkpLCXXfdxaFDh9rct66ujvLy8habiDf5qqiSgrJabAFmxqcoIPuKq8O3YMbBrqoECooOG12OSJfzKDSUlJTgcDiIj49vcXt8fDyFhYWdLiItLY1XXnmFnJwcXn75ZQ4cOMDEiROpqGi9j3t2djaRkZHNW1JSUqefW8QITUMT44f0IdiqSy17NacTjpRAMa22kT5TdEAFl4XsBuCTTZrXIL6nV5xDu+GGG7jtttsYOXIkGRkZfPDBB5SWlvK3v/2t1f1nz55NWVlZ83b4sBK9eJfmoYkL4wyuRNpVUwPfeBweos020mdqGqL45KuT3VqWiBE8Cg2xsbFYLBaKiopa3F5UVHTOSY6eioqK4oILLmDv3r2t3m+z2YiIiGixiXiL8tp6Nh10X8uv0OB7JkW4Q8Oa4r7U2XXppfgWj0KD1Wpl9OjR5ObmNt/mdDrJzc1l/PjxXVZUZWUl+/bto1+/fl12TJHeYtVXJTicLob0DWVgnxCjy5EudnHQfuICTlDjDGLD52uMLkekS3k8PJGVlcXixYtZunQpO3fuZNasWVRVVZGZmQnAjBkzmD17dvP+drudrVu3snXrVux2O0ePHmXr1q0tziI88sgjrFy5kvz8fNauXcvNN9+MxWLhzjvv7IKXKNK7nHmppfgek+mMIYrtewyuRqRrtXMB0dmmT59OcXExc+bMobCwkNTUVHJycponRx46dAiz+XQWKSgo4LLLLmv+fv78+cyfP59rrrmGFStWAHDkyBHuvPNOTpw4Qd++fZkwYQLr1q2jb19diia+xel0sWK3u3X0tcMVGnzVtRGbWHYqgxWHrcwxuhiRLmRyuVwuo4s4X+Xl5URGRlJWVqb5DdKrbT9Sxo2/XU2o1cJncyZjDegVc5HlXKqqIKyxY+efgKD2H1LhCObyL9+g3hXIivsvJDlpaLeWKHI+PPkdqk8skR70ceNVExOGxSow+LBwSw1jQ78E4JPNuvRSfIc+tUR6kOYzeKGAAPjuNZAOeNBSo3lew57W+82IeCOFBpEeUlxRx+dHSgGYpNDgPWw2ePJOyAQCO/6wa8M3ArDuZCKVVWXdU5tID1NoEOkh/9lZhMsFIwdEkhDZgYFx8WpDbEcYbD2K3RXIyo0rjS5HpEsoNIj0kI92uFutZ1zcdY3QpAe4XHCyAsoBD6aNm0wwOdI9n+GjLwq6pzaRHqbQINIDKmrrWbP3BACTR8S3s7f0KtXVcMWjMAuo8+yhkyPWAfDxsRjs9Q1dX5tID1NoEOkBK78qxu5wMjg2lKFxYUaXIz3kspDd9A04SYUjlHVb1xpdjsh5U2gQ6QEf7XCv1zL54nhMJpPB1UhPMZtcXB+xHoCPtu42uBqR86fQINLN7A3O5lUtJ4/QfAZ/0zyv4VAoTqfX99ITP6fQINLN8vafoKKugb7hNi5LijK6HOlh40O3EWau5nh9JJ/v+tzockTOi0KDSDdrumri+hHxmM0amvA3NnNDc8+GjzZ/ZnA1IudHoUGkGzmdLpZ/2TifQVdN+K3Jke6rKD7cr9Ao3k2hQaQbbT1SyvGKOsJsAYwf0sfocqQzAgLg5itgIh61kT7TpPBNBJrq2V/Tl70HtVy2eC+FBpFu1HTVxKQL+2IL6ORvHDGWzQbz7oEf41Eb6TOFW2q4Msw9n+GjDVrASryXQoNIN/roS3WBFLeMiMarKPZ42CFKpBdRaBDpJnuPV7C/uIpAi4lJF/Y1uhzpLJcLquugFo/aSH9desR6TDjZWp5I4fEjXVaeSE9SaBDpJu99fgyACUNjCQ/q5HltMV51NaQ+CPficRvpM8UFljI6ZCcA/1qrBazEOyk0iHQDl8vFe9vcixTdOCrR4Gqkt7gxahUA731ZbXAlIp2j0CDSDb48Vs7+4ipsAWau16WW0uibkasx42BreSKHj2mIQryPQoNIN2gamvjG8DgNTUizvoGlXBm2DYD31n5qcDUinlNoEOliLpeL9z7X0IS07sYod1j4505dRSHeR6FBpIt9driUo6U1hFotXHthnNHlSC+TEZFHoKmeXZVx7DmUb3Q5Ih5RaBDpYk1nGa4fEU+wVQ2dpKWogEquDnOvQfHe2jUGVyPiGYUGkS7kcLp4f5t7PoOGJnyExQJTLodxdNknZtMQxfu7HbhcWi5bvEen/gssXLiQ5ORkgoKCSEtLY8OGDW3uu2PHDm655RaSk5MxmUwsWLDgvI8p0lutP3CC4oo6IoMDmThMDZ18QlAQvPgjeBCwds0hr49YR5Cplv01fdix76uuOahID/A4NCxbtoysrCzmzp3Lli1bGDVqFBkZGRw/frzV/aurq0lJSeGZZ54hIaH1VrqeHlOkt2q6auKGSxKwBuhEnrQu1FLLdRHu5bLfy1tncDUiHefxp9rzzz/PzJkzyczMZMSIESxatIiQkBCWLFnS6v5jx47lN7/5DXfccQc2m61LjinSG9U7nPz7Cw1NSMc0D1HsteB0aohCvINHocFut7N582bS09NPH8BsJj09nby8zq3c1plj1tXVUV5e3mITMdrqvSWUVtcTG2bjihQtg+0zqqrggh/DXbjXn+gik8I3E2au5mhdNJ/t2NR1BxbpRh6FhpKSEhwOB/HxLTvcxcfHU1hY2KkCOnPM7OxsIiMjm7ekpKROPbdIV3pny1EApl6agMVsMrga6e2CzHYmR7iHJv5v3VZjixHpIK8cdJ09ezZlZWXN2+HDh40uSfxcWXU9OTvcIffW0Qqx0jG3xvwHgPfyo6iptRtcjUj7PAoNsbGxWCwWioqKWtxeVFTU5iTH7jimzWYjIiKixSZipH98fhR7g5OL+kVwSX/9PErHXBG6nSRrIRWOED5c94nR5Yi0y6PQYLVaGT16NLm5uc23OZ1OcnNzGT9+fKcK6I5jivS0v21yn+26fcwATCYNTUjHmE0ubot2n21YtlELWEnv5/HwRFZWFosXL2bp0qXs3LmTWbNmUVVVRWZmJgAzZsxg9uzZzfvb7Xa2bt3K1q1bsdvtHD16lK1bt7J3794OH1OkN9tRUMYXR8uxWsxMS+1vdDniZW6JzsWEk7wTCRwqLGr/ASIGCvD0AdOnT6e4uJg5c+ZQWFhIamoqOTk5zRMZDx06hNl8OosUFBRw2WWXNX8/f/585s+fzzXXXMOKFSs6dEyR3uytTe6/EK8fEU90aBd1/xG/0d9azISwrayqvJy3V35C1vQ7jC5JpE0mlw/0MC0vLycyMpKysjLNb5AeVdfgIO1/cimtrueVzLFM0gJVvqe2FqaMhbIvurQr5JneK53ITw79jERbGavm3qmrb6RHefI71CuvnhDpLZZ/WURpdT39IoPUNtpXBQXB4gfgUbolMIC7rXSkpYKCukjWfL65e55EpAsoNIich781Dk3cOnqA/jqUTgsy1zMtagUAf1u7zdhiRM5BoUGkkwpKa1i1pxhwhwaR83FbzHIAPjoSw6mKCoOrEWmdQoNIJ729+QguF1yREsOgPqFGlyPdpaoKRv0UfkCXtpH+ukuC93Nx0F7srkD+sXJ59z2RyHlQaBDphAaHk2Ubm3ozqAOkz6uxQ133P83tjR0i3/isHB+Yoy4+SKFBpBOWf1nE0dIaYkKtfPPSfkaXIz5iWvQnhJhr+KqqL2u3bTG6HJGzKDSIdMKf1+QD8N1xAwkKtBhbjPiMSEsVt0a7u+P+eYUmRErvo9Ag4qEvjpaxIf8kAWYT3x8/yOhyxMfc3ec9AHKPxXKwqNjgakRaUmgQ8VDTWYZvXtqP+IggY4sRnzMk6CiTwjfhwswrH/3H6HJEWlBoEPFASWUd731eAEDmVcnGFiM+KzP2nwC8tctKpZbMll5EoUHEA2+sP4Td4WRUUhSXDYw2uhzpCWYzjBsGF9Fjn5gTwz4jxXaYSkcQb3+S2/4DRHqIQoNIB9kbnLy27iAAP9BZBv8RHAx/eRgep9vaSH+d2eQis3Fuw9KNJ3A6dfml9A4KDSId9MH2YxRX1BEXbuOGS3SZpXSv70R/TLi5kgPV0azYssnockQAhQaRDnG5XPx5zQEAvn/FIKwB+q8j3SvUUssdMR8B8OeV2w2uRsRNn3wiHZC37wSfHynDGmDmu2kDjS5HelJVFaQ9Aj+mW9tIt2ZG7PuYcbCqOJ7t+/b17JOLtEKhQaQDXsjdA8CdY5PoE2YzuBrpcacqwYA1pJKsx7kpaiUAL/xrdc8XIPI1Cg0i7Vi3/wTrD5zEajHz40lDjC5H/MwDccsw4eQ/BbF8cfCw0eWIn1NoEGnHC/9xn2W4fewA+kUGG1yN+JshQUe5MepTAF56f6XB1Yi/U2gQOYcNB06St/8EgRYTsyYNNboc8VM/jXsTE04+PBzNzsPHjC5H/JhCg8g5vJD7FQC3jUmif5TOMogxhgYdYWqke07Di+99bHA14s8UGkTasCn/JGv2niDAbGLWNZrLIMb6abz7bMO/D0WxS2cbxCAKDSJtaLpi4tbRA0iKCTG4GjGM2QyXDIIUDP3EvCDoEN+MXAPAS++ptbQYQ6FBpBWb8k+yak8JAWYT91+ruQx+LTgY/j4bnqLH2ki35SdxbwLwwaFIdh48ZGwx4pcUGkS+xul08dT7XwI6yyC9y/Dgg0yN/BQXZp7+v5W4XFqTQnpWp0LDwoULSU5OJigoiLS0NDZs2HDO/d966y2GDx9OUFAQl156KR988EGL+++55x5MJlOLbcqUKZ0pTeS8vfPZUT4/UkaYLYCsyRcYXY5ICz/vtxSryc6a4zEs/2yH0eWIn/E4NCxbtoysrCzmzp3Lli1bGDVqFBkZGRw/frzV/deuXcudd97Jvffey2effca0adOYNm0aX3zxRYv9pkyZwrFjx5q3v/71r517RSLnoaqugXk5uwC4/9qhxIUHGVyRGK66Gq79BTwI1BldDCRZi/hh7LsA/Pr9L6hrcBhbkPgVj0PD888/z8yZM8nMzGTEiBEsWrSIkJAQlixZ0ur+L7zwAlOmTOHRRx/loosu4qmnnuLyyy/nt7/9bYv9bDYbCQkJzVt0dHTnXpHIeXh5xT6OV9QxMCaEH0xINroc6Q1cLjh6EkqAXjIacF/cW/QNOMnB6nBeWb7K6HLEj3gUGux2O5s3byY9Pf30Acxm0tPTycvLa/UxeXl5LfYHyMjIOGv/FStWEBcXx4UXXsisWbM4ceJEm3XU1dVRXl7eYhM5X4dPVvOHVfsB+MU3L8IWYDG4IpHWhVlqeCxhKQAvrT5JcXkPr6Qlfsuj0FBSUoLD4SA+Pr7F7fHx8RQWFrb6mMLCwnb3nzJlCq+++iq5ubnMmzePlStXcsMNN+BwtH7aLTs7m8jIyOYtKSnJk5ch0qpn/r0Le4OT8Sl9yLg4vv0HiBjoluiPGRn8FZUOG8/9/YP2HyDSBXrF1RN33HEH3/72t7n00kuZNm0a77//Phs3bmTFihWt7j979mzKysqat8OHtYiLnJ8NB07yr+3HMJtgzo0jMJlMRpckck5mk4s5iYsBWLYrkC8OHjW4IvEHHoWG2NhYLBYLRUVFLW4vKioiISGh1cckJCR4tD9ASkoKsbGx7N27t9X7bTYbERERLTaRzqqtdzD779sAuGPcQC7qp58n8Q5jQndyY+RKXJiZ/eZK6h1Oo0sSH+dRaLBarYwePZrc3NPdyJxOJ7m5uYwfP77Vx4wfP77F/gDLly9vc3+AI0eOcOLECfr16+dJeSKd8txHu9lXXEVcuI3HMi40uhwRjzyR+EciLRVsPxXJyx9oFUzpXh4PT2RlZbF48WKWLl3Kzp07mTVrFlVVVWRmZgIwY8YMZs+e3bz/gw8+SE5ODs899xy7du3iySefZNOmTTzwwAMAVFZW8uijj7Ju3Try8/PJzc3lpptuYujQoWRkZHTRyxRp3ab8k/xx9QEAsr9zKVEhBrf8k97HZIKh/aA/0AtHreICT/H/EhcB8OLaCnYcbnsSucj58jg0TJ8+nfnz5zNnzhxSU1PZunUrOTk5zZMdDx06xLFjpxdTufLKK3njjTf4wx/+wKhRo3j77bd59913ueSSSwCwWCxs27aNb3/721xwwQXce++9jB49mlWrVmGz2broZYqcrdrewCNvfY7L5e78eN1FmvworQgJgQ/mwrNAL/1I+nbUSjIi1tLgsvDw6x9jb9AwhXQPk8sH+pCWl5cTGRlJWVmZ5jdIhz35zx28sjaffpFBfPjfVxMRFGh0SdJb7fk9bPyx0VWcU0lDJJN3/46Tjkh+Mj6Uh2+aZHRJ4iU8+R3aK66eEOlpeftO8MrafADm3TJSgUG8XmxAGU/1/x0Av8srZ9vB1i+DFzkfCg3id0oq63j4b1sBuHPcQK6+oK+xBUnvVl0N3/wVPEavaCN9LlOj1vCtyE9xYOHB11ZSXltvdEniYxQaxK/UO5zc//oWCspqSYkN5ZdTLzK6JOntXC7YewyO0mvaSJ/LU/1fJjHwOAcqw/jvP/8bp9MLihavodAgfuXX/9rJ+gMnCbMF8IcZowmzBRhdkkiXig6o4PeDfo3NVEfuQQsLPmi9xb9IZyg0iN/4v81HmucxPHf7KIbGhRtbkEg3uTRkH9kD3IsCvrj6FB9+nm9sQeIzFBrEL2w7Usrsd7YD8NNvDCXj4rY7kor4gu9Ef8I9ff4JQNbfPmNvkRb2k/On0CA+r6C0hv96bTP2BifXDY/jofQLjC5JpEf8MvFPpIVup8phZeYfP6SkspfP5JReT6FBfNrx8lq+u3gdx8pqSekbyv/ekYrZ3Avb+ol0g0CTg98NyqZ/YBEHKkL43u8+oLTabnRZ4sUUGsRnnais464/rif/RDX9o4L5y71p6scgnjOZoH8MxNIr20i3p09AOX9JeYK+ASfZddLK91/+UJdiSqcpNIhPKquu5/t/2sCe45UkRATx15lXkBgVbHRZ4o1CQuCT/4EX6LVtpNsz2FbAGym/JMZSxvZiM5m//4iqugajyxIvpNAgPqe8tp4Zf97Al8fKiQ2z8vrMNAb2CTG6LBFDDQs6zGspjxNhqWTzMbj3Dx9SbVdwEM8oNIhPOXyymlt+t5bPD5cSFRLIX36YxpC+YUaXJdIrXBx8gFcHzyHMXM26ozD9pX9TVF5rdFniRRQaxGdsOXSKm3+3hj3HK4mPsPH6D9MYnqAFzOQ81dTAd7LhCfh0O9w4HxLvB9Nd8O6mcz/02Cn47m/hgofB/D146LWz9/n7RhjzOETNhNAfQOpseG3V2ftMzoY+/+V+3q35Le8/WQk/WQoXPgLB98DAn8JPl0JZ9dnPlxryFa8OfqJ5qGLaCx/xZYEux5SOUWgQn/De5wXc8Yd1lFTaGdEvgnfvv4qLEyONLkt8gdMJXxyE/VBVC6MGwsJ7OvbQugboGwGPT3M/rjUxofDLmyDvSdiWDZnXQOYf4MNtp/epqoUJF8K8O1o/RsEp9zb/u/DFPHjlvyBnG9z7h9b3vzx0N+8MfZghtsMcq7Jw2+9W8PFOLXAl7VMPXfFq9gYnL+R+xcJP9gGQflEcL9xxGaFqDy3d4IZL4YaxHd8/uS+8MMP99ZKVre8zaUTL7x+cAktXwerdkDHSfdv3J7r/zS9u/RiXJMH/PXT6+yHx8Ovb4Xu/gwYHBFjOfswgWyF/H/IIsw79grWVo/jh0o1kXTeYH39jBAEW/T0prdNPhnitPUUV3Py7Nc2B4QdXDeb33x+jwCBey+WC3C9g9zG4evj5HausGiKCWw8MTSIDqlg6eA53xHyIEzPzcw9y+8Jc8kuqzu/JxWfp01W8jtPpYsmaAzz74W7sDU6iQgL59bRLmTqyn9GliXRKWTX0f8A9nGExw+/ugesv7fzxSirgqXfgR99of99Ak4Ps/i8xJmQHTxb8mC0F8M0FH/PLb13Kd9MGYTJ5YXMK6TYKDeJVPj9cytP/+pKN+acAmHRhX569ZSRxEUEGVybSeeFBsPV/oLIWcndA1uuQEnf20EVHlFfD1N/AiP7w5Hc69hiTCW6N+ZgrwrbzyOH/Zl3VSH757g4+2Lqfx28aw0X9NKFY3BQaxCscPlnN/I9284+tBQAEB1p4/FsX8d1xA/WXkHg9sxmGNq6hlpoMOwsg+5+eh4aKGpjyrDuEvPPfEOjhJ/wAazFvpPySJSU38WzhDNbkwzdf+JTbLu/Hw1MuJl7h3O8pNEivVlhWy5I1B3hlbT72BicmE9x8WX8emXyhOjxKz4kOg4bKHns6p8s9VOGJ8mrImAe2QPjnwxBk7dxzm00uftj3XSZH5DGv8G7+VXY1f9tSyHvbCrh3wlDumZBCbJiXtsaU86bQIL3StiOlLFl9gPe3HaPB6QJgfEoffjn1Ii7pr0sppQeFhsL6+bDxx1TWwt7803cdKHb3TIgJg4GxMPtNOHoKXp11ep+mngqVtVBc7v7eGgAjBrhvz/4HjElxX/FQVw8fbIXXVsPLmaePcbISDpVAQan7+93H3P8mRLm38mqY/AxU2+Ev90F5jXsD9yWfnbkYYqCtiIWDnuUHVf/kf479gM3VI/jtiv384dN93JTanx9MHKJhCz9kcrlcLqOLOF/l5eVERkZSVlZGRIR+iL1VWXU9OTuO8fbmI81zFgDGJkcza9IQrr0wTkMRYow9v4eNP2bFl3Dtr8++++6J8MqP4Z5FkF8CKx4/fZ/prrP3HxQL+S+4v378b7BsHRw5CcFWGJ4ID2bA9PGn939lpbt3w9fN/Q48eQtt1gVwYIH70s/z4XLBh+Xjefn4bXxec3pp+fHJ4dw6NoXJF8cTrsXgvJYnv0MVGsRQ5bX1fLLrOO99XsDKr4qpd7h/HAPMJr41sh8/mDCYkQOijC1SpDE0+DuXC7ZUD2dJyU38u+xKnLiv57Ra4BvD47hx1ACuubAvYbrs2asoNEivZW9wsuXQKdbsLWH13hI+P1yK84yfwOEJ4XxrZD9uHZ1EQqQmXUkvUFMDk0ZBxR54DOjkXAFfc8Tel7dOXs97ZVezv25A8+0BZheXJUVx1bA4JgyNZVRSFIFqFtWrKTRIr1Bb72B/cRVfFJSx7Ugp24+UsfNYBXaHs8V+KX1DmXppP24clcgF8eEGVSvShqoqCGtc9OxPgLJsCy4XfFk7mPdKr+bfZRM4aG/ZL8VmgRGJEYwcEM3IAVFc0j+S5NgQbOfqOiU9qttDw8KFC/nNb35DYWEho0aN4qWXXmLcuHFt7v/WW2/xxBNPkJ+fz7Bhw5g3bx7f/OY3m+93uVzMnTuXxYsXU1paylVXXcXLL7/MsGHDOlSPQoMxnE4XJ6rsHCuroaC0hqOltRw5Vc3+4ir2FVdytLSG1n66+oRauWpoLBOGxnLVsFj66yoI6c0UGjxyqC6e1ZWprKm8jDWVIyl1nP2ZbDZBUnQQKX3DSekbxoDoYPpFBtM/KpjEqCCiQ6yYzZq/1FO6NTQsW7aMGTNmsGjRItLS0liwYAFvvfUWu3fvJi4u7qz9165dy9VXX012djbf+ta3eOONN5g3bx5btmzhkksuAWDevHlkZ2ezdOlSBg8ezBNPPMH27dv58ssvCQpq/3+oQkPHuFwuGpwu6h1O6htc1Dkc1NU7qWtwUlvvoK7BQbXdQVWdg2p7A1V2BxW19ZTXNFBeW095TT2nqu2cqLRTUmnnVLUdh/PcPz4RQQGNf2VEcWn/SEYOiGRgTIgmNIr3UGjoNKfLRL69H9urh7GtZhjba4axsyaZCmfoOR8XYIaYkED6hAfRJ9RGdKiViKAAIoIDiQgKJDwogFCbhRBrACFW979BgWZsARZsAWZsgWZsFguBASYCLWYCzCZ95pxDt4aGtLQ0xo4dy29/+1sAnE4nSUlJ/OQnP+HnP//5WftPnz6dqqoq3n///ebbrrjiClJTU1m0aBEul4vExEQefvhhHnnkEQDKysqIj4/nlVde4Y47zl7Wra6ujrq6uhYvOCkpqUtDw7+2HePPaw60u197b97X315Xi/vOuK3xG1fjly5c7n9dTbe5mh/jwoXTBU6Xex+ny+XenOBwunC4XDid7oDgcLpocDpxOF3Nkwy7kskEceE2EqOCSYx0/5WQ0jeMlNhQhsSF0SfUqv+s4t0UGrqUywXFDVHsq0tiX90A8usSKaiP42h9XwrssRQ3xHTL8waawWI2EWA2EWAxYTGbMJvc/1pMJsxmM2aTCbMJTI23mUxgwv0vgMlkwoT7c+/M+5o/4Rrvb/zS/W8rtbT3mdiRT8z7rh3CN4bHd2DP9nkSGjya4mq329m8eTOzZ89uvs1sNpOenk5eXl6rj8nLyyMrK6vFbRkZGbz77rsAHDhwgMLCQtLT05vvj4yMJC0tjby8vFZDQ3Z2Nr/61a88Kd1jReW1bDp4qv0dvZjJBLYAM0GBjek8wNKY2i2E2gIIDrQ0J/uI4AAiggKJCgkkNsxGnzArsWE2YkKtmuQk/sNkOf3bQDrFZII4ayVx1p2MD9/5tXtd2B0mTjoiKWmI5ERDFCUNUZQ2hFHuCKPcGUq5I5QKRyg1ThtVzmCqnUFUO4OodVqpc1mpcwZS57Li+tp6jPVOqHe6aP9PPe9Qkr8Kht/a48/rUWgoKSnB4XAQH98y3cTHx7Nr165WH1NYWNjq/oWFhc33N93W1j5fN3v27BZBpOlMQ1f6xvC4Tncc/Ppnytc/Ys5MmWel0uZ06o6vJk6nW7PpjFRrojEdNyZjkzsZt0jPjam66etAixmrxUxggAmrxYxFp+xEPHPJExCiyye6kxVIaNzaV9+4lYOjFhqqwVGLy1FLQ0M99Q0N1DvqsTc4qXc4cTgcOJxOGhxOHE5wuJyNZ2fB4QSaztq6wNF4mrfprK/TZcLlctEcO1yn44eL02eC4YzbXSa+HlK+Hlk8n1XogrAULrnkMU8f2CW88mJam82Gzda9bUyTY0NJjj33uJuI+ImQEPe/Ix5xd4iUXs0EBDZu0rU8Oq8cGxuLxWKhqKioxe1FRUUkJLSeCxMSEs65f9O/nhxTRKTHhIa65zVUVSkwiN/zKDRYrVZGjx5Nbm5u821Op5Pc3FzGjx/f6mPGjx/fYn+A5cuXN+8/ePBgEhISWuxTXl7O+vXr2zymiIiI9DyPhyeysrK4++67GTNmDOPGjWPBggVUVVWRmeleXWXGjBn079+f7OxsAB588EGuueYannvuOaZOncqbb77Jpk2b+MMf3I3UTSYTDz30EE8//TTDhg1rvuQyMTGRadOmdd0rFRERkfPicWiYPn06xcXFzJkzh8LCQlJTU8nJyWmeyHjo0CHM5tMnMK688kreeOMNHn/8cX7xi18wbNgw3n333eYeDQCPPfYYVVVV/OhHP6K0tJQJEyaQk5PToR4NIiLdqrYWbrnF/fX//R/oc0n8mNpIi4icy5l9GiorNa9BfI4nv0N1gb2IiIh0iEKDiIiIdIhCg4iIiHSIQoOIiIh0iEKDiIiIdIhXtpH+uqYLQMrLyw2uRER8TlXV6a/Ly8HhMK4WkW7Q9LuzIxdT+kRoqKioAOjyRatERFpITDS6ApFuU1FRQWRk5Dn38Yk+DU6nk4KCAsLDw/1y1camVT4PHz6sPhVdQO9n19N72vX0nnYtf34/XS4XFRUVJCYmtmjO2BqfONNgNpsZMGCA0WUYLiIiwu9+2LuT3s+up/e06+k97Vr++n62d4ahiSZCioiISIcoNIiIiEiHKDT4AJvNxty5c7HZbEaX4hP0fnY9vaddT+9p19L72TE+MRFSREREup/ONIiIiEiHKDSIiIhIhyg0iIiISIcoNIiIiEiHKDSIiIhIhyg0+Ki6ujpSU1MxmUxs3brV6HK8Vn5+Pvfeey+DBw8mODiYIUOGMHfuXOx2u9GleY2FCxeSnJxMUFAQaWlpbNiwweiSvFZ2djZjx44lPDycuLg4pk2bxu7du40uy2c888wzmEwmHnroIaNL6bUUGnzUY489RqIW1zlvu3btwul08vvf/54dO3bwv//7vyxatIhf/OIXRpfmFZYtW0ZWVhZz585ly5YtjBo1ioyMDI4fP250aV5p5cqV3H///axbt47ly5dTX1/P5MmTqTpzJU7plI0bN/L73/+ekSNHGl1K7+YSn/PBBx+4hg8f7tqxY4cLcH322WdGl+RTnn32WdfgwYONLsMrjBs3znX//fc3f+9wOFyJiYmu7OxsA6vyHcePH3cBrpUrVxpdilerqKhwDRs2zLV8+XLXNddc43rwwQeNLqnX0pkGH1NUVMTMmTN57bXXCAkJMbocn1RWVkZMTIzRZfR6drudzZs3k56e3nyb2WwmPT2dvLw8AyvzHWVlZQD6eTxP999/P1OnTm3xsyqt84lVLsXN5XJxzz338OMf/5gxY8aQn59vdEk+Z+/evbz00kvMnz/f6FJ6vZKSEhwOB/Hx8S1uj4+PZ9euXQZV5TucTicPPfQQV111FZdcconR5XitN998ky1btrBx40ajS/EKOtPgBX7+859jMpnOue3atYuXXnqJiooKZs+ebXTJvV5H39MzHT16lClTpnDbbbcxc+ZMgyoXcbv//vv54osvePPNN40uxWsdPnyYBx98kNdff52goCCjy/EKWnvCCxQXF3PixIlz7pOSksLtt9/Oe++9h8lkar7d4XBgsVi46667WLp0aXeX6jU6+p5arVYACgoKmDRpEldccQWvvPIKZrPydnvsdjshISG8/fbbTJs2rfn2u+++m9LSUv7xj38YV5yXe+CBB/jHP/7Bp59+yuDBg40ux2u9++673HzzzVgslubbHA4HJpMJs9lMXV1di/tEocGnHDp0iPLy8ubvCwoKyMjI4O233yYtLY0BAwYYWJ33Onr0KNdeey2jR4/mL3/5iz5EPJCWlsa4ceN46aWXAPcp9YEDB/LAAw/w85//3ODqvI/L5eInP/kJ77zzDitWrGDYsGFGl+TVKioqOHjwYIvbMjMzGT58OD/72c807NMKzWnwIQMHDmzxfVhYGABDhgxRYOiko0ePMmnSJAYNGsT8+fMpLi5uvi8hIcHAyrxDVlYWd999N2PGjGHcuHEsWLCAqqoqMjMzjS7NK91///288cYb/OMf/yA8PJzCwkIAIiMjCQ4ONrg67xMeHn5WMAgNDaVPnz4KDG1QaBA5h+XLl7N371727t17VvDSSbr2TZ8+neLiYubMmUNhYSGpqank5OScNTlSOubll18GYNKkSS1u//Of/8w999zT8wWJ39HwhIiIiHSIZnOJiIhIhyg0iIiISIcoNIiIiEiHKDSIiIhIhyg0iIiISIcoNIiIiEiHKDSIiIhIhyg0iIiISIcoNIiIiEiHKDSIiIhIhyg0iIiISIf8f2bZMUdpFXRpAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(6, 4))\n",
    "\n",
    "plt.plot(np.linspace(-5, 5, 100), norm.pdf(np.linspace(-5, 5, 100)))\n",
    "plt.axvline(Z, color='red', linestyle='--')\n",
    "plt.text(Z, 0.01, str(Z)[:6])\n",
    "plt.fill_between(np.linspace(Z, 5, 100), np.zeros(shape=100),\n",
    "                norm.pdf(np.linspace(Z, 5, 100)), color='orange')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "33340924",
   "metadata": {},
   "source": [
    "#### 비율 Z 검정(Propotional Z-test)\n",
    "\n",
    "- 베르누이 분포의 성질과 중심극한정리를 이용한 검정입니다.\n",
    "\n",
    "\n",
    "- 이진형 확률 변수의 1인 비율 $p$에  대한 검정입니다.\n",
    "\n",
    "$H_0: p = p_0$\n",
    "\n",
    "$H_1:$\n",
    "\n",
    "|대립 가설|검정 종류|\n",
    "|---|---|\n",
    "|$$H_1: p < p_0$$|좌측 꼬리(left)|\n",
    "|$$H_1: p > p_0$$|우측 꼬리(right)|\n",
    "|$$H_1: p \\ne p_0$$|양쪽 꼬리(two-sided)|\n",
    "\n",
    "$p$ = 모집단에서 1인 개수 / 모집단의 수 = 모집단의 합 / 모집단의 수\n",
    "\n",
    "$\\bar{p}$ = 표본에서 1인 개수 / 전체 표본수 = 표본의 합 / 전체 표본수\n",
    "\n",
    "즉, 베르누이 분포인 경우에 1인 표본 비율은 표본 평균로 간주 할 수 있습니다.\n",
    "\n",
    "**증거의 확률 분포 및 통계량**\n",
    "\n",
    "$H_0$가 맞다면,\n",
    "\n",
    "> $p=p_0$ 입니다. 베르누이 분포의 성질에 의해, $\\sigma_p^2=p(1-p)$ 입니다.\n",
    ">\n",
    "> 중심극한정리를 적용할 수 있을 만큼 표본수가 충분하다면, \n",
    ">\n",
    "> $H_0$이 맞다는 가정으로, 모분산까지 가정할 수 있어, Z 검정을 적용할 수 있게 됩니다. \n",
    "\n",
    "확률 분포와 검정 통계량\n",
    "\n",
    "> $\\bar{p} \\sim N(p_0, \\frac{p_0(1-p_0)}{n})$, n: 표본수\n",
    ">\n",
    "> $Z = \\frac{\\bar{p} - p_0}{\\sqrt{p_0(1-p_0)/n}} \\sim N(0, 1)$\n",
    "\n",
    "--------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "395e5c7a",
   "metadata": {},
   "source": [
    "**[Ex.2]**\n",
    "\n",
    "<div style=\"border: 1px solid #ddd; padding: 12px; margin-top: 10px\">\n",
    "\n",
    "A 백신 회사에서는 모든 종류의 독감 바이러스에 대한 항체를 포함할 수 없으니, \n",
    "\n",
    "그 해의 백신에 포함될 독감 바이러스 항체를 결정하기 위해 사람들이 보유하고 있는 항체를 조사합니다. \n",
    "\n",
    "먼저 후보군을 선택하여 포함 유무를 판단하고자 합니다.\n",
    "\n",
    "조사 결과 10% 이상 항체를 보유하고 있을 확률이 95% 초과한다면 후보에서 제외합니다 \n",
    "\n",
    "Z 독감 바이러스 항체 보유 여부를 1,600 명의 사람을 대상으로 조사한 결과, 165 명이 항체를 보유한 것으로 나타났습니다.\n",
    "\n",
    "Z 독감 바이러스 항체를 독감 백신에 포함 시킬 후보에 포함시킬지 판단해봅니다.\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ba27b799",
   "metadata": {},
   "source": [
    "$H_0: p = 0.1$\n",
    "\n",
    "$H_1: p > 0.1$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "35dc6526",
   "metadata": {},
   "source": [
    "$Z = \\frac{\\bar{p}-0.1}{\\sqrt{0.1(1 - 0.1)/n}}\\sim N(0, 1)$\n",
    "\n",
    "**우측 검정** 입니다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "65f07817",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "검정통계량(Z): 0.41666666666666513, pvalue: 0.3384611195106902\n"
     ]
    }
   ],
   "source": [
    "p_bar = 165 / 1600\n",
    "\n",
    "p = 0.1\n",
    "n = 1600\n",
    "sigma_p = (p * (1 - p) / n) ** 0.5\n",
    "\n",
    "Z = (p_bar - p) / sigma_p\n",
    "\n",
    "print(\"검정통계량(Z): {}, pvalue: {}\".format(Z, norm.sf(Z))) # sf = 1 - cdf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "d6bf795a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(6, 4))\n",
    "plt.plot(np.linspace(-5, 5, 100), norm.pdf(np.linspace(-5, 5, 100)))\n",
    "plt.axvline(Z, color='red', linestyle='--')\n",
    "plt.text(Z, 0.01, str(Z)[:6])\n",
    "plt.fill_between(np.linspace(Z, 5, 100), np.zeros(shape=100),\n",
    "                norm.pdf(np.linspace(Z, 5, 100)), color='orange')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "48738d5d",
   "metadata": {},
   "source": [
    "$H_0$ not Rejected → 후보에서 제외하지 않습니다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "75b56a76",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.41666666666666513, 0.3384611195106902)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#  statsmodels.stats.proportion.proportions_ztest는 위 검정에 대한 기능을 제공합니다.\n",
    "from statsmodels.stats.proportion import proportions_ztest\n",
    "\n",
    "proportions_ztest(\n",
    "    165, # count:양성(1)인 경우의 수\n",
    "    1600, # nobs: 표본수\n",
    "    0.1, # value: 모비율\n",
    "    'larger', # alternative: 대립 검정 종류 \n",
    "    0.1 # 모분산을 계산할 때의 모비율\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f9a00bb1",
   "metadata": {},
   "source": [
    "### t 검정\n",
    "\n",
    "**가정**\n",
    "\n",
    "1. 모집단이 정규 분포를 따릅니다.\n",
    "\n",
    "\n",
    "2. 각 표본은 서로 독립입니다.\n",
    "\n",
    "-----------------------------\n",
    "\n",
    "**증거의 확률 분포 및 통계량**\n",
    "\n",
    "$H_0$가 맞다면,\n",
    "\n",
    "> $\\mu_{\\bar{X}}=\\mu$\n",
    "\n",
    "확률 분포와 검정 통계량\n",
    "\n",
    "> $t = \\frac{\\bar{X} - \\mu}{s/\\sqrt{n}} \\sim t(n - 1)$, n: 표본수"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0f083211",
   "metadata": {},
   "source": [
    "**[Ex.3]**\n",
    "\n",
    "<div style=\"border: 1px solid #ddd; padding: 12px; margin-top: 10px\">\n",
    "\n",
    "흑맥주 공장에서 맥주의 품질 검사를 하려고 합니다. \n",
    "\n",
    "흑맥주 출하직전에 발효통을 골고루 섞으면서 8잔을 받아, 각 잔의 알코올 도수를 측정합니다. \n",
    "\n",
    "흑맥주의 알코올 도수가 6.5가 아니면 불합격으로 판정을 하는데요. 유의 수준을 5%로 한다면,\n",
    "\n",
    "8잔의 관측값이 다음과 같이 나왔을 때, 해당 발효통의 품질 결과를 판단해봅니다.\n",
    "\n",
    "알코올 측정 결과는 정규분포를 따르고 각 잔의 결과는 서로 독립입니다.\n",
    "\n",
    "```\n",
    "6.03, 6.55, 6.37, 5.92, 6.16, 6.71, 5.69, 6.19\n",
    "```\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cdc1cc94",
   "metadata": {},
   "source": [
    "$H_0: \\mu = 6.5$\n",
    "\n",
    "$H_1: \\mu \\ne 6.5$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0cc31f9e",
   "metadata": {},
   "source": [
    "$t = -|\\frac{\\bar{X} - 6.5}{s/\\sqrt{n}}| \\sim t(n - 1)$\n",
    "\n",
    "**양측 검정** 입니다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "8f5e4229",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "검정통계량(t): -2.5198844093376693, pvalue: 0.039817266144350286\n"
     ]
    }
   ],
   "source": [
    "X = [6.03, 6.55, 6.37, 5.92, 6.16, 6.71, 5.69, 6.19]\n",
    "\n",
    "X_bar = np.mean(X)\n",
    "mu_X_bar = 6.5\n",
    "n = len(X)\n",
    "S = np.std(X, ddof=1) # 표본 평균을 사용합니다.\n",
    "t_stat = -abs(X_bar - mu_X_bar) / (S / (n ** 0.5)) # 양측 검정이고 대칭이라 좌측 확률 영역의 통계량을 구합니다.\n",
    "print(\"검정통계량(t): {}, pvalue: {}\".format(t_stat, t.cdf(t_stat, df=n - 1) * 2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "150b26db",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(6, 4))\n",
    "\n",
    "plt.plot(np.linspace(-5, 5, 100), t.pdf(np.linspace(-5, 5, 100), df=n - 1))\n",
    "\n",
    "plt.axvline(t_stat, color='red', linestyle='--')\n",
    "plt.text(t_stat, 0.01, str(t_stat)[:6])\n",
    "plt.fill_between(np.linspace(-5, t_stat, 100), np.zeros(shape=100),\n",
    "                t.pdf(np.linspace(-5, t_stat, 100), df=n - 1), color='orange')\n",
    "\n",
    "plt.axvline(-t_stat, color='red', linestyle='--')\n",
    "plt.text(-t_stat, 0.01, str(-t_stat)[:6])\n",
    "plt.fill_between(np.linspace(-t_stat, 5, 100), np.zeros(shape=100),\n",
    "                t.pdf(np.linspace(-t_stat, 5, 100), df=n - 1), color='orange')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d9460bbc",
   "metadata": {},
   "source": [
    "$H_0$ Rejected → 통과 실패입니다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "e3a41aa4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ttest_1sampResult(statistic=-2.5198844093376693, pvalue=0.039817266144350286)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# scipy.stats.ttest_1samp 기능을 제공합니다.\n",
    "# 검정장 버젼에서는 양측 검정만 지원됩니다. \n",
    "from scipy.stats import ttest_1samp\n",
    "\n",
    "ttest_1samp(X, 6.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cea31cab",
   "metadata": {},
   "source": [
    "## 2. 서로 다른 두 모집단의 평균"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ff5a8f0f",
   "metadata": {},
   "source": [
    "서로 다른 두 개 범주에 속한 모집단의 평균 $\\mu_1$, $\\mu_2$ 에 대한 검정\n",
    "\n",
    "$H_0: \\mu_1 = \\mu_2$\n",
    "\n",
    "$H_1:$\n",
    "\n",
    "|대립 가설|검정 종류|\n",
    "|---|---|\n",
    "|$$H_1: \\mu_1 < \\mu_2$$|좌측 꼬리(left)|\n",
    "|$$H_1: \\mu_1 > \\mu_2$$|우측 꼬리(right)|\n",
    "|$$H_1: \\mu_1 \\ne \\mu_2$$|양쪽 꼬리(two-sided)|\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "75fdc150",
   "metadata": {},
   "source": [
    "### t-독립성 검정\n",
    "\n",
    "**가정**\n",
    "\n",
    "1. 두 모집단은 정규분포를 따릅니다.\n",
    "\n",
    "\n",
    "2. 각 표본들은 서로 독립입니다.\n",
    "\n",
    "-----------------------\n",
    "\n",
    "가설검정을 아래와 같이 바꿀 수 있습니다.\n",
    "\n",
    "$H_0: \\mu_1 - \\mu_2 = 0$\n",
    "\n",
    "$H_1:$\n",
    "\n",
    "|대립 가설|검정 종류|\n",
    "|---|---|\n",
    "|$$H_1: \\mu_1 - \\mu_2 < 0$$|좌측 꼬리(left)|\n",
    "|$$H_1: \\mu_1 - \\mu_2 > 0$$|우측 꼬리(right)|\n",
    "|$$H_1: \\mu_1 - \\mu_2 \\ne 0$$|양쪽 꼬리(two-sided)|"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "747f34fb",
   "metadata": {},
   "source": [
    "#### Case 1: 모분산이 동일한 경우\n",
    "\n",
    "**증거의 확률 분포 및 통계량**\n",
    "\n",
    "$H_0$가 맞다면, \n",
    "\n",
    "> $\\mu_1 - \\mu_2$도 정규 분포를 따릅니다.\n",
    "\n",
    "확률 분포와 검정 통계량\n",
    "\n",
    "두 표집의 표본분산 이 $S_1^2, S_2^2$ 이라고 하고, 표본수를 $n_1, n_2$ 라고 하면\n",
    "\n",
    "> $S_p^2 = \\frac{(n_1 - 1)S_1^2 + (n_2 - 1)S_2^2}{n_1 + n_2 - 2}$ ← 통합 분산(Pooled variance)라고 합니다.\n",
    ">\n",
    "> $t = \\frac{\\bar{X_1} - \\bar{X_2}}{S_p\\sqrt{1/n_1 + 1/n_2}} \\sim t(n_1 + n_2 - 2)$\n",
    "\n",
    "\n",
    "**유도 과정**\n",
    "\n",
    "<div style=\"border: 1px solid #ddd; padding: 12px; margin-top: 10px\">\n",
    "\n",
    "$\\frac{\\bar{X_1} - \\bar{X_2}}{S_p\\sqrt{1/n_1 + 1/n_2}} = \\frac{\\frac{\\bar{X_1} - \\bar{X_2}}{\\sigma}}{\\frac{S_p}{\\sigma}\\sqrt{1/n_1 + 1/n_2}}$\n",
    "\n",
    "$   = \\frac{\\frac{\\bar{X_1} - \\bar{X_2}}{\\sigma\\sqrt{1/n_1 + 1/n_2}}}{\\frac{S_p}{\\sigma}}$\n",
    "\n",
    "$   = \\frac{Z}{\\sqrt{\\frac{(n_1 + n_2 - 2)S_p^2}{(n_1 + n_2 - 2)\\sigma^2}}} \\sim \\frac{Z}{\\sqrt{\\frac{\\chi_{n_1 + n_2 - 2}^2}{n_1 + n_2 - 2}}} \\sim t(n_1 + n_2 - 2)$\n",
    "\n",
    "> $X_1$와 $X_2$ 는 독립이므로 $\\bar{X_1}, \\bar{X_2}$ 독립입니다. \n",
    ">\n",
    "> 따라서, $V(\\bar{X_1} - \\bar{X_2}) = V(\\bar{X_1}) + (-1)^2V(\\bar{X_2})$\n",
    ">\n",
    "> $V(\\bar{X_1} - \\bar{X_2}) = \\frac{\\sigma^2}{n_1} + \\frac{\\sigma^2}{n_2}=\\sigma^2(1/n_1 + 1/n_2)$, $\\sigma^2$: 모분산\n",
    ">\n",
    "> $\\frac{(n_1 + n_2 - 2)S_p^2}{\\sigma^2} \\sim \\chi^2(n_1 + n_2 - 2)$\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "82d542ec",
   "metadata": {},
   "source": [
    "**[Ex.4]**\n",
    "\n",
    "<div style=\"border: 1px solid #ddd; padding: 12px; margin-top: 10px\">\n",
    "\n",
    "동일한 모델의 배터리의 성능이 북반구와 남반구에서 차이가 있는지를 검정하고자 합니다. \n",
    "\n",
    "북반구에 있는 실험실 A, 남반구에 있는 실험실 B에서 동일한 모델의 배터리를 \n",
    "\n",
    "동일한 여건으로 성능 지속시간을 측정하였습니다. \n",
    "\n",
    "북반구와 남반구에서 성능이 차이가 있는지 판단해봅니다. (유의 수준 5%)\n",
    "\n",
    "표본들의 성능 측정은 독립적으로 이루어집니다. 성능 지속 시간은 정규 분포를 따릅니다.\n",
    "\n",
    "또한 모분산은 같다고 가정합니다.\n",
    "\n",
    "북반구의 지속시간\n",
    "\n",
    "```\n",
    "7.57, 8.40, 8.11, 7.40, 7.77, 8.66, 7.03, 7.83, 8.51, 7.65, 7.73, 7.96\n",
    "```\n",
    "\n",
    "\n",
    "남반구의 지속시간\n",
    "\n",
    "```\n",
    "8.07, 8.65, 8.01, 7.65, 7.54, 7.75, 7.46, 7.67, 7.95, 8.64\n",
    "```\n",
    "    \n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "594bc97b",
   "metadata": {},
   "source": [
    "$H_0: \\mu_1 = \\mu_2$\n",
    "\n",
    "$H_1: \\mu_1 \\ne \\mu_2$\n",
    "\n",
    "$S_p^2 = \\frac{(n_1 - 1)S_1^2 + (n_2 - 1)S_2^2}{n_1 + n_2 - 2} $\n",
    "\n",
    "$t = -|\\frac{\\bar{X_1} - \\bar{X_2}}{S_p\\sqrt{1/n_1 + 1/n_2}}| \\sim t(n_1 + n_2 - 2)$\n",
    "\n",
    "**양측 검정** 입니다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "1c27fd11",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "검정통계량(t): -0.2794606763724717, pvalue: 0.7827609222936273\n"
     ]
    }
   ],
   "source": [
    "X1 = [7.57, 8.40, 8.11, 7.40, 7.77, 8.66, 7.03, 7.83, 8.51, 7.65, 7.73, 7.96]\n",
    "X2 = [8.07, 8.65, 8.01, 7.65, 7.54, 7.75, 7.46, 7.67, 7.95, 8.64]\n",
    "\n",
    "X1_bar, X2_bar = np.mean(X1), np.mean(X2)\n",
    "S1_sq, S2_sq = np.var(X1, ddof=1), np.var(X2, ddof=1)\n",
    "n1, n2 = len(X1), len(X2)\n",
    "Sp_sq = ((n1 - 1) * S1_sq + (n2 - 1) * S2_sq) / (n1 + n2 - 2)\n",
    "\n",
    "# 대칭 분포인 t-분포의 확률 분포에서 좌측 통계량을 모든 경우를 고려해서 구하기 위해 -abs를 적용합니다.\n",
    "t_stat = -abs((X1_bar - X2_bar) / np.sqrt(Sp_sq * (1 / n1 + 1 / n2)))\n",
    "print(\"검정통계량(t): {}, pvalue: {}\".format(t_stat, t.cdf(t_stat, df=n1 + n2 - 2) * 2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "8a21cd82",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(6, 4))\n",
    "\n",
    "plt.plot(np.linspace(-5, 5, 100), t.pdf(np.linspace(-5, 5, 100), df=n - 1))\n",
    "\n",
    "plt.axvline(t_stat, color='red', linestyle='--')\n",
    "plt.text(t_stat, 0.03, str(t_stat)[:6])\n",
    "plt.fill_between(np.linspace(-5, t_stat, 100), np.zeros(shape=100),\n",
    "                t.pdf(np.linspace(-5, t_stat, 100), df=n - 1), color='orange')\n",
    "\n",
    "plt.axvline(-t_stat, color='red', linestyle='--')\n",
    "plt.text(-t_stat, 0.01, str(-t_stat)[:6])\n",
    "plt.fill_between(np.linspace(-t_stat, 5, 100), np.zeros(shape=100),\n",
    "                t.pdf(np.linspace(-t_stat, 5, 100), df=n - 1), color='orange')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5cd98841",
   "metadata": {},
   "source": [
    "$H_0$ not Rejected → 같습니다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "7015616e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ttest_indResult(statistic=-0.2794606763724717, pvalue=0.7827609222936273)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# scipy.stats.ttest_ind 기능을 제공합니다.\n",
    "# 검정장 버젼에서는 양측 검정만 지원됩니다. \n",
    "from scipy.stats import ttest_ind\n",
    "\n",
    "ttest_ind(X1, X2, equal_var=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e6b9af8b",
   "metadata": {},
   "source": [
    "#### Case 2: 모분산이 다를 경우\n",
    "\n",
    "웰치 t-검정(Welch's t-Test)라고도 합니다.\n",
    "\n",
    "**증거의 확률 분포 및 통계량**\n",
    "\n",
    "$\\nu  = \\frac{\\left(S_1^2/n_1 + S_2^2/n_2\\right)^2}{\\left(\\frac{S_1^2}{n_1}\\right)^2/(n_1 - 1) + \\left(\\frac{S_2^2}{n_2}\\right)^2/(n_2 - 1)}$\n",
    "\n",
    "$t = \\frac{\\bar{X_1} - \\bar{X_2}}{\\sqrt{S_1^2/n_1 + S_2^2/n_2}} \\sim t(\\nu)$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f2309014",
   "metadata": {},
   "source": [
    "**[Ex.5]**\n",
    "\n",
    "<div style=\"border: 1px solid #ddd; padding: 12px; margin-top: 10px\">\n",
    "\n",
    "데이터사이언스 강의는 오전과 오후 두 반으로 나누어 강의가 진행됩니다.\n",
    "\n",
    "모두 동일한 내용이고, 강사도 같고 성적은 같다는 생각이 지배적입니다.\n",
    "\n",
    "오전/오후 반의 일부 수강생의 성적을 가지고, 오전 / 오후 반의 성적에 차이가 있는지를 판단해봅니다. (유의 수준 5%)\n",
    "\n",
    "성적은 정규 분포를 따르고, 수강생의 개개인의 성적은 독립임을 가정합니다.\n",
    "    \n",
    "그리고, 두 반의 분산은 같지 않습니다.\n",
    "\n",
    "오전반의 성적\n",
    "\n",
    "```\n",
    "75, 94, 88, 71, 80, 100, 63, 81, 96\n",
    "```\n",
    "\n",
    "오후반의 성적\n",
    "\n",
    "```\n",
    "69, 94, 85, 64, 75, 100, 53, 77, 97, 72, 74, 81, 99, 74, 77, 77\n",
    "```\n",
    "    \n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c4430ab8",
   "metadata": {},
   "source": [
    "$H_0: \\mu_1 = \\mu_2$\n",
    "\n",
    "$H_1: \\mu_1 \\ne \\mu_2$\n",
    "\n",
    "$\\nu  = \\frac{\\left(S_1^2/n_1 + S_2^2/n_2\\right)^2}{\\left(\\frac{S_1^2}{n_1}\\right)^2/(n_1 - 1) + \\left(\\frac{S_2^2}{n_2}\\right)^2/(n_2 - 1)}$\n",
    "\n",
    "$t = -|\\frac{\\bar{X_1} - \\bar{X_2}}{\\sqrt{S_1^2/n_1 + S_2^2/n_2}}| \\sim t(\\nu)$\n",
    "\n",
    "**양측 검정** 입니다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "72625b58",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "검정통계량(t): -0.7340659707882282, pvalue: 0.47263123929211803\n"
     ]
    }
   ],
   "source": [
    "X1 = [75, 94, 88, 71, 80, 100, 63, 81, 96]\n",
    "X2 = [69, 94, 85, 64, 75, 100, 53, 77, 97, 72, 74, 81, 99, 74, 77, 77]\n",
    "\n",
    "X1_bar, X2_bar = np.mean(X1), np.mean(X2)\n",
    "S1_sq, S2_sq = np.var(X1, ddof=1), np.var(X2, ddof=1)\n",
    "n1, n2 = len(X1), len(X2)\n",
    "\n",
    "nu_denom =  ((S1_sq / n1) ** 2) / (n1 - 1) + ((S2_sq / n2) ** 2) / (n2 - 1)\n",
    "nu  = ((S1_sq / n1 + S2_sq / n2) ** 2) / nu_denom\n",
    "\n",
    "t_stat = -abs((X1_bar - X2_bar) / np.sqrt(S1_sq / n1 + S2_sq / n2))\n",
    "print(\"검정통계량(t): {}, pvalue: {}\".format(t_stat, t.cdf(t_stat, df=nu) * 2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "51884cf5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(6, 4))\n",
    "\n",
    "plt.plot(np.linspace(-5, 5, 100), t.pdf(np.linspace(-5, 5, 100), df=n - 1))\n",
    "\n",
    "plt.axvline(t_stat, color='red', linestyle='--')\n",
    "plt.text(t_stat, 0.03, str(t_stat)[:6])\n",
    "plt.fill_between(np.linspace(-5, t_stat, 100), np.zeros(shape=100),\n",
    "                t.pdf(np.linspace(-5, t_stat, 100), df=n - 1), color='orange')\n",
    "\n",
    "plt.axvline(-t_stat, color='red', linestyle='--')\n",
    "plt.text(-t_stat, 0.01, str(-t_stat)[:6])\n",
    "plt.fill_between(np.linspace(-t_stat, 5, 100), np.zeros(shape=100),\n",
    "                t.pdf(np.linspace(-t_stat, 5, 100), df=n - 1), color='orange')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9bbc156b",
   "metadata": {},
   "source": [
    "$H_0$ not Rejected → 같습니다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "945fe93f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ttest_indResult(statistic=0.7340659707882282, pvalue=0.47263123929211803)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# scipy.stats.ttest_ind 기능을 제공합니다.\n",
    "# 검정장 버젼에서는 양측 검정만 지원됩니다. \n",
    "from scipy.stats import ttest_ind\n",
    "\n",
    "ttest_ind(X1, X2, equal_var=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6ce50ae4",
   "metadata": {},
   "source": [
    "### Mann-Whitney U 검정\n",
    "\n",
    "모집단에 대한 가정이 필요하지 않은 비모수 검정법입니다.\n",
    "\n",
    "순위를 기반으로 한 검정법으로, 모집단의 평균에 대한 비교라기 보다는 대소 관계에 대한 비교를 판단합니다.\n",
    "\n",
    "$H_0: P(X_1 > X_2) = P(X_1 < X_2)$(두 모집단은 동일한 분포를 지녔다)\n",
    "\n",
    "$H_1:$\n",
    "\n",
    "|대립 가설|검정 종류|\n",
    "|---|---|\n",
    "|$$H_1: P(X_1 > X_2) < P(X_1 < X_2)$$ (모집단 1이 모집단 2 보다 작은 영역에 분포한다.)|좌측 꼬리(left)|\n",
    "|$$H_1: P(X_1 > X_2) > P(X_1 < X_2)$$ (모집단 1이 모집단 2 보다 큰 영역에 분포한다.)|우측 꼬리(right)|\n",
    "|$$H_1: P(X_1 > X_2) \\ne P(X_1 < X_2)$$ (모집단 1이 모집단 2 보다 다른 영역에 분포한다.)|양쪽 꼬리(two-sided)|\n",
    "\n",
    "\n",
    "**가정**\n",
    "\n",
    "모든 표본은 각각이 독립적입니다.\n",
    "\n",
    "**증거의 확률 분포 및 통계량**\n",
    "\n",
    "$X_1, X_2$ 를 합친 상태에서 순위를 구합니다. (1위부터 시작)\n",
    "\n",
    "$U_1 = R_1 - \\frac{n_1(n_1 + 1)}{2}$, $R_1$: X_1의 순위의 합\n",
    "\n",
    "$U_2 = R_2 - \\frac{n_2(n_2 + 1)}{2}$, $R_2$: X_2의 순위의 합\n",
    "\n",
    "$U = min(U_1, U_2) \\sim N(\\frac{n_1n_2}{2}, \\frac{n_1n_2(n_1 + n_2 + 1)}{12})$ 근사적으로 정규분포를 따릅니다.\n",
    "\n",
    "$Z = \\frac{U - n_1n_2/2}{\\sqrt{n_1n_2(n_1 + n_2 + 1)/12}} \\sim N(0, 1)$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e535cd7f",
   "metadata": {},
   "source": [
    "**[Ex.6]**\n",
    "\n",
    "<div style=\"border: 1px solid #ddd; padding: 12px; margin-top: 10px\">\n",
    "\n",
    "A부서와 임직원의 나이와 B부서의 임직원 나이의 차이를 비교해 봅니다.\n",
    "\n",
    "A부서\n",
    "\n",
    "```\n",
    "25, 35, 38, 49, 51, 43, 29, 54\n",
    "```\n",
    "\n",
    "B부서\n",
    "\n",
    "```\n",
    "28, 42, 45, 31, 48, 43, 25, 55, 33\n",
    "```\n",
    "    \n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6faa652b",
   "metadata": {},
   "source": [
    "$H_0: P(X_1 > X_2) = P(X_1 < X_2)$(두 모집단은 동일한 분포를 지녔다)\n",
    "\n",
    "$H_1: P(X_1 > X_2) \\ne P(X_1 < X_2)$ (모집단 1이 모집단 2 보다 다른 영역에 분포한다.)\n",
    "\n",
    "**양측 검정** 입니다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "0fa0d08f",
   "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>age</th>\n",
       "      <th>dept</th>\n",
       "      <th>rnk</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>25</td>\n",
       "      <td>A</td>\n",
       "      <td>1.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>35</td>\n",
       "      <td>A</td>\n",
       "      <td>7.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>38</td>\n",
       "      <td>A</td>\n",
       "      <td>8.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>49</td>\n",
       "      <td>A</td>\n",
       "      <td>14.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>51</td>\n",
       "      <td>A</td>\n",
       "      <td>15.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>5</td>\n",
       "      <td>43</td>\n",
       "      <td>A</td>\n",
       "      <td>10.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>6</td>\n",
       "      <td>29</td>\n",
       "      <td>A</td>\n",
       "      <td>4.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>7</td>\n",
       "      <td>54</td>\n",
       "      <td>A</td>\n",
       "      <td>16.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>28</td>\n",
       "      <td>B</td>\n",
       "      <td>3.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>42</td>\n",
       "      <td>B</td>\n",
       "      <td>9.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>45</td>\n",
       "      <td>B</td>\n",
       "      <td>12.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>31</td>\n",
       "      <td>B</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>48</td>\n",
       "      <td>B</td>\n",
       "      <td>13.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>5</td>\n",
       "      <td>43</td>\n",
       "      <td>B</td>\n",
       "      <td>10.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>6</td>\n",
       "      <td>25</td>\n",
       "      <td>B</td>\n",
       "      <td>1.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>7</td>\n",
       "      <td>55</td>\n",
       "      <td>B</td>\n",
       "      <td>17.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>8</td>\n",
       "      <td>33</td>\n",
       "      <td>B</td>\n",
       "      <td>6.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   age dept   rnk\n",
       "0   25    A   1.5\n",
       "1   35    A   7.0\n",
       "2   38    A   8.0\n",
       "3   49    A  14.0\n",
       "4   51    A  15.0\n",
       "5   43    A  10.5\n",
       "6   29    A   4.0\n",
       "7   54    A  16.0\n",
       "0   28    B   3.0\n",
       "1   42    B   9.0\n",
       "2   45    B  12.0\n",
       "3   31    B   5.0\n",
       "4   48    B  13.0\n",
       "5   43    B  10.5\n",
       "6   25    B   1.5\n",
       "7   55    B  17.0\n",
       "8   33    B   6.0"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s_A = pd.Series([25, 35, 38, 49, 51, 43, 29, 54], name='age')\n",
    "s_B = pd.Series([28, 42, 45, 31, 48, 43, 25, 55, 33], name='age')\n",
    "\n",
    "df_age = pd.concat([\n",
    "    s_A.to_frame().assign(dept=\"A\"),\n",
    "    s_B.to_frame().assign(dept=\"B\")\n",
    "], axis = 0).assign(\n",
    "    rnk = lambda x: x['age'].rank()\n",
    ")\n",
    "df_age"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "71152e6f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(dept\n",
       " A    40.0\n",
       " B    32.0\n",
       " Name: rnk, dtype: float64,\n",
       " 32.0)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s_U = df_age.groupby('dept')['rnk'].agg(\n",
    "    lambda x: x.sum() - len(x) * (len(x) + 1) / 2\n",
    ")\n",
    "U = s_U.min()\n",
    "s_U, U"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "05a071a4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "검정통계량(U): 32.0, pvalue: 0.7003113729368902\n"
     ]
    }
   ],
   "source": [
    "n1, n2 = df_age['dept'].value_counts()\n",
    "mu_U = n1 * n2 / 2\n",
    "sigma_U = (n1 * n2 * (n1 + n2 + 1) / 12) ** 0.5\n",
    "\n",
    "Z = -abs((U - mu_U) / sigma_U)\n",
    "print(\"검정통계량(U): {}, pvalue: {}\".format(U, norm.cdf(Z) * 2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "c19f8759",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MannwhitneyuResult(statistic=32.0, pvalue=0.6999612764311128)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# scipy.stats.mannwhitneyu\n",
    "from scipy.stats import mannwhitneyu\n",
    "mannwhitneyu(s_B, s_A, use_continuity=False, alternative='two-sided') # use_continuity: Ranking에 보정 루틴적용 여부"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0ddd42f6",
   "metadata": {},
   "source": [
    "$H_0$ not Rejected → 같습니다."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "61520e03",
   "metadata": {},
   "source": [
    "## 3. 동일 개체의 두 모집단 평균\n",
    "\n",
    "동일 개체에서 조치(treatment) 전후의 두 모집단의 평균이 같을 지를 검정합니다.\n",
    "\n",
    "$H_0: \\mu_0 = \\mu_0'$\n",
    "\n",
    "$H_1:$\n",
    "\n",
    "|대립 가설|검정 종류|\n",
    "|---|---|\n",
    "|$$H_1: \\mu_0 < \\mu_0'$$|좌측 꼬리(left)|\n",
    "|$$H_1: \\mu_0 > \\mu_0'$$|우측 꼬리(right)|\n",
    "|$$H_1: \\mu_0 \\ne \\mu_0'$$|양쪽 꼬리(two-sided)|"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "87579c73",
   "metadata": {},
   "source": [
    "### paired t-검정(paired t-test)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bd1f25c3",
   "metadata": {},
   "source": [
    "pair를 이루고 있는 두 표집에서 각 pair의 차로 두 모집단의 평균이 같을 지를 검정합니다.\n",
    "\n",
    "각 pair의 차를 구하고 이를 $X_d$ 라고 합니다. \n",
    "\n",
    "$X_d = X' - X$\n",
    "\n",
    "$H_0: \\mu_d = 0$ \n",
    "\n",
    "$H_1:$\n",
    "\n",
    "|대립 가설|검정 종류|\n",
    "|---|---|\n",
    "|$$H_1: \\mu_d < 0$$|좌측 꼬리(left)|\n",
    "|$$H_1: \\mu_d > 0$$|우측 꼬리(right)|\n",
    "|$$H_1: \\mu_d \\ne 0$$|양쪽 꼬리(two-sided)|\n",
    "\n",
    "**가정**\n",
    "\n",
    "모집단은 정규 분포를 따릅니다.\n",
    "\n",
    "표본은 서로가 독립입니다.\n",
    "\n",
    "--------------------------------------\n",
    "**증거의 확률 분포 및 통계량**\n",
    "\n",
    "$H_0$가 맞다면,\n",
    "\n",
    "> $X_d$도 정규분포를 따릅니다.\n",
    ">\n",
    "> $\\mu_{\\bar{X_d}}=0$ 입니다.\n",
    "\n",
    "$t = \\frac{\\bar{X_d}}{S_d/\\sqrt{n}} \\sim t(n - 1)$, n: pair의 수\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "629b4173",
   "metadata": {},
   "source": [
    "**[Ex.7]**\n",
    "\n",
    "<div style=\"border: 1px solid #ddd; padding: 12px; margin-top: 10px\">\n",
    "\n",
    "S전자는 직원 마음 건강을 위하여 정기적으로 마음 건강 지수를 측정합니다. \n",
    "\n",
    "직원의 마음 건강을 높히기 위해 심리 치료사 지희를 고용했습니다.\n",
    "\n",
    "심리 치료사의 효과를 파악하기 위해,\n",
    "\n",
    "무작위로 16명을 대상으로 지희 상담사에게 상담하기 전과 후의 마음 건강 지수를 측정합니다.\n",
    "\n",
    "마음 건강 지수는 높을 수록 좋은 상태를 나타냅니다. \n",
    "\n",
    "심리 치료 이후 마음 건강 지수가 높아 졌는지를 검정해 봅니다. (유의 수준 5%)\n",
    "\n",
    "치료전 마음 건강 지수\n",
    "\n",
    "```\n",
    "5.91, 8.00, 7.28, 5.49, 6.42, 8.65, 4.57, 6.57, 8.27, 6.13, 6.32, 6.91, 8.49, 6.36, 6.56, 6.57\n",
    "```\n",
    "\n",
    "치료후 마음 건강 지수\n",
    "\n",
    "```\n",
    "5.87, 9.00, 7.92, 5.24, 6.63, 9.98, 3.86, 6.86, 9.40, 6.20, 6.48, 7.36, 9.74, 6.54, 6.83, 6.85\n",
    "```\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "413305d7",
   "metadata": {},
   "source": [
    "$X_d = X' - X$\n",
    "\n",
    "$H_0: X_d = 0$\n",
    "\n",
    "$H_1: X_d > 0$\n",
    "\n",
    "**우측 꼬리** 검정입니다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "43dda6d9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "검정통계량(t): 2.801268271622578, pvalue: 0.006712663916686075\n"
     ]
    }
   ],
   "source": [
    "X = [5.91, 8.00, 7.28, 5.49, 6.42, 8.65, 4.57, 6.57, 8.27, 6.13, 6.32, 6.91, 8.49, 6.36, 6.56, 6.57]\n",
    "X_p = [5.87, 9.00, 7.92, 5.24, 6.63, 9.98, 3.86, 6.86, 9.40, 6.20, 6.48, 7.36, 9.74, 6.54, 6.83, 6.85]\n",
    "\n",
    "Xd = np.array(X_p) - np.array(X)\n",
    "Xd_bar = np.mean(Xd)\n",
    "Xd_std = np.std(Xd, ddof=1)\n",
    "n = len(X)\n",
    "t_stat = Xd_bar / (Xd_std / (n ** 0.5))\n",
    "print(\"검정통계량(t): {}, pvalue: {}\".format(t_stat, t.sf(t_stat, df=n - 1)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "c7200d7d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ttest_relResult(statistic=-2.801268271622578, pvalue=0.01342532783337215)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# scipy.stats.ttest_ind 기능을 제공합니다.\n",
    "# 검정장 버젼에서는 양측 검정만 지원됩니다. \n",
    "from scipy.stats import ttest_rel\n",
    "\n",
    "ttest_rel(X, X_p) # 양측 검정의 결과라 위 결과와 유효하지 않습니다."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1e6154fc",
   "metadata": {},
   "source": [
    "### Wilcoxon 부호순위검정 (Wilcoxon's Signed-rank Test)\n",
    "\n",
    "모집단에 대한 가정이 필요하지 않은 비모수 검정법입니다.\n",
    "\n",
    "짝을 이룬 두 모집단의 분포에 대한 검정입니다.\n",
    "\n",
    "$H_0: P(X_0 > X_0') = P(X_0 < X_0')$(두 모집단은 동일한 분포를 지녔다)\n",
    "\n",
    "|대립 가설|검정 종류|\n",
    "|---|---|\n",
    "|$$H_1: P(X_0 > X_0') < P(X_0 < X_0')$$ (모집단 1이 모집단 2 보다 작은 영역에 분포한다.)|좌측 꼬리(left)|\n",
    "|$$H_1: P(X_0 > X_0') > P(X_0 < X_0')$$ (모집단 1이 모집단 2 보다 큰 영역에 분포한다.)|우측 꼬리(right)|\n",
    "|$$H_1: P(X_0 > X_0') \\ne P(X_0 < X_0')$$ (모집단 1이 모집단 2 보다 다른 영역에 분포한다.)|양쪽 꼬리(two-sided)|\n",
    "\n",
    "\n",
    "**증거의 확률 분포 및 통계량**\n",
    "\n",
    "$X_0' - X_0$ 의 차의 부호에 따라 양이면 1, 음이면 -1인 부호값 sgn을 구합니다.\n",
    "\n",
    "차의 절대값으로 오름 차순으로 순위를 구합니다. 동일값은 해당값들의 순위의 평균을 구해 순위를 교정합니다.\n",
    "\n",
    "차이가 0인 경우 처리 랭킹과 통계량 산출 모두 제외합니다.\n",
    "\n",
    "> $T^+= $ sgn이 1인 순위의 합\n",
    "\n",
    "> $T^-= $ sgn이 -1인 순위의 합\n",
    "\n",
    "\n",
    "양측 검정일 경우, \n",
    "\n",
    "> $T = min(T^+, T^-)$\n",
    "\n",
    "아니면 \n",
    "\n",
    "> $T = T^+$를 사용합니다.\n",
    "\n",
    "$T$는 근사적 정규 분포를 따릅니다. \n",
    "\n",
    "$T \\sim N(\\frac{n(n + 1)}{4}, \\frac{n(n + 1)(2n + 1)}{24})$,  n은 차이가 0이 아닌 표본수\n",
    "\n",
    "$Z = \\frac{T - n(n + 1)/4}{\\sqrt{\\left(n(n + 1)(2n + 1)\\right)/24}} \\sim N(0, 1)$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6f56375d",
   "metadata": {},
   "source": [
    "**[Ex.8]**\n",
    "\n",
    "다음 예제 데이터의 Wilcoxon 부호 검정을 수행해봅니다.\n",
    "\n",
    "$H_0$: $P(x_1 > x_2) = P(x_1 < x_2)$\n",
    "\n",
    "$H_1$: $P(x_1 > x_2) \\ne P(x_1 < x_2)$\n",
    "\n",
    "<div style=\"border: 1px solid #ddd; padding: 12px; margin-top: 10px\">\n",
    "\n",
    "![image.png](data:image/png;base64,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)\n",
    "\n",
    "출처: [Wilcoxon signed-rank test](https://en.wikipedia.org/wiki/Wilcoxon_signed-rank_test)\n",
    "    \n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "823fabbe",
   "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>X</th>\n",
       "      <th>X_p</th>\n",
       "      <th>sgn</th>\n",
       "      <th>a</th>\n",
       "      <th>sgnRank</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>5</td>\n",
       "      <td>140</td>\n",
       "      <td>140</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>125</td>\n",
       "      <td>130</td>\n",
       "      <td>1</td>\n",
       "      <td>5</td>\n",
       "      <td>1.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>9</td>\n",
       "      <td>135</td>\n",
       "      <td>140</td>\n",
       "      <td>1</td>\n",
       "      <td>5</td>\n",
       "      <td>1.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>122</td>\n",
       "      <td>115</td>\n",
       "      <td>-1</td>\n",
       "      <td>7</td>\n",
       "      <td>-3.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>6</td>\n",
       "      <td>124</td>\n",
       "      <td>115</td>\n",
       "      <td>-1</td>\n",
       "      <td>9</td>\n",
       "      <td>-4.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>10</td>\n",
       "      <td>145</td>\n",
       "      <td>135</td>\n",
       "      <td>-1</td>\n",
       "      <td>10</td>\n",
       "      <td>-5.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>8</td>\n",
       "      <td>137</td>\n",
       "      <td>125</td>\n",
       "      <td>-1</td>\n",
       "      <td>12</td>\n",
       "      <td>-6.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>110</td>\n",
       "      <td>125</td>\n",
       "      <td>1</td>\n",
       "      <td>15</td>\n",
       "      <td>7.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>7</td>\n",
       "      <td>123</td>\n",
       "      <td>140</td>\n",
       "      <td>1</td>\n",
       "      <td>17</td>\n",
       "      <td>8.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>120</td>\n",
       "      <td>140</td>\n",
       "      <td>1</td>\n",
       "      <td>20</td>\n",
       "      <td>9.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      X  X_p  sgn   a  sgnRank\n",
       "5   140  140    0   0      NaN\n",
       "3   125  130    1   5      1.5\n",
       "9   135  140    1   5      1.5\n",
       "2   122  115   -1   7     -3.0\n",
       "6   124  115   -1   9     -4.0\n",
       "10  145  135   -1  10     -5.0\n",
       "8   137  125   -1  12     -6.0\n",
       "1   110  125    1  15      7.0\n",
       "7   123  140    1  17      8.0\n",
       "4   120  140    1  20      9.0"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X =   [110, 122, 125, 120, 140, 124, 123, 137, 135, 145]\n",
    "X_p = [125, 115, 130, 140, 140, 115, 140, 125, 140, 135]\n",
    "\n",
    "df_wilcoxon = pd.DataFrame(\n",
    "    {'X': X,'X_p': X_p}, index = np.arange(1, len(X) + 1)\n",
    ").assign(\n",
    "    sgn  = lambda x: np.where(x['X_p'] == x['X'],  0, np.where(x['X_p'] > x['X'], 1, -1)),\n",
    "    a =  lambda x: (x['X_p'] - x['X']).abs()\n",
    ").sort_values('a').assign(\n",
    "    sgnRank = lambda x: x.loc[x['sgn'] != 0].pipe(lambda y: y['sgn'] * y['a'].rank())\n",
    ")\n",
    "df_wilcoxon"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "53509ccd",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "검정통계량(T): 18.0, pvalue: 0.5939546753269146\n"
     ]
    }
   ],
   "source": [
    "T_plus = df_wilcoxon.loc[df_wilcoxon['sgn'] > 0, 'sgnRank'].sum()\n",
    "T_minus = -df_wilcoxon.loc[df_wilcoxon['sgn'] < 0, 'sgnRank'].sum()\n",
    "\n",
    "T = min(T_plus, T_minus)\n",
    "n = (df_wilcoxon['sgn'] != 0).sum()\n",
    "\n",
    "mu_T = n * (n + 1) / 4\n",
    "sigma_T = (n * (n + 1) * (2 * n + 1) / 24) ** 0.5\n",
    "\n",
    "print(\"검정통계량(T): {}, pvalue: {}\".format(T, norm.cdf(-abs(T_minus - mu_T) / sigma_T) * 2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "b4e7243b",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\users\\user\\python3.7\\lib\\site-packages\\scipy\\stats\\morestats.py:2971: UserWarning: Sample size too small for normal approximation.\n",
      "  warnings.warn(\"Sample size too small for normal approximation.\")\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "WilcoxonResult(statistic=18.0, pvalue=0.5936305914425295)"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.stats import wilcoxon\n",
    "wilcoxon(X, X_p, correction=False, alternative='two-sided',  mode='approx', zero_method='wilcox')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fc9ffe8a",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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