4. ADP 20회 통계분석 기초 통계 분석.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 통계 분석 모음 교차, 분산, 상관, 연관, t검정 등\n",
    "\n",
    "사실 ADP를 진행하면서 실기를 진행하셨던 분들의 후기를 보면 \n",
    "\n",
    "통계 분석이 단순히 통계 분석만 하는 경우는 거의 없었다.\n",
    "\n",
    "하더라도 해당 분석을 진행하고 이를 활용해서 추가적으로 분류 분석을 진행하는 식이었다.\n",
    "\n",
    "그것도 아니라면 아예 시계열 분석으로만 진행을 하거나 였다.\n",
    "\n",
    "사실 데이터 마이닝과 떼어넣고 이야기 하기 애매하기에\n",
    "\n",
    "통계분석 part를 시계열 분석, 각종 검증, 데이터 활용 및 샘플링으로 나누어서 포스팅 하는 것을 생각하였다.\n",
    "\n",
    "그 중에서 두번째인 각종 검증을 간단히 모아보았다. 이론적 설명 보다는 python으로 구현하는 코드를 위주로 해놓았다"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-03-13T11:47:59.268504Z",
     "start_time": "2021-03-13T11:47:58.563834Z"
    }
   },
   "outputs": [],
   "source": [
    "import os\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "pd.set_option('display.max_row', 500)\n",
    "pd.set_option('display.max_columns', 30)\n",
    "from pandas import DataFrame\n",
    "\n",
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")\n",
    "\n",
    "from scipy import stats"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 교차분석"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "하나의 변수만 포함된 일원 카이제곱검정(one-way chi-squared test) (적합성 검정)\n",
    "\n",
    "xo는 본래 값이고, xe는 기대값이다.\n",
    "\n",
    "하나의 변수만 사용을 하기 때문에, 기대값을 직접 입력을 해줘야 하며\n",
    "\n",
    "(해당 변수만 그대로 바로 기대값으로 사용시, 기대값이 다 똑같다.)\n",
    "\n",
    "귀무 가설은 실제 값과 기대값은 다르다 입니다.\n",
    "\n",
    "(시험에 해당 일원 카이 제곱은 나올 가능성이 적습니다. 하지만 two-way와 비교를 하기 위해서 넣었습니다.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-03-03T13:30:15.653125Z",
     "start_time": "2021-03-03T13:30:15.646129Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     Item A  Item B  Item C\n",
      "Obs     324      78     261\n",
      "Exp     371      80     212\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Power_divergenceResult(statistic=17.329649595687332, pvalue=0.00017254977751013492)"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.stats import chisquare #교차분석\n",
    "xo, xe = [324, 78, 261], [371, 80, 212]\n",
    "xc = DataFrame([xo, xe], columns=['Item A', 'Item B', 'Item C'], \n",
    "               index=['Obs', 'Exp'])\n",
    "print(xc)\n",
    "\n",
    "result = chisquare(xo, f_exp=xe)\n",
    "result"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "pvalue가 0.05 이하로, 실제 값과 기대값의 차이가 있다는 것을 확인할 수 있었습니다.\n",
    "\n",
    "다음으로는 교차분석이 나올 경우, 수행할 가능성이 높은 two-way 카이제곱 검정입니다. (독립성, 동일성 검정)\n",
    "\n",
    "두 변수 간의 차이가 있느냐 없느냐를 보는 것으로\n",
    "\n",
    "예시로는 성별과 아이템 종류를 사용해보겠습니다.\n",
    "\n",
    "귀무 가설은 성별과 아이템의 종류는 관련성이 없다 이며,\n",
    "\n",
    "현재 결과에서는 pvalue 값이 0.05 이하이므로, 성별과 아이템의 종류는 서로 관련성이 있다는 것을 볼 수 있습니다."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "출력 값 : chi-square 값, pvalue, degree of freedom, array(expected value)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-03-13T11:48:04.188696Z",
     "start_time": "2021-03-13T11:48:04.157807Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "        Item 1  Item 2  Item 3\n",
      "Female     269      83     215\n",
      "Male       155      57     181\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(7.094264414804222,\n",
       " 0.028807134195296135,\n",
       " 2,\n",
       " array([[250.425 ,  82.6875, 233.8875],\n",
       "        [173.575 ,  57.3125, 162.1125]]))"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xf, xm = [269, 83, 215], [155, 57, 181]\n",
    "x = DataFrame([xf, xm], columns=['Item 1', 'Item 2', 'Item 3'], \n",
    "              index=['Female', 'Male'])\n",
    "print(x)\n",
    "\n",
    "stats.chi2_contingency(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 분산분석\n",
    "\n",
    "그룹간 단순하게 F검정으로 분산 분석을 하는 방법과\n",
    "\n",
    "여러 변수들과 함께 검정을 해야되는 경우 anova 검증하는 방법이 있다.\n",
    "\n",
    "기본적인 귀무 가설은 해당 변수의 그룹간에 차이가 없다 이다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-03-13T15:47:04.198990Z",
     "start_time": "2021-03-13T15:47:03.086317Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "F_onewayResult(statistic=3.7113359882669763, pvalue=0.043589334959178244)"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from statsmodels.formula.api import ols\n",
    "from statsmodels.stats.anova import anova_lm\n",
    "\n",
    "import urllib #데이터 불러오기 용도\n",
    "url = 'https://raw.githubusercontent.com/thomas-haslwanter/statsintro_python/master/ipynb/Data/data_altman/altman_910.txt'\n",
    "data = np.genfromtxt(urllib.request.urlopen(url), delimiter=',')\n",
    "\n",
    "# Sort them into groups, according to column 1\n",
    "group1, group2, group3 = data[data[:,1]==1,0], data[data[:,1]==2,0], data[data[:,1]==3,0]\n",
    "\n",
    "stats.f_oneway(group1, group2, group3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "단순히 그룹간에 F검정을 하는 경우와 anova 검정을 사용해서 검증을 하는 방법이 있는데\n",
    "\n",
    "일원 분산 분석과 anova는 애초에 결과가 같을 수 밖에 없다"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-03-03T13:37:05.679349Z",
     "start_time": "2021-03-03T13:37:05.660349Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                df        sum_sq      mean_sq         F    PR(>F)\n",
      "C(treatment)   2.0  15515.766414  7757.883207  3.711336  0.043589\n",
      "Residual      19.0  39716.097222  2090.320906       NaN       NaN\n"
     ]
    }
   ],
   "source": [
    "df = pd.DataFrame(data, columns=['value', 'treatment'])    \n",
    "\n",
    "# the \"C\" indicates categorical data\n",
    "model = ols('value ~ C(treatment)', df).fit()\n",
    "print(anova_lm(model))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-03-13T16:13:25.375840Z",
     "start_time": "2021-03-13T16:13:25.371841Z"
    }
   },
   "source": [
    "다중 분산 분석을 하는 경우, 식에 교호작용까지 같이 넣어서 분석을 하는 경우\n",
    "\n",
    "그 결과까지 볼 수 있는데, 여기서는 pvalue 가 0.32정도로 fetus와 observer 변수간에는 교호작용이 없다는 귀무가설을 기각하지 못한다"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-03-03T13:40:19.610414Z",
     "start_time": "2021-03-03T13:40:19.416731Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                        df      sum_sq     mean_sq            F        PR(>F)\n",
      "C(fetus)               2.0  324.008889  162.004444  2113.101449  1.051039e-27\n",
      "C(observer)            3.0    1.198611    0.399537     5.211353  6.497055e-03\n",
      "C(fetus):C(observer)   6.0    0.562222    0.093704     1.222222  3.295509e-01\n",
      "Residual              24.0    1.840000    0.076667          NaN           NaN\n"
     ]
    }
   ],
   "source": [
    "inFile = 'altman_12_6.txt'\n",
    "url_base = 'https://raw.githubusercontent.com/thomas-haslwanter/statsintro_python/master/ipynb/Data/data_altman/'\n",
    "url = url_base + inFile\n",
    "data = np.genfromtxt(urllib.request.urlopen(url), delimiter=',')\n",
    "\n",
    "# Bring them in dataframe-format\n",
    "df = pd.DataFrame(data, columns=['head_size', 'fetus', 'observer'])\n",
    "\n",
    "formula = 'head_size ~ C(fetus) + C(observer) + C(fetus):C(observer)'\n",
    "lm = ols(formula, df).fit()\n",
    "print(anova_lm(lm))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 상관분석"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-03-13T11:56:32.265696Z",
     "start_time": "2021-03-13T11:56:32.253696Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                hour  attendance    weight        iq   library\n",
      "hour        1.000000    0.492917 -0.362082  0.791026  0.673212\n",
      "attendance  0.492917    1.000000 -0.029190  0.588915  0.341568\n",
      "weight     -0.362082   -0.029190  1.000000 -0.295475  0.128588\n",
      "iq          0.791026    0.588915 -0.295475  1.000000  0.436244\n",
      "library     0.673212    0.341568  0.128588  0.436244  1.000000\n"
     ]
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "##########데이터 로드\n",
    "df = pd.DataFrame([\n",
    "        ['A01', 2, 1, 60, 139, 'country', 0, 'fail'],\n",
    "        ['A02', 3, 2, 80, 148, 'country', 0, 'fail'],\n",
    "        ['A03', 3, 4, 50, 149, 'country', 0, 'fail'],\n",
    "        ['A04', 5, 5, 40, 151, 'country', 0, 'pass'],\n",
    "        ['A05', 7, 5, 35, 154, 'city', 0, 'pass'],\n",
    "        ['A06', 2, 5, 45, 149, 'country', 0, 'fail'],\n",
    "        ['A07',8, 9, 40, 155, 'city', 1, 'pass'],\n",
    "        ['A08', 9, 10, 70, 155, 'city', 3, 'pass'],\n",
    "        ['A09', 6, 12, 55, 154, 'city', 0, 'pass'],\n",
    "        ['A10', 9, 2, 40, 156, 'city', 1, 'pass'],\n",
    "        ['A11', 6, 10, 60, 153, 'city', 0, 'pass'],\n",
    "        ['A12', 2, 4, 75, 151, 'country', 0, 'fail']\n",
    "    ], columns=['ID', 'hour', 'attendance', 'weight', 'iq', 'region', 'library', 'pass'])\n",
    "\n",
    "##########데이터 분석\n",
    "\n",
    "corr = df.corr(method='pearson')\n",
    "print(corr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "상관분석은 크게 어려운 것이 없이, 단순하게 corr을 이용하면 되고,\n",
    "\n",
    "시각화의 경우도 heatmap을 그리면 완성입니다.\n",
    "\n",
    "하지만 시각화의 경우, 단순하게 heatmap만 그리고 끝내는 것보다는\n",
    "\n",
    "자기 자신과의 상관관계가 1인 것은 제거를 해주고 \n",
    "\n",
    "좀 더 명확하게 관계가 드러날 수 있게 하는 것이 개인적으로는 좋다고 생각됩니다.\n",
    "\n",
    "해당 분석이 시험에 나온다면, 전체적인 변수들간의 관계, 그리고 시각화 이외에는 나올 것이 없을 것으로 보입니다.\n",
    "\n",
    "추가적으로 분석을 더 하자면 이와 관련된 다중공선성이 나올 수 있지만\n",
    "\n",
    "그것은 데이터 마이닝쪽 회귀 분석을 하면서 보도록 하겠습니다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-03-13T11:57:15.943807Z",
     "start_time": "2021-03-13T11:57:15.621791Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x648 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.heatmap(corr, cmap='viridis')\n",
    "plt.show();\n",
    "\n",
    "sns.set(style=\"white\")\n",
    "mask=np.zeros_like(corr,dtype=np.bool)\n",
    "mask[np.triu_indices_from(mask)]=True\n",
    "\n",
    "f,ax=plt.subplots(figsize=(12,9))\n",
    "cmap=sns.diverging_palette(200,10,as_cmap=True)\n",
    "sns.heatmap(corr,mask=mask,cmap=cmap,center=0,square=True,\n",
    "            linewidths=0.5,cbar_kws={\"shrink\":1},annot=True);\n",
    "#annot는 히트맵 안에 숫자 생성해주는 것\n",
    "#글자 잘림은 subplots 사이즈 등 조절하면 쉽게 조절 가능"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 연관 분석"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "분석용 데이터는 해당 사이트에서 구하였습니다.\n",
    "\n",
    "https://tjansry354.tistory.com/10\n",
    "\n",
    "해당 데이터를 가공하였던 설명입니다.\n",
    "\n",
    "----------------------------------------------\n",
    "\n",
    "연관분석 함수를 쓰려면 DataFrame을 list로 만들어야합니다.\n",
    "\n",
    "그럼 다른 데이터는 지우고, item_name을 order_id에 따라 그룹짓도록 하겠습니다.\n",
    "\n",
    "order_id가 1834까지 있기 때문에, 리스트의 크기를 1835로 해서 2차원 리스트를 만듭니다.\n",
    "\n",
    "order_id가 1부터 시작이다 보니, 0은 null값으로 들어갔군요. pop()으로 제거하고 계속하겠습니다.\n",
    "\n",
    "그리고 한테이블에 같은 메뉴를 다수로 시킨 경우도 있으니, 중복값을 제거하는 set()도 사용합니다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-03-13T16:16:31.919620Z",
     "start_time": "2021-03-13T16:16:31.452952Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Izze',\n",
       " 'Chips and Tomatillo-Green Chili Salsa',\n",
       " 'Nantucket Nectar',\n",
       " 'Chips and Fresh Tomato Salsa']"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from mlxtend.preprocessing import TransactionEncoder\n",
    "from mlxtend.frequent_patterns import apriori, association_rules\n",
    "\n",
    "df1 = pd.read_csv(\"chipotle.tsv\",error_bad_lines=False, sep='\\t')\n",
    "\n",
    "df_tmp=df1[['order_id','item_name']]\n",
    "df_tmp_arr=[[]for i in range(1835)]\n",
    "num=0\n",
    "for i in df_tmp['item_name'] :\n",
    "    df_tmp_arr[df_tmp['order_id'][num]].append(i)\n",
    "    num+=1\n",
    "    \n",
    "df_tmp_arr.pop(0)\n",
    "num=0\n",
    "for i in df_tmp_arr :\n",
    "    df_tmp_arr[num] = list(set(df_tmp_arr[num]))\n",
    "    num+=1\n",
    "df_tmp_arr[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-03-13T16:16:36.139957Z",
     "start_time": "2021-03-13T16:16:36.124962Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>support</th>\n",
       "      <th>itemsets</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.083969</td>\n",
       "      <td>(Bottled Water)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.051254</td>\n",
       "      <td>(Canned Soda)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.150491</td>\n",
       "      <td>(Canned Soft Drink)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.335333</td>\n",
       "      <td>(Chicken Bowl)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.266630</td>\n",
       "      <td>(Chicken Burrito)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.053435</td>\n",
       "      <td>(Chicken Salad Bowl)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.058342</td>\n",
       "      <td>(Chicken Soft Tacos)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.113413</td>\n",
       "      <td>(Chips)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.059978</td>\n",
       "      <td>(Chips and Fresh Tomato Salsa)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.258451</td>\n",
       "      <td>(Chips and Guacamole)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0.055071</td>\n",
       "      <td>(Side of Chips)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>0.102508</td>\n",
       "      <td>(Steak Bowl)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>0.186478</td>\n",
       "      <td>(Steak Burrito)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>0.060523</td>\n",
       "      <td>(Canned Soft Drink, Chicken Bowl)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>0.066521</td>\n",
       "      <td>(Chips, Chicken Bowl)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>0.081243</td>\n",
       "      <td>(Chips and Guacamole, Chicken Bowl)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>0.062159</td>\n",
       "      <td>(Chicken Burrito, Chips and Guacamole)</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     support                                itemsets\n",
       "0   0.083969                         (Bottled Water)\n",
       "1   0.051254                           (Canned Soda)\n",
       "2   0.150491                     (Canned Soft Drink)\n",
       "3   0.335333                          (Chicken Bowl)\n",
       "4   0.266630                       (Chicken Burrito)\n",
       "5   0.053435                    (Chicken Salad Bowl)\n",
       "6   0.058342                    (Chicken Soft Tacos)\n",
       "7   0.113413                                 (Chips)\n",
       "8   0.059978          (Chips and Fresh Tomato Salsa)\n",
       "9   0.258451                   (Chips and Guacamole)\n",
       "10  0.055071                         (Side of Chips)\n",
       "11  0.102508                            (Steak Bowl)\n",
       "12  0.186478                         (Steak Burrito)\n",
       "13  0.060523       (Canned Soft Drink, Chicken Bowl)\n",
       "14  0.066521                   (Chips, Chicken Bowl)\n",
       "15  0.081243     (Chips and Guacamole, Chicken Bowl)\n",
       "16  0.062159  (Chicken Burrito, Chips and Guacamole)"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "te = TransactionEncoder()\n",
    "#주어진 코드에서 fit 함수를 통해 dataset은 고유한 라벨을 갖게 되고 , \n",
    "#transform함수를 통해서 파이썬 리스트를 one-hot 인코딩 된 numPy 배열로 변환합니다.\n",
    "te_ary = te.fit(df_tmp_arr).transform(df_tmp_arr) \n",
    "df = pd.DataFrame(te_ary, columns=te.columns_)\n",
    "\n",
    "frequent_itemsets = apriori(df, min_support=0.05, use_colnames=True)\n",
    "frequent_itemsets"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "apriori에 가공된 데이터를 넣고 최소한의 support를 지정해주면 위와 같은 결과가 나온다\n",
    "\n",
    "여기서 쉼표로 구분이 없는 것들은 연관성의 메인은 아니고\n",
    "\n",
    "조건절과 결과절을 연결 할 수 있는 것은 쉼표가 있는 것들이다."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "antecedents : 조건절\n",
    "\n",
    "consequents : 결과절\n",
    "\n",
    "→만일 (조건절)이라면 (결과절)\n",
    "\n",
    "lift가 1이면 두 항목은 독립\n",
    "\n",
    "1보다 크면 양의 상관관계, 1보다 작으면 음의 상관관계(우연보다 낮은 확률)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-03-03T14:53:22.222115Z",
     "start_time": "2021-03-03T14:53:22.196115Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>antecedents</th>\n",
       "      <th>consequents</th>\n",
       "      <th>antecedent support</th>\n",
       "      <th>consequent support</th>\n",
       "      <th>support</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>(Canned Soft Drink)</td>\n",
       "      <td>(Chicken Bowl)</td>\n",
       "      <td>0.150491</td>\n",
       "      <td>0.335333</td>\n",
       "      <td>0.060523</td>\n",
       "      <td>0.402174</td>\n",
       "      <td>1.199328</td>\n",
       "      <td>0.010059</td>\n",
       "      <td>1.111807</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>(Chicken Bowl)</td>\n",
       "      <td>(Canned Soft Drink)</td>\n",
       "      <td>0.335333</td>\n",
       "      <td>0.150491</td>\n",
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       "      <td>0.180488</td>\n",
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       "      <td>0.010059</td>\n",
       "      <td>1.036604</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>(Chips)</td>\n",
       "      <td>(Chicken Bowl)</td>\n",
       "      <td>0.113413</td>\n",
       "      <td>0.335333</td>\n",
       "      <td>0.066521</td>\n",
       "      <td>0.586538</td>\n",
       "      <td>1.749124</td>\n",
       "      <td>0.028490</td>\n",
       "      <td>1.607568</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>(Chicken Bowl)</td>\n",
       "      <td>(Chips)</td>\n",
       "      <td>0.335333</td>\n",
       "      <td>0.113413</td>\n",
       "      <td>0.066521</td>\n",
       "      <td>0.198374</td>\n",
       "      <td>1.749124</td>\n",
       "      <td>0.028490</td>\n",
       "      <td>1.105985</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           antecedents          consequents  antecedent support  \\\n",
       "0  (Canned Soft Drink)       (Chicken Bowl)            0.150491   \n",
       "1       (Chicken Bowl)  (Canned Soft Drink)            0.335333   \n",
       "2              (Chips)       (Chicken Bowl)            0.113413   \n",
       "3       (Chicken Bowl)              (Chips)            0.335333   \n",
       "\n",
       "   consequent support   support  confidence      lift  leverage  conviction  \n",
       "0            0.335333  0.060523    0.402174  1.199328  0.010059    1.111807  \n",
       "1            0.150491  0.060523    0.180488  1.199328  0.010059    1.036604  \n",
       "2            0.335333  0.066521    0.586538  1.749124  0.028490    1.607568  \n",
       "3            0.113413  0.066521    0.198374  1.749124  0.028490    1.105985  "
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "association_rules(frequent_itemsets, metric=\"lift\", min_threshold=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-03-03T15:07:54.829611Z",
     "start_time": "2021-03-03T15:07:54.810577Z"
    }
   },
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>antecedents</th>\n",
       "      <th>consequents</th>\n",
       "      <th>antecedent support</th>\n",
       "      <th>consequent support</th>\n",
       "      <th>support</th>\n",
       "      <th>confidence</th>\n",
       "      <th>lift</th>\n",
       "      <th>leverage</th>\n",
       "      <th>conviction</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>(Canned Soft Drink)</td>\n",
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       "      <td>0.150491</td>\n",
       "      <td>0.335333</td>\n",
       "      <td>0.060523</td>\n",
       "      <td>0.402174</td>\n",
       "      <td>1.199328</td>\n",
       "      <td>0.010059</td>\n",
       "      <td>1.111807</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>(Chicken Bowl)</td>\n",
       "      <td>(Canned Soft Drink)</td>\n",
       "      <td>0.335333</td>\n",
       "      <td>0.150491</td>\n",
       "      <td>0.060523</td>\n",
       "      <td>0.180488</td>\n",
       "      <td>1.199328</td>\n",
       "      <td>0.010059</td>\n",
       "      <td>1.036604</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>(Chips)</td>\n",
       "      <td>(Chicken Bowl)</td>\n",
       "      <td>0.113413</td>\n",
       "      <td>0.335333</td>\n",
       "      <td>0.066521</td>\n",
       "      <td>0.586538</td>\n",
       "      <td>1.749124</td>\n",
       "      <td>0.028490</td>\n",
       "      <td>1.607568</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>(Chicken Bowl)</td>\n",
       "      <td>(Chips)</td>\n",
       "      <td>0.335333</td>\n",
       "      <td>0.113413</td>\n",
       "      <td>0.066521</td>\n",
       "      <td>0.198374</td>\n",
       "      <td>1.749124</td>\n",
       "      <td>0.028490</td>\n",
       "      <td>1.105985</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>(Chips and Guacamole)</td>\n",
       "      <td>(Chicken Bowl)</td>\n",
       "      <td>0.258451</td>\n",
       "      <td>0.335333</td>\n",
       "      <td>0.081243</td>\n",
       "      <td>0.314346</td>\n",
       "      <td>0.937416</td>\n",
       "      <td>-0.005424</td>\n",
       "      <td>0.969392</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>(Chicken Bowl)</td>\n",
       "      <td>(Chips and Guacamole)</td>\n",
       "      <td>0.335333</td>\n",
       "      <td>0.258451</td>\n",
       "      <td>0.081243</td>\n",
       "      <td>0.242276</td>\n",
       "      <td>0.937416</td>\n",
       "      <td>-0.005424</td>\n",
       "      <td>0.978653</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>(Chips and Guacamole)</td>\n",
       "      <td>(Chicken Burrito)</td>\n",
       "      <td>0.258451</td>\n",
       "      <td>0.266630</td>\n",
       "      <td>0.062159</td>\n",
       "      <td>0.240506</td>\n",
       "      <td>0.902022</td>\n",
       "      <td>-0.006752</td>\n",
       "      <td>0.965603</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>(Chicken Burrito)</td>\n",
       "      <td>(Chips and Guacamole)</td>\n",
       "      <td>0.266630</td>\n",
       "      <td>0.258451</td>\n",
       "      <td>0.062159</td>\n",
       "      <td>0.233129</td>\n",
       "      <td>0.902022</td>\n",
       "      <td>-0.006752</td>\n",
       "      <td>0.966979</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             antecedents            consequents  antecedent support  \\\n",
       "0    (Canned Soft Drink)         (Chicken Bowl)            0.150491   \n",
       "1         (Chicken Bowl)    (Canned Soft Drink)            0.335333   \n",
       "2                (Chips)         (Chicken Bowl)            0.113413   \n",
       "3         (Chicken Bowl)                (Chips)            0.335333   \n",
       "4  (Chips and Guacamole)         (Chicken Bowl)            0.258451   \n",
       "5         (Chicken Bowl)  (Chips and Guacamole)            0.335333   \n",
       "6  (Chips and Guacamole)      (Chicken Burrito)            0.258451   \n",
       "7      (Chicken Burrito)  (Chips and Guacamole)            0.266630   \n",
       "\n",
       "   consequent support   support  confidence      lift  leverage  conviction  \n",
       "0            0.335333  0.060523    0.402174  1.199328  0.010059    1.111807  \n",
       "1            0.150491  0.060523    0.180488  1.199328  0.010059    1.036604  \n",
       "2            0.335333  0.066521    0.586538  1.749124  0.028490    1.607568  \n",
       "3            0.113413  0.066521    0.198374  1.749124  0.028490    1.105985  \n",
       "4            0.335333  0.081243    0.314346  0.937416 -0.005424    0.969392  \n",
       "5            0.258451  0.081243    0.242276  0.937416 -0.005424    0.978653  \n",
       "6            0.266630  0.062159    0.240506  0.902022 -0.006752    0.965603  \n",
       "7            0.258451  0.062159    0.233129  0.902022 -0.006752    0.966979  "
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "association_rules(frequent_itemsets, metric=\"confidence\", min_threshold=0.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### t검정\n",
    "\n",
    "t검정은 3종류로 하나의 표본이 특정 값과 차이가 있는지 없는지를 검증하는 단일표본 t 검정\n",
    "\n",
    "두 집단간의 차이가 있는지 검증하는 독립표본 t 검정 (A그룹 약 복용 / B그룹 약 미 복용)\n",
    "\n",
    "한 집단의 전과 후를 비교하는 대응표본 t 검정으로 나뉩니다. (A그룹 약 복용 전 / B그룹 약 복용 후)\n",
    "\n",
    "기본적으로 귀무가설은 표본과 해당 값은 차이가 없다, 두 집단은 차이가 없다, 해당 그룹의 전과 후는 차이가 없다 입니다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-03-13T12:07:29.213702Z",
     "start_time": "2021-03-13T12:07:29.196179Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ttest_1sampResult(statistic=-2.3501608059776435, pvalue=0.029721802204110182)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dat_M = [117, 108, 105, 89, 101, 93, 96, 108, 108, 94, 93, 112, 92, 91, 100, 96, 120, 86, 96, 95]\n",
    "dat_F = [121, 101, 102, 114, 103, 105, 101, 131, 96, 109, 109, 113, 115, 94, 108, 96, 110, 112, 120, 100]\n",
    "\n",
    "stats.ttest_1samp(dat_M, 105) #일표본 t 검정"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "독립표본의 경우, 두 집단을 비교하는 stats.ttest_ind 함수 안에 equal_var 이라는 옵션이 있습니다.\n",
    "\n",
    "바로, 두 집단이 등분산인지 이분산인지 표시를 해주는 옵션으로\n",
    "\n",
    "이는 일원 분산 분석을 수행해서 결과를 확인 후 결정하면 됩니다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-03-13T12:08:17.063919Z",
     "start_time": "2021-03-13T12:08:17.051401Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "F_onewayResult(statistic=7.131964809384164, pvalue=0.011082895240510133)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Ttest_indResult(statistic=-2.670573872669349, pvalue=0.01108318824471652)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(stats.f_oneway(dat_M, dat_F)) # -> 검증결과 pvalue 0.01로 분산 다름 확인 완료\n",
    "\n",
    "#독립표본 t검정\n",
    "stats.ttest_ind(dat_M, dat_F, equal_var=False) #마지막 옵션은 분산 동일 여부"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "대응표본"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-03-13T12:08:24.547522Z",
     "start_time": "2021-03-13T12:08:24.529498Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ttest_relResult(statistic=-2.9868874599588247, pvalue=0.007578486289181322)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.ttest_rel(dat_M, dat_F)"
   ]
  }
 ],
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