Jupyter 데이터 분석 사례 (인코고등학교 중간고사 성적)

데이터분석사례-중간고사성적.ipynb.json

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 성적 데이터 분석\n",
    "\n",
    "인코고등학교 1학년의 중간고사 성적이 나왔습니다. 1반과 2반 두개의 반으로 구성되어 있고, 학생은 각각 6명입니다. 이 성적 데이터로 간단한 데이터 분석을 하고자 합니다. \n",
    "\n",
    "본 Jupyter Notebook은 보시는 것처럼 문서와 파이썬 코드가 각각 섞여서 사용됩니다. 먼저, 데이터 분석에 필요한 파이썬 모듈들을 임포트합니다. (\"#\" 는 주석표시를 의미합니다. 본 코드는 Python 3으로 작성되어 한국어 표시 등이 더 편리합니다.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np  ## 백터, 행렬 데이터 전문 모듈 numpy\n",
    "import pandas as pd  ## 고수준 데이터 모델 (DataFrame) 모듈 pandas\n",
    "import matplotlib.pyplot as plt  ## 차트 그리기 모듈 matplotlib\n",
    "import scipy.stats as stats      ## 통계 등 과학용 모듈 scipy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "엑셀 파일을 불러옵니다. pandas의 read_excel 함수를 이용합니다. df라는 변수에 엑셀쉬트를 DataFrame으로 만듭니다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>반</th>\n",
       "      <th>이름</th>\n",
       "      <th>국어</th>\n",
       "      <th>영어</th>\n",
       "      <th>수학</th>\n",
       "      <th>과학</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>성춘향</td>\n",
       "      <td>67</td>\n",
       "      <td>87</td>\n",
       "      <td>90</td>\n",
       "      <td>98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>이몽룡</td>\n",
       "      <td>45</td>\n",
       "      <td>45</td>\n",
       "      <td>56</td>\n",
       "      <td>98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>향단이</td>\n",
       "      <td>95</td>\n",
       "      <td>59</td>\n",
       "      <td>96</td>\n",
       "      <td>88</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>방자</td>\n",
       "      <td>65</td>\n",
       "      <td>94</td>\n",
       "      <td>89</td>\n",
       "      <td>98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>월매</td>\n",
       "      <td>45</td>\n",
       "      <td>65</td>\n",
       "      <td>78</td>\n",
       "      <td>98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1</td>\n",
       "      <td>변학도</td>\n",
       "      <td>78</td>\n",
       "      <td>76</td>\n",
       "      <td>98</td>\n",
       "      <td>89</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>2</td>\n",
       "      <td>홍길동</td>\n",
       "      <td>87</td>\n",
       "      <td>67</td>\n",
       "      <td>65</td>\n",
       "      <td>56</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>2</td>\n",
       "      <td>임꺽정</td>\n",
       "      <td>89</td>\n",
       "      <td>98</td>\n",
       "      <td>78</td>\n",
       "      <td>78</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>2</td>\n",
       "      <td>전우치</td>\n",
       "      <td>100</td>\n",
       "      <td>78</td>\n",
       "      <td>56</td>\n",
       "      <td>65</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>2</td>\n",
       "      <td>일지매</td>\n",
       "      <td>99</td>\n",
       "      <td>89</td>\n",
       "      <td>87</td>\n",
       "      <td>87</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>2</td>\n",
       "      <td>심청</td>\n",
       "      <td>98</td>\n",
       "      <td>45</td>\n",
       "      <td>56</td>\n",
       "      <td>54</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>2</td>\n",
       "      <td>콩쥐</td>\n",
       "      <td>65</td>\n",
       "      <td>89</td>\n",
       "      <td>87</td>\n",
       "      <td>78</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    반   이름   국어  영어  수학  과학\n",
       "0   1  성춘향   67  87  90  98\n",
       "1   1  이몽룡   45  45  56  98\n",
       "2   1  향단이   95  59  96  88\n",
       "3   1   방자   65  94  89  98\n",
       "4   1   월매   45  65  78  98\n",
       "5   1  변학도   78  76  98  89\n",
       "6   2  홍길동   87  67  65  56\n",
       "7   2  임꺽정   89  98  78  78\n",
       "8   2  전우치  100  78  56  65\n",
       "9   2  일지매   99  89  87  87\n",
       "10  2   심청   98  45  56  54\n",
       "11  2   콩쥐   65  89  87  78"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_excel('성적표.xlsx')\n",
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "엑셀쉬트를 잘 읽어들였고, 또 화면에 잘 표시합니다. \n",
    "\n",
    "여기에 기본적인 통계인 총점과 평균을 추가해서, 평균으로 정렬해보겠습니다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>반</th>\n",
       "      <th>이름</th>\n",
       "      <th>국어</th>\n",
       "      <th>영어</th>\n",
       "      <th>수학</th>\n",
       "      <th>과학</th>\n",
       "      <th>총점</th>\n",
       "      <th>평균</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>2</td>\n",
       "      <td>일지매</td>\n",
       "      <td>99</td>\n",
       "      <td>89</td>\n",
       "      <td>87</td>\n",
       "      <td>87</td>\n",
       "      <td>362</td>\n",
       "      <td>90.50</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>방자</td>\n",
       "      <td>65</td>\n",
       "      <td>94</td>\n",
       "      <td>89</td>\n",
       "      <td>98</td>\n",
       "      <td>346</td>\n",
       "      <td>86.50</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>2</td>\n",
       "      <td>임꺽정</td>\n",
       "      <td>89</td>\n",
       "      <td>98</td>\n",
       "      <td>78</td>\n",
       "      <td>78</td>\n",
       "      <td>343</td>\n",
       "      <td>85.75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>성춘향</td>\n",
       "      <td>67</td>\n",
       "      <td>87</td>\n",
       "      <td>90</td>\n",
       "      <td>98</td>\n",
       "      <td>342</td>\n",
       "      <td>85.50</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1</td>\n",
       "      <td>변학도</td>\n",
       "      <td>78</td>\n",
       "      <td>76</td>\n",
       "      <td>98</td>\n",
       "      <td>89</td>\n",
       "      <td>341</td>\n",
       "      <td>85.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>향단이</td>\n",
       "      <td>95</td>\n",
       "      <td>59</td>\n",
       "      <td>96</td>\n",
       "      <td>88</td>\n",
       "      <td>338</td>\n",
       "      <td>84.50</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>2</td>\n",
       "      <td>콩쥐</td>\n",
       "      <td>65</td>\n",
       "      <td>89</td>\n",
       "      <td>87</td>\n",
       "      <td>78</td>\n",
       "      <td>319</td>\n",
       "      <td>79.75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>2</td>\n",
       "      <td>전우치</td>\n",
       "      <td>100</td>\n",
       "      <td>78</td>\n",
       "      <td>56</td>\n",
       "      <td>65</td>\n",
       "      <td>299</td>\n",
       "      <td>74.75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>월매</td>\n",
       "      <td>45</td>\n",
       "      <td>65</td>\n",
       "      <td>78</td>\n",
       "      <td>98</td>\n",
       "      <td>286</td>\n",
       "      <td>71.50</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>2</td>\n",
       "      <td>홍길동</td>\n",
       "      <td>87</td>\n",
       "      <td>67</td>\n",
       "      <td>65</td>\n",
       "      <td>56</td>\n",
       "      <td>275</td>\n",
       "      <td>68.75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>2</td>\n",
       "      <td>심청</td>\n",
       "      <td>98</td>\n",
       "      <td>45</td>\n",
       "      <td>56</td>\n",
       "      <td>54</td>\n",
       "      <td>253</td>\n",
       "      <td>63.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>이몽룡</td>\n",
       "      <td>45</td>\n",
       "      <td>45</td>\n",
       "      <td>56</td>\n",
       "      <td>98</td>\n",
       "      <td>244</td>\n",
       "      <td>61.00</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    반   이름   국어  영어  수학  과학   총점     평균\n",
       "9   2  일지매   99  89  87  87  362  90.50\n",
       "3   1   방자   65  94  89  98  346  86.50\n",
       "7   2  임꺽정   89  98  78  78  343  85.75\n",
       "0   1  성춘향   67  87  90  98  342  85.50\n",
       "5   1  변학도   78  76  98  89  341  85.25\n",
       "2   1  향단이   95  59  96  88  338  84.50\n",
       "11  2   콩쥐   65  89  87  78  319  79.75\n",
       "8   2  전우치  100  78  56  65  299  74.75\n",
       "4   1   월매   45  65  78  98  286  71.50\n",
       "6   2  홍길동   87  67  65  56  275  68.75\n",
       "10  2   심청   98  45  56  54  253  63.25\n",
       "1   1  이몽룡   45  45  56  98  244  61.00"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "subjects = ['국어', '영어', '수학', '과학']\n",
    "df['총점'] = df[subjects].sum(axis=1)\n",
    "df['평균']= df['총점'] / len(subjects)\n",
    "df.sort_values(['평균'], ascending=[False])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "일지매가 전교 1등이네요. \n",
    "\n",
    "총점으로 막대그래프를 그려볼까요? 그래프를 그리기전, matplotlib에서 한국어가 잘 표시되기 위해 다음을 실행합니다. (OS X에서 테스트 중인데, 기본 폰트에 한국어가 없나봅니다.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import matplotlib\n",
    "matplotlib.rc('font', family='AppleGothic')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "자료를 평균으로 내림차순 정렬하고, 각 데이터의 이름을 `이름` 필드를 사용하도록 한 후, 막대그래프를 그려봅니다. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x10e927358>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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pqFdpI3pNHy1M+uFOutJk1tfikzyC9rk9h3bqGtoAIn9Cu1PNdarq6bOsaajr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\nJKkT/x/Ma7iRvWD2igAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e96a278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sorted_df = df.sort_values(['평균'], ascending=[False])\n",
    "sorted_df.index = sorted_df['이름']\n",
    "sorted_df['평균'].plot(kind='bar', figsize=(8, 4))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "막대그래프로 평균점수를 보니까, 2위 그룹들이 비슷비슷하네요. 일지매는 방심하면 안되겠네요."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1반과 2반의 점수 비교\n",
    "\n",
    "그럼 이번에는 1반과 2반중 어느반이 더 잘했나 볼까요? 담임선생님들 이것에 민감하죠?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(79.041666666666671, 77.125)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "일반 = df[df['반'] == 1]\n",
    "이반 = df[df['반'] == 2]\n",
    "일반평균 = 일반['총점'].sum() / (6 * 4)\n",
    "이반평균 = 이반['총점'].sum() / (6 * 4)\n",
    "일반평균, 이반평균"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1반이 평균이 높네요. (파이썬 3은 변수명을 한국어로 쓸 수 도 있습니다. \"1반\" 이라고 변수를 쓰고 싶었지만, 파이썬 변수 명명 규칙이 숫자로 시작하면 안되기 때문에 그냥 저렇게 표시합니다.) \n",
    "\n",
    "1반 선생님 좋아합니다. 그걸 보고있던 2반 선생님이 \"별 차이도 안나는구먼 뭘\" 이라고 합니다. \n",
    "\n",
    "정말 두 반의 평균은 차이가 없는 걸까요? 서로 독립적인 두 집단에서 얻어진 수치형 자료로 부터 두 집단의 차이가 유의한지를 파악하는데는 독립표본 [t-검정](https://en.wikipedia.org/wiki/Student%27s_t-test) (two independent sample t-test)이 유용합니다. scipy의 ttest_ind 함수를 이용하여 바로 계산이 가능합니다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ttest_indResult(statistic=0.31996022820984599, pvalue=0.755583336185639)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.ttest_ind(일반['평균'], 이반['평균'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`p value > 0.005` 이므로 두 집단이 차이가 없다는 영가설을 채택합니다. 즉 1반과 2반은 사실 유의한 점수차이가 없습니다. 오차수준에 의한 차이라고 봐야겠네요. 1반 선생님 그렇게 좋아하시면 아니될 듯.\n",
    "\n",
    "혹시 과목별로는 차이가 있을까요? 과목별로도 확인해보겠습니다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "국어 Ttest_indResult(statistic=-2.490140665442242, pvalue=0.031982494983816424)\n",
      "영어 Ttest_indResult(statistic=-0.61569071526315811, pvalue=0.55185337815288071)\n",
      "수학 Ttest_indResult(statistic=1.4961318778859336, pvalue=0.1654958420079056)\n",
      "과학 Ttest_indResult(statistic=4.3284425553317547, pvalue=0.0014931977711732465)\n"
     ]
    }
   ],
   "source": [
    "for subject in subjects:\n",
    "    print(subject, stats.ttest_ind(일반[subject], 이반[subject]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "과학 과목은 p value < 0.005 입니다. 차이가 많이 나네요. 평균이 어떻길래."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(94.833333333333329, 69.666666666666671)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "일반['과학'].sum() / 6, 이반['과학'].sum() / 6"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "역시 차이가 많이 났군요. 1반 학생들은 과학에 소질이 많은 것 같습니다. \n",
    "\n",
    "## 과목별 비교 \n",
    "\n",
    "과목별로 다른 특징이 있는 것 같습니다. 먼저 전체 데이터를 막대그래프로 그려보겠습니다. 앞서 그렸던 성적별 막대그래프를 과목별로 각각 그려보겠습니다. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x10ea60978>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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/Av3AthT7l4cotpVtgGnA6zNzTduKbCIi/iwz/xgRe2fmLRHxDeCIzByIiMdl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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ea029b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sorted_df[subjects].plot(kind='bar', figsize=(10, 6))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "일지매는 전체적으로 점수가 고르게 높은데, 2등부터는 약간 들쑥날쑥하네요. 과목별 점수 분포를 볼까요? boxplot으로 그려보겠습니다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x10eb57160>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ebf8518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df[subjects].boxplot(return_type='axes')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1반과 2반을 각각 boxplot으로 그려봅시다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x10ed6f828>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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e2wUUxa/PdEroZYqc+43AX0t6G/1M/ZKIuF/SJcAuSQeBPcDWBM9lZmZr8LlfRizXukbJ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\nkP8Hry8M933dJTEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ea23160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "일반[subjects].boxplot(return_type='axes')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x10ef7e160>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ef23ef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "이반[subjects].boxplot(return_type='axes')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "확실히, 1반의 과학점수가 좋네요. 분포 차이도 크지 않습니다. 대신 2반은 국어점수가 좋습니다."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## 과목별 상관도 \n",
    "\n",
    "보통 수학 점수가 높으면 과학 점수가 높을 것이라고 기대할 수 있습니다. 국어 점수가 높으면 영어 점수가 높을 것이라고도 기대할 수 있죠. 언어능력, 수리능력이 별개의 특징처럼 생각될 수 도 있기 때문입니다. 여기 학생들도 그런지 살펴볼까요."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x10f017438>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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SM8NDktTM8JAkNTM8JEnNDA9JUjPDQ5LUzPAQg8GAmZntzMxsZzAY9F2OpDHgSYIb3GAw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\nD0lSs/8PSPCZ5YrtSRsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10efa3e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df.plot(kind='scatter', x='수학', y='과학')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "수학점수가 높으면 과학점수도 높아 보입니다. 어느정도 상관관계가 보이네요. 얼마나 상관관계가 있을까요? 이렇때 상관계수를 구해볼 수 있습니다. [피어슨 상관계수](https://en.wikipedia.org/wiki/Pearson_product-moment_correlation_coefficient)를 구해볼까요? scipy의 stats 모듈에 함수가 있습니다. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.56328905970677512, 0.05650580486155532)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.pearsonr(df['수학'], df['과학'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "앞 숫자가 상관계수 뒷 숫자가 p-value를 의미합니다. 상관계수가 0.5보다 높으므로, 관계가 있긴 하지만 p > 0.05 이므로, 유의한 상관관계가 있지는 않네요. 데이터가 좀 더 많아지면, p-value가 의미있어지는 경우가 많습니다. 이 경우는 데이터 n수가 작아서 의미를 찾기 어려운 것 같습니다. 국어와 영어는 어떨까요?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x10edfba58>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f15f898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df.plot(kind='scatter', x='국어', y='영어')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.10566562777973997, 0.74379595518578356)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.pearsonr(df['국어'], df['영어'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "상관관계가 아주 약간 있어보이지만 별로 없네요. 이 경우도, 데이터가 많으면 좀 더 충분한 관계를 밝혀낼 수 있을 것 같습니다. \n",
    "\n",
    "## 학생별 성적 패턴 분석\n",
    "\n",
    "학생별로 어떤 학생은 수학을 잘하면서 과학을 잘하지만 영어는 약할 수 있고, 또 어떤 학생은 다른 패턴으로 잘하는 과목에 대한 특징이 있을 수 있습니다. 학생들끼리 이러한 성적 패턴이 얼마나 비슷한지 비교해 볼 수 있을까요? 이를 확인할 수 있는 다양한 방법이 있습니다. 대표적인 방법으로 [주성분분석 (Principle component analysis)](https://ko.wikipedia.org/wiki/주성분_분석)이 있습니다. 학생별로 4과목이라는 특성을 두개로 축약한 후, 2차원 평면에 표시하면, 그 종합적인 차이를 한눈에 알 수 있습니다. \n",
    "\n",
    "PCA 분석은 [scikit-learn](http://scikit-learn.org/stable/)이라는 라이브러리를 설치하고 수행할 수 있습니다. \n",
    "\n",
    "PCA 분석의 입력자료는 4과목의 성적데이터 입니다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>국어</th>\n",
       "      <th>영어</th>\n",
       "      <th>수학</th>\n",
       "      <th>과학</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>67</td>\n",
       "      <td>87</td>\n",
       "      <td>90</td>\n",
       "      <td>98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>45</td>\n",
       "      <td>45</td>\n",
       "      <td>56</td>\n",
       "      <td>98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>95</td>\n",
       "      <td>59</td>\n",
       "      <td>96</td>\n",
       "      <td>88</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>65</td>\n",
       "      <td>94</td>\n",
       "      <td>89</td>\n",
       "      <td>98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>45</td>\n",
       "      <td>65</td>\n",
       "      <td>78</td>\n",
       "      <td>98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>78</td>\n",
       "      <td>76</td>\n",
       "      <td>98</td>\n",
       "      <td>89</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>87</td>\n",
       "      <td>67</td>\n",
       "      <td>65</td>\n",
       "      <td>56</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>89</td>\n",
       "      <td>98</td>\n",
       "      <td>78</td>\n",
       "      <td>78</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>100</td>\n",
       "      <td>78</td>\n",
       "      <td>56</td>\n",
       "      <td>65</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>99</td>\n",
       "      <td>89</td>\n",
       "      <td>87</td>\n",
       "      <td>87</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>98</td>\n",
       "      <td>45</td>\n",
       "      <td>56</td>\n",
       "      <td>54</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>65</td>\n",
       "      <td>89</td>\n",
       "      <td>87</td>\n",
       "      <td>78</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     국어  영어  수학  과학\n",
       "0    67  87  90  98\n",
       "1    45  45  56  98\n",
       "2    95  59  96  88\n",
       "3    65  94  89  98\n",
       "4    45  65  78  98\n",
       "5    78  76  98  89\n",
       "6    87  67  65  56\n",
       "7    89  98  78  78\n",
       "8   100  78  56  65\n",
       "9    99  89  87  87\n",
       "10   98  45  56  54\n",
       "11   65  89  87  78"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[subjects]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "이 데이터를 정규화합니다. 전체 데이터를 최대, 최소를 기준으로 재 정리합니다. 정규화하는 함수는 scikit-learn 라이브러리에서 제공됩니다. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.55809652,  0.72621778,  0.78954203,  1.01066629],\n",
       "       [-1.70024754, -1.68176748, -1.44749373,  1.01066629],\n",
       "       [ 0.89555023, -0.87910573,  1.18431305,  0.36897341],\n",
       "       [-0.66192843,  1.12754865,  0.72374686,  1.01066629],\n",
       "       [-1.70024754, -0.53510783,  0.        ,  1.01066629],\n",
       "       [ 0.01297899,  0.09555497,  1.31590339,  0.43314269],\n",
       "       [ 0.48022259, -0.42044187, -0.8553372 , -1.68444381],\n",
       "       [ 0.5840545 ,  1.35688058,  0.        , -0.27271947],\n",
       "       [ 1.15513001,  0.21022093, -1.44749373, -1.10692022],\n",
       "       [ 1.10321405,  0.84088374,  0.59215653,  0.30480412],\n",
       "       [ 1.0512981 , -1.68176748, -1.44749373, -1.81278239],\n",
       "       [-0.66192843,  0.84088374,  0.59215653, -0.27271947]])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.preprocessing import StandardScaler\n",
    "X_std = StandardScaler().fit_transform(df[subjects])\n",
    "X_std"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "위 행렬데이터가 PCA의 입력으로 사용됩니다. PCA 분석 함수는 scikit-learn 라이브러리에 있습니다. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-1.56591653, -0.09168753],\n",
       "       [ 0.11774518,  2.93515218],\n",
       "       [-0.20727166, -0.38845514],\n",
       "       [-1.71984653, -0.24234692],\n",
       "       [-1.11185524,  1.70512415],\n",
       "       [-1.03327136, -0.43547978],\n",
       "       [ 1.88205338, -0.20323602],\n",
       "       [-0.10118555, -1.27408337],\n",
       "       [ 1.88020684, -0.64411706],\n",
       "       [-0.39554448, -1.36047251],\n",
       "       [ 2.98704605,  0.37256038],\n",
       "       [-0.7321601 , -0.37295837]])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "pca = PCA(n_components=2)\n",
    "Y = pca.fit_transform(X_std)\n",
    "Y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`Y` 변수에 4과목(4차원)을 2차원으로 축약한 데이터 값이 저장됩니다. 보통 제1주성분, 제2주성분이라고도 합니다. 이를 원래 데이터(df)에 추가합니다.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>반</th>\n",
       "      <th>이름</th>\n",
       "      <th>국어</th>\n",
       "      <th>영어</th>\n",
       "      <th>수학</th>\n",
       "      <th>과학</th>\n",
       "      <th>총점</th>\n",
       "      <th>평균</th>\n",
       "      <th>PC1</th>\n",
       "      <th>PC2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>성춘향</td>\n",
       "      <td>67</td>\n",
       "      <td>87</td>\n",
       "      <td>90</td>\n",
       "      <td>98</td>\n",
       "      <td>342</td>\n",
       "      <td>85.50</td>\n",
       "      <td>-1.565917</td>\n",
       "      <td>-0.091688</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>이몽룡</td>\n",
       "      <td>45</td>\n",
       "      <td>45</td>\n",
       "      <td>56</td>\n",
       "      <td>98</td>\n",
       "      <td>244</td>\n",
       "      <td>61.00</td>\n",
       "      <td>0.117745</td>\n",
       "      <td>2.935152</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>향단이</td>\n",
       "      <td>95</td>\n",
       "      <td>59</td>\n",
       "      <td>96</td>\n",
       "      <td>88</td>\n",
       "      <td>338</td>\n",
       "      <td>84.50</td>\n",
       "      <td>-0.207272</td>\n",
       "      <td>-0.388455</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>방자</td>\n",
       "      <td>65</td>\n",
       "      <td>94</td>\n",
       "      <td>89</td>\n",
       "      <td>98</td>\n",
       "      <td>346</td>\n",
       "      <td>86.50</td>\n",
       "      <td>-1.719847</td>\n",
       "      <td>-0.242347</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>월매</td>\n",
       "      <td>45</td>\n",
       "      <td>65</td>\n",
       "      <td>78</td>\n",
       "      <td>98</td>\n",
       "      <td>286</td>\n",
       "      <td>71.50</td>\n",
       "      <td>-1.111855</td>\n",
       "      <td>1.705124</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1</td>\n",
       "      <td>변학도</td>\n",
       "      <td>78</td>\n",
       "      <td>76</td>\n",
       "      <td>98</td>\n",
       "      <td>89</td>\n",
       "      <td>341</td>\n",
       "      <td>85.25</td>\n",
       "      <td>-1.033271</td>\n",
       "      <td>-0.435480</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>2</td>\n",
       "      <td>홍길동</td>\n",
       "      <td>87</td>\n",
       "      <td>67</td>\n",
       "      <td>65</td>\n",
       "      <td>56</td>\n",
       "      <td>275</td>\n",
       "      <td>68.75</td>\n",
       "      <td>1.882053</td>\n",
       "      <td>-0.203236</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>2</td>\n",
       "      <td>임꺽정</td>\n",
       "      <td>89</td>\n",
       "      <td>98</td>\n",
       "      <td>78</td>\n",
       "      <td>78</td>\n",
       "      <td>343</td>\n",
       "      <td>85.75</td>\n",
       "      <td>-0.101186</td>\n",
       "      <td>-1.274083</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>2</td>\n",
       "      <td>전우치</td>\n",
       "      <td>100</td>\n",
       "      <td>78</td>\n",
       "      <td>56</td>\n",
       "      <td>65</td>\n",
       "      <td>299</td>\n",
       "      <td>74.75</td>\n",
       "      <td>1.880207</td>\n",
       "      <td>-0.644117</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>2</td>\n",
       "      <td>일지매</td>\n",
       "      <td>99</td>\n",
       "      <td>89</td>\n",
       "      <td>87</td>\n",
       "      <td>87</td>\n",
       "      <td>362</td>\n",
       "      <td>90.50</td>\n",
       "      <td>-0.395544</td>\n",
       "      <td>-1.360473</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>2</td>\n",
       "      <td>심청</td>\n",
       "      <td>98</td>\n",
       "      <td>45</td>\n",
       "      <td>56</td>\n",
       "      <td>54</td>\n",
       "      <td>253</td>\n",
       "      <td>63.25</td>\n",
       "      <td>2.987046</td>\n",
       "      <td>0.372560</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>2</td>\n",
       "      <td>콩쥐</td>\n",
       "      <td>65</td>\n",
       "      <td>89</td>\n",
       "      <td>87</td>\n",
       "      <td>78</td>\n",
       "      <td>319</td>\n",
       "      <td>79.75</td>\n",
       "      <td>-0.732160</td>\n",
       "      <td>-0.372958</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    반   이름   국어  영어  수학  과학   총점     평균       PC1       PC2\n",
       "0   1  성춘향   67  87  90  98  342  85.50 -1.565917 -0.091688\n",
       "1   1  이몽룡   45  45  56  98  244  61.00  0.117745  2.935152\n",
       "2   1  향단이   95  59  96  88  338  84.50 -0.207272 -0.388455\n",
       "3   1   방자   65  94  89  98  346  86.50 -1.719847 -0.242347\n",
       "4   1   월매   45  65  78  98  286  71.50 -1.111855  1.705124\n",
       "5   1  변학도   78  76  98  89  341  85.25 -1.033271 -0.435480\n",
       "6   2  홍길동   87  67  65  56  275  68.75  1.882053 -0.203236\n",
       "7   2  임꺽정   89  98  78  78  343  85.75 -0.101186 -1.274083\n",
       "8   2  전우치  100  78  56  65  299  74.75  1.880207 -0.644117\n",
       "9   2  일지매   99  89  87  87  362  90.50 -0.395544 -1.360473\n",
       "10  2   심청   98  45  56  54  253  63.25  2.987046  0.372560\n",
       "11  2   콩쥐   65  89  87  78  319  79.75 -0.732160 -0.372958"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca_df = pd.DataFrame(Y)\n",
    "pca_df.index = df.index\n",
    "pca_df.columns = ['PC1', 'PC2']\n",
    "df2 = pd.concat([df, pca_df], axis=1)\n",
    "df2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "위 데이터의 PC1, PC2 값으로 scatter plot을 그려봅니다. 1반과 2반의 차이를 알아보기 위해, 각각을 그룹핑하고, 다른 색으로 표시합니다. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f9e4da0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def draw_groups(groups, loc):\n",
    "    fig, ax = plt.subplots()\n",
    "    ax.margins(0.1)\n",
    "\n",
    "    for name, group in groups:\n",
    "        ax.plot(group['PC1'], group['PC2'], marker='o', linestyle='', ms=8, label=name)\n",
    "\n",
    "    ax.legend(numpoints=1, loc=loc)\n",
    "    \n",
    "draw_groups(df2.groupby('반'), loc='upper left')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "위 scatter plot에 의하면 `PC1 < 0, PC2 <0` 에 있는 7명의 학생이 어느 정도 비슷한 패턴을 갖는 것으로 보입니다. 이후, 교육 방침을 정하거나, 장래 희망 상담등을 할 때, 이 결과를 이용할 수 있을 것으로 보입니다.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "여기까지, 성적 데이터 분석을 통한 데이터 분석 사례 소개를 마칩니다. 이 예제는 성적이지만, 실제 실무적으로 유사한 데이터가 많습니다. 이들을 분석하는데 도움이 되시길 바랍니다. \n",
    "\n",
    "--김형용, Insilicogen. Inc., 2016-01-22"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}