ABtesting_gamedesign.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Mobile Games A/B Testing with Cookie Cats\n",
    "\n",
    "Project Description\n",
    "Cookie Cats is a hugely popular mobile puzzle game developed by Tactile Entertainment. It's a classic \"connect three\" style puzzle game where the player must connect tiles of the same color in order to clear the board and win the level. It also features singing cats. We're not kidding! Check out this short demo:\n",
    "\n",
    "As players progress through the game they will encounter gates that force them to wait some time before they can progress or make an in-app purchase. In this project, we will analyze the result of an A/B test where the first gate in Cookie Cats was moved from level 30 to level 40. In particular, we will analyze the impact on player retention."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dataset is collected from https://www.datacamp.com/projects/184"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import statsmodels as sms\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_csv('cookie_cats.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "---------- Display information about column types and number of null values ----------\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>userid</th>\n",
       "      <th>version</th>\n",
       "      <th>sum_gamerounds</th>\n",
       "      <th>retention_1</th>\n",
       "      <th>retention_7</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>column type</th>\n",
       "      <td>int64</td>\n",
       "      <td>object</td>\n",
       "      <td>int64</td>\n",
       "      <td>bool</td>\n",
       "      <td>bool</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>null values (nb)</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>null values (%)</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 userid version sum_gamerounds retention_1 retention_7\n",
       "column type       int64  object          int64        bool        bool\n",
       "null values (nb)      0       0              0           0           0\n",
       "null values (%)       0       0              0           0           0"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "tab_info = pd.DataFrame(df.dtypes).T.rename(index={0:'column type'})\n",
    "tab_info = tab_info.append(pd.DataFrame(df.isnull().sum()).T.rename(index={0:'null values (nb)'}))\n",
    "tab_info = tab_info.append(pd.DataFrame(df.isnull().sum()/df.shape[0]*100).T.\n",
    "                         rename(index={0:'null values (%)'}))\n",
    "print ('-' * 10 + \" Display information about column types and number of null values \" + '-' * 10 )\n",
    "print \n",
    "display(tab_info)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2. The AB-test data\n",
    "The data we have is from 90,189 players that installed the game while the AB-test was running. The variables are:\n",
    "\n",
    "userid - a unique number that identifies each player.\n",
    "version - whether the player was put in the control group (gate_30 - a gate at level 30) or the group with the moved gate (gate_40 - a gate at level 40).\n",
    "sum_gamerounds - the number of game rounds played by the player during the first 14 days after install.\n",
    "retention_1 - did the player come back and play 1 day after installing?\n",
    "retention_7 - did the player come back and play 7 days after installing?\n",
    "When a player installed the game, he or she was randomly assigned to either gate_30 or gate_40. As a sanity check, let's see if there are roughly the same number of players in each AB group."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>userid</th>\n",
       "      <th>version</th>\n",
       "      <th>sum_gamerounds</th>\n",
       "      <th>retention_1</th>\n",
       "      <th>retention_7</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>116</td>\n",
       "      <td>gate_30</td>\n",
       "      <td>3</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>337</td>\n",
       "      <td>gate_30</td>\n",
       "      <td>38</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>377</td>\n",
       "      <td>gate_40</td>\n",
       "      <td>165</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>483</td>\n",
       "      <td>gate_40</td>\n",
       "      <td>1</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>488</td>\n",
       "      <td>gate_40</td>\n",
       "      <td>179</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   userid  version  sum_gamerounds  retention_1  retention_7\n",
       "0     116  gate_30               3        False        False\n",
       "1     337  gate_30              38         True        False\n",
       "2     377  gate_40             165         True        False\n",
       "3     483  gate_40               1        False        False\n",
       "4     488  gate_40             179         True         True"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "#df['retention_1'] = df['retention_1'].map({True: 1, False: 0})\n",
    "#df['retention_7'] = df['retention_7'].map({True: 1, False: 0})\n",
    "df[['retention_1','retention_7']] = df[['retention_1','retention_7']].astype(int)\n",
    "df['version'] = df['version'].map({'gate_30': \"Control\", 'gate_40':\"Experimental\" })"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>userid</th>\n",
       "      <th>version</th>\n",
       "      <th>sum_gamerounds</th>\n",
       "      <th>retention_1</th>\n",
       "      <th>retention_7</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>116</td>\n",
       "      <td>Control</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>337</td>\n",
       "      <td>Control</td>\n",
       "      <td>38</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>377</td>\n",
       "      <td>Experimental</td>\n",
       "      <td>165</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>483</td>\n",
       "      <td>Experimental</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>488</td>\n",
       "      <td>Experimental</td>\n",
       "      <td>179</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   userid       version  sum_gamerounds  retention_1  retention_7\n",
       "0     116       Control               3            0            0\n",
       "1     337       Control              38            1            0\n",
       "2     377  Experimental             165            1            0\n",
       "3     483  Experimental               1            0            0\n",
       "4     488  Experimental             179            1            1"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "count_df = df.groupby('version')['userid'].count().head(100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of Users Percentage\n",
      "--------------------------------------------------\n",
      "Experimental    50.437415\n",
      "Control         49.562585\n",
      "Name: version, dtype: float64\n",
      "Number of Users values count\n",
      "--------------------------------------------------\n",
      "Experimental    45489\n",
      "Control         44700\n",
      "Name: version, dtype: int64\n"
     ]
    }
   ],
   "source": [
    "x = df['version'].value_counts()\n",
    "print(\"Number of Users Percentage\\n{}\\n{}\\nNumber of Users values count\\n{}\\n{}\".format(\n",
    "      50*\"-\", x / len(df.index) * 100, 50*\"-\", x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "plot_df = df.groupby('sum_gamerounds')['userid'].count().head(100).reset_index()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'User Count')"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e0a2eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "ax = plot_df.plot(x ='sum_gamerounds' ,y ='userid')\n",
    "ax.set_xlabel('Sum Gamerounds', fontsize=14)\n",
    "ax.set_ylabel('User Count',  fontsize=14)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def ecdf(data):\n",
    "    n= len(data)\n",
    "    x = np.sort(data)\n",
    "    y = np.arange(1,n+1)/n\n",
    "    return x,y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a1ebb58d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_test , y_test = ecdf(df['sum_gamerounds'])\n",
    "mean = np.mean(df['sum_gamerounds'])\n",
    "std = np.std(df['sum_gamerounds'])\n",
    "\n",
    "samples = np.random.poisson(mean,  size=100000)\n",
    "\n",
    "x_normal , y_normal = ecdf(samples)\n",
    "\n",
    "_ =plt.plot(x_test, y_test, marker='.', linestyle='none')\n",
    "_ =plt.plot(x_normal , y_normal, marker='.', linestyle='none')\n",
    "_ = plt.xlabel('Sum Gamerounds', fontsize=14)\n",
    "_ = plt.ylabel('Probability', fontsize=14)\n",
    "_ = plt.xlim(-200,200)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11474efd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Generate sample data\n",
    "y1 = df['sum_gamerounds'][df['version']=='Control']\n",
    "y2 = df['sum_gamerounds'][df['version']=='Experimental']\n",
    "\n",
    "\n",
    "# Plot regular histograms\n",
    "plt.figure()\n",
    "plt.hist(y1, facecolor='blue', range=[0,100], alpha = .5, bins =20, align='mid', label='Control Group', normed = True)\n",
    "plt.hist(y2, facecolor='pink', range=[0,100], alpha = .5,bins =20, align='mid', label='Experimental Group', normed = True)\n",
    "\n",
    "plt.xlabel('Sum Gamerounds', fontsize=14)\n",
    "plt.ylabel('User Count', fontsize=14)\n",
    "plt.grid(color='black', linestyle='-', linewidth=.1, axis = 'y')\n",
    "plt.legend(loc='upper right')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_cr = df.groupby('version').agg({'retention_1':sum , 'retention_7':sum,'userid':'count'}).reset_index()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>version</th>\n",
       "      <th>retention_1</th>\n",
       "      <th>retention_7</th>\n",
       "      <th>userid</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Control</td>\n",
       "      <td>20034</td>\n",
       "      <td>8502</td>\n",
       "      <td>44700</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Experimental</td>\n",
       "      <td>20119</td>\n",
       "      <td>8279</td>\n",
       "      <td>45489</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        version  retention_1  retention_7  userid\n",
       "0       Control        20034         8502   44700\n",
       "1  Experimental        20119         8279   45489"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_cr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_cr['Conversion_rate1'] = df_cr['retention_1']/(df_cr['userid'])\n",
    "df_cr['Conversion_rate7'] = df_cr['retention_7']/(df_cr['userid'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>version</th>\n",
       "      <th>retention_1</th>\n",
       "      <th>retention_7</th>\n",
       "      <th>userid</th>\n",
       "      <th>Conversion_rate1</th>\n",
       "      <th>Conversion_rate7</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Control</td>\n",
       "      <td>20034</td>\n",
       "      <td>8502</td>\n",
       "      <td>44700</td>\n",
       "      <td>0.448188</td>\n",
       "      <td>0.190201</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Experimental</td>\n",
       "      <td>20119</td>\n",
       "      <td>8279</td>\n",
       "      <td>45489</td>\n",
       "      <td>0.442283</td>\n",
       "      <td>0.182000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        version  retention_1  retention_7  userid  Conversion_rate1  \\\n",
       "0       Control        20034         8502   44700          0.448188   \n",
       "1  Experimental        20119         8279   45489          0.442283   \n",
       "\n",
       "   Conversion_rate7  \n",
       "0          0.190201  \n",
       "1          0.182000  "
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_cr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>userid</th>\n",
       "      <th>version</th>\n",
       "      <th>sum_gamerounds</th>\n",
       "      <th>retention_1</th>\n",
       "      <th>retention_7</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>116</td>\n",
       "      <td>Control</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>337</td>\n",
       "      <td>Control</td>\n",
       "      <td>38</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>377</td>\n",
       "      <td>Experimental</td>\n",
       "      <td>165</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>483</td>\n",
       "      <td>Experimental</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>488</td>\n",
       "      <td>Experimental</td>\n",
       "      <td>179</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   userid       version  sum_gamerounds  retention_1  retention_7\n",
       "0     116       Control               3            0            0\n",
       "1     337       Control              38            1            0\n",
       "2     377  Experimental             165            1            0\n",
       "3     483  Experimental               1            0            0\n",
       "4     488  Experimental             179            1            1"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It appears that there was a slight decrease in 1-day retention when the gate was moved to level 40 (44.2%) compared to the control when it was at level 30 (44.8%). It's a small change, but even small changes in retention can have a large impact. But while we are certain of the difference in the data, how certain should we be that a gate at level 40 will be worse in the future?\n",
    "\n",
    "There are a couple of ways we can get at the certainty of these retention numbers. Here we will use bootstrapping: We will repeatedly re-sample our dataset (with replacement) and calculate 1-day retention for those samples. The variation in 1-day retention will give us an indication of how uncertain the retention numbers are."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1147beac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "boot_1d = []\n",
    "iterations =500\n",
    "for i in range(iterations):\n",
    "    boot_mean = df.sample(frac=1, replace=True).groupby('version')['retention_1'].mean()\n",
    "    boot_1d.append(boot_mean)\n",
    "    \n",
    "# Transforming the list to a DataFrame\n",
    "boot_1d = pd.DataFrame(boot_1d)\n",
    "    \n",
    "# A Kernel Density Estimate plot of the bootstrap distributions\n",
    "# ... YOUR CODE FOR TASK 6 ...\n",
    "\n",
    "_=  boot_1d.plot.kde() "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>version</th>\n",
       "      <th>Control</th>\n",
       "      <th>Experimental</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>retention_1</th>\n",
       "      <td>0.448811</td>\n",
       "      <td>0.443628</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>retention_1</th>\n",
       "      <td>0.445459</td>\n",
       "      <td>0.440185</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>retention_1</th>\n",
       "      <td>0.452219</td>\n",
       "      <td>0.439168</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>retention_1</th>\n",
       "      <td>0.447803</td>\n",
       "      <td>0.443191</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>retention_1</th>\n",
       "      <td>0.450079</td>\n",
       "      <td>0.443688</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "version       Control  Experimental\n",
       "retention_1  0.448811      0.443628\n",
       "retention_1  0.445459      0.440185\n",
       "retention_1  0.452219      0.439168\n",
       "retention_1  0.447803      0.443191\n",
       "retention_1  0.450079      0.443688"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "boot_1d.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "7. Zooming in on the difference\n",
    "These two distributions above represent the bootstrap uncertainty over what the underlying 1-day retention could be for the two AB-groups. Just eyeballing this plot, we can see that there seems to be some evidence of a difference, albeit small. Let's zoom in on the difference in 1-day retention\n",
    "\n",
    "(Note that in this notebook we have limited the number of bootstrap replication to 500 to keep the calculations quick. In \"production\" we would likely increase this to a much larger number, say, 10 000.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compare how much larger (in%) Control results is compared to Experimental results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a1ebc0198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "boot_1d['diff'] = (boot_1d['Control']- boot_1d['Experimental'])/boot_1d['Experimental']*100\n",
    "ax = boot_1d['diff'].plot.kde()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    ". The probability of a difference¶\n",
    "\n",
    "From this chart, we can see that the most likely % difference is around 1% - 2%, and that most of the distribution is above 0%, in favor of a gate at level 30. But what is the probability that the difference is above 0%? Let's calculate that as well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.958\n"
     ]
    }
   ],
   "source": [
    "# Calculating the probability that 1-day retention is greater when the gate is at level 30\n",
    "prob = (boot_1d['diff'] > 0).sum() / len(boot_1d['diff'])\n",
    "# Pretty printing the probability\n",
    "print(prob)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a1e9af588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "boot_7d = []\n",
    "iterations =500\n",
    "for i in range(iterations):\n",
    "    boot_mean = df.sample(frac=1, replace=True).groupby('version')['retention_7'].mean()\n",
    "    boot_7d.append(boot_mean)\n",
    "    \n",
    "# Transforming the list to a DataFrame\n",
    "boot_7d = pd.DataFrame(boot_7d)\n",
    "    \n",
    "# A Kernel Density Estimate plot of the bootstrap distributions\n",
    "# ... YOUR CODE FOR TASK 6 ...\n",
    "\n",
    "_=  boot_7d.plot.kde() "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,0,'% Difference in means')"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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enBm8sFvfb4nWePssHgdeBqYBn3D36939B+7+BaBojNViQE3C42qgcbyFuXtj8LMeeAFYOUqb+9291t1rKyoqxrtpyUANbcMn5KXXngXAVedVsHF/Kyd6dVEkic549yz+1d2Xu/tX3f0wgJnlAwT/+x/NRmCpmS0yszzgVmBco5rMrHR4+2ZWDlwB7BxnrSLv09DaTW62Mae4IOpSTtuvnFdB/6Dz6t7mqEuRDDbesPifoyxbf6oV3H0AuBN4GtgFPOzuO8zsHjO7HsDM1phZDLgZuM/MdgSrLwPqzGwb8DzwNXdXWMgZi7V1UVVSSHbWaEdHU1vtgjKm52Xzwls6FCXRyTnVk2Y2l3indKGZreTdfohi4oekTsndnwSeHLHs7oT7G4kfnhq53qvAhcm2LzJeDW3daXkICiAvJ4vLzynn5T0KC4nOKcMC+BjxTu1q4O8Tlh8H/iKkmkQm3IGWk1x3YWXUZZyxy5fM4pmdR4m1daXViYUydZwyLNz9QeBBM7vR3R+bpJpEJlR7Vx/tXf0sKp8edSln7AOLZwHwWn0r1asVFjL5kh2G+oy7fxdYaGZfHPm8u//9KKuJpJS3m08CsHBW+obFeXNmUDotl/X1Ldy4+n1HbkVCl+ww1PBv11jDY0VS3v6WICzSeM8iK8u4dNEsNtS3RF2KZKhkh6HuC35+ZXLKEZl4bzd3kWWpf9GjZD6wuIyndhyhobUrbTvrJX2N96S8e82s2MxyzexZM2s2s8+EXZzIRNjffJJ5JYXk52RHXcpZuWxJOQCvvd0acSWSicZ7nsU17t4J/BrxM7PPBf5baFWJTKD9LSfTunN72NLZRZRNz9OhKInEeMNieLLAjwPfd3f910bSgrvzdvPJtO7cHpaVZaxeUMrmA21RlyIZaLxh8Z9m9iZQCzxrZhVAT3hliUyM1pN9HO8ZSOvO7USrF5RS33yS1pN9UZciGWa8U5TfBVwG1Lp7P3CSEdemEElFwyOhFpVPjQ7h1QtKAbR3IZMu2dDZRMuIn2+RuM6/T3A9IhOqvin9z7FIdGHVTHKzjU0H27h6+Zyoy5EMMq6wMLPvAEuArcBgsNhRWEiK23PsBHnZWcyfIkNNC3KzWT5vJpu0ZyGTbLx7FrXAcnc/nYsXiURuz9HjLK6YTk72uK/zlfJWzy/l/752gP7BIXKn0PuS1Dbeb9obwNwwCxEJw1tHT3DunBlRlzGhVi8opXdgiJ2NnVGXIhlkvGFRDuw0s6fN7InhW5iFiZytk70DHGrvZunsqTVbzaoFJQA6FCWTaryHob4cZhEiYdh77AQAS6fYnkXlzEKqSgrZfLCN32ZR1OVIhhhXWLj7i2a2AFjq7j83s2lAes+dIFPennfCYmrtWQCsnF+i4bMyqcY7N9TvAo8C9wWLqoAfhlWUyETYc/Q4edlZLJgiI6ESrV5QSmNHD4c7uqMuRTLEePss/hC4AugEcPc9wOywihKZCHuOnZhyI6GGrZo/fHJee8SVSKYY729Rr7u/M79AcGKehtFKStt95PiU668YtqyymPycLLYc1KEomRzjDYsXzewvgEIz+yjwCPCf4ZUlcnbau/o41N7N8sriqEsJRV5OFhdWzWSzwkImyXjD4i6gCdgO/B7wJPBXYRUlcraGz0FYMW9qhgXAqgWlvNHYSe/AYPLGImdpvKOhhszsh8AP3b0p5JpEztqODAiLlTUl3B+cnLcy6MMQCcsp9yws7stm1gy8Cew2syYzu3tyyhM5M280dlA5s4BZRflRlxKaVcMz0B5UJ7eEL9lhqD8mPgpqjbvPcvcy4FLgCjP7k9CrEzlDOxo7WTFvZtRlhGpOcQHzZhaok1smRbKw+K/Abe7+9vACd68HPhM8J5JyuvoG2Nd0Ykofghq2ckEpW7RnIZMgWVjkunvzyIVBv0XuKO1FIrfr8HHc4YKqqb1nAfF+i0Pt3Rzt1IUrJVzJwuJU127UdR0lJb1xqAOY2p3bw4b7LXQoSsKWLCwuNrPOUW7HgQsno0CR07X5YBtzivOpnFkQdSmhWzGvmLzsLHVyS+hOGRbunu3uxaPcZrh70sNQZrbOzHab2V4zu2uU5z9kZpvNbMDMbhrx3O1mtie43X76b00y1aYDbayaX4qZRV1K6PJzsllRVaw9CwldaJPmmFk28E3gWmA5cJuZLR/R7CDwWeB7I9YtA75EfOTVWuBLZqaB5JLUseM9xNq635k7KROsml/K67EO+gaGoi5FprAwZ1hbC+x19/pgXqmHgBsSG7j7fnd/HRj5Lf8Y8Iy7t7p7G/AMsC7EWmWKGJ5Yb/hYfiZYOb+E3oEh3jyiK+dJeMIMiyqgIeFxLFgW9rqSwbYcbCMvO4sLqqZ+5/awd2eg1aEoCU+YYTHaAePxzlQ7rnXN7A4zqzOzuqYmzUIi8c7tFVXF5OdkzrW55pUUMre4gC0N6uSW8IQZFjGgJuFxNdA4keu6+/3uXuvutRUVFWdcqEwNfQNDbIt1ZFR/xbCV80s0A62EKsyw2AgsNbNFZpYH3Ao8Mc51nwauMbPSoGP7mmCZyJh2NMY7eTMxLFbNL6WhtZum471RlyJTVGhh4e4DwJ3E/8jvAh529x1mdo+ZXQ9gZmvMLAbcDNxnZjuCdVuBvyYeOBuBe4JlImPaUB//iqxZlHlhsXJ+CaCT8yQ845qi/Ey5+5PEr32RuOzuhPsbiR9iGm3dB4AHwqxPppb19S2cM7uI2TOm/sl4I11QNZPcbGPzwXauWTE36nJkCpp6FyeWjNQ/OETd/lYuWzwr6lIiUZCbzfJKnZwn4VFYyJTweqyDrr5BLluSmWEBsDI4OW9gUCfnycRTWMiUsKG+BYAPZOieBcRPROzuH+TNI8ejLkWmIIWFTAnr97Vw/twZlE3Pi7qUyKysUSe3hEdhIWmvd2CQugOtGb1XAVBdWkjFjHzNQCuhUFhI2tvW0EFP/1DGh4WZsbKmRHsWEgqFhaS99ftaMIMPLC6LupTIrVpQyv6WLlpO6OQ8mVgKC0l76+ubWTa3mJJpmdtfMaw2mG13437tXcjEUlhIWuvpH2TzwfaMHjKb6KLqEgpys3jt7ZaoS5EpRmEhaW3LwXb6BoYy9mS8kfJyslg1v5TX6jU7jkwshYWktfX1LWQZrFV/xTsuXTSLXUc66ejqj7oUmUIUFpLWNuxr4YKqmRQXJL0kfMa4dHEZ7rBxv/YuZOIoLCRtdfcNsqWhLeOHzI50SU0JeTlZ75zVLjIRFBaStjYdaKN/0NVfMUJBbjaX1JTw2tvas5CJo7CQtLW+vpnsLKN2YeZdvyKZDywqY0djB5096reQiaGwkLT1i70tXFJTwgz1V7zPpYtnMeSwSedbyARRWEha6ujuZ3usnSvOKY+6lJS0an4pudmmfguZMAoLSUsb6lsYcrhSYTGqwrxsVtaU8sq+5qhLkSlCYSFp6ZW9zUzLi3fkyug+uLScNw51ap4omRAKC0lLv9jbzNpFZeTl6Cs8liuXxve6XtmnQ1Fy9vSbJmmnsb2b+qaTOgSVxEXVJRQX5PCLPU1RlyJTgMJC0s4re+PH4dW5fWrZWcYV55Tz8p5m3D3qciTNKSwk7byyt5nyojzOmzMj6lJS3pVLyznc0cO+ppNRlyJpTmEhacXdeWVfC5cvKScry6IuJ+V9aGkFAC/rUJScJYWFpJU9x07QdLxX/RXjVFM2jQWzpvGLPRpCK2dHYSFpZfiP3hVLFRbjdeU55Wyob6FvYCjqUiSNKSwkrbyyt5lF5dOpKimMupS0cdV5sznZN8gvNbGgnAWFhaSN3oFB1te3cMU5mmX2dFx5Tjn5OVn8fNfRqEuRNKawkLTxy7db6eob5MPnz466lLRSmJfNFeeU8+ybRzWEVs5YqGFhZuvMbLeZ7TWzu0Z5Pt/MfhA8/5qZLQyWLzSzbjPbGtz+Jcw6JT08/2YTeTlZXLZY/RWn6yPLZtPQ2s2eYyeiLkXSVGhhYWbZwDeBa4HlwG1mtnxEs88Bbe5+DvAPwN8mPLfP3S8Jbp8Pq05JHy/sPsZli2dRmJcddSlp5yPnzwHQoSg5Y2HuWawF9rp7vbv3AQ8BN4xocwPwYHD/UeAjZqbB8/I++5tPUt98kl89ryLqUtLS3JkFXFBVzLO7jkVdiqSpMMOiCmhIeBwLlo3axt0HgA5guPdykZltMbMXzeyDo72Amd1hZnVmVtfUpJOOprIXdsf/yF11nvorztRHzp/D5oNtmoVWzkiYYTHaHsLI3rWx2hwG5rv7SuCLwPfMrPh9Dd3vd/dad6+tqND/OKey53c3sbh8OgvLp0ddStr66PI5uMNzb2rvQk5fmGERA2oSHlcDjWO1MbMcYCbQ6u697t4C4O6bgH3AuSHWKinsRO8A6+tbtFdxllbMK6aqpJCn3jgSdSmShsIMi43AUjNbZGZ5wK3AEyPaPAHcHty/CXjO3d3MKoIOcsxsMbAUqA+xVklhz715jL6BIdZdMDfqUtKamfHxC+fy0p4mOrr7oy5H0kxoYRH0QdwJPA3sAh529x1mdo+ZXR80+zdglpntJX64aXh47YeA181sG/GO78+7u04/zVA/3X6Yihn5rF5QGnUpae+6i+bRP+g8s1OjouT05IS5cXd/EnhyxLK7E+73ADePst5jwGNh1ibpoatvgOd3H+Pm1TVka5bZs3Zx9UyqSgr5yeuN3LS6OupyJI3oDG5JaS/sbqKnf4hrL9QhqIlgZvzaRZW8vKeZ9q6+qMuRNKKwkJT2k+2HmTU9j7ULy6IuZcq47qJKBoacn+3QoSgZP4WFpKzOnn5+vvMo6y6YS062vqoT5cKqmSyYNY0fbj0UdSmSRvQbKCnrx9sO0zswxM21Nckby7iZGb++sppX97XQ0NoVdTmSJhQWkrIe3dTA0tlFXFw9M+pSppwbV1dhBo9v1t6FjI/CQlLSvqYTbD7Yzk2rq9F0YROvunQaly+ZxaObGxga0rTlkpzCQlLSdzccIDfb+NSqkdOJyUS5eXUNDa3dvKYr6Mk4KCwk5Rzv6eeRuhjXXVjJ7BkFUZczZX1sxVxm5OfwSF1D8saS8RQWknIe3RTjRO8An71iUdSlTGmFedncsHIeP95+WDPRSlIKC0kpA4ND/J9X9nNJTQmX1JREXc6Ud/tlC+kbGOKhjdq7kFNTWEhK+eHWRg62dvEHVy2JupSMsHTODK48p5zvrD9A/+BQ1OVIClNYSMoYGBzin5/bw/LKYj66fE7U5WSM2y9fyJHOHp7eoanLZWwKC0kZP9rayIGWLv6fq5dquOwk+vD5s1kwaxr3vViPu4bRyugUFpISevoH+ftn3mJ5ZTHXaK9iUmVnGX9w1RK2H+rghd26PLGMTmEhKeH+l+o51N7N//i15dqriMCnVlZTVVLIPz67R3sXMiqFhUTucEc333phHx+/cC6XLZkVdTkZKS8ni9+/aglbG9p5aU9z1OVIClJYSKTcna88sZNBd/782mVRl5PRbq6tprq0kK8+uYsBjYySERQWEqmfbD/MUzuO8MWPnktN2bSoy8lo+TnZ/MXHl/HmkeP8QGd1ywgKC4lMy4levvSjHVxUPZPfuVJna6eCay+Yy9pFZfzdz96io6s/6nIkhSgsJBJDQ86fPbKN4z0D3HvTRbq4UYowM770ieV0dPdzz493Rl2OpBD9hkok/vUX9Ty/u4m/vG4Z588tjrocSbBi3kz+4KolPLY5xs90op4EFBYy6V7d18y9T+1m3Yq5/NfLFkRdjoziCx9eyrLKYv77Y6/ranoCKCxkku09doLPf2cTi8qnc+/NF+mcihSVl5PF//ubqxgYcu74zia6+gaiLkkiprCQSdPY3s1vffuX5OVk8cBn11BckBt1SXIKi8qn80+3rWT3kU5+99/r6OkfjLokiZDCQiZFrK2LW+5fT/vJfv7t9jUaJpsmfvW82Xz9pot5ZW8Lv/vvdRzv0QipTKWwkNBtj3Vw07fW09HVz3d/51Iu1nUq0sqNq6u598aLeHVfCzd9a736MDKUwkJCMzTkfGf9fm76l1fJzjIeuuMyBUWa+vSaGr79W2to7Ojm4//0Mo9timkOqQyjsJBQbNzfyi33r+d//GgHaxeV8aM7r2D5PA21WZIwAAALP0lEQVSRTWcfXFrBT77wQc6fO4M/fWQbn/m319jR2BF1WTJJLMz/HZjZOuAfgWzgX939ayOezwf+HVgNtAC3uPv+4Lk/Bz4HDAJ/5O5Pn+q1amtrva6ubsLfg4zP4JCz63AnG+pb+NHWRrYf6qC8KJ8/u+ZcbllTo1FPU8hgsMf4jWf30NHdz7UXzOVzVy5i1fxS/TunITPb5O61SduFFRZmlg28BXwUiAEbgdvcfWdCmz8ALnL3z5vZrcCn3P0WM1sOfB9YC8wDfg6c6+5jDsdQWITH3Wnr6qehtYuGti4OtXVzpLOHIx09HO7o4WhnD8eO9zI4FP8uLa8s5tO11dyyZj6FedkRVy9h6eju574X9/HdDQfo7Bng/Lkz+MTF87hm+RzOmV102sHROzBI68k+Wk704Q6FeVkU5edSMSOf7CyFUFhSISwuA77s7h8LHv85gLt/NaHN00Gb9WaWAxwBKoC7Etsmthvr9RQWZ2ZoyDnRN0BHVz/tXf00dnTT0NpFrK2bWFsXDa3xnyf73pvTRfk5zJ1ZQOXMAuYUx38uqSji0sVlVM4sjOjdSBRO9g7w+OYY/7HlEJsPtgNQMi2Xi6pLWFA2jcqSAqblZpOTnUVX3wDHewZo7+qn5WQvzcf7aD7RS/OJXjp7Rj+XIzvLmBt8x+aVFDKvpJCqknfvV8zIpyg/h/ycLO3ZnIHxhkVOiDVUAYlTV8aAS8dq4+4DZtYBzAqWbxixblUYRbZ39XHTv8QzaDg434lP572PR2nj77TxhDbv/Tly3VOtn7jOyDacss3odSV7X119AwyN8v+F6XnZ1JRNo6ZsGpefM4ua0mlUlxZSUxb/OUPnSEhgen4O/+WyhfyXyxZyqL2bV/Y0U3eglTcOdbLlYBvHR4RAlsGMglzKi/IoL8pnWWUx5UV5zCrKp7won1lFeWSb0d0/SGdPP4fbe2hs7+ZQezdbG9r56RuH6R98/5c2O8uYlpdNQW422WZkGWRlGVlmZGcZZpA1RcNkWWUx/3zbylBfI8ywGO1fZeS/8FhtxrMuZnYHcAfA/PnzT7c+IP4FO2/OjPdVNFzA8P9UEguycbR5dzs26jrvXTaizSgbev9rJrYYq837P8aRrzk9P5uZhbnv3ObOLKCmdBol03L1vzQ5bVUlhXx6TQ2fXlPzzrKuvgF6+ofoHxxien4O0/Oyz+q7NTTkNJ/opbEjHiLNJ3o50TvAyd4BTvYO0jswyNAQDLoz5M7QkDPk8cfv/ysyNdSUhr83H2ZYxICahMfVQOMYbWLBYaiZQOs418Xd7wfuh/hhqDMpckZBLt/8zVVnsqqIjMO0vBym5U3c9rKyjNnFBcwuLuASDcWeNGEOnd0ILDWzRWaWB9wKPDGizRPA7cH9m4DnPH7M5AngVjPLN7NFwFLglyHWKiIipxDankXQB3En8DTxobMPuPsOM7sHqHP3J4B/A75jZnuJ71HcGqy7w8weBnYCA8AfnmoklIiIhCvU8ywmk0ZDiYicvvGOhtIZ3CIikpTCQkREklJYiIhIUgoLERFJSmEhIiJJTZnRUGbWBBwI+WXKgeaQXyOd6fMZmz6bU9PnM7awP5sF7l6RrNGUCYvJYGZ14xlilqn0+YxNn82p6fMZW6p8NjoMJSIiSSksREQkKYXF6bk/6gJSnD6fsemzOTV9PmNLic9GfRYiIpKU9ixERCQphcVpMrMvm9khM9sa3D4edU1RM7N1ZrbbzPaa2V1R15NqzGy/mW0Pvi8ZPdulmT1gZsfM7I2EZWVm9oyZ7Ql+lkZZY5TG+HxS4m+OwuLM/IO7XxLcnoy6mCiZWTbwTeBaYDlwm5ktj7aqlPSrwfcl8iGQEfs2sG7EsruAZ919KfBs8DhTfZv3fz6QAn9zFBZyttYCe9293t37gIeAGyKuSVKUu79E/No1iW4AHgzuPwh8clKLSiFjfD4pQWFxZu40s9eDXcaM3WUOVAENCY9jwTJ5lwM/M7NNwXXj5b3muPthgODn7IjrSUWR/81RWIzCzH5uZm+McrsB+BawBLgEOAz8XaTFRs9GWaYhdu91hbuvIn6o7g/N7ENRFyRpJSX+5oR2WdV05u5Xj6edmf1/wI9DLifVxYCahMfVQGNEtaQkd28Mfh4zs/8gfujupWirSilHzazS3Q+bWSVwLOqCUom7Hx2+H+XfHO1ZnKbgyzzsU8AbY7XNEBuBpWa2yMzyiF9H/YmIa0oZZjbdzGYM3weuQd+ZkZ4Abg/u3w78KMJaUk6q/M3RnsXpu9fMLiF+qGU/8HvRlhMtdx8wszuBp4Fs4AF33xFxWalkDvAfZgbx37fvuftT0ZYUHTP7PnAVUG5mMeBLwNeAh83sc8BB4OboKozWGJ/PVanwN0dncIuISFI6DCUiIkkpLEREJCmFhYiIJKWwEBGRpBQWIiKSlMJCImdmFWb2i+As+U8mLP+Rmc0bY53EmTj3mNnjiRMYmtm/Dj82s5vNbJeZPR88/n4wdcKfhP3ezoSZzTOzR6OuQySRhs5K5Mzsj4Bu4pMQPuXuV5jZJ4BV7v6VMdb5MnDC3f938PgW4B+BC929aUTbp4C/dffnzWwu8Jq7LziN+nLcfeBM3pvIVKE9C0kF/UAhkA8MmVkO8MfA18e7AXf/AfAz4DcAzOwFM6s1s7uBK4F/MbOvB21mB3skHzSzJWb2VDDJ38tmdn6w/rfN7O+DvZG/Dc7EfsDMNprZlmCeMMzss8FezVPBHs69wzUF1/nYbGbbzOzZYNmo20lkZguHr2dwqu2PWGe/mf0vM1tvZnVmtsrMnjazfWb2+YR2/y147dfN7CsJy38YfAY7Eic7NLMTZvY3wXvYYGZzguU3B3uC28xMU5dkAnfXTbdIb8BM4CdAHfAR4I+A25Os82Xgz0Ys+2PgW8H9F4DaUe4vBN5IWOdZYGlw/1LgueD+t4nPwZMdPP5fwGeC+yXAW8B04LNAffAeCoADxOfKqiA+G++iYJ2yU21nxPt4p8axtj/K57Ef+P3g/j8ArwMzgjqOBcuvIX49ZyP+H8UfAx8aUV8h8ekkZgWPHfhEcP9e4K+C+9uBquH3EfV3SLfwb5ruQyLn7h3AdQDB9Mv/Hfj1YNK0UuDv3H39ODY12gy4Yzc2KwIuBx4JpuOA+N7NsEfcfTC4fw1wvZn9WfC4AJgf3H82eA+Y2U5gQVD3S+7+dvAeW5NsZ9cpSh1t+w2jtBuek2s7UOTux4HjZtZjZiXBa18DbAnaFQFLiU9q+Edm9qlgeU2wvAXo492J6zYBHw3uvwJ828weBh4/Re0yRSgsJNXcDfwNcBvxP07fIz6x3K+OY92VxPdOxisLaHf3S8Z4/mTCfQNudPfdiQ3M7FKgN2HRIPHfK2P0qdpH3U4So23/VO2GRqwzlFDTV939vvcUZHYVcDVwmbt3mdkLxEMMoN/dh9/HO6/t7p8P3vt1wFYzu8TdW07jPUmaUZ+FpAwzWwrMc/cXgWnE/8g57/7hOtW6NxL/X/P3x/t67t4JvG1mNwfbMDO7eIzmTwNfsGAXxMxWJtn8euBXzGxR0L7sDLczkZ4GfjvYo8LMqsxsNvFDXG1BUJwPfCDZhsxsibu/5u53A828d5p6mYIUFpJK/gb4q+D+94kfr98A/O8x2v/J8NBZ4DPAh33ESKhx+E3gc2a2DdjB2JeE/WsgF3g96Hz+61NtNKjjDuDxYNs/OJPtTCR3/xnxPbX1ZrYdeJR4v8ZTQI6ZvR7Us2Ecm/u6mW0P3sNLwLaQypYUoaGzIiKSlPYsREQkKYWFiIgkpbAQEZGkFBYiIpKUwkJERJJSWIiISFIKCxERSUphISIiSf3/awfekS/WpEUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a1e9712b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "boot_7d['diff'] = (boot_7d['Control']- boot_7d['Experimental'])/boot_7d['Experimental']*100\n",
    "\n",
    "ax = boot_7d['diff'].plot.kde()\n",
    "ax.set_xlabel('% Difference in means')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calculating the probability that 7-day retention is greater when the gate is at level 30\n",
    "prob = (boot_7d['diff'] > 0).sum() / len(boot_7d['diff'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We keep the gate at level 30 which is the Control group. It gave us a more succesful output"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.998"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Calculating the probability that 7-day retention is greater when the gate is at level 30\n",
    "prob"
   ]
  }
 ],
 "metadata": {
  "hide_input": false,
  "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": "3.6.4"
  }
 },
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