Case Study 1- Missing Values and Outliers.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "b71b6c1c",
   "metadata": {},
   "source": [
    "# Missing Values and Outliers"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "75e01129",
   "metadata": {},
   "source": [
    "### Missing Values"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "98214e3e",
   "metadata": {},
   "source": [
    "### Business Undestanding"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1ab875ee",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "0300dd00",
   "metadata": {},
   "source": [
    "### Initial Setup"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1ef31a59",
   "metadata": {},
   "source": [
    "Goal:\n",
    "\n",
    "Survey analysis: calculate Pearson correlaion w/ missing values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "b48bcf6e",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Required libraries\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "3ebaea5a",
   "metadata": {},
   "outputs": [
    {
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       "      <th></th>\n",
       "      <th>ID</th>\n",
       "      <th>V1</th>\n",
       "      <th>V2</th>\n",
       "      <th>V3</th>\n",
       "      <th>V4</th>\n",
       "      <th>V5</th>\n",
       "      <th>V6</th>\n",
       "      <th>V7</th>\n",
       "      <th>V8</th>\n",
       "      <th>V9</th>\n",
       "      <th>V10</th>\n",
       "      <th>V11</th>\n",
       "      <th>V12</th>\n",
       "      <th>V13</th>\n",
       "      <th>V14</th>\n",
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       "  </thead>\n",
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       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>201</td>\n",
       "      <td>3.3</td>\n",
       "      <td>0.9</td>\n",
       "      <td>8.6</td>\n",
       "      <td>4</td>\n",
       "      <td>2.1</td>\n",
       "      <td>1.8</td>\n",
       "      <td>6.3</td>\n",
       "      <td>41</td>\n",
       "      <td>4.5</td>\n",
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       "      <th>1</th>\n",
       "      <td>202</td>\n",
       "      <td>.</td>\n",
       "      <td>0.4</td>\n",
       "      <td>4</td>\n",
       "      <td>2.5</td>\n",
       "      <td>1.2</td>\n",
       "      <td>1.7</td>\n",
       "      <td>5.2</td>\n",
       "      <td>35</td>\n",
       "      <td>3.3</td>\n",
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       "      <td>1</td>\n",
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       "      <td>1</td>\n",
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       "      <th>2</th>\n",
       "      <td>203</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>9.1</td>\n",
       "      <td>7.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>3.4</td>\n",
       "      <td>.</td>\n",
       "      <td>55</td>\n",
       "      <td>5.2</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>204</td>\n",
       "      <td>.</td>\n",
       "      <td>2.5</td>\n",
       "      <td>8.1</td>\n",
       "      <td>3.1</td>\n",
       "      <td>4</td>\n",
       "      <td>1.9</td>\n",
       "      <td>5.4</td>\n",
       "      <td>51</td>\n",
       "      <td>3.9</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>205</td>\n",
       "      <td>5.1</td>\n",
       "      <td>1.4</td>\n",
       "      <td>7.1</td>\n",
       "      <td>4.8</td>\n",
       "      <td>3.3</td>\n",
       "      <td>2.6</td>\n",
       "      <td>3.8</td>\n",
       "      <td>49</td>\n",
       "      <td>4.9</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
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      "text/plain": [
       "    ID   V1   V2   V3   V4   V5   V6   V7  V8   V9 V10 V11  V12  V13  V14\n",
       "0  201  3.3  0.9  8.6    4  2.1  1.8  6.3  41  4.5   0   1    0    0    2\n",
       "1  202    .  0.4    4  2.5  1.2  1.7  5.2  35  3.3   0   1    0    0    1\n",
       "2  203    3    1  9.1  7.1  3.5  3.4    .  55  5.2   0   1    1    0    3\n",
       "3  204    .  2.5  8.1  3.1    4  1.9  5.4  51  3.9   0   0    0    1    3\n",
       "4  205  5.1  1.4  7.1  4.8  3.3  2.6  3.8  49  4.9   0   1    0    0    2"
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     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Read data from csv file\n",
    "data = pd.read_csv('Data\\cs_01.csv')\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "6fb0a55e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(79, 15)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "ea4dc18d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 79 entries, 0 to 78\n",
      "Data columns (total 15 columns):\n",
      " #   Column  Non-Null Count  Dtype \n",
      "---  ------  --------------  ----- \n",
      " 0   ID      79 non-null     int64 \n",
      " 1   V1      79 non-null     object\n",
      " 2   V2      79 non-null     object\n",
      " 3   V3      79 non-null     object\n",
      " 4   V4      79 non-null     object\n",
      " 5   V5      79 non-null     object\n",
      " 6   V6      79 non-null     object\n",
      " 7   V7      79 non-null     object\n",
      " 8   V8      79 non-null     object\n",
      " 9   V9      79 non-null     object\n",
      " 10  V10     79 non-null     object\n",
      " 11  V11     79 non-null     object\n",
      " 12  V12     79 non-null     int64 \n",
      " 13  V13     79 non-null     int64 \n",
      " 14  V14     79 non-null     int64 \n",
      "dtypes: int64(4), object(11)\n",
      "memory usage: 9.4+ KB\n"
     ]
    }
   ],
   "source": [
    "data.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "6bd6b94a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "ID     0\n",
       "V1     0\n",
       "V2     0\n",
       "V3     0\n",
       "V4     0\n",
       "V5     0\n",
       "V6     0\n",
       "V7     0\n",
       "V8     0\n",
       "V9     0\n",
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       "V12    0\n",
       "V13    0\n",
       "V14    0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Step 1: Determine the type of MVs\n",
    "#Know the cause\n",
    "np.sum(data.isnull())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "bc40e028",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "ID      0\n",
       "V1     19\n",
       "V2     11\n",
       "V3      5\n",
       "V4      5\n",
       "V5      4\n",
       "V6      3\n",
       "V7      5\n",
       "V8      4\n",
       "V9      3\n",
       "V10     2\n",
       "V11     1\n",
       "V12     0\n",
       "V13     0\n",
       "V14     0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(data == '.')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "76bce1bb",
   "metadata": {},
   "outputs": [],
   "source": [
    "data[data == '.'] = np.nan"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "5ee01ad0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "ID      0\n",
       "V1     19\n",
       "V2     11\n",
       "V3      5\n",
       "V4      5\n",
       "V5      4\n",
       "V6      3\n",
       "V7      5\n",
       "V8      4\n",
       "V9      3\n",
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       "V12     0\n",
       "V13     0\n",
       "V14     0\n",
       "dtype: int64"
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     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "np.sum(data.isnull())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "42484863",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 79 entries, 0 to 78\n",
      "Data columns (total 15 columns):\n",
      " #   Column  Non-Null Count  Dtype \n",
      "---  ------  --------------  ----- \n",
      " 0   ID      79 non-null     int64 \n",
      " 1   V1      60 non-null     object\n",
      " 2   V2      68 non-null     object\n",
      " 3   V3      74 non-null     object\n",
      " 4   V4      74 non-null     object\n",
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      " 6   V6      76 non-null     object\n",
      " 7   V7      74 non-null     object\n",
      " 8   V8      75 non-null     object\n",
      " 9   V9      76 non-null     object\n",
      " 10  V10     77 non-null     object\n",
      " 11  V11     78 non-null     object\n",
      " 12  V12     79 non-null     int64 \n",
      " 13  V13     79 non-null     int64 \n",
      " 14  V14     79 non-null     int64 \n",
      "dtypes: int64(4), object(11)\n",
      "memory usage: 9.4+ KB\n"
     ]
    }
   ],
   "source": [
    "data.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "c4c1884b",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Change data type of columns\n",
    "data[data.columns[1 : ]] = data.iloc[:, 1 : ].apply(lambda col: col.astype('float'), axis = 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "9559298a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 79 entries, 0 to 78\n",
      "Data columns (total 15 columns):\n",
      " #   Column  Non-Null Count  Dtype  \n",
      "---  ------  --------------  -----  \n",
      " 0   ID      79 non-null     int64  \n",
      " 1   V1      60 non-null     float64\n",
      " 2   V2      68 non-null     float64\n",
      " 3   V3      74 non-null     float64\n",
      " 4   V4      74 non-null     float64\n",
      " 5   V5      75 non-null     float64\n",
      " 6   V6      76 non-null     float64\n",
      " 7   V7      74 non-null     float64\n",
      " 8   V8      75 non-null     float64\n",
      " 9   V9      76 non-null     float64\n",
      " 10  V10     77 non-null     float64\n",
      " 11  V11     78 non-null     float64\n",
      " 12  V12     79 non-null     float64\n",
      " 13  V13     79 non-null     float64\n",
      " 14  V14     79 non-null     float64\n",
      "dtypes: float64(14), int64(1)\n",
      "memory usage: 9.4 KB\n"
     ]
    }
   ],
   "source": [
    "data.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "e498730a",
   "metadata": {},
   "outputs": [
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       "      <th></th>\n",
       "      <th>freq</th>\n",
       "      <th>pct</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
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       "      <th>V1</th>\n",
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       "      <th>V2</th>\n",
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       "      <th>V7</th>\n",
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       "      <th>V5</th>\n",
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       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
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       "      <th>V13</th>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
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       "      <th>V14</th>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
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      "text/plain": [
       "     freq   pct\n",
       "V1     19  24.1\n",
       "V2     11  13.9\n",
       "V3      5   6.3\n",
       "V4      5   6.3\n",
       "V7      5   6.3\n",
       "V5      4   5.1\n",
       "V8      4   5.1\n",
       "V6      3   3.8\n",
       "V9      3   3.8\n",
       "V10     2   2.5\n",
       "V11     1   1.3\n",
       "ID      0   0.0\n",
       "V12     0   0.0\n",
       "V13     0   0.0\n",
       "V14     0   0.0"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Step 2: Determine the extent of MVs\n",
    "#Summary of MVs in each column\n",
    "mvs_summary = pd.DataFrame({'freq' : np.sum(data.isnull())})\n",
    "mvs_summary['pct'] = round(mvs_summary['freq'] / data.shape[0] * 100, 1)\n",
    "mvs_summary.sort_values(by = 'pct', ascending = False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "cb683c3f",
   "metadata": {},
   "outputs": [
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       "      <th>9</th>\n",
       "      <td>210</td>\n",
       "      <td>4.1</td>\n",
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       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>60</th>\n",
       "      <td>261</td>\n",
       "      <td>3.6</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>6.2</td>\n",
       "      <td>4.5</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>62</th>\n",
       "      <td>263</td>\n",
       "      <td>3.6</td>\n",
       "      <td>NaN</td>\n",
       "      <td>9.9</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>4.9</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>225</td>\n",
       "      <td>4.7</td>\n",
       "      <td>1.3</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3.0</td>\n",
       "      <td>2.6</td>\n",
       "      <td>6.8</td>\n",
       "      <td>54.0</td>\n",
       "      <td>5.9</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td>248</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>6.4</td>\n",
       "      <td>5.3</td>\n",
       "      <td>3.0</td>\n",
       "      <td>2.5</td>\n",
       "      <td>7.1</td>\n",
       "      <td>46.0</td>\n",
       "      <td>4.5</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>236</td>\n",
       "      <td>2.9</td>\n",
       "      <td>2.6</td>\n",
       "      <td>7.7</td>\n",
       "      <td>7.0</td>\n",
       "      <td>2.8</td>\n",
       "      <td>3.6</td>\n",
       "      <td>7.7</td>\n",
       "      <td>47.0</td>\n",
       "      <td>4.2</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>239</td>\n",
       "      <td>4.3</td>\n",
       "      <td>1.8</td>\n",
       "      <td>7.6</td>\n",
       "      <td>5.4</td>\n",
       "      <td>3.1</td>\n",
       "      <td>2.5</td>\n",
       "      <td>4.4</td>\n",
       "      <td>46.0</td>\n",
       "      <td>5.6</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td>242</td>\n",
       "      <td>5.1</td>\n",
       "      <td>1.9</td>\n",
       "      <td>9.2</td>\n",
       "      <td>5.8</td>\n",
       "      <td>3.6</td>\n",
       "      <td>2.3</td>\n",
       "      <td>4.5</td>\n",
       "      <td>60.0</td>\n",
       "      <td>6.1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>243</td>\n",
       "      <td>4.1</td>\n",
       "      <td>1.1</td>\n",
       "      <td>9.3</td>\n",
       "      <td>5.5</td>\n",
       "      <td>2.5</td>\n",
       "      <td>2.7</td>\n",
       "      <td>7.4</td>\n",
       "      <td>47.0</td>\n",
       "      <td>5.3</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>78</th>\n",
       "      <td>279</td>\n",
       "      <td>3.1</td>\n",
       "      <td>2.6</td>\n",
       "      <td>9.9</td>\n",
       "      <td>3.5</td>\n",
       "      <td>3.2</td>\n",
       "      <td>1.2</td>\n",
       "      <td>5.4</td>\n",
       "      <td>43.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>79 rows × 16 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     ID   V1   V2   V3   V4   V5   V6   V7    V8   V9  V10  V11  V12  V13   \n",
       "9   210  4.1  3.7  5.9  NaN  NaN  NaN  NaN   NaN  NaN  NaN  0.0  1.0  0.0  \\\n",
       "60  261  3.6  NaN  NaN  6.2  4.5  NaN  NaN   NaN  NaN  1.0  NaN  1.0  1.0   \n",
       "62  263  3.6  NaN  9.9  NaN  NaN  NaN  NaN   NaN  4.9  NaN  1.0  0.0  0.0   \n",
       "24  225  4.7  1.3  NaN  NaN  3.0  2.6  6.8  54.0  5.9  0.0  1.0  0.0  0.0   \n",
       "47  248  NaN  NaN  6.4  5.3  3.0  2.5  7.1  46.0  4.5  1.0  0.0  1.0  0.0   \n",
       "..  ...  ...  ...  ...  ...  ...  ...  ...   ...  ...  ...  ...  ...  ...   \n",
       "35  236  2.9  2.6  7.7  7.0  2.8  3.6  7.7  47.0  4.2  0.0  1.0  1.0  1.0   \n",
       "38  239  4.3  1.8  7.6  5.4  3.1  2.5  4.4  46.0  5.6  0.0  1.0  0.0  1.0   \n",
       "41  242  5.1  1.9  9.2  5.8  3.6  2.3  4.5  60.0  6.1  0.0  1.0  0.0  0.0   \n",
       "42  243  4.1  1.1  9.3  5.5  2.5  2.7  7.4  47.0  5.3  0.0  1.0  0.0  1.0   \n",
       "78  279  3.1  2.6  9.9  3.5  3.2  1.2  5.4  43.0  5.0  0.0  1.0  0.0  1.0   \n",
       "\n",
       "    V14  mvs  \n",
       "9   2.0    7  \n",
       "60  2.0    7  \n",
       "62  3.0    7  \n",
       "24  3.0    2  \n",
       "47  2.0    2  \n",
       "..  ...  ...  \n",
       "35  2.0    0  \n",
       "38  3.0    0  \n",
       "41  3.0    0  \n",
       "42  3.0    0  \n",
       "78  3.0    0  \n",
       "\n",
       "[79 rows x 16 columns]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Summary of MVs for each case\n",
    "data.loc[:, 'mvs'] = data.apply(lambda row: np.sum(row.isnull()), axis = 1)\n",
    "data.sort_values(by = 'mvs', ascending = False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "4e346ca7",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Decision: remove V1 and cases with 50% mvs\n",
    "data.drop(columns = 'V1', inplace = True)\n",
    "data.drop(index = [9, 60, 62], inplace = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "6ee65cc6",
   "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>freq</th>\n",
       "      <th>pct</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>V2</th>\n",
       "      <td>9</td>\n",
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       "      <th>V3</th>\n",
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       "      <th>V4</th>\n",
       "      <td>3</td>\n",
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       "    <tr>\n",
       "      <th>V5</th>\n",
       "      <td>2</td>\n",
       "      <td>2.6</td>\n",
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       "      <th>V7</th>\n",
       "      <td>2</td>\n",
       "      <td>2.6</td>\n",
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       "    <tr>\n",
       "      <th>V8</th>\n",
       "      <td>1</td>\n",
       "      <td>1.3</td>\n",
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       "    <tr>\n",
       "      <th>V9</th>\n",
       "      <td>1</td>\n",
       "      <td>1.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ID</th>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>V6</th>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>V10</th>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>V11</th>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>V12</th>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>V13</th>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>V14</th>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mvs</th>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     freq   pct\n",
       "V2      9  11.8\n",
       "V3      4   5.3\n",
       "V4      3   3.9\n",
       "V5      2   2.6\n",
       "V7      2   2.6\n",
       "V8      1   1.3\n",
       "V9      1   1.3\n",
       "ID      0   0.0\n",
       "V6      0   0.0\n",
       "V10     0   0.0\n",
       "V11     0   0.0\n",
       "V12     0   0.0\n",
       "V13     0   0.0\n",
       "V14     0   0.0\n",
       "mvs     0   0.0"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Summary of MVs in each column\n",
    "mvs_summary = pd.DataFrame({'freq' : np.sum(data.isnull())})\n",
    "mvs_summary['pct'] = round(mvs_summary['freq'] / data.shape[0] * 100, 1)\n",
    "mvs_summary.sort_values(by = 'pct', ascending = False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "cbde502a",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th>ID</th>\n",
       "      <th>V2</th>\n",
       "      <th>V3</th>\n",
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       "      <th>V11</th>\n",
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       "      <th>V13</th>\n",
       "      <th>V14</th>\n",
       "      <th>mvs</th>\n",
       "      <th>if_v2_null</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>74</th>\n",
       "      <td>275</td>\n",
       "      <td>NaN</td>\n",
       "      <td>9.9</td>\n",
       "      <td>6.5</td>\n",
       "      <td>3.0</td>\n",
       "      <td>2.7</td>\n",
       "      <td>6.9</td>\n",
       "      <td>58.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
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       "      <td>1</td>\n",
       "      <td>1</td>\n",
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       "    <tr>\n",
       "      <th>75</th>\n",
       "      <td>276</td>\n",
       "      <td>0.7</td>\n",
       "      <td>8.1</td>\n",
       "      <td>6.0</td>\n",
       "      <td>2.2</td>\n",
       "      <td>2.1</td>\n",
       "      <td>8.4</td>\n",
       "      <td>40.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>76</th>\n",
       "      <td>277</td>\n",
       "      <td>2.4</td>\n",
       "      <td>9.6</td>\n",
       "      <td>5.0</td>\n",
       "      <td>3.3</td>\n",
       "      <td>3.2</td>\n",
       "      <td>8.5</td>\n",
       "      <td>47.0</td>\n",
       "      <td>5.2</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
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       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>77</th>\n",
       "      <td>278</td>\n",
       "      <td>NaN</td>\n",
       "      <td>8.8</td>\n",
       "      <td>5.3</td>\n",
       "      <td>3.5</td>\n",
       "      <td>2.5</td>\n",
       "      <td>7.1</td>\n",
       "      <td>71.0</td>\n",
       "      <td>6.2</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>78</th>\n",
       "      <td>279</td>\n",
       "      <td>2.6</td>\n",
       "      <td>9.9</td>\n",
       "      <td>3.5</td>\n",
       "      <td>3.2</td>\n",
       "      <td>1.2</td>\n",
       "      <td>5.4</td>\n",
       "      <td>43.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
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       "      <td>3.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     ID   V2   V3   V4   V5   V6   V7    V8   V9  V10  V11  V12  V13  V14   \n",
       "74  275  NaN  9.9  6.5  3.0  2.7  6.9  58.0  6.0  0.0  1.0  0.0  0.0  3.0  \\\n",
       "75  276  0.7  8.1  6.0  2.2  2.1  8.4  40.0  5.0  0.0  1.0  1.0  0.0  2.0   \n",
       "76  277  2.4  9.6  5.0  3.3  3.2  8.5  47.0  5.2  0.0  1.0  0.0  1.0  2.0   \n",
       "77  278  NaN  8.8  5.3  3.5  2.5  7.1  71.0  6.2  0.0  1.0  1.0  0.0  3.0   \n",
       "78  279  2.6  9.9  3.5  3.2  1.2  5.4  43.0  5.0  0.0  1.0  0.0  1.0  3.0   \n",
       "\n",
       "    mvs  if_v2_null  \n",
       "74    1           1  \n",
       "75    0           0  \n",
       "76    0           0  \n",
       "77    1           1  \n",
       "78    0           0  "
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Step 3: Diagnose the randomness of the MVs processes\n",
    "#Create a list of conditions\n",
    "conditions = [data['V2'].isnull(), data['V2'].notnull()]\n",
    "#Create a list of the values needed to assign for each condition\n",
    "values = [1, 0]\n",
    "#Create a new column and use np.select to assign values to it using the lists as arguments\n",
    "data['if_v2_null'] = np.select(conditions, values)\n",
    "data.tail()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "688faf1c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7.9\n",
      "7.4\n"
     ]
    }
   ],
   "source": [
    "#Evaluate the randomness of the MVs in V2 from V3 perspective\n",
    "print(round(data.loc[data['if_v2_null'] == 0, 'V3'].mean(), 1))\n",
    "print(round(data.loc[data['if_v2_null'] == 1, 'V3'].mean(), 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "17866e29",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ttest_indResult(statistic=0.8458114458768, pvalue=0.40053997816689313)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#T-test for the means of two independent samples\n",
    "    #H0: mu_1 = mu_2\n",
    "    #H1: mu_1 # mu_2\n",
    "#If p-value < 0.05 reject H0\n",
    "#Note : Normality assumption is needed.\n",
    "from scipy.stats import ttest_ind\n",
    "ttest_ind(data.loc[(data['if_v2_null'] == 0) & (data['V3'].notnull()), 'V3'],\n",
    "          data.loc[(data['if_v2_null'] == 1) & (data['V3'].notnull()), 'V3'],\n",
    "          alternative = 'two-sided')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "37b4c637",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Box plot for evaluating the randomness of the MVs in V2 from V3 perspective\n",
    "plt.boxplot([data.loc[(data['if_v2_null'] == 0) & (data['V3'].notnull()), 'V3'],\n",
    "             data.loc[(data['if_v2_null'] == 1) & (data['V3'].notnull()), 'V3']])\n",
    "plt.xticks(ticks = [1, 2], labels = [0, 1])\n",
    "plt.title('MVs in V2 \\n from V3 perspective')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "4530e9d4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "Index: 76 entries, 0 to 78\n",
      "Data columns (total 16 columns):\n",
      " #   Column      Non-Null Count  Dtype  \n",
      "---  ------      --------------  -----  \n",
      " 0   ID          76 non-null     int64  \n",
      " 1   V2          67 non-null     float64\n",
      " 2   V3          72 non-null     float64\n",
      " 3   V4          73 non-null     float64\n",
      " 4   V5          74 non-null     float64\n",
      " 5   V6          76 non-null     float64\n",
      " 6   V7          74 non-null     float64\n",
      " 7   V8          75 non-null     float64\n",
      " 8   V9          75 non-null     float64\n",
      " 9   V10         76 non-null     float64\n",
      " 10  V11         76 non-null     float64\n",
      " 11  V12         76 non-null     float64\n",
      " 12  V13         76 non-null     float64\n",
      " 13  V14         76 non-null     float64\n",
      " 14  mvs         76 non-null     int64  \n",
      " 15  if_v2_null  76 non-null     int32  \n",
      "dtypes: float64(13), int32(1), int64(2)\n",
      "memory usage: 9.8 KB\n"
     ]
    }
   ],
   "source": [
    "data.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "ee9e9178",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>var</th>\n",
       "      <th>v2_null</th>\n",
       "      <th>v2_not_null</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>V3</td>\n",
       "      <td>7.4</td>\n",
       "      <td>7.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>V4</td>\n",
       "      <td>6.1</td>\n",
       "      <td>5.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>V5</td>\n",
       "      <td>3.5</td>\n",
       "      <td>3.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>V6</td>\n",
       "      <td>3.1</td>\n",
       "      <td>2.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>V7</td>\n",
       "      <td>8.0</td>\n",
       "      <td>6.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>V8</td>\n",
       "      <td>52.4</td>\n",
       "      <td>46.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>V9</td>\n",
       "      <td>5.1</td>\n",
       "      <td>4.8</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  var  v2_null  v2_not_null\n",
       "0  V3      7.4          7.9\n",
       "1  V4      6.1          5.1\n",
       "2  V5      3.5          3.0\n",
       "3  V6      3.1          2.6\n",
       "4  V7      8.0          6.8\n",
       "5  V8     52.4         46.7\n",
       "6  V9      5.1          4.8"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Evaluate the randomness of the MVs in V2 from other numeric variables perspective\n",
    "mvs_in_v2 = pd.DataFrame({'var' : data.columns[2 : 9],\n",
    "                          'v2_null' : [0] * 7,\n",
    "                          'v2_not_null' : [0] * 7})\n",
    "for i in range(2, 9):\n",
    "    mvs_in_v2.iloc[i - 2, 1] = round(data.loc[data['if_v2_null'] == 1, data.columns[i]].mean(), 1)\n",
    "    mvs_in_v2.iloc[i - 2, 2] = round(data.loc[data['if_v2_null'] == 0, data.columns[i]].mean(), 1)\n",
    "mvs_in_v2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "13390d06",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>if_v2_null</th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>V10</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0.0</th>\n",
       "      <td>50</td>\n",
       "      <td>6</td>\n",
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       "    <tr>\n",
       "      <th>1.0</th>\n",
       "      <td>17</td>\n",
       "      <td>3</td>\n",
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       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "if_v2_null   0  1\n",
       "V10              \n",
       "0.0         50  6\n",
       "1.0         17  3"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Evaluate the randomness of the MVs in V2 from V10 perspective\n",
    "#Cross tabulation analysis\n",
    "cross_tab = round(pd.crosstab(data['V10'], data['if_v2_null']), 2)\n",
    "cross_tab"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "120e0acd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>if_v2_null</th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>V10</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0.0</th>\n",
       "      <td>0.89</td>\n",
       "      <td>0.11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1.0</th>\n",
       "      <td>0.85</td>\n",
       "      <td>0.15</td>\n",
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      ],
      "text/plain": [
       "if_v2_null     0     1\n",
       "V10                   \n",
       "0.0         0.89  0.11\n",
       "1.0         0.85  0.15"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Evaluate the randomness of the MVs in V2 from V10 perspective\n",
    "#Cross tabulation analysis\n",
    "cross_tab_pct = round(pd.crosstab(data['V10'], data['if_v2_null'], normalize = 'index'), 2)\n",
    "cross_tab_pct"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "2c5bbd1b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Chi2ContingencyResult(statistic=0.01125325752191425, pvalue=0.9155177905952596, dof=1, expected_freq=array([[49.36842105,  6.63157895],\n",
       "       [17.63157895,  2.36842105]]))"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Two categorical variables\n",
    "#Chi-Square test for cross tab\n",
    "    #H0: MVs in V2 are independent from V10\n",
    "    #H1: MVs in V2 are related to V10\n",
    "#If p-value < 0.05 reject H0\n",
    "from scipy.stats import chi2_contingency\n",
    "chi2_contingency(cross_tab)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "8e1f6a57",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th>ID</th>\n",
       "      <th>V2</th>\n",
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       "      <th>V14</th>\n",
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       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>201</td>\n",
       "      <td>0.9</td>\n",
       "      <td>8.6</td>\n",
       "      <td>4.0</td>\n",
       "      <td>2.1</td>\n",
       "      <td>1.8</td>\n",
       "      <td>6.3</td>\n",
       "      <td>41.0</td>\n",
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       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.0</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>202</td>\n",
       "      <td>0.4</td>\n",
       "      <td>4.0</td>\n",
       "      <td>2.5</td>\n",
       "      <td>1.2</td>\n",
       "      <td>1.7</td>\n",
       "      <td>5.2</td>\n",
       "      <td>35.0</td>\n",
       "      <td>3.3</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>203</td>\n",
       "      <td>1.0</td>\n",
       "      <td>9.1</td>\n",
       "      <td>7.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>3.4</td>\n",
       "      <td>NaN</td>\n",
       "      <td>55.0</td>\n",
       "      <td>5.2</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>204</td>\n",
       "      <td>2.5</td>\n",
       "      <td>8.1</td>\n",
       "      <td>3.1</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.9</td>\n",
       "      <td>5.4</td>\n",
       "      <td>51.0</td>\n",
       "      <td>3.9</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>3.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>205</td>\n",
       "      <td>1.4</td>\n",
       "      <td>7.1</td>\n",
       "      <td>4.8</td>\n",
       "      <td>3.3</td>\n",
       "      <td>2.6</td>\n",
       "      <td>3.8</td>\n",
       "      <td>49.0</td>\n",
       "      <td>4.9</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    ID   V2   V3   V4   V5   V6   V7    V8   V9  V10  V11  V12  V13  V14\n",
       "0  201  0.9  8.6  4.0  2.1  1.8  6.3  41.0  4.5  0.0  1.0  0.0  0.0  2.0\n",
       "1  202  0.4  4.0  2.5  1.2  1.7  5.2  35.0  3.3  0.0  1.0  0.0  0.0  1.0\n",
       "2  203  1.0  9.1  7.1  3.5  3.4  NaN  55.0  5.2  0.0  1.0  1.0  0.0  3.0\n",
       "3  204  2.5  8.1  3.1  4.0  1.9  5.4  51.0  3.9  0.0  0.0  0.0  1.0  3.0\n",
       "4  205  1.4  7.1  4.8  3.3  2.6  3.8  49.0  4.9  0.0  1.0  0.0  0.0  2.0"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Remove temporary variables: mvs and if_v2_null\n",
    "data.drop(columns = ['mvs', 'if_v2_null'], inplace = True)\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "5901bf2e",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>V7</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>V8</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>V9</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  var  comp_case  mean_sub  mice\n",
       "0  V2          0         0     0\n",
       "1  V3          0         0     0\n",
       "2  V4          0         0     0\n",
       "3  V5          0         0     0\n",
       "4  V6          0         0     0\n",
       "5  V7          0         0     0\n",
       "6  V8          0         0     0\n",
       "7  V9          0         0     0"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Step 4: Select the imputation method\n",
    "#Create a dataframe to save mean of numeric variables \n",
    "# for different imputation methods\n",
    "mean_imput_methods = pd.DataFrame({'var' : data.columns[1 : 9],\n",
    "                                   'comp_case' : [0] * 8,\n",
    "                                   'mean_sub': [0] * 8,\n",
    "                                   'mice': [0] * 8})\n",
    "mean_imput_methods"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "ee548230",
   "metadata": {},
   "outputs": [
    {
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       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>V6</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>V7</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>V8</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>V9</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  var  comp_case  mean_sub  mice\n",
       "0  V2          0         0     0\n",
       "1  V3          0         0     0\n",
       "2  V4          0         0     0\n",
       "3  V5          0         0     0\n",
       "4  V6          0         0     0\n",
       "5  V7          0         0     0\n",
       "6  V8          0         0     0\n",
       "7  V9          0         0     0"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Create a dataframe to save std of numeric variables \n",
    "# for different imputation methods\n",
    "std_imput_methods = pd.DataFrame({'var' : data.columns[1 : 9],\n",
    "                                  'comp_case' : [0] * 8,\n",
    "                                  'mean_sub': [0] * 8,\n",
    "                                  'mice': [0] * 8})\n",
    "std_imput_methods"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "d8a65cc7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(56, 14)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "ID     0\n",
       "V2     0\n",
       "V3     0\n",
       "V4     0\n",
       "V5     0\n",
       "V6     0\n",
       "V7     0\n",
       "V8     0\n",
       "V9     0\n",
       "V10    0\n",
       "V11    0\n",
       "V12    0\n",
       "V13    0\n",
       "V14    0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Method 1: complete case approach\n",
    "data_complete_case = data.dropna(axis = 0, inplace = False)\n",
    "print(data_complete_case.shape)\n",
    "np.sum(data_complete_case.isnull())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "15fc4400",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>var</th>\n",
       "      <th>comp_case</th>\n",
       "      <th>mean_sub</th>\n",
       "      <th>mice</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>V2</td>\n",
       "      <td>2.04</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>V3</td>\n",
       "      <td>7.93</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>V4</td>\n",
       "      <td>5.08</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>V5</td>\n",
       "      <td>3.00</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>V6</td>\n",
       "      <td>2.56</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>V7</td>\n",
       "      <td>6.80</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>V8</td>\n",
       "      <td>46.95</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>V9</td>\n",
       "      <td>4.81</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  var  comp_case  mean_sub  mice\n",
       "0  V2       2.04         0     0\n",
       "1  V3       7.93         0     0\n",
       "2  V4       5.08         0     0\n",
       "3  V5       3.00         0     0\n",
       "4  V6       2.56         0     0\n",
       "5  V7       6.80         0     0\n",
       "6  V8      46.95         0     0\n",
       "7  V9       4.81         0     0"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean_imput_methods['comp_case'] = list(round(data_complete_case.iloc[:, 1 : 9].mean(), 2))\n",
    "mean_imput_methods"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "f3b89e36",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>var</th>\n",
       "      <th>comp_case</th>\n",
       "      <th>mean_sub</th>\n",
       "      <th>mice</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>V2</td>\n",
       "      <td>0.90</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>V3</td>\n",
       "      <td>1.56</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>V4</td>\n",
       "      <td>1.22</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>V5</td>\n",
       "      <td>0.89</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>V6</td>\n",
       "      <td>0.73</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>V7</td>\n",
       "      <td>1.66</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>V8</td>\n",
       "      <td>9.12</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>V9</td>\n",
       "      <td>0.91</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  var  comp_case  mean_sub  mice\n",
       "0  V2       0.90         0     0\n",
       "1  V3       1.56         0     0\n",
       "2  V4       1.22         0     0\n",
       "3  V5       0.89         0     0\n",
       "4  V6       0.73         0     0\n",
       "5  V7       1.66         0     0\n",
       "6  V8       9.12         0     0\n",
       "7  V9       0.91         0     0"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "std_imput_methods['comp_case'] = list(round(data_complete_case.iloc[:, 1 : 9].std(), 2))\n",
    "std_imput_methods"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "26601d44",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Method 2: mean substitution\n",
    "data_mean_sub = data.copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "029131df",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(76, 14)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "ID     0\n",
       "V2     0\n",
       "V3     0\n",
       "V4     0\n",
       "V5     0\n",
       "V6     0\n",
       "V7     0\n",
       "V8     0\n",
       "V9     0\n",
       "V10    0\n",
       "V11    0\n",
       "V12    0\n",
       "V13    0\n",
       "V14    0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Substiude NAs w/ mean of each column\n",
    "data_mean_sub.iloc[:, 1 : 9] = data_mean_sub.iloc[:, 1 : 9].fillna(data_mean_sub.iloc[:, 1 : 9].mean())\n",
    "print(data_mean_sub.shape)\n",
    "np.sum(data_mean_sub.isnull())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "de9c5a60",
   "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>var</th>\n",
       "      <th>comp_case</th>\n",
       "      <th>mean_sub</th>\n",
       "      <th>mice</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>V2</td>\n",
       "      <td>2.04</td>\n",
       "      <td>1.98</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>V3</td>\n",
       "      <td>7.93</td>\n",
       "      <td>7.79</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>V4</td>\n",
       "      <td>5.08</td>\n",
       "      <td>5.20</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>V5</td>\n",
       "      <td>3.00</td>\n",
       "      <td>3.04</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>V6</td>\n",
       "      <td>2.56</td>\n",
       "      <td>2.62</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>V7</td>\n",
       "      <td>6.80</td>\n",
       "      <td>6.90</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>V8</td>\n",
       "      <td>46.95</td>\n",
       "      <td>47.37</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>V9</td>\n",
       "      <td>4.81</td>\n",
       "      <td>4.87</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  var  comp_case  mean_sub  mice\n",
       "0  V2       2.04      1.98     0\n",
       "1  V3       7.93      7.79     0\n",
       "2  V4       5.08      5.20     0\n",
       "3  V5       3.00      3.04     0\n",
       "4  V6       2.56      2.62     0\n",
       "5  V7       6.80      6.90     0\n",
       "6  V8      46.95     47.37     0\n",
       "7  V9       4.81      4.87     0"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean_imput_methods['mean_sub'] = list(round(data_mean_sub.iloc[:, 1 : 9].mean(), 2))\n",
    "mean_imput_methods"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "fcf7869d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>var</th>\n",
       "      <th>comp_case</th>\n",
       "      <th>mean_sub</th>\n",
       "      <th>mice</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>V2</td>\n",
       "      <td>0.90</td>\n",
       "      <td>0.83</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>V3</td>\n",
       "      <td>1.56</td>\n",
       "      <td>1.60</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>V4</td>\n",
       "      <td>1.22</td>\n",
       "      <td>1.20</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>V5</td>\n",
       "      <td>0.89</td>\n",
       "      <td>0.84</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>V6</td>\n",
       "      <td>0.73</td>\n",
       "      <td>0.74</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>V7</td>\n",
       "      <td>1.66</td>\n",
       "      <td>1.58</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>V8</td>\n",
       "      <td>9.12</td>\n",
       "      <td>9.19</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>V9</td>\n",
       "      <td>0.91</td>\n",
       "      <td>0.87</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  var  comp_case  mean_sub  mice\n",
       "0  V2       0.90      0.83     0\n",
       "1  V3       1.56      1.60     0\n",
       "2  V4       1.22      1.20     0\n",
       "3  V5       0.89      0.84     0\n",
       "4  V6       0.73      0.74     0\n",
       "5  V7       1.66      1.58     0\n",
       "6  V8       9.12      9.19     0\n",
       "7  V9       0.91      0.87     0"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "std_imput_methods['mean_sub'] = list(round(data_mean_sub.iloc[:, 1 : 9].std(), 2))\n",
    "std_imput_methods"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "b670a8a2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(76, 14)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "ID     0\n",
       "V2     0\n",
       "V3     0\n",
       "V4     0\n",
       "V5     0\n",
       "V6     0\n",
       "V7     0\n",
       "V8     0\n",
       "V9     0\n",
       "V10    0\n",
       "V11    0\n",
       "V12    0\n",
       "V13    0\n",
       "V14    0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Method 3: MICE\n",
    "#%pip install miceforest (uses lightgbm as a backend)\n",
    "from miceforest import ImputationKernel\n",
    "\n",
    "mice_kernel = ImputationKernel(data = data, save_all_iterations = True, random_state = 123)\n",
    "#Run the kernel on the data for 5 iterations\n",
    "mice_kernel.mice(5)\n",
    "#Create the imputed data\n",
    "data_mice_imputation = mice_kernel.complete_data()\n",
    "print(data_mice_imputation.shape)\n",
    "np.sum(data_mice_imputation.isnull())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "7c251cd6",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>var</th>\n",
       "      <th>comp_case</th>\n",
       "      <th>mean_sub</th>\n",
       "      <th>mice</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>V2</td>\n",
       "      <td>2.04</td>\n",
       "      <td>1.98</td>\n",
       "      <td>2.04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>V3</td>\n",
       "      <td>7.93</td>\n",
       "      <td>7.79</td>\n",
       "      <td>7.80</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>V4</td>\n",
       "      <td>5.08</td>\n",
       "      <td>5.20</td>\n",
       "      <td>5.19</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>V5</td>\n",
       "      <td>3.00</td>\n",
       "      <td>3.04</td>\n",
       "      <td>3.04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>V6</td>\n",
       "      <td>2.56</td>\n",
       "      <td>2.62</td>\n",
       "      <td>2.62</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>V7</td>\n",
       "      <td>6.80</td>\n",
       "      <td>6.90</td>\n",
       "      <td>6.89</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>V8</td>\n",
       "      <td>46.95</td>\n",
       "      <td>47.37</td>\n",
       "      <td>47.33</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>V9</td>\n",
       "      <td>4.81</td>\n",
       "      <td>4.87</td>\n",
       "      <td>4.86</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  var  comp_case  mean_sub   mice\n",
       "0  V2       2.04      1.98   2.04\n",
       "1  V3       7.93      7.79   7.80\n",
       "2  V4       5.08      5.20   5.19\n",
       "3  V5       3.00      3.04   3.04\n",
       "4  V6       2.56      2.62   2.62\n",
       "5  V7       6.80      6.90   6.89\n",
       "6  V8      46.95     47.37  47.33\n",
       "7  V9       4.81      4.87   4.86"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean_imput_methods['mice'] = list(round(data_mice_imputation.iloc[:, 1 : 9].mean(), 2))\n",
    "mean_imput_methods"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "7aed0980",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th>mean_sub</th>\n",
       "      <th>mice</th>\n",
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       "      <th>0</th>\n",
       "      <td>V2</td>\n",
       "      <td>0.90</td>\n",
       "      <td>0.83</td>\n",
       "      <td>0.88</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>V3</td>\n",
       "      <td>1.56</td>\n",
       "      <td>1.60</td>\n",
       "      <td>1.64</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>V4</td>\n",
       "      <td>1.22</td>\n",
       "      <td>1.20</td>\n",
       "      <td>1.21</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>V5</td>\n",
       "      <td>0.89</td>\n",
       "      <td>0.84</td>\n",
       "      <td>0.84</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>V6</td>\n",
       "      <td>0.73</td>\n",
       "      <td>0.74</td>\n",
       "      <td>0.74</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>V7</td>\n",
       "      <td>1.66</td>\n",
       "      <td>1.58</td>\n",
       "      <td>1.59</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>V8</td>\n",
       "      <td>9.12</td>\n",
       "      <td>9.19</td>\n",
       "      <td>9.20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>V9</td>\n",
       "      <td>0.91</td>\n",
       "      <td>0.87</td>\n",
       "      <td>0.88</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  var  comp_case  mean_sub  mice\n",
       "0  V2       0.90      0.83  0.88\n",
       "1  V3       1.56      1.60  1.64\n",
       "2  V4       1.22      1.20  1.21\n",
       "3  V5       0.89      0.84  0.84\n",
       "4  V6       0.73      0.74  0.74\n",
       "5  V7       1.66      1.58  1.59\n",
       "6  V8       9.12      9.19  9.20\n",
       "7  V9       0.91      0.87  0.88"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "std_imput_methods['mice'] = list(round(data_mice_imputation.iloc[:, 1 : 9].std(), 2))\n",
    "std_imput_methods"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "9d85c82b",
   "metadata": {},
   "outputs": [
    {
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       "      <th>V4</th>\n",
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       "      <td>0.20</td>\n",
       "      <td>0.75</td>\n",
       "      <td>0.43</td>\n",
       "      <td>0.16</td>\n",
       "      <td>0.19</td>\n",
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       "    <tr>\n",
       "      <th>V5</th>\n",
       "      <td>0.39</td>\n",
       "      <td>0.03</td>\n",
       "      <td>0.20</td>\n",
       "      <td>1.00</td>\n",
       "      <td>0.19</td>\n",
       "      <td>-0.01</td>\n",
       "      <td>0.42</td>\n",
       "      <td>0.11</td>\n",
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       "    <tr>\n",
       "      <th>V6</th>\n",
       "      <td>0.20</td>\n",
       "      <td>-0.19</td>\n",
       "      <td>0.75</td>\n",
       "      <td>0.19</td>\n",
       "      <td>1.00</td>\n",
       "      <td>0.49</td>\n",
       "      <td>0.14</td>\n",
       "      <td>0.04</td>\n",
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       "    <tr>\n",
       "      <th>V7</th>\n",
       "      <td>0.29</td>\n",
       "      <td>-0.24</td>\n",
       "      <td>0.43</td>\n",
       "      <td>-0.01</td>\n",
       "      <td>0.49</td>\n",
       "      <td>1.00</td>\n",
       "      <td>-0.22</td>\n",
       "      <td>-0.33</td>\n",
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       "    <tr>\n",
       "      <th>V8</th>\n",
       "      <td>0.13</td>\n",
       "      <td>0.48</td>\n",
       "      <td>0.16</td>\n",
       "      <td>0.42</td>\n",
       "      <td>0.14</td>\n",
       "      <td>-0.22</td>\n",
       "      <td>1.00</td>\n",
       "      <td>0.48</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>V9</th>\n",
       "      <td>-0.30</td>\n",
       "      <td>0.68</td>\n",
       "      <td>0.19</td>\n",
       "      <td>0.11</td>\n",
       "      <td>0.04</td>\n",
       "      <td>-0.33</td>\n",
       "      <td>0.48</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      V2    V3    V4    V5    V6    V7    V8    V9\n",
       "V2  1.00 -0.08  0.11  0.39  0.20  0.29  0.13 -0.30\n",
       "V3 -0.08  1.00 -0.03  0.03 -0.19 -0.24  0.48  0.68\n",
       "V4  0.11 -0.03  1.00  0.20  0.75  0.43  0.16  0.19\n",
       "V5  0.39  0.03  0.20  1.00  0.19 -0.01  0.42  0.11\n",
       "V6  0.20 -0.19  0.75  0.19  1.00  0.49  0.14  0.04\n",
       "V7  0.29 -0.24  0.43 -0.01  0.49  1.00 -0.22 -0.33\n",
       "V8  0.13  0.48  0.16  0.42  0.14 -0.22  1.00  0.48\n",
       "V9 -0.30  0.68  0.19  0.11  0.04 -0.33  0.48  1.00"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Step 5: correlation analysis\n",
    "#Method 1: complete case approach\n",
    "round(data_complete_case.iloc[:, 1 : 9].corr(), 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "fc28ce62",
   "metadata": {},
   "outputs": [
    {
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       "      <td>0.37</td>\n",
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       "      <td>0.22</td>\n",
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       "      <td>1.00</td>\n",
       "      <td>0.26</td>\n",
       "      <td>0.04</td>\n",
       "      <td>0.47</td>\n",
       "      <td>0.17</td>\n",
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       "    <tr>\n",
       "      <th>V6</th>\n",
       "      <td>0.16</td>\n",
       "      <td>-0.18</td>\n",
       "      <td>0.76</td>\n",
       "      <td>0.26</td>\n",
       "      <td>1.00</td>\n",
       "      <td>0.43</td>\n",
       "      <td>0.21</td>\n",
       "      <td>0.09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>V7</th>\n",
       "      <td>0.24</td>\n",
       "      <td>-0.19</td>\n",
       "      <td>0.40</td>\n",
       "      <td>0.04</td>\n",
       "      <td>0.43</td>\n",
       "      <td>1.00</td>\n",
       "      <td>-0.13</td>\n",
       "      <td>-0.24</td>\n",
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       "    <tr>\n",
       "      <th>V8</th>\n",
       "      <td>0.12</td>\n",
       "      <td>0.50</td>\n",
       "      <td>0.22</td>\n",
       "      <td>0.47</td>\n",
       "      <td>0.21</td>\n",
       "      <td>-0.13</td>\n",
       "      <td>1.00</td>\n",
       "      <td>0.53</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>V9</th>\n",
       "      <td>-0.29</td>\n",
       "      <td>0.61</td>\n",
       "      <td>0.24</td>\n",
       "      <td>0.17</td>\n",
       "      <td>0.09</td>\n",
       "      <td>-0.24</td>\n",
       "      <td>0.53</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      V2    V3    V4    V5    V6    V7    V8    V9\n",
       "V2  1.00 -0.10  0.07  0.37  0.16  0.24  0.12 -0.29\n",
       "V3 -0.10  1.00 -0.03  0.05 -0.18 -0.19  0.50  0.61\n",
       "V4  0.07 -0.03  1.00  0.26  0.76  0.40  0.22  0.24\n",
       "V5  0.37  0.05  0.26  1.00  0.26  0.04  0.47  0.17\n",
       "V6  0.16 -0.18  0.76  0.26  1.00  0.43  0.21  0.09\n",
       "V7  0.24 -0.19  0.40  0.04  0.43  1.00 -0.13 -0.24\n",
       "V8  0.12  0.50  0.22  0.47  0.21 -0.13  1.00  0.53\n",
       "V9 -0.29  0.61  0.24  0.17  0.09 -0.24  0.53  1.00"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Method 2: mean substitution\n",
    "round(data_mean_sub.iloc[:, 1 : 9].corr(), 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "d0e59574",
   "metadata": {},
   "outputs": [
    {
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       "    </tr>\n",
       "    <tr>\n",
       "      <th>V4</th>\n",
       "      <td>0.12</td>\n",
       "      <td>-0.01</td>\n",
       "      <td>1.00</td>\n",
       "      <td>0.26</td>\n",
       "      <td>0.77</td>\n",
       "      <td>0.41</td>\n",
       "      <td>0.23</td>\n",
       "      <td>0.24</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>V5</th>\n",
       "      <td>0.40</td>\n",
       "      <td>0.08</td>\n",
       "      <td>0.26</td>\n",
       "      <td>1.00</td>\n",
       "      <td>0.27</td>\n",
       "      <td>0.05</td>\n",
       "      <td>0.47</td>\n",
       "      <td>0.20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>V6</th>\n",
       "      <td>0.22</td>\n",
       "      <td>-0.14</td>\n",
       "      <td>0.77</td>\n",
       "      <td>0.27</td>\n",
       "      <td>1.00</td>\n",
       "      <td>0.43</td>\n",
       "      <td>0.21</td>\n",
       "      <td>0.10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>V7</th>\n",
       "      <td>0.32</td>\n",
       "      <td>-0.15</td>\n",
       "      <td>0.41</td>\n",
       "      <td>0.05</td>\n",
       "      <td>0.43</td>\n",
       "      <td>1.00</td>\n",
       "      <td>-0.11</td>\n",
       "      <td>-0.24</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>V8</th>\n",
       "      <td>0.13</td>\n",
       "      <td>0.53</td>\n",
       "      <td>0.23</td>\n",
       "      <td>0.47</td>\n",
       "      <td>0.21</td>\n",
       "      <td>-0.11</td>\n",
       "      <td>1.00</td>\n",
       "      <td>0.55</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>V9</th>\n",
       "      <td>-0.27</td>\n",
       "      <td>0.64</td>\n",
       "      <td>0.24</td>\n",
       "      <td>0.20</td>\n",
       "      <td>0.10</td>\n",
       "      <td>-0.24</td>\n",
       "      <td>0.55</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      V2    V3    V4    V5    V6    V7    V8    V9\n",
       "V2  1.00 -0.12  0.12  0.40  0.22  0.32  0.13 -0.27\n",
       "V3 -0.12  1.00 -0.01  0.08 -0.14 -0.15  0.53  0.64\n",
       "V4  0.12 -0.01  1.00  0.26  0.77  0.41  0.23  0.24\n",
       "V5  0.40  0.08  0.26  1.00  0.27  0.05  0.47  0.20\n",
       "V6  0.22 -0.14  0.77  0.27  1.00  0.43  0.21  0.10\n",
       "V7  0.32 -0.15  0.41  0.05  0.43  1.00 -0.11 -0.24\n",
       "V8  0.13  0.53  0.23  0.47  0.21 -0.11  1.00  0.55\n",
       "V9 -0.27  0.64  0.24  0.20  0.10 -0.24  0.55  1.00"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Method 3: MICE\n",
    "round(data_mice_imputation.iloc[:, 1 : 9].corr(), 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "b799175d",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Summary\n",
    "#   The missing data process is MCAR\n",
    "#   Imputation is the most logical course of action\n",
    "#   Correlations differ slightly across imputation techniques"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9a1d6f7c",
   "metadata": {},
   "source": [
    "### Outliers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "6a4ec8e8",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Problem of Masking\n",
    "x = np.array([2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 1000])\n",
    "y = np.array([2, 2, 3, 3, 3, 4, 4, 4, 10000, 100000])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "6ea7c0ec",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[False False False False False False False False False False False False\n",
      " False False False  True]\n",
      "[False False False False False False False False False False]\n"
     ]
    }
   ],
   "source": [
    "#Classic method for outlier detection\n",
    "#|(x - mean)/ sd| > 3\n",
    "print(abs((x - np.mean(x))/ np.std(x) > 3))\n",
    "print(abs((y - np.mean(y))/ np.std(y) > 3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "b1e1d2c6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[False False False False False False False False False False False False\n",
      " False False False  True]\n",
      "[False False False False False False False False  True  True]\n"
     ]
    }
   ],
   "source": [
    "#Tukey's method\n",
    "from scipy.stats import iqr\n",
    "#x > q(0.75) + 1.5 * IQR(x)\n",
    "#x < q(0.25) - 1.5 * IQR(x)\n",
    "print(x > np.quantile(x, 0.75) + 1.5 * iqr(x))\n",
    "print(y > np.quantile(y, 0.75) + 1.5 * iqr(y))"
   ]
  }
 ],
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