Method 2 - Frequentist T-Test Analysis of AB Testing results on Conversion Rate and CTR.ipynb

{
 "cells": [
  {
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   "source": [
    "#@author Rachel Peng\n",
    "#@version 1.0\n",
    "#@changelog\n",
    "#version 1.0\n",
    "#Initial version\n",
    "\n",
    "# Import the packages\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from scipy import stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Load data\n",
    "df_e = pd.read_csv('Experiment Data.csv', skiprows=1, usecols = ['Impressions','Clicks','Conversions'])\n",
    "df_c = pd.read_csv('Control Data.csv', skiprows=1, usecols = ['Impressions','Clicks','Conversions'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Impressions</th>\n",
       "      <th>Clicks</th>\n",
       "      <th>Conversions</th>\n",
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       "      <th>3</th>\n",
       "      <td>109</td>\n",
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       "      <th>4</th>\n",
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       "      <th>5</th>\n",
       "      <td>3</td>\n",
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       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
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       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>5</td>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
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       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>1</td>\n",
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       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
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       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
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       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>7</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
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       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>32</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
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       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
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       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
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       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
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       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
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       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>15</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
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       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2006</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2007</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2008</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2010</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2011</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2014</th>\n",
       "      <td>65</td>\n",
       "      <td>5</td>\n",
       "      <td>0.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2019</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2021</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2022</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2025</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2026</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2027</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2028</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2029</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2030</th>\n",
       "      <td>30</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2031</th>\n",
       "      <td>324594</td>\n",
       "      <td>1414</td>\n",
       "      <td>82.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2032</th>\n",
       "      <td>1251081</td>\n",
       "      <td>5253</td>\n",
       "      <td>793.67</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2033</th>\n",
       "      <td>2925346</td>\n",
       "      <td>9925</td>\n",
       "      <td>1,120.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2034</th>\n",
       "      <td>372149</td>\n",
       "      <td>5702</td>\n",
       "      <td>941.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2035</th>\n",
       "      <td>2553197</td>\n",
       "      <td>4223</td>\n",
       "      <td>179.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>2036 rows × 3 columns</p>\n",
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      "text/plain": [
       "      Impressions  Clicks Conversions\n",
       "0               0       0         0.0\n",
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       "7               0       0         0.0\n",
       "8               4       0         0.0\n",
       "9               5       0         0.0\n",
       "10              0       0         0.0\n",
       "11              1       0         0.0\n",
       "12              1       0         0.0\n",
       "13              3       0         0.0\n",
       "14              2       0         0.0\n",
       "15              0       0         0.0\n",
       "16              4       0         0.0\n",
       "17              7       0         0.0\n",
       "18              0       0         0.0\n",
       "19             32       0         0.0\n",
       "20              1       0         0.0\n",
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       "23              0       0         0.0\n",
       "24              0       0         0.0\n",
       "25              1       0         0.0\n",
       "26              0       0         0.0\n",
       "27              0       0         0.0\n",
       "28              0       0         0.0\n",
       "29             15       0         0.0\n",
       "...           ...     ...         ...\n",
       "2006            0       0         0.0\n",
       "2007            0       0         0.0\n",
       "2008            0       0         0.0\n",
       "2009            0       0         0.0\n",
       "2010            0       0         0.0\n",
       "2011            0       0         0.0\n",
       "2012            0       0         0.0\n",
       "2013            0       0         0.0\n",
       "2014           65       5         0.5\n",
       "2015            0       0         0.0\n",
       "2016            0       0         0.0\n",
       "2017            0       0         0.0\n",
       "2018            0       0         0.0\n",
       "2019            0       0         0.0\n",
       "2020            0       0         0.0\n",
       "2021            0       0         0.0\n",
       "2022            0       0         0.0\n",
       "2023            0       0         0.0\n",
       "2024            0       0         0.0\n",
       "2025            0       0         0.0\n",
       "2026            0       0         0.0\n",
       "2027            0       0         0.0\n",
       "2028            0       0         0.0\n",
       "2029            0       0         0.0\n",
       "2030           30       0         0.0\n",
       "2031       324594    1414       82.25\n",
       "2032      1251081    5253      793.67\n",
       "2033      2925346    9925     1,120.0\n",
       "2034       372149    5702       941.0\n",
       "2035      2553197    4223       179.0\n",
       "\n",
       "[2036 rows x 3 columns]"
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   "cell_type": "code",
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       "      <th>4</th>\n",
       "      <td>12</td>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
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       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>97</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
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       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
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       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>101</td>\n",
       "      <td>2</td>\n",
       "      <td>0.0</td>\n",
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       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
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       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>5</td>\n",
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       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>128</td>\n",
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       "      <td>0.0</td>\n",
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       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>232</td>\n",
       "      <td>7</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>80</td>\n",
       "      <td>2</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>113</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>6</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>18</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>44</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2014</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2019</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2021</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2022</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2025</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2026</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2027</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2028</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2029</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2030</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2031</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2032</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2033</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2034</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2035</th>\n",
       "      <td>34</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2036</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2037</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2038</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2039</th>\n",
       "      <td>489885</td>\n",
       "      <td>1784</td>\n",
       "      <td>164.83</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2040</th>\n",
       "      <td>1251081</td>\n",
       "      <td>5253</td>\n",
       "      <td>793.67</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2041</th>\n",
       "      <td>2925346</td>\n",
       "      <td>9925</td>\n",
       "      <td>1,120.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2042</th>\n",
       "      <td>372149</td>\n",
       "      <td>5702</td>\n",
       "      <td>941.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2043</th>\n",
       "      <td>2553197</td>\n",
       "      <td>4223</td>\n",
       "      <td>179.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>2044 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      Impressions  Clicks Conversions\n",
       "0               0       0         0.0\n",
       "1               3       0         0.0\n",
       "2               0       0         0.0\n",
       "3               0       0         0.0\n",
       "4              12       0         0.0\n",
       "5               0       0         0.0\n",
       "6               2       0         0.0\n",
       "7               2       0         0.0\n",
       "8              97       1         0.0\n",
       "9               0       0         0.0\n",
       "10            101       2         0.0\n",
       "11              0       0         0.0\n",
       "12              5       0         0.0\n",
       "13            128       2         0.0\n",
       "14              1       0         0.0\n",
       "15            232       7         0.0\n",
       "16              0       0         0.0\n",
       "17              0       0         0.0\n",
       "18             80       2         1.0\n",
       "19              0       0         0.0\n",
       "20              0       0         0.0\n",
       "21              2       0         0.0\n",
       "22            113       1         0.0\n",
       "23              6       0         0.0\n",
       "24              2       0         0.0\n",
       "25              0       0         0.0\n",
       "26             18       0         0.0\n",
       "27              0       0         0.0\n",
       "28             44       1         0.0\n",
       "29              0       0         0.0\n",
       "...           ...     ...         ...\n",
       "2014            0       0         0.0\n",
       "2015            0       0         0.0\n",
       "2016            0       0         0.0\n",
       "2017            0       0         0.0\n",
       "2018            0       0         0.0\n",
       "2019            0       0         0.0\n",
       "2020            0       0         0.0\n",
       "2021            0       0         0.0\n",
       "2022            0       0         0.0\n",
       "2023            0       0         0.0\n",
       "2024            0       0         0.0\n",
       "2025            0       0         0.0\n",
       "2026            0       0         0.0\n",
       "2027            1       0         0.0\n",
       "2028            0       0         0.0\n",
       "2029            0       0         0.0\n",
       "2030            0       0         0.0\n",
       "2031            0       0         0.0\n",
       "2032            0       0         0.0\n",
       "2033            0       0         0.0\n",
       "2034            0       0         0.0\n",
       "2035           34       0         0.0\n",
       "2036            0       0         0.0\n",
       "2037            0       0         0.0\n",
       "2038            0       0         0.0\n",
       "2039       489885    1784      164.83\n",
       "2040      1251081    5253      793.67\n",
       "2041      2925346    9925     1,120.0\n",
       "2042       372149    5702       941.0\n",
       "2043      2553197    4223       179.0\n",
       "\n",
       "[2044 rows x 3 columns]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Drop last 5 rows\n",
    "df_e.drop(df_e.tail(5).index,inplace=True) \n",
    "df_c.drop(df_c.tail(5).index,inplace=True) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Impressions</th>\n",
       "      <th>Clicks</th>\n",
       "      <th>Conversions</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>12</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>97</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>101</td>\n",
       "      <td>2</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>5</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>128</td>\n",
       "      <td>2</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>232</td>\n",
       "      <td>7</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>80</td>\n",
       "      <td>2</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>113</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>6</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>18</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>44</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2010</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2011</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2014</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2019</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2021</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2022</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2025</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2026</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2027</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2028</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2029</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2030</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2031</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2032</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2033</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2034</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2035</th>\n",
       "      <td>34</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2036</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2037</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2038</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>2039 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      Impressions  Clicks Conversions\n",
       "0               0       0         0.0\n",
       "1               3       0         0.0\n",
       "2               0       0         0.0\n",
       "3               0       0         0.0\n",
       "4              12       0         0.0\n",
       "5               0       0         0.0\n",
       "6               2       0         0.0\n",
       "7               2       0         0.0\n",
       "8              97       1         0.0\n",
       "9               0       0         0.0\n",
       "10            101       2         0.0\n",
       "11              0       0         0.0\n",
       "12              5       0         0.0\n",
       "13            128       2         0.0\n",
       "14              1       0         0.0\n",
       "15            232       7         0.0\n",
       "16              0       0         0.0\n",
       "17              0       0         0.0\n",
       "18             80       2         1.0\n",
       "19              0       0         0.0\n",
       "20              0       0         0.0\n",
       "21              2       0         0.0\n",
       "22            113       1         0.0\n",
       "23              6       0         0.0\n",
       "24              2       0         0.0\n",
       "25              0       0         0.0\n",
       "26             18       0         0.0\n",
       "27              0       0         0.0\n",
       "28             44       1         0.0\n",
       "29              0       0         0.0\n",
       "...           ...     ...         ...\n",
       "2009            0       0         0.0\n",
       "2010            0       0         0.0\n",
       "2011            0       0         0.0\n",
       "2012            0       0         0.0\n",
       "2013            0       0         0.0\n",
       "2014            0       0         0.0\n",
       "2015            0       0         0.0\n",
       "2016            0       0         0.0\n",
       "2017            0       0         0.0\n",
       "2018            0       0         0.0\n",
       "2019            0       0         0.0\n",
       "2020            0       0         0.0\n",
       "2021            0       0         0.0\n",
       "2022            0       0         0.0\n",
       "2023            0       0         0.0\n",
       "2024            0       0         0.0\n",
       "2025            0       0         0.0\n",
       "2026            0       0         0.0\n",
       "2027            1       0         0.0\n",
       "2028            0       0         0.0\n",
       "2029            0       0         0.0\n",
       "2030            0       0         0.0\n",
       "2031            0       0         0.0\n",
       "2032            0       0         0.0\n",
       "2033            0       0         0.0\n",
       "2034            0       0         0.0\n",
       "2035           34       0         0.0\n",
       "2036            0       0         0.0\n",
       "2037            0       0         0.0\n",
       "2038            0       0         0.0\n",
       "\n",
       "[2039 rows x 3 columns]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'6.25'"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_c['Conversions'].values.max()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'7.0'"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_e['Conversions'].values.max()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Calculate the total amount of Conversions, clicks and impressions for Experiment group\n",
    "SumConv_e = int (df_e['Conversions'].astype(float).sum())\n",
    "SumClick_e = int (df_e['Clicks'].astype(float).sum())\n",
    "SumImpr_e = int( df_e['Impressions'].astype(float).sum())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total Conversions of Experiment Group 82\n",
      "Total Clicks of Experiment Group 1414\n",
      "Total Impressions of Experiment Group 324594\n"
     ]
    }
   ],
   "source": [
    "# Print out the total amount of Conversions, clicks and impressions for Experiment group\n",
    "print('Total Conversions of Experiment Group', SumConv_e)\n",
    "print('Total Clicks of Experiment Group', SumClick_e)\n",
    "print('Total Impressions of Experiment Group', SumImpr_e)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Calculate the total amount of Conversions, clicks and impressions for Control group\n",
    "SumConv_c = int (df_c['Conversions'].astype(float).sum())\n",
    "SumClick_c = int (df_c['Clicks'].astype(float).sum())\n",
    "SumImpr_c = int( df_c['Impressions'].astype(float).sum())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "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>Clicks</th>\n",
       "      <th>Conversions</th>\n",
       "      <th>Conversion Rate</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
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       "    <tr>\n",
       "      <th>1384</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1385</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1386</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1387</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1388</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1389</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1390</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1391</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1392</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1393</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1394</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1395</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1396</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1397</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1398</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1399</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1400</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1401</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1402</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1403</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1404</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1405</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1406</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1407</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1408</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1409</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1410</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1411</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1412</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1413</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>1414 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      Clicks  Conversions  Conversion Rate\n",
       "0        1.0          1.0              1.0\n",
       "1        1.0          1.0              1.0\n",
       "2        1.0          1.0              1.0\n",
       "3        1.0          1.0              1.0\n",
       "4        1.0          1.0              1.0\n",
       "5        1.0          1.0              1.0\n",
       "6        1.0          1.0              1.0\n",
       "7        1.0          1.0              1.0\n",
       "8        1.0          1.0              1.0\n",
       "9        1.0          1.0              1.0\n",
       "10       1.0          1.0              1.0\n",
       "11       1.0          1.0              1.0\n",
       "12       1.0          1.0              1.0\n",
       "13       1.0          1.0              1.0\n",
       "14       1.0          1.0              1.0\n",
       "15       1.0          1.0              1.0\n",
       "16       1.0          1.0              1.0\n",
       "17       1.0          1.0              1.0\n",
       "18       1.0          1.0              1.0\n",
       "19       1.0          1.0              1.0\n",
       "20       1.0          1.0              1.0\n",
       "21       1.0          1.0              1.0\n",
       "22       1.0          1.0              1.0\n",
       "23       1.0          1.0              1.0\n",
       "24       1.0          1.0              1.0\n",
       "25       1.0          1.0              1.0\n",
       "26       1.0          1.0              1.0\n",
       "27       1.0          1.0              1.0\n",
       "28       1.0          1.0              1.0\n",
       "29       1.0          1.0              1.0\n",
       "...      ...          ...              ...\n",
       "1384     1.0          0.0              0.0\n",
       "1385     1.0          0.0              0.0\n",
       "1386     1.0          0.0              0.0\n",
       "1387     1.0          0.0              0.0\n",
       "1388     1.0          0.0              0.0\n",
       "1389     1.0          0.0              0.0\n",
       "1390     1.0          0.0              0.0\n",
       "1391     1.0          0.0              0.0\n",
       "1392     1.0          0.0              0.0\n",
       "1393     1.0          0.0              0.0\n",
       "1394     1.0          0.0              0.0\n",
       "1395     1.0          0.0              0.0\n",
       "1396     1.0          0.0              0.0\n",
       "1397     1.0          0.0              0.0\n",
       "1398     1.0          0.0              0.0\n",
       "1399     1.0          0.0              0.0\n",
       "1400     1.0          0.0              0.0\n",
       "1401     1.0          0.0              0.0\n",
       "1402     1.0          0.0              0.0\n",
       "1403     1.0          0.0              0.0\n",
       "1404     1.0          0.0              0.0\n",
       "1405     1.0          0.0              0.0\n",
       "1406     1.0          0.0              0.0\n",
       "1407     1.0          0.0              0.0\n",
       "1408     1.0          0.0              0.0\n",
       "1409     1.0          0.0              0.0\n",
       "1410     1.0          0.0              0.0\n",
       "1411     1.0          0.0              0.0\n",
       "1412     1.0          0.0              0.0\n",
       "1413     1.0          0.0              0.0\n",
       "\n",
       "[1414 rows x 3 columns]"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Convert data in Experiment group to 0, 1\n",
    "dfE_1 = pd.DataFrame(columns=['Clicks','Conversions'])\n",
    "dfE_1['Clicks'] = np.ones(int (SumClick_e)).tolist() \n",
    "dfE_1['Conversions'] = np.ones(int(SumConv_e)).tolist() + np.zeros(int (SumClick_e-SumConv_e) ).tolist()\n",
    "dfE_1['Conversion Rate'] = dfE_1['Conversions']/dfE_1['Clicks']\n",
    "dfE_1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Clicks</th>\n",
       "      <th>Impressions</th>\n",
       "      <th>CTR</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>324564</th>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>324565</th>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>324566</th>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>324567</th>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>324568</th>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>324569</th>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>324570</th>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>324571</th>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>324572</th>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>324573</th>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>324574</th>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>324575</th>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>324576</th>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>324577</th>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>324578</th>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>324579</th>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>324580</th>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>324581</th>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>324582</th>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>324583</th>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>324584</th>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>324585</th>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>324586</th>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>324587</th>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>324588</th>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>324589</th>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>324590</th>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>324591</th>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>324592</th>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>324593</th>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>324594 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "        Clicks  Impressions  CTR\n",
       "0          1.0          1.0  1.0\n",
       "1          1.0          1.0  1.0\n",
       "2          1.0          1.0  1.0\n",
       "3          1.0          1.0  1.0\n",
       "4          1.0          1.0  1.0\n",
       "5          1.0          1.0  1.0\n",
       "6          1.0          1.0  1.0\n",
       "7          1.0          1.0  1.0\n",
       "8          1.0          1.0  1.0\n",
       "9          1.0          1.0  1.0\n",
       "10         1.0          1.0  1.0\n",
       "11         1.0          1.0  1.0\n",
       "12         1.0          1.0  1.0\n",
       "13         1.0          1.0  1.0\n",
       "14         1.0          1.0  1.0\n",
       "15         1.0          1.0  1.0\n",
       "16         1.0          1.0  1.0\n",
       "17         1.0          1.0  1.0\n",
       "18         1.0          1.0  1.0\n",
       "19         1.0          1.0  1.0\n",
       "20         1.0          1.0  1.0\n",
       "21         1.0          1.0  1.0\n",
       "22         1.0          1.0  1.0\n",
       "23         1.0          1.0  1.0\n",
       "24         1.0          1.0  1.0\n",
       "25         1.0          1.0  1.0\n",
       "26         1.0          1.0  1.0\n",
       "27         1.0          1.0  1.0\n",
       "28         1.0          1.0  1.0\n",
       "29         1.0          1.0  1.0\n",
       "...        ...          ...  ...\n",
       "324564     0.0          1.0  0.0\n",
       "324565     0.0          1.0  0.0\n",
       "324566     0.0          1.0  0.0\n",
       "324567     0.0          1.0  0.0\n",
       "324568     0.0          1.0  0.0\n",
       "324569     0.0          1.0  0.0\n",
       "324570     0.0          1.0  0.0\n",
       "324571     0.0          1.0  0.0\n",
       "324572     0.0          1.0  0.0\n",
       "324573     0.0          1.0  0.0\n",
       "324574     0.0          1.0  0.0\n",
       "324575     0.0          1.0  0.0\n",
       "324576     0.0          1.0  0.0\n",
       "324577     0.0          1.0  0.0\n",
       "324578     0.0          1.0  0.0\n",
       "324579     0.0          1.0  0.0\n",
       "324580     0.0          1.0  0.0\n",
       "324581     0.0          1.0  0.0\n",
       "324582     0.0          1.0  0.0\n",
       "324583     0.0          1.0  0.0\n",
       "324584     0.0          1.0  0.0\n",
       "324585     0.0          1.0  0.0\n",
       "324586     0.0          1.0  0.0\n",
       "324587     0.0          1.0  0.0\n",
       "324588     0.0          1.0  0.0\n",
       "324589     0.0          1.0  0.0\n",
       "324590     0.0          1.0  0.0\n",
       "324591     0.0          1.0  0.0\n",
       "324592     0.0          1.0  0.0\n",
       "324593     0.0          1.0  0.0\n",
       "\n",
       "[324594 rows x 3 columns]"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Convert data in Experiment group to 0, 1\n",
    "dfE_2 = pd.DataFrame(columns=['Clicks','Impressions'])\n",
    "dfE_2['Impressions'] = np.ones(int (SumImpr_e)).tolist() \n",
    "dfE_2['Clicks'] = np.ones(int(SumClick_e)).tolist() + np.zeros(int (SumImpr_e-SumClick_e) ).tolist()\n",
    "dfE_2['CTR'] = dfE_2['Clicks']/dfE_2['Impressions']\n",
    "dfE_2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Clicks</th>\n",
       "      <th>Conversions</th>\n",
       "      <th>Conversion Rate</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
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       "      <th>0</th>\n",
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       "      <td>1.0</td>\n",
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       "      <th>4</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
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       "      <th>5</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
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       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
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       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
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       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
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       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
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       "    <tr>\n",
       "      <th>1754</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1755</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1756</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1757</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1758</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1759</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1760</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1761</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1762</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1763</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
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       "    <tr>\n",
       "      <th>1764</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1765</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1766</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1767</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1768</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1769</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1770</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1771</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1772</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1773</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1774</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1775</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1776</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1777</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1778</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1779</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1780</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1781</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1782</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1783</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>1784 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      Clicks  Conversions  Conversion Rate\n",
       "0        1.0          1.0              1.0\n",
       "1        1.0          1.0              1.0\n",
       "2        1.0          1.0              1.0\n",
       "3        1.0          1.0              1.0\n",
       "4        1.0          1.0              1.0\n",
       "5        1.0          1.0              1.0\n",
       "6        1.0          1.0              1.0\n",
       "7        1.0          1.0              1.0\n",
       "8        1.0          1.0              1.0\n",
       "9        1.0          1.0              1.0\n",
       "10       1.0          1.0              1.0\n",
       "11       1.0          1.0              1.0\n",
       "12       1.0          1.0              1.0\n",
       "13       1.0          1.0              1.0\n",
       "14       1.0          1.0              1.0\n",
       "15       1.0          1.0              1.0\n",
       "16       1.0          1.0              1.0\n",
       "17       1.0          1.0              1.0\n",
       "18       1.0          1.0              1.0\n",
       "19       1.0          1.0              1.0\n",
       "20       1.0          1.0              1.0\n",
       "21       1.0          1.0              1.0\n",
       "22       1.0          1.0              1.0\n",
       "23       1.0          1.0              1.0\n",
       "24       1.0          1.0              1.0\n",
       "25       1.0          1.0              1.0\n",
       "26       1.0          1.0              1.0\n",
       "27       1.0          1.0              1.0\n",
       "28       1.0          1.0              1.0\n",
       "29       1.0          1.0              1.0\n",
       "...      ...          ...              ...\n",
       "1754     1.0          0.0              0.0\n",
       "1755     1.0          0.0              0.0\n",
       "1756     1.0          0.0              0.0\n",
       "1757     1.0          0.0              0.0\n",
       "1758     1.0          0.0              0.0\n",
       "1759     1.0          0.0              0.0\n",
       "1760     1.0          0.0              0.0\n",
       "1761     1.0          0.0              0.0\n",
       "1762     1.0          0.0              0.0\n",
       "1763     1.0          0.0              0.0\n",
       "1764     1.0          0.0              0.0\n",
       "1765     1.0          0.0              0.0\n",
       "1766     1.0          0.0              0.0\n",
       "1767     1.0          0.0              0.0\n",
       "1768     1.0          0.0              0.0\n",
       "1769     1.0          0.0              0.0\n",
       "1770     1.0          0.0              0.0\n",
       "1771     1.0          0.0              0.0\n",
       "1772     1.0          0.0              0.0\n",
       "1773     1.0          0.0              0.0\n",
       "1774     1.0          0.0              0.0\n",
       "1775     1.0          0.0              0.0\n",
       "1776     1.0          0.0              0.0\n",
       "1777     1.0          0.0              0.0\n",
       "1778     1.0          0.0              0.0\n",
       "1779     1.0          0.0              0.0\n",
       "1780     1.0          0.0              0.0\n",
       "1781     1.0          0.0              0.0\n",
       "1782     1.0          0.0              0.0\n",
       "1783     1.0          0.0              0.0\n",
       "\n",
       "[1784 rows x 3 columns]"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Convert data in Control group to 0, 1\n",
    "dfC_1 = pd.DataFrame(columns=['Clicks','Conversions'])\n",
    "dfC_1['Clicks'] = np.ones(int (SumClick_c)).tolist() \n",
    "dfC_1['Conversions'] = np.ones(int(SumConv_c)).tolist() + np.zeros(int (SumClick_c-SumConv_c) ).tolist()\n",
    "dfC_1['Conversion Rate'] = dfC_1['Conversions']/dfC_1['Clicks']\n",
    "dfC_1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
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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>Clicks</th>\n",
       "      <th>Impressions</th>\n",
       "      <th>CTR</th>\n",
       "    </tr>\n",
       "  </thead>\n",
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       "    <tr>\n",
       "      <th>489880</th>\n",
       "      <td>0.0</td>\n",
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       "      <th>489881</th>\n",
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       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>489885 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "        Clicks  Impressions  CTR\n",
       "0          1.0          1.0  1.0\n",
       "1          1.0          1.0  1.0\n",
       "2          1.0          1.0  1.0\n",
       "3          1.0          1.0  1.0\n",
       "4          1.0          1.0  1.0\n",
       "5          1.0          1.0  1.0\n",
       "6          1.0          1.0  1.0\n",
       "7          1.0          1.0  1.0\n",
       "8          1.0          1.0  1.0\n",
       "9          1.0          1.0  1.0\n",
       "10         1.0          1.0  1.0\n",
       "11         1.0          1.0  1.0\n",
       "12         1.0          1.0  1.0\n",
       "13         1.0          1.0  1.0\n",
       "14         1.0          1.0  1.0\n",
       "15         1.0          1.0  1.0\n",
       "16         1.0          1.0  1.0\n",
       "17         1.0          1.0  1.0\n",
       "18         1.0          1.0  1.0\n",
       "19         1.0          1.0  1.0\n",
       "20         1.0          1.0  1.0\n",
       "21         1.0          1.0  1.0\n",
       "22         1.0          1.0  1.0\n",
       "23         1.0          1.0  1.0\n",
       "24         1.0          1.0  1.0\n",
       "25         1.0          1.0  1.0\n",
       "26         1.0          1.0  1.0\n",
       "27         1.0          1.0  1.0\n",
       "28         1.0          1.0  1.0\n",
       "29         1.0          1.0  1.0\n",
       "...        ...          ...  ...\n",
       "489855     0.0          1.0  0.0\n",
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       "489857     0.0          1.0  0.0\n",
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       "489860     0.0          1.0  0.0\n",
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       "489862     0.0          1.0  0.0\n",
       "489863     0.0          1.0  0.0\n",
       "489864     0.0          1.0  0.0\n",
       "489865     0.0          1.0  0.0\n",
       "489866     0.0          1.0  0.0\n",
       "489867     0.0          1.0  0.0\n",
       "489868     0.0          1.0  0.0\n",
       "489869     0.0          1.0  0.0\n",
       "489870     0.0          1.0  0.0\n",
       "489871     0.0          1.0  0.0\n",
       "489872     0.0          1.0  0.0\n",
       "489873     0.0          1.0  0.0\n",
       "489874     0.0          1.0  0.0\n",
       "489875     0.0          1.0  0.0\n",
       "489876     0.0          1.0  0.0\n",
       "489877     0.0          1.0  0.0\n",
       "489878     0.0          1.0  0.0\n",
       "489879     0.0          1.0  0.0\n",
       "489880     0.0          1.0  0.0\n",
       "489881     0.0          1.0  0.0\n",
       "489882     0.0          1.0  0.0\n",
       "489883     0.0          1.0  0.0\n",
       "489884     0.0          1.0  0.0\n",
       "\n",
       "[489885 rows x 3 columns]"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Convert data in Control group to 0, 1\n",
    "dfC_2 = pd.DataFrame(columns=['Clicks','Impressions'])\n",
    "dfC_2['Impressions'] = np.ones(int (SumImpr_c)).tolist() \n",
    "dfC_2['Clicks'] = np.ones(int(SumClick_c)).tolist() + np.zeros(int (SumImpr_c-SumClick_c) ).tolist()\n",
    "dfC_2['CTR'] = dfC_2['Clicks']/dfC_2['Impressions']\n",
    "dfC_2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ttest_ind: t = 3.67061  p = 0.000245931\n"
     ]
    }
   ],
   "source": [
    "from scipy.stats import ttest_ind, ttest_ind_from_stats\n",
    "from scipy.special import stdtr\n",
    "# Use scipy.stats.ttest_ind.\n",
    "t, p = ttest_ind(dfC_1['Conversion Rate'], dfE_1['Conversion Rate'], equal_var=False)\n",
    "print(\"ttest_ind: t = %g  p = %g\" % (t, p))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "t-statistics and p-value: t = -4.95817  p = 7.11775e-07\n"
     ]
    }
   ],
   "source": [
    "# Use scipy.stats.ttest_ind.\n",
    "t, p = ttest_ind(dfC_2['CTR'], dfE_2['CTR'], equal_var=False)\n",
    "print(\"t-statistics and p-value: t = %g  p = %g\" % (t, p))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Calculate Means of CTR in both groups\n",
    "dfC_CR_Mean = dfC_1['Conversion Rate'].mean()\n",
    "dfE_CR_Mean = dfE_1['Conversion Rate'].mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean of Conversion Rate in Control Group 0.09192825112107623\n",
      "Mean of Conversion Rate in Experiment Group 0.05799151343705799\n"
     ]
    }
   ],
   "source": [
    "# Print out Means of CTR in both groups\n",
    "print('Mean of Conversion Rate in Control Group', dfC_CR_Mean)\n",
    "print('Mean of Conversion Rate in Experiment Group', dfE_CR_Mean)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Calculate Means of CTR in both groups\n",
    "dfC_CTR_Mean = dfC_2['CTR'].mean()\n",
    "dfE_CTR_Mean = dfE_2['CTR'].mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean of CTR in Control Group 0.0036416710044194045\n",
      "Mean of CTR in Experiment Group 0.004356211143767291\n"
     ]
    }
   ],
   "source": [
    "# Print out Means of CTR in both groups\n",
    "print('Mean of CTR in Control Group', dfC_CTR_Mean)\n",
    "print('Mean of CTR in Experiment Group', dfE_CTR_Mean)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.23372740063231248"
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.std(dfE_1['Conversion Rate'].values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYAAAAD8CAYAAAB+UHOxAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x116ce1898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Histogram graph of Conversion Rate in Control Group\n",
    "import matplotlib.pyplot as plt\n",
    "dfC_1['Conversion Rate'].hist()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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b+p4gyXcA/xH4Z1X1v5OctOsybbXM+XYzXCJiZmaGwWAw9txmNsJNFx4b+/Hj6jPnvhYX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\nACSpUQaAJDXKAJCkRv0/0K0snUvW9IwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1163676d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Histogram graph of Conversion Rate in Experiment Group\n",
    "dfE_1['Conversion Rate'].hist()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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VUuBAucS0FVgWEaeWG+DLgK1l22sRsbQ8NXXlhGN160OS1JCe12Ii4mvACDAvIsZoPwV1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\nQ0OSVM3QkCRVMzQkSdUMDUlStf8Huwn9pQELUO0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x115eb3780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Histogram graph of CTR in Control Group\n",
    "dfC_2['CTR'].hist()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x116cf4e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Histogram graph of CTR in Experiment Group\n",
    "dfE_2['CTR'].hist()\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}