ch10 scipy.stats f_oneway, statsmodels ols, anova_lm, pairwise_tukeyhsd.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "4f37daa8",
   "metadata": {},
   "source": [
    "# 10차시 모평균 비교에 관한 가설검정: One way ANOVA\n",
    "\n",
    "## 01 일원 분산 분석(One Way ANOVA) 개요\n",
    "\n",
    "### 일원 분산 분석의 특징\n",
    "\n",
    "- 수치형 종속변수와 명목형 독립변수가 각각 1개 일 때 실시하는 분석\n",
    "- 종속변수로 나뉘어지는 그룹이 2개 이상일 때 사용\n",
    "- 귀무가설을 기각하는 경우 사후 검정(Post-hoc)을 실시\n",
    "\n",
    "### 가설\n",
    "\n",
    "- 귀무가설(H0): 집단 간 평균이 같음\n",
    "- 대립가설(H1): 평균이 같지 않은 집단이 한 쌍 이상 존재\n",
    "\n",
    "### 일원 분산 분석의 사후 검정\n",
    "\n",
    "- 사후 검정 방법으로는 Tukey's HSD, Duncan's MRT, Scheffe's test가 있다.\n",
    "- 실습 해볼 사후 검정은 Tukey's HSD이다.\n",
    "- 모든 집단 간 독립 2 표본 t-검정을 하는 것과 유사하며 어던 집단 간 평균이 유의하게 차이 나는지 알 수 있다."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f285f591",
   "metadata": {},
   "source": [
    "## 주요 함수 및 메서드 소개\n",
    "\n",
    "### 02 일원 분산 분석 - f_oneway()\n",
    "\n",
    "- 일원 분산 분석을 수행하는 scipy의 함수\n",
    "- 입력은 각각의 집단을 pandas의 series로 하는 것을 권장\n",
    "- 출력은 검정통계량과 p-value 두 개 이며 하나의 객체에 할당할 경우 튜플로 저장됨"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "8ce46597",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "from scipy.stats import f_oneway"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "0f2c2eb7",
   "metadata": {},
   "outputs": [
    {
     "data": {
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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>carat</th>\n",
       "      <th>cut</th>\n",
       "      <th>color</th>\n",
       "      <th>clarity</th>\n",
       "      <th>depth</th>\n",
       "      <th>table</th>\n",
       "      <th>price</th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "      <th>z</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.23</td>\n",
       "      <td>Ideal</td>\n",
       "      <td>E</td>\n",
       "      <td>SI2</td>\n",
       "      <td>61.5</td>\n",
       "      <td>55.0</td>\n",
       "      <td>326</td>\n",
       "      <td>3.95</td>\n",
       "      <td>3.98</td>\n",
       "      <td>2.43</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.21</td>\n",
       "      <td>Premium</td>\n",
       "      <td>E</td>\n",
       "      <td>SI1</td>\n",
       "      <td>59.8</td>\n",
       "      <td>61.0</td>\n",
       "      <td>326</td>\n",
       "      <td>3.89</td>\n",
       "      <td>3.84</td>\n",
       "      <td>2.31</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.23</td>\n",
       "      <td>Good</td>\n",
       "      <td>E</td>\n",
       "      <td>VS1</td>\n",
       "      <td>56.9</td>\n",
       "      <td>65.0</td>\n",
       "      <td>327</td>\n",
       "      <td>4.05</td>\n",
       "      <td>4.07</td>\n",
       "      <td>2.31</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.29</td>\n",
       "      <td>Premium</td>\n",
       "      <td>I</td>\n",
       "      <td>VS2</td>\n",
       "      <td>62.4</td>\n",
       "      <td>58.0</td>\n",
       "      <td>334</td>\n",
       "      <td>4.20</td>\n",
       "      <td>4.23</td>\n",
       "      <td>2.63</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.31</td>\n",
       "      <td>Good</td>\n",
       "      <td>J</td>\n",
       "      <td>SI2</td>\n",
       "      <td>63.3</td>\n",
       "      <td>58.0</td>\n",
       "      <td>335</td>\n",
       "      <td>4.34</td>\n",
       "      <td>4.35</td>\n",
       "      <td>2.75</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   carat      cut color clarity  depth  table  price     x     y     z\n",
       "0   0.23    Ideal     E     SI2   61.5   55.0    326  3.95  3.98  2.43\n",
       "1   0.21  Premium     E     SI1   59.8   61.0    326  3.89  3.84  2.31\n",
       "2   0.23     Good     E     VS1   56.9   65.0    327  4.05  4.07  2.31\n",
       "3   0.29  Premium     I     VS2   62.4   58.0    334  4.20  4.23  2.63\n",
       "4   0.31     Good     J     SI2   63.3   58.0    335  4.34  4.35  2.75"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv(\"강의자료/실습파일/diamonds.csv\")\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "e7b96732",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['E', 'I', 'J', 'H', 'F', 'G', 'D'], dtype=object)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[\"color\"].unique()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "3d341f2b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "621.846\n",
      "0.0\n"
     ]
    }
   ],
   "source": [
    "stat, p = f_oneway(df.loc[df[\"color\"] == \"E\", \"price\"],\n",
    "                  df.loc[df[\"color\"] == \"I\", \"price\"],\n",
    "                  df.loc[df[\"color\"] == \"J\", \"price\"])\n",
    "print(stat.round(3))\n",
    "print(p.round(3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "b0782021",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>color</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>D</td>\n",
       "      <td>3169.954096</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>E</td>\n",
       "      <td>3076.752475</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>F</td>\n",
       "      <td>3724.886397</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>G</td>\n",
       "      <td>3999.135671</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>H</td>\n",
       "      <td>4486.669196</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>I</td>\n",
       "      <td>5091.874954</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>J</td>\n",
       "      <td>5323.818020</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  color        price\n",
       "0     D  3169.954096\n",
       "1     E  3076.752475\n",
       "2     F  3724.886397\n",
       "3     G  3999.135671\n",
       "4     H  4486.669196\n",
       "5     I  5091.874954\n",
       "6     J  5323.818020"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.groupby(\"color\")[\"price\"].mean().reset_index()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e6310a14",
   "metadata": {},
   "source": [
    "### 일원 분산 분석 - ols(), anova_lm()\n",
    "\n",
    "- statsmodels의 일원 분산 분석을 수행하는 함수\n",
    "- ols() 함수는 모델을 생성하고 적합\n",
    "- anova_lm() 함수는 적합된 모델 정보를 기반으로 일원 분산 분석표를 보여줌\n",
    "- ols() 함수에 수식 입력 시 독립변수에 C() 함수 사용 권장"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "96d0a26c",
   "metadata": {},
   "outputs": [],
   "source": [
    "from statsmodels.formula.api import ols\n",
    "from statsmodels.stats.anova import anova_lm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "da08181c",
   "metadata": {},
   "outputs": [
    {
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>datetime</th>\n",
       "      <th>season</th>\n",
       "      <th>holiday</th>\n",
       "      <th>workingday</th>\n",
       "      <th>weather</th>\n",
       "      <th>temp</th>\n",
       "      <th>atemp</th>\n",
       "      <th>humidity</th>\n",
       "      <th>windspeed</th>\n",
       "      <th>casual</th>\n",
       "      <th>registered</th>\n",
       "      <th>count</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2011-01-01 00:00:00</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>9.84</td>\n",
       "      <td>14.395</td>\n",
       "      <td>81</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3</td>\n",
       "      <td>13</td>\n",
       "      <td>16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2011-01-01 01:00:00</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>9.02</td>\n",
       "      <td>13.635</td>\n",
       "      <td>80</td>\n",
       "      <td>0.0</td>\n",
       "      <td>8</td>\n",
       "      <td>32</td>\n",
       "      <td>40</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2011-01-01 02:00:00</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>9.02</td>\n",
       "      <td>13.635</td>\n",
       "      <td>80</td>\n",
       "      <td>0.0</td>\n",
       "      <td>5</td>\n",
       "      <td>27</td>\n",
       "      <td>32</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2011-01-01 03:00:00</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>9.84</td>\n",
       "      <td>14.395</td>\n",
       "      <td>75</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3</td>\n",
       "      <td>10</td>\n",
       "      <td>13</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2011-01-01 04:00:00</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>9.84</td>\n",
       "      <td>14.395</td>\n",
       "      <td>75</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              datetime  season  holiday  workingday  weather  temp   atemp  \\\n",
       "0  2011-01-01 00:00:00       1        0           0        1  9.84  14.395   \n",
       "1  2011-01-01 01:00:00       1        0           0        1  9.02  13.635   \n",
       "2  2011-01-01 02:00:00       1        0           0        1  9.02  13.635   \n",
       "3  2011-01-01 03:00:00       1        0           0        1  9.84  14.395   \n",
       "4  2011-01-01 04:00:00       1        0           0        1  9.84  14.395   \n",
       "\n",
       "   humidity  windspeed  casual  registered  count  \n",
       "0        81        0.0       3          13     16  \n",
       "1        80        0.0       8          32     40  \n",
       "2        80        0.0       5          27     32  \n",
       "3        75        0.0       3          10     13  \n",
       "4        75        0.0       0           1      1  "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bike = pd.read_csv(\"강의자료/실습파일/bike.csv\")\n",
    "bike.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "05209b3e",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>df</th>\n",
       "      <th>sum_sq</th>\n",
       "      <th>mean_sq</th>\n",
       "      <th>F</th>\n",
       "      <th>PR(&gt;F)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>season</th>\n",
       "      <td>1.0</td>\n",
       "      <td>44221.657301</td>\n",
       "      <td>44221.657301</td>\n",
       "      <td>780.591754</td>\n",
       "      <td>5.879560e-166</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Residual</th>\n",
       "      <td>10884.0</td>\n",
       "      <td>616594.417651</td>\n",
       "      <td>56.651453</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "               df         sum_sq       mean_sq           F         PR(>F)\n",
       "season        1.0   44221.657301  44221.657301  780.591754  5.879560e-166\n",
       "Residual  10884.0  616594.417651     56.651453         NaN            NaN"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = ols(formula = 'temp ~ season', data = bike).fit()  # fit: 학습\n",
    "anova_lm(model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "e25ebd97",
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>df</th>\n",
       "      <th>sum_sq</th>\n",
       "      <th>mean_sq</th>\n",
       "      <th>F</th>\n",
       "      <th>PR(&gt;F)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>C(season)</th>\n",
       "      <td>3.0</td>\n",
       "      <td>412885.270005</td>\n",
       "      <td>137628.423335</td>\n",
       "      <td>6040.687453</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Residual</th>\n",
       "      <td>10882.0</td>\n",
       "      <td>247930.804947</td>\n",
       "      <td>22.783570</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                df         sum_sq        mean_sq            F  PR(>F)\n",
       "C(season)      3.0  412885.270005  137628.423335  6040.687453     0.0\n",
       "Residual   10882.0  247930.804947      22.783570          NaN     NaN"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = ols(formula = 'temp ~ C(season)', data = bike).fit() # C(): Categorical, 시즌 변수는 명목형이다, 숫자형의 경우 꼭 C() 사용할 것\n",
    "anova_lm(model) # F: 검정통계량 / PR: 검정통계량보다 큰 값이 나올 확률"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "517a9d09",
   "metadata": {},
   "source": [
    "### 사후검정 - pairwise_tukeyhsd()\n",
    "\n",
    "- statsmodels의 Tukey 사후검정을 실시하는 함수\n",
    "- 함수 내에 종속변수와 독립변수를 차례대로 선언\n",
    "- 결과를 출력하기 위해서 print() 함수를 반드시 사용\n",
    "- reject 변수의 True는 귀무가설(두 집단의 평균 차이가 유의미하게 나지 않음)을 기각하는 것"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "0c9d3539",
   "metadata": {},
   "outputs": [],
   "source": [
    "from statsmodels.stats.multicomp import pairwise_tukeyhsd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "df6ca43d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " Multiple Comparison of Means - Tukey HSD, FWER=0.05 \n",
      "=====================================================\n",
      "group1 group2 meandiff p-adj  lower    upper   reject\n",
      "-----------------------------------------------------\n",
      "     1      2   10.293   0.0   9.9598  10.6262   True\n",
      "     1      3  16.2586   0.0  15.9254  16.5918   True\n",
      "     1      4   4.1187   0.0   3.7856   4.4519   True\n",
      "     2      3   5.9656   0.0   5.6339   6.2974   True\n",
      "     2      4  -6.1742   0.0   -6.506  -5.8425   True\n",
      "     3      4 -12.1399   0.0 -12.4716 -11.8081   True\n",
      "-----------------------------------------------------\n"
     ]
    }
   ],
   "source": [
    "result = pairwise_tukeyhsd(bike[\"temp\"], bike[\"season\"])\n",
    "print(result)  # reject: FWER 0.05 기준이 적용됨"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bf771e1d",
   "metadata": {},
   "source": [
    "## Q1. 분산분석 시 사용하는 함수 또는 라이브러리와 관련 없는 것은?\n",
    "1. ANOVA (답)\n",
    "2. f_oneway\n",
    "3. ols\n",
    "4. statsmodels"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a1e7a75c",
   "metadata": {},
   "source": [
    "## Q2. 계절별 기온 평균을 분산분석 시 검정통계량은?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "79535028",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>datetime</th>\n",
       "      <th>season</th>\n",
       "      <th>holiday</th>\n",
       "      <th>workingday</th>\n",
       "      <th>weather</th>\n",
       "      <th>temp</th>\n",
       "      <th>atemp</th>\n",
       "      <th>humidity</th>\n",
       "      <th>windspeed</th>\n",
       "      <th>casual</th>\n",
       "      <th>registered</th>\n",
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       "  </thead>\n",
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       "      <td>2011-01-01 00:00:00</td>\n",
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       "      <td>2011-01-01 01:00:00</td>\n",
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       "      <td>0</td>\n",
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       "      <td>80</td>\n",
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       "      <td>8</td>\n",
       "      <td>32</td>\n",
       "      <td>40</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2011-01-01 02:00:00</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>9.02</td>\n",
       "      <td>13.635</td>\n",
       "      <td>80</td>\n",
       "      <td>0.0</td>\n",
       "      <td>5</td>\n",
       "      <td>27</td>\n",
       "      <td>32</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2011-01-01 03:00:00</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>9.84</td>\n",
       "      <td>14.395</td>\n",
       "      <td>75</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3</td>\n",
       "      <td>10</td>\n",
       "      <td>13</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2011-01-01 04:00:00</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>9.84</td>\n",
       "      <td>14.395</td>\n",
       "      <td>75</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              datetime  season  holiday  workingday  weather  temp   atemp  \\\n",
       "0  2011-01-01 00:00:00       1        0           0        1  9.84  14.395   \n",
       "1  2011-01-01 01:00:00       1        0           0        1  9.02  13.635   \n",
       "2  2011-01-01 02:00:00       1        0           0        1  9.02  13.635   \n",
       "3  2011-01-01 03:00:00       1        0           0        1  9.84  14.395   \n",
       "4  2011-01-01 04:00:00       1        0           0        1  9.84  14.395   \n",
       "\n",
       "   humidity  windspeed  casual  registered  count  \n",
       "0        81        0.0       3          13     16  \n",
       "1        80        0.0       8          32     40  \n",
       "2        80        0.0       5          27     32  \n",
       "3        75        0.0       3          10     13  \n",
       "4        75        0.0       0           1      1  "
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q2 = pd.read_csv(\"강의자료/실습파일/bike.csv\")\n",
    "Q2.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "99c8bcb6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 10886 entries, 0 to 10885\n",
      "Data columns (total 12 columns):\n",
      " #   Column      Non-Null Count  Dtype  \n",
      "---  ------      --------------  -----  \n",
      " 0   datetime    10886 non-null  object \n",
      " 1   season      10886 non-null  int64  \n",
      " 2   holiday     10886 non-null  int64  \n",
      " 3   workingday  10886 non-null  int64  \n",
      " 4   weather     10886 non-null  int64  \n",
      " 5   temp        10886 non-null  float64\n",
      " 6   atemp       10886 non-null  float64\n",
      " 7   humidity    10886 non-null  int64  \n",
      " 8   windspeed   10886 non-null  float64\n",
      " 9   casual      10886 non-null  int64  \n",
      " 10  registered  10886 non-null  int64  \n",
      " 11  count       10886 non-null  int64  \n",
      "dtypes: float64(3), int64(8), object(1)\n",
      "memory usage: 1020.7+ KB\n"
     ]
    }
   ],
   "source": [
    "Q2.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "3c9c4efa",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>df</th>\n",
       "      <th>sum_sq</th>\n",
       "      <th>mean_sq</th>\n",
       "      <th>F</th>\n",
       "      <th>PR(&gt;F)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>C(season)</th>\n",
       "      <td>3.0</td>\n",
       "      <td>412885.270005</td>\n",
       "      <td>137628.423335</td>\n",
       "      <td>6040.687453</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Residual</th>\n",
       "      <td>10882.0</td>\n",
       "      <td>247930.804947</td>\n",
       "      <td>22.783570</td>\n",
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      ],
      "text/plain": [
       "                df         sum_sq        mean_sq            F  PR(>F)\n",
       "C(season)      3.0  412885.270005  137628.423335  6040.687453     0.0\n",
       "Residual   10882.0  247930.804947      22.783570          NaN     NaN"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "formula = \"temp ~ C(season)\"  # C() 범주형 변수임을 명시\n",
    "lm = ols(formula, Q2).fit()\n",
    "anova_lm(lm)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c094cd45",
   "metadata": {},
   "source": [
    "## Q3. 요일별 registered의 평균을 사후검정 했을 때 평균이 유의미하게 차이 나지 않는 조합은 총 몇개 인가?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "58886551",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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       "      <td>32</td>\n",
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       "      <th>3</th>\n",
       "      <td>2011-01-01 03:00:00</td>\n",
       "      <td>1</td>\n",
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       "      <td>0</td>\n",
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       "      <td>13</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2011-01-01 04:00:00</td>\n",
       "      <td>1</td>\n",
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       "      <td>1</td>\n",
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       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              datetime  season  holiday  workingday  weather  temp   atemp  \\\n",
       "0  2011-01-01 00:00:00       1        0           0        1  9.84  14.395   \n",
       "1  2011-01-01 01:00:00       1        0           0        1  9.02  13.635   \n",
       "2  2011-01-01 02:00:00       1        0           0        1  9.02  13.635   \n",
       "3  2011-01-01 03:00:00       1        0           0        1  9.84  14.395   \n",
       "4  2011-01-01 04:00:00       1        0           0        1  9.84  14.395   \n",
       "\n",
       "   humidity  windspeed  casual  registered  count  \n",
       "0        81        0.0       3          13     16  \n",
       "1        80        0.0       8          32     40  \n",
       "2        80        0.0       5          27     32  \n",
       "3        75        0.0       3          10     13  \n",
       "4        75        0.0       0           1      1  "
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q3 = pd.read_csv(\"강의자료/실습파일/bike.csv\")\n",
    "Q3.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "677fc350",
   "metadata": {},
   "outputs": [
    {
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2011-01-01 02:00:00</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>9.02</td>\n",
       "      <td>13.635</td>\n",
       "      <td>80</td>\n",
       "      <td>0.0</td>\n",
       "      <td>5</td>\n",
       "      <td>27</td>\n",
       "      <td>32</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2011-01-01 03:00:00</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>9.84</td>\n",
       "      <td>14.395</td>\n",
       "      <td>75</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3</td>\n",
       "      <td>10</td>\n",
       "      <td>13</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2011-01-01 04:00:00</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>9.84</td>\n",
       "      <td>14.395</td>\n",
       "      <td>75</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             datetime  season  holiday  workingday  weather  temp   atemp  \\\n",
       "0 2011-01-01 00:00:00       1        0           0        1  9.84  14.395   \n",
       "1 2011-01-01 01:00:00       1        0           0        1  9.02  13.635   \n",
       "2 2011-01-01 02:00:00       1        0           0        1  9.02  13.635   \n",
       "3 2011-01-01 03:00:00       1        0           0        1  9.84  14.395   \n",
       "4 2011-01-01 04:00:00       1        0           0        1  9.84  14.395   \n",
       "\n",
       "   humidity  windspeed  casual  registered  count  weekday  \n",
       "0        81        0.0       3          13     16        5  \n",
       "1        80        0.0       8          32     40        5  \n",
       "2        80        0.0       5          27     32        5  \n",
       "3        75        0.0       3          10     13        5  \n",
       "4        75        0.0       0           1      1        5  "
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q3[\"datetime\"] = pd.to_datetime(Q3[\"datetime\"])\n",
    "Q3[\"weekday\"] = Q3[\"datetime\"].dt.weekday\n",
    "Q3.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "95696b46",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " Multiple Comparison of Means - Tukey HSD, FWER=0.05  \n",
      "======================================================\n",
      "group1 group2 meandiff p-adj   lower    upper   reject\n",
      "------------------------------------------------------\n",
      "     0      1   6.1979  0.913   -9.719  22.1148  False\n",
      "     0      2    5.343 0.9559 -10.5429  21.2289  False\n",
      "     0      3  12.7424 0.2132  -3.1384  28.6232  False\n",
      "     0      4   6.2956 0.9074  -9.6473  22.2386  False\n",
      "     0      5 -27.5063    0.0 -43.3093 -11.7034   True\n",
      "     0      6 -36.7583    0.0 -52.5736 -20.9429   True\n",
      "     1      2  -0.8549    1.0 -16.7718   15.062  False\n",
      "     1      3   6.5445 0.8895  -9.3673  22.4562  False\n",
      "     1      4   0.0977    1.0 -15.8761  16.0715  False\n",
      "     1      5 -33.7042    0.0 -49.5383 -17.8702   True\n",
      "     1      6 -42.9562    0.0 -58.8026 -27.1097   True\n",
      "     2      3   7.3994 0.8159  -8.4814  23.2802  False\n",
      "     2      4   0.9526    1.0 -14.9903  16.8956  False\n",
      "     2      5 -32.8493    0.0 -48.6523 -17.0464   True\n",
      "     2      6 -42.1013    0.0 -57.9166 -26.2859   True\n",
      "     3      4  -6.4467 0.8971 -22.3846   9.4911  False\n",
      "     3      5 -40.2487    0.0 -56.0465 -24.4509   True\n",
      "     3      6 -49.5006    0.0 -65.3109 -33.6904   True\n",
      "     4      5  -33.802    0.0 -49.6623 -17.9417   True\n",
      "     4      6 -43.0539    0.0 -58.9265 -27.1813   True\n",
      "     5      6  -9.2519 0.5929 -24.9839   6.4801  False\n",
      "------------------------------------------------------\n"
     ]
    }
   ],
   "source": [
    "result = pairwise_tukeyhsd(Q3[\"registered\"], Q3[\"weekday\"])\n",
    "print(result)"
   ]
  }
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