h345a.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# ハンバーガー統計学 + Python (第3章〜第5章)\n",
    "[ハンバーガー統計学にようこそ！](http://kogolab.chillout.jp/elearn/hamburger/index.html)\n",
    "のページを読み進めながら、以下の課題を Python を使って解いてください。\n",
    "\n",
    "* [アイスクリーム統計学・第１章〜第３章（散布図と相関、相関係数、無相関検定）](http://nbviewer.jupyter.org/github/maskot1977/ipython_notebook/blob/master/%E3%82%A2%E3%82%A4%E3%82%B9%E3%82%AF%E3%83%AA%E3%83%BC%E3%83%A0%E7%B5%B1%E8%A8%88%E5%AD%A6%E3%83%BB%E7%AC%AC%EF%BC%91%E7%AB%A0%E3%80%9C%E7%AC%AC%EF%BC%93%E7%AB%A0.ipynb)\n",
    "* [アイスクリーム統計学・第４章〜第６章（単回帰、偏相関、重回帰）](http://nbviewer.jupyter.org/github/maskot1977/ipython_notebook/blob/master/%E3%82%A2%E3%82%A4%E3%82%B9%E3%82%AF%E3%83%AA%E3%83%BC%E3%83%A0%E7%B5%B1%E8%A8%88%E5%AD%A6%E3%83%BB%E7%AC%AC%EF%BC%94%E7%AB%A0%E3%80%9C%E7%AC%AC%EF%BC%96%E7%AB%A0.ipynb)\n",
    "* [アイスクリーム統計学・第７章〜第９章（相関行列、因子分析1、因子分析2）](http://nbviewer.jupyter.org/github/maskot1977/ipython_notebook/blob/master/%E3%82%A2%E3%82%A4%E3%82%B9%E3%82%AF%E3%83%AA%E3%83%BC%E3%83%A0%E7%B5%B1%E8%A8%88%E5%AD%A6%E3%83%BB%E7%AC%AC%EF%BC%97%E7%AB%A0%E3%80%9C%E7%AC%AC%EF%BC%99%E7%AB%A0.ipynb)\n",
    "* [アイスクリーム統計学・第１０章（主成分分析とクラスター分析）](http://nbviewer.jupyter.org/github/maskot1977/ipython_notebook/blob/master/%E3%82%A2%E3%82%A4%E3%82%B9%E3%82%AF%E3%83%AA%E3%83%BC%E3%83%A0%E7%B5%B1%E8%A8%88%E5%AD%A6%E3%83%BB%E7%AC%AC%EF%BC%91%EF%BC%90%E7%AB%A0.ipynb)\n",
    "* [ハンバーガー統計学・第１章〜第２章（平均と分散、信頼区間）](http://nbviewer.jupyter.org/github/maskot1977/ipython_notebook/blob/master/%E3%83%8F%E3%83%B3%E3%83%8F%E3%82%99%E3%83%BC%E3%82%AB%E3%82%99%E3%83%BC%E7%B5%B1%E8%A8%88%E5%AD%A6%E3%83%BB%E7%AC%AC%EF%BC%91%E7%AB%A0%E3%80%9C%E7%AC%AC%EF%BC%92%E7%AB%A0.ipynb)\n",
    "* [ハンバーガー統計学・第３章〜第５章（カイ２乗検定、t検定 （対応なし・対応あり））](http://nbviewer.jupyter.org/github/maskot1977/ipython_notebook/blob/master/%E3%83%8F%E3%83%B3%E3%83%8F%E3%82%99%E3%83%BC%E3%82%AB%E3%82%99%E3%83%BC%E7%B5%B1%E8%A8%88%E5%AD%A6%E3%83%BB%E7%AC%AC%EF%BC%93%E7%AB%A0%E3%80%9C%E7%AC%AC%EF%BC%95%E7%AB%A0.ipynb)\n",
    "* [ハンバーガー統計学・第６章〜第７章（分散分析 (１要因、２要因) ）](http://nbviewer.jupyter.org/github/maskot1977/ipython_notebook/blob/master/%E3%83%8F%E3%83%B3%E3%83%8F%E3%82%99%E3%83%BC%E3%82%AB%E3%82%99%E3%83%BC%E7%B5%B1%E8%A8%88%E5%AD%A6%E3%83%BB%E7%AC%AC%EF%BC%96%E7%AB%A0%E3%80%9C%E7%AC%AC%EF%BC%97%E7%AB%A0.ipynb)\n",
    "* [ハンバーガー統計学・第８章 (分布と仮説検定)](http://nbviewer.jupyter.org/github/maskot1977/ipython_notebook/blob/master/%E3%83%8F%E3%83%B3%E3%83%8F%E3%82%99%E3%83%BC%E3%82%AB%E3%82%99%E3%83%BC%E7%B5%B1%E8%A8%88%E5%AD%A6%E3%83%BB%E7%AC%AC%EF%BC%98%E7%AB%A0.ipynb)\n",
    "\n",
    "### Jupyter Notebook (IPython Notebook) とは\n",
    "* Python という名のプログラミング言語が使えるプログラミング環境。計算コードと計算結果を同じ場所に時系列で保存できるので、実験系における実験ノートのように、いつどんな処理を行って何を得たのか記録して再現するのに便利。\n",
    "* [当学演習室での Jupyter Notebook の起動方法](https://raw.githubusercontent.com/maskot1977/-/master/%E6%BC%94%E7%BF%92%E5%AE%A4.txt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. [カイ２乗検定](http://kogolab.chillout.jp/elearn/hamburger/chap3/sec0.html)\n",
    "本文を読んで概念を学んでください。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.1　[チキンの売り上げは少ないのか](http://kogolab.chillout.jp/elearn/hamburger/chap3/sec1.html)\n",
    "本文を読んで概念を学んでください。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.2　[カイ２乗値とカイ２乗分布](http://kogolab.chillout.jp/elearn/hamburger/chap3/sec2.html)\n",
    "本文を読んで概念を学んでください。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.3　[カイ２乗検定](http://kogolab.chillout.jp/elearn/hamburger/chap3/sec3.html)\n",
    "本文を読んで概念を学んでください。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.4　[実践編：ハンバーガーを入れてみる](http://kogolab.chillout.jp/elearn/hamburger/chap3/sec4.html)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__課題3.4__: 下表をもとに、ワクワクとモグモグのポテト・チキン・ハンバーガーの売れ方に違いがあるかをカイ２乗検定で調べたいと思います。以下の問いに答えてください。\n",
    "<table border=1 bgcolor=\"#FFFFFF\" cellpadding=\"0\" cellspacing=\"0\" align=center>\n",
    "  <caption>表3.9　ポテトとチキンとハンバーガーの売り上げ数</caption>\n",
    "  <tr> \n",
    "    <th width=100 height=30 bgcolor=\"#CCCC99\"> お店 </th>\n",
    "    <th width=81 height=30 bgcolor=\"#FFFFCC\"> ポテト </th>\n",
    "    <th width=100 height=30 bgcolor=\"#FFCCCC\"> チキン </th>\n",
    "    <th width=100 height=30 bgcolor=\"#99FFCC\">ハンバーガー</th>\n",
    "    <th width=100 height=30 bgcolor=\"#CCCCCC\">合計</th>\n",
    "  </tr>\n",
    "  <tr align=center> \n",
    "    <td width=100 height=30 bgcolor=\"#CCCC99\"> ワクワク </td>\n",
    "    <td width=100 height=30 bgcolor=\"#FFFFFF\"> 435</td>\n",
    "    <td width=100 height=30 bgcolor=\"#FFFFFF\">165</td>\n",
    "    <td width=100 height=30 bgcolor=\"#FFFFFF\">650</td>\n",
    "    <td width=100 height=30 bgcolor=\"#CCCCCC\">1250</td>\n",
    "  </tr>\n",
    "  <tr align=center> \n",
    "    <td width=119 height=30 bgcolor=\"#CCCC99\"> モグモグ </td>\n",
    "    <td width=81 height=30 bgcolor=\"#FFFFFF\"> 265</td>\n",
    "    <td width=100 height=30 bgcolor=\"#FFFFFF\">135</td>\n",
    "    <td width=100 height=30 bgcolor=\"#FFFFFF\">350</td>\n",
    "    <td width=100 height=30 bgcolor=\"#CCCCCC\">750</td>\n",
    "  </tr>\n",
    "  <tr align=center bgcolor=\"#CCCCCC\"> \n",
    "    <td width=119 height=30>合計</td>\n",
    "    <td width=81 height=30>700</td>\n",
    "    <td width=100 height=30>300</td>\n",
    "    <td width=100 height=30>1000</td>\n",
    "    <td width=100 height=30>2000</td>\n",
    "  </tr>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* 帰無仮説と対立仮説は何か、説明してください。\n",
    "  * 帰無仮説：\n",
    "  * 対立仮説："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 帰無仮説： ワクワクとモグモグのポテト・チキン・ハンバーガーの売れ方に違いはない。\n",
    "# 対立仮説：ワクワクとモグモグのポテト・チキン・ハンバーガーの売れ方に違いがある。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* 帰無仮説に基づいて、モグモグとワクワクの、ポテトとチキンとハンバーガーの売上数の期待度数を求めてください（下表の６つの空欄）。\n",
    "<table border=1 bgcolor=\"#FFFFFF\" cellpadding=\"0\" cellspacing=\"0\" align=center>\n",
    "  <caption>表3.10　ポテトとチキンとハンバーガーの売り上げの期待度数</caption>\n",
    "  <tr> \n",
    "    <th width=100 height=30 bgcolor=\"#CCCC99\"> お店 </th>\n",
    "    <th width=81 height=30 bgcolor=\"#FFFFCC\"> ポテト </th>\n",
    "    <th width=100 height=30 bgcolor=\"#FFCCCC\"> チキン </th>\n",
    "    <th width=100 height=30 bgcolor=\"#99FFCC\">ハンバーガー</th>\n",
    "    <th width=100 height=30 bgcolor=\"#CCCCCC\">合計</th>\n",
    "  </tr>\n",
    "  <tr align=center> \n",
    "    <td width=100 height=30 bgcolor=\"#CCCC99\"> ワクワク </td>\n",
    "    <td width=100 height=30 bgcolor=\"#FFFFFF\">　 </td>\n",
    "    <td width=100 height=30 bgcolor=\"#FFFFFF\">　</td>\n",
    "    <td width=100 height=30 bgcolor=\"#FFFFFF\">　</td>\n",
    "    <td width=100 height=30 bgcolor=\"#CCCCCC\">1250</td>\n",
    "  </tr>\n",
    "  <tr align=center> \n",
    "    <td width=119 height=30 bgcolor=\"#CCCC99\"> モグモグ </td>\n",
    "    <td width=81 height=30 bgcolor=\"#FFFFFF\">　 </td>\n",
    "    <td width=100 height=30 bgcolor=\"#FFFFFF\">　</td>\n",
    "    <td width=100 height=30 bgcolor=\"#FFFFFF\">　</td>\n",
    "    <td width=100 height=30 bgcolor=\"#CCCCCC\">750</td>\n",
    "  </tr>\n",
    "  <tr align=center bgcolor=\"#CCCCCC\"> \n",
    "    <td width=119 height=30>合計</td>\n",
    "    <td width=81 height=30>700</td>\n",
    "    <td width=100 height=30>300</td>\n",
    "    <td width=100 height=30>1000</td>\n",
    "    <td width=100 height=30>2000</td>\n",
    "  </tr>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(437.5, 187.5, 625.0)\n",
      "(262.5, 112.5, 375.0)\n"
     ]
    }
   ],
   "source": [
    "wp = 1250. * 700. / 2000.\n",
    "wc = 1250. * 300. / 2000.\n",
    "wb = 1250. * 1000. / 2000.\n",
    "mp = 750. * 700. / 2000.\n",
    "mc = 750. * 300. / 2000.\n",
    "mb = 750. * 1000. / 2000.\n",
    "print (wp, wc, wb) #ワクワクポテト、ワクワクチキン、ワクワクバーガー\n",
    "print (mp, mc, mb) #モグモグポテト、モグモグチキン、モグモグバーガー"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* 観測度数と期待度数を元にして、カイ２乗値を計算してください（全部で6個の空欄について計算します）。\n",
    "  * カイ２乗値＝（（（観測度数－期待度数）の２乗）÷期待度数）の総和"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(0.014285714285714285, 2.7, 1.0)\n",
      "(0.023809523809523808, 4.5, 1.6666666666666667)\n",
      "9.90476190476\n"
     ]
    }
   ],
   "source": [
    "kwp = (435. - wp) ** 2 / wp\n",
    "kwc = (165. - wc) ** 2 / wc\n",
    "kwb = (650. - wb) ** 2 / wb\n",
    "kmp = (265. - mp) ** 2 / mp\n",
    "kmc = (135. - mc) ** 2 / mc\n",
    "kmb = (350. - mb) ** 2 / mb\n",
    "print (kwp, kwc, kwb) #ワクワクポテト、ワクワクチキン、ワクワクバーガー\n",
    "print (kmp, kmc, kmb) #モグモグポテト、モグモグチキン、モグモグバーガー\n",
    "kai = kwp + kwc + kwb + kmp + kmc + kmb\n",
    "print (kai) # カイ２乗値"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* 自由度を求めてください。\n",
    "  * 自由度＝（行の数－1）×（列の数－1）"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2\n"
     ]
    }
   ],
   "source": [
    "jiyudo = (2 - 1) * (3 - 1)\n",
    "print (jiyudo)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* ここでは、有意水準をちょっと厳しくして、1%としましょう。カイ２乗分布表を用いて、有意水準を満たすカイ２乗値を探してください。\n",
    "<table border=1 bgcolor=\"#FFFFFF\" cellpadding=\"0\" cellspacing=\"0\" align=center>\n",
    "  <caption>表3.8　カイ２乗分布表</caption>\n",
    "  <tr> \n",
    "    <th width=100 height=30 bgcolor=\"#CCCCCC\"> ↓自由度／確率→</th>\n",
    "    <th width=81 height=30 bgcolor=\"#FFFFCC\"> 0.05</th>\n",
    "    <th width=100 height=30 bgcolor=\"#FFCCCC\"> 0.01</th>\n",
    "  </tr>\n",
    "  <tr align=center> \n",
    "    <td width=100 height=30 bgcolor=\"#CCCCCC\"> 1</td>\n",
    "    <td width=100 height=30 bgcolor=\"#FFFFFF\"> 3.84</td>\n",
    "    <td width=100 height=30 bgcolor=\"#FFFFFF\">6.63</td>\n",
    "  </tr>\n",
    "  <tr align=center> \n",
    "    <td width=119 height=30 bgcolor=\"#CCCCCC\"> 2</td>\n",
    "    <td width=81 height=30> 5.99</td>\n",
    "    <td width=100 height=30>9.21</td>\n",
    "  </tr>\n",
    "  <tr align=center bgcolor=\"#CCCCCC\"> \n",
    "    <td width=119 height=30 bgcolor=\"#CCCCCC\">3</td>\n",
    "    <td width=81 height=30 bgcolor=\"#FFFFFF\">7.81</td>\n",
    "    <td width=100 height=30 bgcolor=\"#FFFFFF\">11.34</td>\n",
    "  </tr>\n",
    "  <tr align=center bgcolor=\"#CCCCCC\"> \n",
    "    <td width=119 height=30 bgcolor=\"#CCCCCC\">4</td>\n",
    "    <td width=81 height=30 bgcolor=\"#FFFFFF\">9.49</td>\n",
    "    <td width=100 height=30 bgcolor=\"#FFFFFF\">13.28</td>\n",
    "  </tr>\n",
    "  <tr align=center bgcolor=\"#CCCCCC\"> \n",
    "    <td width=119 height=30 bgcolor=\"#CCCCCC\">5</td>\n",
    "    <td width=81 height=30 bgcolor=\"#FFFFFF\">11.07</td>\n",
    "    <td width=100 height=30 bgcolor=\"#FFFFFF\">15.09</td>\n",
    "  </tr>\n",
    "  <tr align=center bgcolor=\"#CCCCCC\"> \n",
    "    <td width=119 height=30 bgcolor=\"#CCCCCC\">…以下続く…</td>\n",
    "    <td width=81 height=30 bgcolor=\"#FFFFFF\">…</td>\n",
    "    <td width=100 height=30 bgcolor=\"#FFFFFF\">…</td>\n",
    "  </tr>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9.21"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "9.21"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* 計算したカイ２乗値と、表から得られた「有意水準を満たすカイ２乗値」を比べてください。\n",
    "  * 計算したカイ２乗値がもし表の値よりも大きければ、それは、1%よりも小さい確率でしか起こらないことが起こったということです。したがって帰無仮説が間違っていたと考え、帰無仮説を棄却します。\n",
    "  * もし表の値よりも小さければ、それは、1%よりも大きい確率で起こりうることだということです。したがって帰無仮説を採択します。\n",
    "* 結論はどうなったか説明してください。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 計算したカイ２乗値は、1%有意水準を満たすカイ２乗値よりも大きかった。\n",
    "# それは、1%よりも小さい確率でしか起こらないことが起こったということを意味する。\n",
    "# したがって帰無仮説が間違っていたと考え、帰無仮説を棄却する。\n",
    "# つまり、ワクワクとモグモグのポテト・チキン・ハンバーガーの売れ方には違いがある。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.9　[通過テスト](http://kogolab.chillout.jp/elearn/hamburger/chap3/sec9.html)\n",
    "本文を読んで、通過テストの問題を解いてください。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# (1)　この検定での帰無仮説を言いなさい。\n",
    "\n",
    "# 桜組と桃組とで、国語と算数のどちらが好きかに違いはない。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# (2)　この検定での対立仮説を言いなさい。\n",
    "\n",
    "# 桜組と桃組とで、国語と算数のどちらが好きかに違いがある。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(19.764705882352942, 22.235294117647058)\n",
      "(12.235294117647058, 13.764705882352942)\n"
     ]
    }
   ],
   "source": [
    "# (3)　帰無仮説が成立するときの期待度数を求めなさい。\n",
    "sk = 42. * 32. / 68.\n",
    "mk = 42. * 36. / 68.\n",
    "ss = 26. * 32. / 68.\n",
    "ms = 26. * 36. / 68.\n",
    "print (sk, mk) #桜組で国語が好き、桃組で国語が好き\n",
    "print (ss, ms) #桜組で算数が好き、桃組で算数が好き"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(0.9075630252100837, 0.80672268907563)\n",
      "(1.4660633484162893, 1.3031674208144792)\n",
      "4.48351648352\n"
     ]
    }
   ],
   "source": [
    "# (4)　カイ２乗値を求めなさい（小数点以下第3位を四捨五入）。\n",
    "ksk = (24. - sk) ** 2 / sk\n",
    "kmk = (18. - mk)** 2 / mk\n",
    "kss = (8. - ss) ** 2 / ss\n",
    "kms = (18. - ms) ** 2 / ms\n",
    "print (ksk, kmk) #桜組で国語が好き、桃組で国語が好き\n",
    "print (kss, kms) #桜組で算数が好き、桃組で算数が好き\n",
    "kai = ksk + kmk + kss + kms\n",
    "print (kai) # カイ２乗値"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# (5)　有意水準を1%としたとき、このカイ２乗値から言えることを書きなさい。\n",
    "\n",
    "# 自由度は (2 - 1) * (2 - 1) = 1 なので、1%有意水準を満たすカイ２乗値は　6.63　である。\n",
    "# 計算したカイ２乗値は、1%有意水準を満たすカイ２乗値よりも大きかった。\n",
    "# それは、1%よりも小さい確率でしか起こらないことが起こったということを意味する。\n",
    "# したがって帰無仮説が間違っていたと考え、帰無仮説を棄却する。\n",
    "# つまり、桜組と桃組とで、国語と算数のどちらが好きかに違いがある。\n",
    "# 桜組の担任は、大学で国語を専門とした先生で、一方、桃組の担任は数学を専門とした先生であった。\n",
    "# 担任の先生の専門が、担当クラスの子どもの科目の好みに影響することがわかった。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. [t検定（対応なし）](http://kogolab.chillout.jp/elearn/hamburger/chap4/sec0.html)\n",
    "本文を読んで概念を学んでください。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.1　[ハンバーガーの味を評価する](http://kogolab.chillout.jp/elearn/hamburger/chap4/sec1.html)\n",
    "本文を読んで概念を学んでください。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.2　[平均差の信頼区間](http://kogolab.chillout.jp/elearn/hamburger/chap4/sec2.html)\n",
    "本文を読んで概念を学んでください。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.3　[t検定](http://kogolab.chillout.jp/elearn/hamburger/chap4/sec3.html)\n",
    "まずは本文を読んで概念を学んでください。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__課題4.3__：ワクワクバーガーとモグモグバーガーの評価に差があるかどうか、下表の空欄を埋めながら検定を進めてください。\n",
    "<table border=1 bgcolor=\"#FFFFFF\" cellpadding=\"0\" cellspacing=\"0\" align=center>\n",
    "  <tr align=\"center\"> \n",
    "    <th width=120 height=30 bgcolor=\"#ffffcc\"> ワクワクバーガーを食べた女子高生</th>\n",
    "    <th width=120 height=30 bgcolor=\"#ffffcc\"> 点数</th>\n",
    "    <th width=120 height=30 bgcolor=\"#ffcccc\"> モグモグバーガーを食べた女子高生</th>\n",
    "    <th width=120 height=30 bgcolor=\"#ffcccc\"> 点数</th>\n",
    "  </tr>\n",
    "  <tr align=center> \n",
    "    <td width=120 height=30 bgcolor=\"#cccccc\"> 1</td>\n",
    "    <td width=120 height=30 bgcolor=\"#FFFFFF\"> 70</td>\n",
    "    <td width=120 height=30 bgcolor=\"#cccccc\"> 1</td>\n",
    "    <td width=120 height=30> 85</td>\n",
    "  </tr>\n",
    "  <tr align=center> \n",
    "    <td width=120 height=30 bgcolor=\"#cccccc\">2</td>\n",
    "    <td width=120 height=30 bgcolor=\"#FFFFFF\">75</td>\n",
    "    <td width=120 height=30 bgcolor=\"#cccccc\">2</td>\n",
    "    <td width=120 height=30>80</td>\n",
    "  </tr>\n",
    "  <tr align=center> \n",
    "    <td width=120 height=30 bgcolor=\"#cccccc\">3</td>\n",
    "    <td width=120 height=30 bgcolor=\"#FFFFFF\">70</td>\n",
    "    <td width=120 height=30 bgcolor=\"#cccccc\">3</td>\n",
    "    <td width=120 height=30>95</td>\n",
    "  </tr>\n",
    "  <tr align=center> \n",
    "    <td width=120 height=30 bgcolor=\"#cccccc\">4</td>\n",
    "    <td width=120 height=30 bgcolor=\"#FFFFFF\">85</td>\n",
    "    <td width=120 height=30 bgcolor=\"#cccccc\">4</td>\n",
    "    <td width=120 height=30>70</td>\n",
    "  </tr>\n",
    "  <tr align=center> \n",
    "    <td width=120 height=30 bgcolor=\"#cccccc\">5</td>\n",
    "    <td width=120 height=30 bgcolor=\"#FFFFFF\">90</td>\n",
    "    <td width=120 height=30 bgcolor=\"#cccccc\">5</td>\n",
    "    <td width=120 height=30>80</td>\n",
    "  </tr>\n",
    "  <tr align=center> \n",
    "    <td width=120 height=30 bgcolor=\"#cccccc\">6</td>\n",
    "    <td width=120 height=30 bgcolor=\"#FFFFFF\">70</td>\n",
    "    <td width=120 height=30 bgcolor=\"#cccccc\">6</td>\n",
    "    <td width=120 height=30>75</td>\n",
    "  </tr>\n",
    "  <tr align=center> \n",
    "    <td width=120 height=30 bgcolor=\"#cccccc\">7</td>\n",
    "    <td width=120 height=30 bgcolor=\"#FFFFFF\">80</td>\n",
    "    <td width=120 height=30 bgcolor=\"#cccccc\">7</td>\n",
    "    <td width=120 height=30>80</td>\n",
    "  </tr>\n",
    "  <tr align=center> \n",
    "    <td width=120 height=30 bgcolor=\"#cccccc\">8</td>\n",
    "    <td width=120 height=30 bgcolor=\"#FFFFFF\">75</td>\n",
    "    <td width=120 height=30 bgcolor=\"#cccccc\">8</td>\n",
    "    <td width=120 height=30>90</td>\n",
    "  </tr>\n",
    "  <tr align=center> \n",
    "    <td width=120 height=30 bgcolor=\"#ffffcc\">標本平均</td>\n",
    "    <td width=120 height=30 bgcolor=\"#ffffff\"></td>\n",
    "    <td width=120 height=30 bgcolor=\"#ffcccc\">標本平均</td>\n",
    "    <td width=120 height=30 bgcolor=\"#ffffff\"></td>\n",
    "  </tr>\n",
    "  <tr align=center> \n",
    "    <td width=120 height=30 bgcolor=\"#ffffcc\">標本分散</td>\n",
    "    <td width=120 height=30 bgcolor=\"#ffffff\"></td>\n",
    "    <td width=120 height=30 bgcolor=\"#ffcccc\">標本分散</td>\n",
    "    <td width=120 height=30 bgcolor=\"#ffffff\"></td>\n",
    "  </tr>\n",
    "  <tr align=center> \n",
    "    <td width=120 height=30 bgcolor=\"#ffffcc\">平均偏差の平方和</td>\n",
    "    <td width=120 height=30 bgcolor=\"#ffffff\"></td>\n",
    "    <td width=120 height=30 bgcolor=\"#ffcccc\">平均偏差の平方和</td>\n",
    "    <td width=120 height=30 bgcolor=\"#ffffff\"></td>\n",
    "  </tr>\n",
    "  <tr align=center> \n",
    "    <td width=120 height=30 bgcolor=\"#cccccc\">推定母分散</td>\n",
    "    <td width=120 height=30 bgcolor=\"#ffffff\" colspan=\"3\"></td>\n",
    "  </tr>\n",
    "  <tr align=center> \n",
    "    <td width=120 height=30 bgcolor=\"#cccccc\">差の標準誤差</td>\n",
    "    <td width=120 height=30 bgcolor=\"#ffffff\" colspan=\"3\"></td>\n",
    "  </tr>\n",
    "  <tr align=center> \n",
    "    <td width=120 height=30 bgcolor=\"#cccccc\">t値</td>\n",
    "    <td width=120 height=30 bgcolor=\"#ffffff\" colspan=\"3\"></td>\n",
    "  </tr>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* ワクワクバーガー、モグモグバーガーの評価点の平均値（標本平均）をそれぞれ求めてください。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "wakuwaku =   [70, 75, 70, 85, 90, 70, 80, 75]\n",
    "mogumogu = [85, 80, 95, 70, 80, 75, 80, 90] "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 平均値を求める関数\n",
    "def average(list):\n",
    "    sum = 0.0\n",
    "    n = 0.0\n",
    "    for x in list:\n",
    "        sum += x\n",
    "        n += 1.0\n",
    "    return sum / n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "76.875\n",
      "81.875\n"
     ]
    }
   ],
   "source": [
    "print (average(wakuwaku)) #ワクワクバーガーの評価点の平均\n",
    "print (average(mogumogu)) #モグモグバーガーの評価点の平均"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* ワクワクバーガー、モグモグバーガーの評価点の分散値（標本分散）をそれぞれ求めてください。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 分散を求める関数\n",
    "def variance(list):\n",
    "    ave = average(list)\n",
    "    sum = 0.0\n",
    "    n = 0.0\n",
    "    for x in list:\n",
    "        sum += (x - ave) ** 2.0\n",
    "        n += 1.0\n",
    "    return sum / n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "49.609375\n",
      "55.859375\n"
     ]
    }
   ],
   "source": [
    "print (variance(wakuwaku)) #ワクワクバーガーの評価点の分散\n",
    "print (variance(mogumogu)) #モグモグバーガーの評価点の分散"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* ワクワクバーガー、モグモグバーガーの評価点の平均偏差の平方和をそれぞれ求めてください。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 平均偏差の平方和を求める関数\n",
    "def sum_square(list):\n",
    "    ave = average(list)\n",
    "    sum = 0.0\n",
    "    for x in list:\n",
    "        sum += (x - ave) ** 2.0\n",
    "    return sum"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "396.875\n",
      "446.875\n"
     ]
    }
   ],
   "source": [
    "print (sum_square(wakuwaku)) #ワクワクバーガーの評価点の平均偏差の平方和\n",
    "print (sum_square(mogumogu)) #モグモグバーガーの評価点の平均偏差の平方和"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* 推定母分散を求めてください。\n",
    "  * __推定母分散__ ＝（標本Aの平均偏差の平方和＋標本Bの平均偏差の平方和）／（（標本数A－1）＋（標本数B－1））"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def population_variance(list1, list2):\n",
    "    return (sum_square(list1) + sum_square(list2)) / ((len(list1) - 1) + (len(list2) - 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "60.267857142857146"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "population_variance(wakuwaku, mogumogu)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* ｔ値を求めてください。\n",
    "  * __t__ ＝（標本平均の差）／sqrt（推定母分散×（（1／標本数A）＋（1／標本数B））"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import math\n",
    "def get_t_value(list1, list2):\n",
    "    return (average(list1) - average(list2)) / math.sqrt(population_variance(list1, list2) *\n",
    "                                                        (1. / len(list1) + 1. /len(list2)) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.2881223774390613"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "get_t_value(wakuwaku, mogumogu)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* 自由度を求めてください。\n",
    "  * t検定の場合は、（標本数A-1）と（標本数B-1）を足したものが自由度になります。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def freedom_t(list1, list2):\n",
    "    return (len(list1) - 1) + (len(list2) - 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "14"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "freedom_t(wakuwaku, mogumogu)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* 下記のt分布表を用いて、t検定の結果を説明してください。\n",
    "<table width=\"50%\" border=\"1\" align=\"center\" cellpadding=\"2\" cellspacing=\"0\">\n",
    "  <tr bgcolor=\"#FFFFCC\"> \n",
    "    <td width=\"32%\"> <div align=\"right\">自由度</div></td>\n",
    "    <td width=\"34%\"> <div align=\"right\">有意水準5%</div></td>\n",
    "    <td width=\"34%\"> <div align=\"right\">有意水準1%</div></td>\n",
    "  </tr>\n",
    "  <tr> \n",
    "    <td bgcolor=\"#CCCCCC\"><div align=\"right\">1</div></td>\n",
    "    <td><div align=\"right\">12.706</div></td>\n",
    "    <td><div align=\"right\">63.657</div></td>\n",
    "  </tr>\n",
    "  <tr> \n",
    "    <td bgcolor=\"#CCCCCC\"><div align=\"right\">2</div></td>\n",
    "    <td><div align=\"right\">4.303</div></td>\n",
    "    <td><div align=\"right\">9.925</div></td>\n",
    "  </tr>\n",
    "  <tr> \n",
    "    <td bgcolor=\"#CCCCCC\"><div align=\"right\">3</div></td>\n",
    "    <td><div align=\"right\">3.182</div></td>\n",
    "    <td><div align=\"right\">5.841</div></td>\n",
    "  </tr>\n",
    "  <tr> \n",
    "    <td bgcolor=\"#CCCCCC\"><div align=\"right\">4</div></td>\n",
    "    <td><div align=\"right\">2.776</div></td>\n",
    "    <td><div align=\"right\">4.604</div></td>\n",
    "  </tr>\n",
    "  <tr> \n",
    "    <td bgcolor=\"#CCCCCC\"><div align=\"right\">5</div></td>\n",
    "    <td><div align=\"right\">2.571</div></td>\n",
    "    <td><div align=\"right\">4.032</div></td>\n",
    "  </tr>\n",
    "  <tr> \n",
    "    <td bgcolor=\"#CCCCCC\"><div align=\"right\">6</div></td>\n",
    "    <td><div align=\"right\">2.447</div></td>\n",
    "    <td><div align=\"right\">3.707</div></td>\n",
    "  </tr>\n",
    "  <tr> \n",
    "    <td bgcolor=\"#CCCCCC\"><div align=\"right\">7</div></td>\n",
    "    <td><div align=\"right\">2.365</div></td>\n",
    "    <td><div align=\"right\">3.499</div></td>\n",
    "  </tr>\n",
    "  <tr> \n",
    "    <td bgcolor=\"#CCCCCC\"><div align=\"right\">8</div></td>\n",
    "    <td><div align=\"right\">2.306</div></td>\n",
    "    <td><div align=\"right\">3.355</div></td>\n",
    "  </tr>\n",
    "  <tr> \n",
    "    <td bgcolor=\"#CCCCCC\"><div align=\"right\">9</div></td>\n",
    "    <td><div align=\"right\">2.262</div></td>\n",
    "    <td><div align=\"right\">3.250</div></td>\n",
    "  </tr>\n",
    "  <tr> \n",
    "    <td bgcolor=\"#CCCCCC\"><div align=\"right\">10</div></td>\n",
    "    <td><div align=\"right\">2.226</div></td>\n",
    "    <td><div align=\"right\">3.169</div></td>\n",
    "  </tr>\n",
    "  <tr> \n",
    "    <td bgcolor=\"#eeeeee\"> <div align=\"right\">11</div></td>\n",
    "    <td><div align=\"right\">2.201</div></td>\n",
    "    <td><div align=\"right\">3.106</div></td>\n",
    "  </tr>\n",
    "  <tr> \n",
    "    <td bgcolor=\"#eeeeee\"> <div align=\"right\">12</div></td>\n",
    "    <td><div align=\"right\">2.179</div></td>\n",
    "    <td><div align=\"right\">3.055</div></td>\n",
    "  </tr>\n",
    "  <tr> \n",
    "    <td bgcolor=\"#eeeeee\"> <div align=\"right\">13</div></td>\n",
    "    <td><div align=\"right\">2.160</div></td>\n",
    "    <td><div align=\"right\">3.021</div></td>\n",
    "  </tr>\n",
    "  <tr> \n",
    "    <td bgcolor=\"#eeeeee\"> <div align=\"right\">14</div></td>\n",
    "    <td>\n",
    "<div align=\"right\">2.145</div></td>\n",
    "    <td>\n",
    "<div align=\"right\">2.977</div></td>\n",
    "  </tr>\n",
    "  <tr> \n",
    "    <td bgcolor=\"#eeeeee\"> <div align=\"right\">15</div></td>\n",
    "    <td><div align=\"right\">2.131</div></td>\n",
    "    <td><div align=\"right\">2.947</div></td>\n",
    "  </tr>\n",
    "  <tr> \n",
    "    <td bgcolor=\"#eeeeee\"> <div align=\"right\">16</div></td>\n",
    "    <td><div align=\"right\">2.120</div></td>\n",
    "    <td><div align=\"right\">2.921</div></td>\n",
    "  </tr>\n",
    "  <tr> \n",
    "    <td bgcolor=\"#eeeeee\"> <div align=\"right\">17</div></td>\n",
    "    <td><div align=\"right\">2.110</div></td>\n",
    "    <td><div align=\"right\">2.898</div></td>\n",
    "  </tr>\n",
    "  <tr> \n",
    "    <td bgcolor=\"#eeeeee\"> <div align=\"right\">18</div></td>\n",
    "    <td><div align=\"right\">2.101</div></td>\n",
    "    <td><div align=\"right\">2.878</div></td>\n",
    "  </tr>\n",
    "  <tr> \n",
    "    <td bgcolor=\"#eeeeee\"> <div align=\"right\">19</div></td>\n",
    "    <td><div align=\"right\">2.093</div></td>\n",
    "    <td><div align=\"right\">2.861</div></td>\n",
    "  </tr>\n",
    "  <tr> \n",
    "    <td bgcolor=\"#eeeeee\"> <div align=\"right\">20</div></td>\n",
    "    <td><div align=\"right\">2.086</div></td>\n",
    "    <td><div align=\"right\">2.845</div></td>\n",
    "  </tr>\n",
    "  <tr> \n",
    "    <td bgcolor=\"#CCCCCC\"><div align=\"right\">21</div></td>\n",
    "    <td><div align=\"right\">2.080</div></td>\n",
    "    <td><div align=\"right\">2.831</div></td>\n",
    "  </tr>\n",
    "  <tr> \n",
    "    <td bgcolor=\"#CCCCCC\"><div align=\"right\">22</div></td>\n",
    "    <td><div align=\"right\">2.074</div></td>\n",
    "    <td><div align=\"right\">2.819</div></td>\n",
    "  </tr>\n",
    "  <tr> \n",
    "    <td bgcolor=\"#CCCCCC\"><div align=\"right\">23</div></td>\n",
    "    <td><div align=\"right\">2.069</div></td>\n",
    "    <td><div align=\"right\">2.807</div></td>\n",
    "  </tr>\n",
    "  <tr> \n",
    "    <td bgcolor=\"#CCCCCC\"><div align=\"right\">24</div></td>\n",
    "    <td><div align=\"right\">2.064</div></td>\n",
    "    <td><div align=\"right\">2.797</div></td>\n",
    "  </tr>\n",
    "  <tr> \n",
    "    <td bgcolor=\"#CCCCCC\"><div align=\"right\">25</div></td>\n",
    "    <td><div align=\"right\">2.060</div></td>\n",
    "    <td><div align=\"right\">2.787</div></td>\n",
    "  </tr>\n",
    "  <tr> \n",
    "    <td bgcolor=\"#CCCCCC\"><div align=\"right\">26</div></td>\n",
    "    <td><div align=\"right\">2.056</div></td>\n",
    "    <td><div align=\"right\">2.779</div></td>\n",
    "  </tr>\n",
    "  <tr> \n",
    "    <td bgcolor=\"#CCCCCC\"><div align=\"right\">27</div></td>\n",
    "    <td><div align=\"right\">2.052</div></td>\n",
    "    <td><div align=\"right\">2.771</div></td>\n",
    "  </tr>\n",
    "  <tr> \n",
    "    <td bgcolor=\"#CCCCCC\"><div align=\"right\">28</div></td>\n",
    "    <td><div align=\"right\">2.048</div></td>\n",
    "    <td><div align=\"right\">2.763</div></td>\n",
    "  </tr>\n",
    "  <tr> \n",
    "    <td bgcolor=\"#CCCCCC\"><div align=\"right\">29</div></td>\n",
    "    <td><div align=\"right\">2.045</div></td>\n",
    "    <td><div align=\"right\">2.756</div></td>\n",
    "  </tr>\n",
    "  <tr> \n",
    "    <td bordercolor=\"#CCCCCC\" bgcolor=\"#eeeeee\"> <div align=\"right\">30</div></td>\n",
    "    <td><div align=\"right\">2.042</div></td>\n",
    "    <td><div align=\"right\">2.750</div></td>\n",
    "  </tr>\n",
    "  <tr> \n",
    "    <td bordercolor=\"#CCCCCC\" bgcolor=\"#eeeeee\"> <div align=\"right\">40</div></td>\n",
    "    <td><div align=\"right\">2.021</div></td>\n",
    "    <td><div align=\"right\">2.704</div></td>\n",
    "  </tr>\n",
    "  <tr> \n",
    "    <td bordercolor=\"#CCCCCC\" bgcolor=\"#eeeeee\"> <div align=\"right\">60</div></td>\n",
    "    <td><div align=\"right\">2.000</div></td>\n",
    "    <td><div align=\"right\">2.660</div></td>\n",
    "  </tr>\n",
    "  <tr> \n",
    "    <td bordercolor=\"#CCCCCC\" bgcolor=\"#eeeeee\"> <div align=\"right\">120</div></td>\n",
    "    <td><div align=\"right\">1.980</div></td>\n",
    "    <td><div align=\"right\">2.617</div></td>\n",
    "  </tr>\n",
    "  <tr> \n",
    "    <td bordercolor=\"#CCCCCC\" bgcolor=\"#eeeeee\"> <div align=\"right\">∞</div></td>\n",
    "    <td><div align=\"right\">1.960</div></td>\n",
    "    <td><div align=\"right\">2.576</div></td>\n",
    "  </tr>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 計算したt値は -1.29 だった。\n",
    "# 一方、自由度は14なので、有意水準5%を満たすt値は　-2.145 である。\n",
    "# 計算したt値は -2.145 を下回らないので棄却域に入らない。\n",
    "# それは、5%よりも大きい確率で起こりうることを意味する。\n",
    "# したがって帰無仮説は棄却できない。\n",
    "# つまり、ワクワクバーガー（全体）とモグモグバーガー（全体）のおいしさの評価点には差があるとは言えない。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.4　[実践編：ポテトの評価は？](http://kogolab.chillout.jp/elearn/hamburger/chap4/sec4.html)\n",
    "__課題4.4__：下表を用いて、ワクワクポテトとモグモグポテトの評価に差があるかどうかを検定してください。\n",
    "<table border=1 bgcolor=\"#FFFFFF\" cellpadding=\"0\" cellspacing=\"0\" align=center>\n",
    "  <tr align=\"center\"> \n",
    "    <th width=120 height=30 bgcolor=\"#ffffcc\"> ワクワクポテトを食べた女子高生</th>\n",
    "    <th width=120 height=30 bgcolor=\"#ffffcc\"> 点数</th>\n",
    "    <th width=120 height=30 bgcolor=\"#ffcccc\"> モグモグポテトを食べた女子高生</th>\n",
    "    <th width=120 height=30 bgcolor=\"#ffcccc\"> 点数</th>\n",
    "  </tr>\n",
    "  <tr align=center> \n",
    "    <td width=120 height=30 bgcolor=\"#cccccc\"> 1</td>\n",
    "    <td width=120 height=30 bgcolor=\"#FFFFFF\"> 80</td>\n",
    "    <td width=120 height=30 bgcolor=\"#cccccc\"> 1</td>\n",
    "    <td width=120 height=30> 75</td>\n",
    "  </tr>\n",
    "  <tr align=center> \n",
    "    <td width=120 height=30 bgcolor=\"#cccccc\">2</td>\n",
    "    <td width=120 height=30 bgcolor=\"#FFFFFF\">75</td>\n",
    "    <td width=120 height=30 bgcolor=\"#cccccc\">2</td>\n",
    "    <td width=120 height=30>65</td>\n",
    "  </tr>\n",
    "  <tr align=center> \n",
    "    <td width=120 height=30 bgcolor=\"#cccccc\">3</td>\n",
    "    <td width=120 height=30 bgcolor=\"#FFFFFF\">80</td>\n",
    "    <td width=120 height=30 bgcolor=\"#cccccc\">3</td>\n",
    "    <td width=120 height=30>80</td>\n",
    "  </tr>\n",
    "  <tr align=center> \n",
    "    <td width=120 height=30 bgcolor=\"#cccccc\">4</td>\n",
    "    <td width=120 height=30 bgcolor=\"#FFFFFF\">95</td>\n",
    "    <td width=120 height=30 bgcolor=\"#cccccc\">4</td>\n",
    "    <td width=120 height=30>85</td>\n",
    "  </tr>\n",
    "  <tr align=center> \n",
    "    <td width=120 height=30 bgcolor=\"#cccccc\">5</td>\n",
    "    <td width=120 height=30 bgcolor=\"#FFFFFF\">90</td>\n",
    "    <td width=120 height=30 bgcolor=\"#cccccc\">5</td>\n",
    "    <td width=120 height=30>75</td>\n",
    "  </tr>\n",
    "  <tr align=center> \n",
    "    <td width=120 height=30 bgcolor=\"#cccccc\">6</td>\n",
    "    <td width=120 height=30 bgcolor=\"#FFFFFF\">80</td>\n",
    "    <td width=120 height=30 bgcolor=\"#cccccc\">6</td>\n",
    "    <td width=120 height=30>80</td>\n",
    "  </tr>\n",
    "  <tr align=center> \n",
    "    <td width=120 height=30 bgcolor=\"#cccccc\">7</td>\n",
    "    <td width=120 height=30 bgcolor=\"#FFFFFF\">85</td>\n",
    "    <td width=120 height=30 bgcolor=\"#cccccc\">7</td>\n",
    "    <td width=120 height=30>80</td>\n",
    "  </tr>\n",
    "  <tr align=center> \n",
    "    <td width=120 height=30 bgcolor=\"#cccccc\">8</td>\n",
    "    <td width=120 height=30 bgcolor=\"#FFFFFF\">90</td>\n",
    "    <td width=120 height=30 bgcolor=\"#cccccc\">8</td>\n",
    "    <td width=120 height=30>70</td>\n",
    "  </tr>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "wakuwaku =   [80, 75, 80, 95, 90, 80, 85, 90]\n",
    "mogumogu = [75, 65, 80, 85, 75, 80, 80, 70]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "84.375"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "average(wakuwaku)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "76.25"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "average(mogumogu)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.463060426921489"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "get_t_value(wakuwaku, mogumogu)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "14"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "freedom_t(wakuwaku, mogumogu)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 計算したt値は 2.46 だった。\n",
    "# 一方、自由度は14なので、有意水準5%を満たすt値は　2.145 である。\n",
    "# 計算したt値は 2.145 を上回り棄却域に入った。\n",
    "# それは、帰無仮説を仮定した場合に5%よりも小さい確率でしか起こりえないことが起こったを意味する。\n",
    "# したがって帰無仮説は棄却でき、\n",
    "# ワクワクポテト（全体）とモグモグポテト（全体）のおいしさの評価点には差があると言える。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.9　[通過テスト](http://kogolab.chillout.jp/elearn/hamburger/chap4/sec9.html)\n",
    "本文を読んで、問題を解いてください。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sakura = [7, 8, 10, 5, 8, 7, 9, 5, 6, 9, 10, 6, 7, 8, 7, 9, 10, 6]\n",
    "momo = [9, 9, 6, 10, 9, 8, 10, 7, 9, 10, 6, 8, 9, 9, 10, 7, 8, 8, 10, 9]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# (1)　この検定での帰無仮説を言いなさい。\n",
    "\n",
    "# 桜組と桃組で平均点に差がない。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# (2)　この検定での対立仮説を言いなさい。\n",
    "\n",
    "# 桜組と桃組で平均点に差がある。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.9730501898890833"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# (3)　t値を求めなさい（小数点以下第3位を四捨五入）。\n",
    "\n",
    "get_t_value(sakura, momo)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "36"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "freedom_t(sakura, momo)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# (4)　有意水準を1%としたとき、このt値から言えることを書きなさい。\n",
    "\n",
    "# 計算したt値は -1.97 だった。\n",
    "# 一方、自由度は36なので、有意水準1%を満たすt値は　-2.750 〜 -2.704 の間である。\n",
    "# 計算したt値は棄却域に入らなかった。\n",
    "# それは、帰無仮説を仮定した場合に1%よりも大きい確率で起こりうるを意味する。\n",
    "# したがって帰無仮説は棄却できず、\n",
    "# 桜組と桃組で平均点に差が出たとは言えない。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5.　[t検定（対応あり）](http://kogolab.chillout.jp/elearn/hamburger/chap5/sec0.html)\n",
    "本文を読んで概念を学んでください。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5.1　[１人に２種類を評価してもらう](http://kogolab.chillout.jp/elearn/hamburger/chap5/sec1.html)\n",
    "本文を読んで概念を学んでください。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5.2　[対応があるとは？](http://kogolab.chillout.jp/elearn/hamburger/chap5/sec2.html)\n",
    "本文を読んで概念を学んでください。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5.3　[対応のあるt検定](http://kogolab.chillout.jp/elearn/hamburger/chap5/sec3.html)\n",
    "まずは本文を読んで概念を学んでください。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__課題4.3__：ワクワクバーガーとモグモグバーガーの評価に差があるかどうか、下表の空欄を埋めながら検定を進めてください。\n",
    "<table border=1 bgcolor=\"#FFFFFF\" cellpadding=\"0\" cellspacing=\"0\" align=center>\n",
    "  <caption>&nbsp;\n",
    "  </caption>\n",
    "  <tr align=\"center\"> \n",
    "    <th width=120 height=30 bgcolor=\"#ffffcc\"> 女子高生</th>\n",
    "    <th width=120 height=30 bgcolor=\"#ffffcc\"> ワクワクバーガーの点数</th>\n",
    "    <th width=120 height=30 bgcolor=\"#ffcccc\"> モグモグバーガーの点数</th>\n",
    "    <th width=120 bgcolor=\"#CCFFFF\">点数の差</th>\n",
    "  </tr>\n",
    "  <tr align=center> \n",
    "    <td width=120 height=30 bgcolor=\"#cccccc\"> 1</td>\n",
    "    <td width=120 height=30 bgcolor=\"#FFFFFF\"> 90</td>\n",
    "    <td width=120 height=30> 95</td>\n",
    "    <td width=120></td>\n",
    "  </tr>\n",
    "  <tr align=center> \n",
    "    <td width=120 height=30 bgcolor=\"#cccccc\">2</td>\n",
    "    <td width=120 height=30 bgcolor=\"#FFFFFF\">75</td>\n",
    "    <td width=120 height=30>80</td>\n",
    "    <td width=120></td>\n",
    "  </tr>\n",
    "  <tr align=center> \n",
    "    <td width=120 height=30 bgcolor=\"#cccccc\">3</td>\n",
    "    <td width=120 height=30 bgcolor=\"#FFFFFF\">75</td>\n",
    "    <td width=120 height=30>80</td>\n",
    "    <td width=120></td>\n",
    "  </tr>\n",
    "  <tr align=center> \n",
    "    <td width=120 height=30 bgcolor=\"#cccccc\">4</td>\n",
    "    <td width=120 height=30 bgcolor=\"#FFFFFF\">75</td>\n",
    "    <td width=120 height=30>80</td>\n",
    "    <td width=120></td>\n",
    "  </tr>\n",
    "  <tr align=center> \n",
    "    <td width=120 height=30 bgcolor=\"#cccccc\">5</td>\n",
    "    <td width=120 height=30 bgcolor=\"#FFFFFF\">80</td>\n",
    "    <td width=120 height=30>75</td>\n",
    "    <td width=120></td>\n",
    "  </tr>\n",
    "  <tr align=center> \n",
    "    <td width=120 height=30 bgcolor=\"#cccccc\">6</td>\n",
    "    <td width=120 height=30 bgcolor=\"#FFFFFF\">65</td>\n",
    "    <td width=120 height=30>75</td>\n",
    "    <td width=120></td>\n",
    "  </tr>\n",
    "  <tr align=center> \n",
    "    <td width=120 height=30 bgcolor=\"#cccccc\">7</td>\n",
    "    <td width=120 height=30 bgcolor=\"#FFFFFF\">75</td>\n",
    "    <td width=120 height=30>80</td>\n",
    "    <td width=120></td>\n",
    "  </tr>\n",
    "  <tr align=center> \n",
    "    <td width=120 height=30 bgcolor=\"#cccccc\">8</td>\n",
    "    <td width=120 height=30 bgcolor=\"#FFFFFF\">80</td>\n",
    "    <td width=120 height=30>85</td>\n",
    "    <td width=120></td>\n",
    "  </tr>\n",
    "  <tr align=center> \n",
    "    <td width=120 height=30 bgcolor=\"#ffffcc\">平均</td>\n",
    "    <td width=120 height=30></td>\n",
    "    <td width=120 height=30></td>\n",
    "    <td width=120></td>\n",
    "  </tr>\n",
    "  <tr align=center> \n",
    "    <td width=120 height=30 bgcolor=\"#ffffcc\"> 標本分散</td>\n",
    "    <td width=120 height=30></td>\n",
    "    <td width=120 height=30></td>\n",
    "    <td width=120></td>\n",
    "  </tr>\n",
    "  <tr align=center> \n",
    "    <td width=120 height=30 bgcolor=\"#ffffcc\"> 不偏分散</td>\n",
    "    <td width=120 height=30></td>\n",
    "    <td width=120 height=30></td>\n",
    "    <td width=120></td>\n",
    "  </tr>\n",
    "  <tr align=center> \n",
    "    <td width=120 height=30 bgcolor=\"#ffffcc\" colspan=\"3\"> 差の標準誤差</td>\n",
    "    <td width=120></td>\n",
    "  </tr>\n",
    "  <tr align=center> \n",
    "    <td width=120 height=30 bgcolor=\"#ffffcc\" colspan=\"3\"> t値</td>\n",
    "    <td width=120></td>\n",
    "  </tr>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* ８人の女子高生の「点数の差」をそれぞれ求めてください。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "wakuwaku =   [90, 75, 75, 75, 80, 65, 75, 80]\n",
    "mogumogu = [95, 80, 80, 80, 75, 75, 80, 85]\n",
    "sa = []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "for w, m in zip(wakuwaku, mogumogu):\n",
    "    sa.append(w - m)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-5, -5, -5, -5, 5, -10, -5, -5]"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sa"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* ワクワクバーガーの点数の平均、モグモグバーガーの点数の平均、点数の差の平均をそれぞれ求めてください。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "76.875\n",
      "81.25\n",
      "-4.375\n"
     ]
    }
   ],
   "source": [
    "print (average(wakuwaku)) # ワクワクバーガーの点数の平均\n",
    "print (average(mogumogu)) # モグモグバーガーの点数の平均\n",
    "print (average(sa)) # 点数の差の平均"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* ワクワクバーガーの点数の標本分散、モグモグバーガーの点数の標本分散、点数の差の標本分散をそれぞれ求めてください。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "43.359375\n",
      "35.9375\n",
      "15.234375\n"
     ]
    }
   ],
   "source": [
    "print (variance(wakuwaku)) # ワクワクバーガーの点数の標本分散\n",
    "print (variance(mogumogu)) # モグモグバーガーの点数の標本分散\n",
    "print (variance(sa)) # 点数の差の標本分散"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* ワクワクバーガーの点数の不偏分散、モグモグバーガーの点数の不偏分散、点数の差の不偏分散をそれぞれ求めてください。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 不偏分散を求める関数\n",
    "def unbiased_variance(list):\n",
    "    ave = average(list)\n",
    "    sum = 0.0\n",
    "    n = 0.0\n",
    "    for x in list:\n",
    "        sum += (x - ave) ** 2.0\n",
    "        n += 1.0\n",
    "    return sum / (n - 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "49.5535714286\n",
      "41.0714285714\n",
      "17.4107142857\n"
     ]
    }
   ],
   "source": [
    "print (unbiased_variance(wakuwaku)) # ワクワクバーガーの点数の不偏分散\n",
    "print (unbiased_variance(mogumogu)) # モグモグバーガーの点数の不偏分散\n",
    "print (unbiased_variance(sa)) # 点数の差の不偏分散"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* 差の標準誤差を求めてください。\n",
    "  * 差の標準誤差＝sqrt（差の不偏分散／標本数）＝sqrt（（差の標本分散／（標本数－1））"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import math\n",
    "def unbiased_standard_error(list):\n",
    "    n = 0\n",
    "    for x in list:\n",
    "        n += 1\n",
    "    return math.sqrt(unbiased_variance(sa) / n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.4752421108802058"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "unbiased_standard_error(sa)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* t値を求めてください。\n",
    "  * t＝平均の差／sqrt（不偏分散／標本数）＝平均の差／sqrt（標本分散／（標本数－1））"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-2.965614910077132"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(average(wakuwaku) - average(mogumogu)) / unbiased_standard_error(sa)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# これまでの計算を関数として書き直すと\n",
    "def get_t_value2(list1, list2):\n",
    "    sa = []\n",
    "    for x1, x2 in zip(list1, list2):\n",
    "        sa.append(x1 - x2)\n",
    "    return (average(list1) - average(list2)) / unbiased_standard_error(sa)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-2.965614910077132"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "get_t_value2(wakuwaku, mogumogu)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* t分布表を用いて、t検定の結果を説明してください。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 計算したt値は -2.97 だった。\n",
    "# 一方、自由度（標本数から１を引いた値）は7なので、有意水準5%を満たすt値は　-2.365 である。\n",
    "# 計算したt値は -2.365 を下回るので棄却域に入る。\n",
    "# それは、5%よりも小さい確率でしか起こりえないことを意味する。\n",
    "# したがって帰無仮説は棄却できる。\n",
    "# つまり、ワクワクバーガー（全体）とモグモグバーガー（全体）のおいしさの評価点に差があると言える。\n",
    "# ところが、有意水準1%とした場合、それを満たすt値は　-3.449である。\n",
    "# 計算したt値は -3.449 を下回らないので棄却域に入らず、帰無仮説は棄却できない。\n",
    "# つまり、ワクワクバーガー（全体）とモグモグバーガー（全体）のおいしさの評価点に差があるとは言えない。\n",
    "# 最終的な結論として、この差は有意に大きいが、有意水準5%~1%の範囲に収まる範囲の差であると言える。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5.4　[実践編：新作バーガー！](http://kogolab.chillout.jp/elearn/hamburger/chap5/sec4.html)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__課題5.4__：下表を用いて、改善前と改善後で差があるかどうかを検定してください。\n",
    "<table border=1 bgcolor=\"#FFFFFF\" cellpadding=\"0\" cellspacing=\"0\" align=center>\n",
    "  <caption>&nbsp;\n",
    "  </caption>\n",
    "  <tr align=\"center\"> \n",
    "    <th width=120 height=30 bgcolor=\"#ffffcc\"> 女子高生</th>\n",
    "    <th width=120 height=30 bgcolor=\"#ffffcc\"> 改善前</th>\n",
    "    <th width=120 height=30 bgcolor=\"#ffcccc\"> 改善後</th>\n",
    "  </tr>\n",
    "  <tr align=center> \n",
    "    <td width=120 height=30 bgcolor=\"#cccccc\"> 1</td>\n",
    "    <td width=120 height=30 bgcolor=\"#FFFFFF\"> 65</td>\n",
    "    <td width=120 height=30> 80</td>\n",
    "  </tr>\n",
    "  <tr align=center> \n",
    "    <td width=120 height=30 bgcolor=\"#cccccc\">2</td>\n",
    "    <td width=120 height=30 bgcolor=\"#FFFFFF\">70</td>\n",
    "    <td width=120 height=30>90</td>\n",
    "  </tr>\n",
    "  <tr align=center> \n",
    "    <td width=120 height=30 bgcolor=\"#cccccc\">3</td>\n",
    "    <td width=120 height=30 bgcolor=\"#FFFFFF\">85</td>\n",
    "    <td width=120 height=30>80</td>\n",
    "  </tr>\n",
    "  <tr align=center> \n",
    "    <td width=120 height=30 bgcolor=\"#cccccc\">4</td>\n",
    "    <td width=120 height=30 bgcolor=\"#FFFFFF\">70</td>\n",
    "    <td width=120 height=30>90</td>\n",
    "  </tr>\n",
    "  <tr align=center> \n",
    "    <td width=120 height=30 bgcolor=\"#cccccc\">5</td>\n",
    "    <td width=120 height=30 bgcolor=\"#FFFFFF\">80</td>\n",
    "    <td width=120 height=30>90</td>\n",
    "  </tr>\n",
    "  <tr align=center> \n",
    "    <td width=120 height=30 bgcolor=\"#cccccc\">6</td>\n",
    "    <td width=120 height=30 bgcolor=\"#FFFFFF\">80</td>\n",
    "    <td width=120 height=30>85</td>\n",
    "  </tr>\n",
    "  <tr align=center> \n",
    "    <td width=120 height=30 bgcolor=\"#cccccc\">7</td>\n",
    "    <td width=120 height=30 bgcolor=\"#FFFFFF\">80</td>\n",
    "    <td width=120 height=30>80</td>\n",
    "  </tr>\n",
    "  <tr align=center> \n",
    "    <td width=120 height=30 bgcolor=\"#cccccc\">8</td>\n",
    "    <td width=120 height=30 bgcolor=\"#FFFFFF\">70</td>\n",
    "    <td width=120 height=30>90</td>\n",
    "  </tr>\n",
    "  <tr align=center bgcolor=\"#FFFFFF\"> \n",
    "    <td width=120 height=30 bgcolor=\"#CCCCCC\">9</td>\n",
    "    <td width=120 height=30>80</td>\n",
    "    <td width=120 height=30>85</td>\n",
    "  </tr>\n",
    "  <tr align=center bgcolor=\"#FFFFFF\"> \n",
    "    <td width=120 height=30 bgcolor=\"#CCCCCC\"> 10</td>\n",
    "    <td width=120 height=30>70</td>\n",
    "    <td width=120 height=30>80</td>\n",
    "  </tr>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "before = [65, 70, 85, 70, 80, 80, 80, 70, 80, 70]\n",
    "after    = [80, 90, 80, 90, 90, 85, 80, 90, 85, 80]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-7.578647467450735"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "get_t_value2(before, after)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 計算したt値は -7.57 だった。\n",
    "# 一方、自由度（標本数から１を引いた値）は9なので、有意水準5%を満たすt値は　-2.262 である。\n",
    "# 計算したt値は -2.262 を下回るので棄却域に入る。\n",
    "# それは、5%よりも小さい確率でしか起こりえないことを意味する。\n",
    "# したがって帰無仮説は棄却できる。\n",
    "# つまり、ワクワクバーガー（全体）とモグモグバーガー（全体）のおいしさの評価点に差があると言える。\n",
    "# 同様に、有意水準1%とした場合、それを満たすt値は　-3.250であり、この場合も帰無仮説を棄却できる。\n",
    "# 最終的な結論として、改善前と改善後は十分な差があると言える。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5.9　[通過テスト](http://kogolab.chillout.jp/elearn/hamburger/chap5/sec9.html)\n",
    "<p> テストの点数データ（10点満点）は次のようになった。これを対応のあるt検定によって分析したい。</p>\n",
    "<p>柳組18人の点数：</p>\n",
    "<table width=\"80%\" border=\"1\" align=\"center\" cellpadding=\"1\" cellspacing=\"0\">\n",
    "  <tr bgcolor=\"#CCCCCC\"> \n",
    "    <td width=\"10%\" bgcolor=\"#FFFF99\"> <div align=\"center\">事前テスト</div></td>\n",
    "    <td width=\"5%\"> <div align=\"center\">9</div></td>\n",
    "    <td width=\"5%\"> <div align=\"center\">8</div></td>\n",
    "    <td width=\"5%\"> <div align=\"center\">10</div></td>\n",
    "    <td width=\"5%\"><div align=\"center\">7</div></td>\n",
    "    <td width=\"5%\"><div align=\"center\">5</div></td>\n",
    "    <td width=\"5%\"><div align=\"center\">9</div></td>\n",
    "    <td width=\"5%\"><div align=\"center\">10</div></td>\n",
    "    <td width=\"5%\"><div align=\"center\">10</div></td>\n",
    "    <td width=\"5%\"><div align=\"center\">8</div></td>\n",
    "    <td width=\"5%\"><div align=\"center\">10</div></td>\n",
    "    <td width=\"5%\"><div align=\"center\">10</div></td>\n",
    "    <td width=\"5%\"><div align=\"center\">6</div></td>\n",
    "    <td width=\"5%\"><div align=\"center\">8</div></td>\n",
    "    <td width=\"5%\"><div align=\"center\">9</div></td>\n",
    "    <td width=\"5%\"><div align=\"center\">10</div></td>\n",
    "    <td width=\"5%\"><div align=\"center\">9</div></td>\n",
    "    <td width=\"5%\"> <div align=\"center\">10</div></td>\n",
    "    <td width=\"5%\"><div align=\"center\">9</div></td>\n",
    "  </tr>\n",
    "  <tr bgcolor=\"#CCCCCC\"> \n",
    "    <td bgcolor=\"#FFFF99\"><div align=\"center\">事後テスト</div></td>\n",
    "    <td width=\"5%\"><div align=\"center\">9</div></td>\n",
    "    <td width=\"5%\"><div align=\"center\">9</div></td>\n",
    "    <td width=\"5%\"><div align=\"center\">10</div></td>\n",
    "    <td width=\"5%\"><div align=\"center\">7</div></td>\n",
    "    <td width=\"5%\"><div align=\"center\">6</div></td>\n",
    "    <td width=\"5%\"><div align=\"center\">10</div></td>\n",
    "    <td width=\"5%\"><div align=\"center\">10</div></td>\n",
    "    <td width=\"5%\"><div align=\"center\">9</div></td>\n",
    "    <td width=\"5%\"><div align=\"center\">8</div></td>\n",
    "    <td width=\"5%\"><div align=\"center\">10</div></td>\n",
    "    <td width=\"5%\"><div align=\"center\">7</div></td>\n",
    "    <td width=\"5%\"><div align=\"center\">8</div></td>\n",
    "    <td width=\"5%\"><div align=\"center\">10</div></td>\n",
    "    <td width=\"5%\"><div align=\"center\">10</div></td>\n",
    "    <td width=\"5%\"><div align=\"center\">10</div></td>\n",
    "    <td width=\"5%\"><div align=\"center\">10</div></td>\n",
    "    <td width=\"5%\"><div align=\"center\">10</div></td>\n",
    "    <td width=\"5%\"><div align=\"center\">10</div></td>\n",
    "  </tr>\n",
    "</table>\n",
    "<p>&nbsp;</p>\n",
    "<p> (1)　この検定での帰無仮説を言いなさい。</p>\n",
    "<p>(2)　この検定での対立仮説を言いなさい。</p>\n",
    "<p>(3)　t値を求めなさい（小数点以下第3位を四捨五入）。</p>\n",
    "<p>(4)　有意水準を1%としたとき、このt値から言えることは何か。</p>\n",
    "<p>(5)　以上の検定の結果を、わかりやすいことばで説明しなさい。</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# (1)　この検定での帰無仮説を言いなさい。\n",
    "\n",
    "# 事前テストと事後テストとで点数の平均に差はない。\n",
    "\n",
    "# (2)　この検定での対立仮説を言いなさい。\n",
    "\n",
    "# 事前テストと事後テストとで点数の平均に差がある。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.33892741829453"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# (3)　t値を求めなさい\n",
    "before = [9, 8, 10, 7, 5, 9, 10, 10, 8, 10, 10, 6, 8, 9, 10, 9, 10, 9]\n",
    "after = [9, 9, 10, 7, 6, 10, 10, 9, 8, 10, 7, 8, 10, 10, 10, 10, 10, 10]\n",
    "get_t_value2(before, after)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# (4)　有意水準を1%としたとき、このt値から言えることは何か。\n",
    "\n",
    "# 計算したt値は -0.33 だった。\n",
    "# 一方、自由度（標本数から１を引いた値）は17なので、有意水準1%を満たすt値は　-2.898 である。\n",
    "# 計算したt値は -2.898 を下回らないので棄却域に入らない。\n",
    "# つまり帰無仮説は棄却できない。\n",
    "# したがって、事前テストと事後テストとで点数の平均に差があったとは言えない。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__今日の課題提出__：計算結果を.ipynb ファイル（または.jsonファイル）として保存し、指定したアドレスまでメールしてください。メールタイトルは「__ハンバーガー統計学345__」とし、メール本文に学籍番号と氏名を明記のこと。また、感想も書いてくれると喜びます。今後の講義の改善につながるかも知れません。"
   ]
  }
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