ab-testing-cookie-cats.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "31ad0177-cadf-4a9e-ad15-1045cadc98aa",
   "metadata": {},
   "source": [
    "# AB Testing Mobile Game "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4cd12765-790f-49a1-b9cf-af02c3aff720",
   "metadata": {},
   "source": [
    "<p>This project is based on a mini project from <a href=\"https://www.datacamp.com/projects/184\">Datacamp</a>.</p>\n",
    "<p><a href=\"https://www.facebook.com/cookiecatsgame\">Cookie Cats</a> is a hugely popular mobile puzzle game developed by <a href=\"http://tactile.dk\">Tactile Entertainment</a>. It's a classic \"connect three\"-style puzzle game where the player must connect tiles of the same color to clear the board and win the level. It also features singing cats. Check out this short demo:</p>\n",
    "<p><a href=\"https://youtu.be/GaP5f0jVTWE\"><img src=\"https://s3.amazonaws.com/assets.datacamp.com/production/project_184/img/cookie_cats_video.jpeg\" style=\"width: 500px\"></a></p>\n",
    "<p>As players progress through the levels of the game, they will <strong>occasionally encounter gates that force them to wait a non-trivial amount of time or make an in-app purchase to progress</strong>. In addition to driving in-app purchases, these gates serve the important purpose of giving players an enforced break from playing the game, hopefully resulting in that the player's enjoyment of the game being increased and prolonged.<p>But where should the gates be placed? Initially the first gate was placed at level 30. <strong>In this project, we're going to analyze an AB-test where we moved the first gate in Cookie Cats from level 30 to level 40. In particular, we will look at the impact on player retention.</strong> </p>\n",
    "<p><img src=\"https://s3.amazonaws.com/assets.datacamp.com/production/project_184/img/cc_gates.png\" alt=\"\"></p>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f630073d-a441-4d73-bc9a-484638310165",
   "metadata": {},
   "source": [
    "<p>The data is from 90,189 players that installed the game while the AB-test was running. The variables are:</p>\n",
    "<ul>\n",
    "<li><code>userid</code> - a unique number that identifies each player.</li>\n",
    "<li><code>version</code> - whether the player was put in the control group (<code>gate_30</code> - a gate at level 30) or the test group (<code>gate_40</code> - a gate at level 40).</li>\n",
    "<li><code>sum_gamerounds</code> - the number of game rounds played by the player during the first week after installation\n",
    "<li><code>retention_1</code> - did the player come back and play 1 day after installing?</li>\n",
    "<li><code>retention_7</code> - did the player come back and play 7 days after installing?</li>\n",
    "</ul>\n",
    "<p>When a player installed the game, he or she was randomly assigned to either <code>gate_30</code> or <code>gate_40</code>. </p>\n",
    "\n",
    "### AB Testing Process\n",
    "\n",
    "1. Understanding business problem & data\n",
    "2. Detect and resolve problems in the data (Missing Value, Outliers, Unexpected Value)\n",
    "3. Look summary stats and plots\n",
    "4. Apply hypothesis testing and check assumptions\n",
    "    - Check Normality & Homogeneity\n",
    "    - Apply tests (Shapiro, Levene Test, T-Test, Welch Test, Mann Whitney U Test)\n",
    "5. Evaluate the results\n",
    "6. Make inferences \n",
    "7. Recommend business decision to your customer/director/ceo etc. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c26ad1db-94b9-4106-ba67-33dd6d5a521c",
   "metadata": {},
   "source": [
    "## <font color=\"darkcyan\">Libraries and Packages</font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "4852df58-4c77-4a9b-a078-eb4b021e577a",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Data Visualization\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import pandas as pd \n",
    "import numpy as np\n",
    "\n",
    "# Hypothesis Testing\n",
    "from scipy.stats import shapiro\n",
    "import scipy.stats as stats\n",
    "\n",
    "# Configuration\n",
    "import warnings\n",
    "pd.options.display.float_format = '{:.4f}'.format\n",
    "pd.set_option('display.max_columns', None)\n",
    "# Plotting setup\n",
    "sns.set(style=\"darkgrid\",color_codes=True)\n",
    "warnings.filterwarnings('ignore')\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e6ae4b0e-def0-4aa2-8674-b2406a728785",
   "metadata": {},
   "source": [
    "## <font color=\"darkcyan\">Loading the data</font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "220b2329-6473-4b22-9751-a13964fa817b",
   "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>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": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# load dataset\n",
    "df = pd.read_csv(\"cookie_cats.csv\")    \n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "80574bdf-2065-4bd9-a3a7-40e255247c9d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(90189, 5)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Check shape of data\n",
    "df.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "89d2a5d5-09aa-4f25-8100-b82c9938db13",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(90189,)\n"
     ]
    }
   ],
   "source": [
    "# Check unique user_id's in dataset\n",
    "print(df.userid.unique().shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "5c8d4e71-a89c-44cb-9ac9-2f944463e9fc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "userid            0\n",
       "version           0\n",
       "sum_gamerounds    0\n",
       "retention_1       0\n",
       "retention_7       0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Check is there any null value  \n",
    "df.isnull().sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "9c4602e7-49f3-4ab5-bb58-5baf28088005",
   "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>count</th>\n",
       "      <th>median</th>\n",
       "      <th>std</th>\n",
       "      <th>mean</th>\n",
       "      <th>max</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>version</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>gate_30</th>\n",
       "      <td>44700</td>\n",
       "      <td>17</td>\n",
       "      <td>256.7164</td>\n",
       "      <td>52.4563</td>\n",
       "      <td>49854</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gate_40</th>\n",
       "      <td>45489</td>\n",
       "      <td>16</td>\n",
       "      <td>103.2944</td>\n",
       "      <td>51.2988</td>\n",
       "      <td>2640</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         count  median      std    mean    max\n",
       "version                                       \n",
       "gate_30  44700      17 256.7164 52.4563  49854\n",
       "gate_40  45489      16 103.2944 51.2988   2640"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.groupby('version').sum_gamerounds.agg(['count','median','std','mean','max'])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "279f6469-3763-4e6c-8b88-e37207afcecc",
   "metadata": {},
   "source": [
    "## <font color=\"darkcyan\">Detect and Delete Outliers</font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "09fa406a-8e45-4c35-bf5e-dae7a6074465",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='version', ylabel='sum_gamerounds'>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.rcParams['figure.figsize'] = (16, 8)\n",
    "\n",
    "sns.boxplot(x = df.version, y = df.sum_gamerounds)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "c50e52f7-abdf-44d7-8fb7-e2f6cbb92061",
   "metadata": {},
   "outputs": [],
   "source": [
    "df = df[df['sum_gamerounds'] < 4800]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "89e13e8f-1f82-48ed-b7ae-fbdeb2fb31a0",
   "metadata": {},
   "source": [
    "## <font color=\"darkcyan\">Look summary stats and plots</font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "abb519c6-bcd3-4083-9356-f97b8f9edc97",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Distribution of Two Groups')"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x432 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(1, 3, figsize = (18,6))\n",
    "\n",
    "\n",
    "df[(df.version == \"gate_30\")].hist(\"sum_gamerounds\", ax = axes[0], color = \"steelblue\")\n",
    "df[(df.version == \"gate_40\")].hist(\"sum_gamerounds\", ax = axes[1], color = \"red\")\n",
    "sns.boxplot(x = df.version, y = df.sum_gamerounds)\n",
    "\n",
    "axes[0].set_title(\"Distribution of Gate 30 (A)\", fontsize = 15)\n",
    "axes[1].set_title(\"Distribution of Gate 40 (B)\", fontsize = 15)\n",
    "axes[2].set_title(\"Distribution of Two Groups\", fontsize = 15)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "89d12f24-b0d4-487c-ae94-482b8728f441",
   "metadata": {},
   "source": [
    "<a id='details'></a>\n",
    "<h1 style=\"color:DarkSlateBlue\" >SOME DETAILS</h1>\n",
    "\n",
    "**The users installed the game but 3994 users never played the game!** Some reasons might explain this situation.\n",
    "\n",
    "- They have no free time to play game\n",
    "- Users might prefer to play other games or they play other games already\n",
    "- Some users don't like the app etc.\n",
    "- You can comment below for this users also\n",
    "- The gmae might have some issuse in some phones \n",
    "\n",
    "**The number of users decreases as the levels progress**\n",
    "\n",
    "- Most of users played the game at early stage and they didn't progress.\n",
    "- Tactile Entertainment should learn why users churn playing the game.\n",
    "- Doing research and collecting data about the game and users would help to understand user churn\n",
    "- The difficulty of the game can be measured\n",
    "- Gifts might help player retention"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "1a185fba-bc66-4c55-8ce5-d046089562f2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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N07JX97pdPMk7e+uuS5tCYBCq+UCSq9Za9+zW3ycbD3Q+cdL+1jsLfhDOOCvtPTmk+95xybRjwfXSpv8YuFqSd3ahoJX08EwOIp1/3Oi+27wj7Rg88Pu0EMQ+tdaLdlOa7Jv2+vYH8G+T5FUr2ehN8Mq0UMWpaUGQ/WqtB9Ra90t7z180sv6DSilXHrehUsqhaQO9/ffi1UkuU2vdp/vueNG0z+nf0r5fjqtkMuplaftT0vbrxya5aLfNg2utO6f1Ja/s3We7JP+9Of3bGJdP8m/d5V+nhQl27/qr3dL63F/01r9iNqNiUud/kly2d/2dafv8Ll3fPvhcXCvJ20bu+7AuqHC+bkqJN/cWXXnS9/YR/corP661fr1/42odt7ugxnszHGR8X5LDu77mwLQ+9EFp+/Bs2ncQAAC2MqZOAAC48DopyU1rrcf1F3Zlz59SSjk9C2eLzya5c9og16iHZPgs+P9N8i+jJXhrmzf8v0op789CNYXZJEeXUg5ZwRLJgx+fX5vkgaNntddav1hKuWFa2OBK3eKrl1IuV2v9yQq1YbnWpf2IfcNa6/mhgq708ue6s0G/0Fv/0mk/yt+s1vrl/oZqrd8ppdwsyf+lhQeSFvqYJmyQJP9Va33EyDb/nOSlpZTPpp2VOjiT71mllDePzp1bSrlohgdZfpE2D/XQfMG11nPTzsj9VNqP7oOBxruVUt5Za31vFjeYQ/5lSV6adrbtZdJ+OP/Uks90vIenzV0+8Jkkt6u1Dp05Xms9MclzurLvn0gr+5206Tg+XGv92iY+/tbirlk44/cvae/fUEWGbmDjY6WUr6WFiwaDJvdNC2GMelaGz1x9Sq11o0HgLgzwjN5ru0/agNnRWfoM8cE+8bMkj0ryubQBjyMyHLQ/qnf57bXW+41px2lJ/qOU8sMsDICuSxu8fsIS7VhJg/+3fzTJHUbLWtdav1faFCUfSQvuJG1/vHHagNBamUty51rru/sLu77+TaWU/0sLGQ3el7ul9QNDSimHp+07A99M8g+11j+ObPeMJO8ppXw0yduzMHj/+FLKu2qt39nUJ9JNA/H03qJfp30mfj7Shu8luUMp5akZCR1N2O6OaWG/gZ8kuX6t9W+j69Zaf5E2rcAP0p7fwO3Twn6LGZyFfM9a69C6tdaTumPM4Vn4DA8G4l9ea33oyPqnpYUPd0sbBEzaseaaaWen95/fDl3bBvvwqUluUmv9/sg257r73rqU8qQshENukBYwWckw4KCP+GTaa//DtEHyOyT5fG+9u2Q4AHJskpuPHu+6/fDl3XebT6QNWifJPUspH6q19t+rLWn7tOos1+sFrJKcf/x6VCnlj1l4rWfSzoL/wZhtvSDDFR0eUmsd+qx23x2fX0r5TNprO24KkPN1A839ChsPr7W+cnS97jP2z9130sd2iw9JC4B8fLHHWIbB98Zj0/bP80Mj3feU95ZSPp/k01k4Bh1ZSrlNrfUDy32wbuqOW/UWvanWutF0E9336G+mfSc6LS3kkrTP822SvHzkLkdn+Lve3dOmepnUjp2yMN3C4P6jVuu4/eQsfG9KkhfUWh/bX6H73vWq7jvi59KmagIAYCujogEAwIXXv4yGDEa8LMOl+682ukJ3pmH/h8FvpP0APXGe31rr8Rk+4/iiaWfxr6TfJPnn0ZBBrw2DMyr7rrPCbViuf+uHDPpqrV/M8Nl0SfLS0ZBBb/0/Z/gM1UO7Aa2lfCkLZ/WN2+6xaWWyB3bK+LOQH552Jl7Syn/fYTRkMLLdubTASn/waeKP4yOeU2t9WK31Z7XWM2qt36+1PmZTgiullF0zvD//NskdR0MGI23/Ydr+PCg/PpM2BcQF3WV6l38yGjLoq7X+Ka0qx3xagOmXXdjkfKWUi2RhkCRJ3jVusGJku99N0p9e5fBSyq0mrd9zapIb1Fo/UGs9vdb6u1rr20YGWPvP7wtZRK31I0m+kxbu+WkWBqW2pDOS3Gs0ZDDQfYaeOrJ4rfu0/x4NGfR1Z85+srdoo2NM53FZGCg/PcltR0MGI9s9M22AbTAgPJPND4Y8PMOl9u81GjIYacMzk3xwiu3eLAvTYSTJk8aFDEa2/Y60z9nAoZPWHfG+0ZBBb5vnpU0n0HdiFjkeZOPKM+POnr5PkgP710dDBmPa8uy00vsDj17hs9eTFii4Za31G91x45e11hfWWr/VW+eZvct/TQuc/S4TdMfv22e43P9TusoIa+VBoyGDES/I8Pe8jfqMUsohSW7bW/Su0ZBBX631m1moKrWYS2f4N8lF++Ekz08rpf+XtDDEvlM8xnKckeT2/ZBBX9fn3DnD0xks9vlYzB17lweVHJbyXyPXN/rc11p/kOR7vUV3X2L/u10WKgpsyEiVhtU6bpdSdknygN6ib6RVw5i0zV+kBfwAANgKCRoAAFw4Hb/U2eLdgNa3e4sOHLPaTdPKpQ48d9Lg/si2v5U2L+vAHSetu4ne0J2Ftpivj1zfZ+xaW8aJtdalSv0fO3L9jUus/9OR63tN0Y6nTfH+vSPDoYdxZerv27v8oaUGlpLzz9x7RW/RNUopBy1xt78lee5S216GG2f4dfrP7uzdRdVaP5/hM8eP3Nz5m7cCf+pdPryUcqVJK3b+Nwul3q9ba/39yO13zvAZsc/OdN6TNuA5ME1f8fJa60lLrPOn3uU7l1ImTcExcESSnWqtl621PmqKNqy099ZaT11ine9kYU7rZG37tGS6s9D7YaldSil79m/swj/9eblfP8V7m1rrX5O8vrfoH7uz6zdVfwqEL3Sf+aU8bYp1vp022PfIJC/J8AD7Yvohh10mrjVs4uBwZ/QY87Za6zlj12xGjzEXGbNOP0T4/Vrrh8esM87LepcvluTvprzftJ7RhSvG6qYQ6IeRXtsNdi6q1lozfFb4YVm6Cstq+U2WOOO/e3/7U9+M6zPumIUpkJKNp80Y541pVT8W86eR6/cct9JAN9C/T61191rr4bXW0WDM5nrNYuGhrg0/zXA1kRuUUvbfhMd6bVrVoCemhYsmBlh6fjZyfdLn/g29ywdleIqgUf3X/BNj+tbVOm7fcmS7L1rqu2et9XMZqZgCAMDWQdAAAODCaXSQfZL+YOG4HzVvMHL9M8tow5d6l6+zwmcsTvP8Rn/Y3WkFH3+5vjnFOv2zDs/O8Dzk44yehb/UINsfaq1Lvn+1TefQLxV8uVLK+WcWllIum6T/w/unl9pmz5dGrt9w7FoLvt4NKK6Um45cX07J6/6ZwjNZuu1bu/7Zpdsn+WIp5RmT5vCutZ6zRBWJfl/xx9pKzC+p29/6gwvTvK7TTJvRf343TPL1Usq9+vvySDv+Mk2IahUt2ad1A6d/6C1ayz7t9131miXXG7k+epz5+wxP+bip/ckOSa69jPuer5RS0ua0H1hqSpck55/ZOzo4OLrOibXW99daX1JrfeQSA/uD9uyc4aoa006J+Y0lbv/zyPWlpppY9BjTtfPqvUXLee++nIUqMcnK9qdnZukBy9FjwduWsf3RqhE3WsZ9V9I3uv5zKf3vQuP6jH7f/YeuEsmiur5yqc/JL9KqBg08oZTy7lLKkV1J/3HbHd1HV9Kbp1zvfb3LM0muv9wHqrUeV2t9e631ubXWaYIbSQuB9KuFTfrcvzlJP2h7j3ErlVL2S3Lz3qLXj1lttY7b/e3Op037M42JFXIAAFg70/6HFACAbctSZ5oN9Ac9xp3xe9Xe5fkk32ljMlPZs3d5x7SzFo+f9s5LWPL51VrPHmnrWoZwJ04r0NMfMDhtikHP5Q6KfnvpVc43WqHgClmY2/qqI7c9qZTy8Cm3O/oeXGrsWgumCWgsR3+H+O00Z04v0pbLrUB71tLHk3wlC2dD7pFWmv+ppZTfpQ0afirJJ2utvx2/iSH9/WK3UsqiA7Aj+mfZHlxKmV1i/59mv3huWjnwQTn8q6adhTtfSvle2vP7ZNrZ62OnK9jCpu2zz+5dXss+bVOOMcnGx5nR/uQVpZRpKiUkG4erLpWly7OPc/jI9aUG4Pu+lemnNhhSSlmXVknokCSXTTs7/upJrpHh5zbN+/yXboqTxYwOSv9h7FqdWuvcEsf7K2X4N6f7lFJuO2nlJSx1LFiOH0wR6Og/sQ0ZPut/Kd9OO/4O3pe1OhasVJ9xhd7l0aoXi/neYjfWWs8rpTwzrRrOwB26v7NLKV9JO8Z8Ism3pwxNbKpzskR7e0b3hSuMXWsTddNcHZS2z5e0z9E106Ym6VeWGPu5r7WeUkr5SBamu7hTKeVhYyp43DULn8/TMhwgHVit43b/NTt+sempRnxvGY8PAMAWImgAAHDhdMYKbad/9u9M2py7m2rvrFzQYNofLfvWch7l05e5/tlLr7Jso2cWL+bkkev9aQJGzwi/aPe3KZaafmA5bZ5G/4fx5YQMko0rZFygp06otc53g4IfzMbzdu+fdpbkPZKklPL9tLNX39KVlh6nv19sl03vK2bSpreYNI3A6dMEA2qt3y+l3DktXLDnyPav2v09OsmZpZRPJ3lXknevcAWN5big9WmrcYxJxk/hM61N/UyOPuZo/7eYaUqiJzl/PvQ7JblZkiunBQxW6jeb5R5jks0/zoy+d3tn09+DlexPpzlu9I8Fp9Vap34taq1nllJOz0K/slbHgpXqM/oVik5ZxrZOXGqFWuurSikXS/LkJOt6N+2QVgniRmnl+k8ppXw4rcrQJ7upllbS76apJtIZ/fzvtzkPXEq5dNqg/w3SBuAvns3vu9+QhaDBPklukWR02pJ79S6/dcI+vlrH7VXbpwAA2PJMnQAAcOG0UmeG7bFC20mSXVdwWyv9I/RqmzhX9Bb0t81Yt3927ZbcJ/60go+VJLv3Li93QHn0Ndl5M9uy5mqtf0hy3ST3TfLVTO43Dk/y9CS1lHLMhOkHttR+8adpN1Jr/WDa2cb/mckDGDsluXXavOsnlFIeMu32V9gFrU/blo4xo5/lxaYIGbVkv1pKmSmlPC7JCUlemeT/JblMxocMTkkrjf5/y2hDsjbHmK3hvRvnT1OssznHgmT4fV+rY8FK9Rk79i4vJ0A0Vbil1vr0tDP235zJr/W+SY5K8tEkx5ZSbryMdkxj6lBGN0VQv39balqqsUope5RSXp/2Wf73tGkMDsz4kMHPkvxXpq9U9aEMVyS5+8hjl7TKKANHT9jOan2GV3WfAgBgy1LRAACAzdH/gfDYWuvY+dsvTLpy1xdEOy69yvlGB31O610e/dH46rXW5ZQaX46VLqXcH+RY7sDWbiPXV+qM7tUy1X7alTo+OsnR3Zmnt0w74/qIbHwm50xalYMrl1KuPzKf9hlZGLz7YK31Npve9EUta5+otf4+yWNKKY9NG3g5Mm1+9msn2X5k9YskeXkp5YBa61NWorEsafRztHet9Y9buA2jYYHl9A27TLHOG5Pcc2TZeUl+kuS4JLX79ztJftpVG/lU2nQKW7PR9+7/1VrfsyYtGTZNH7E5x4Jk+Hiw2ceCNf5ecVYWwhLT7M8Do/3nRLXW7ya5ZzdtwBFJ/iHJjbPxdAFJcvkkHyul3KbW+rFltGcxU4cFSim7jrRp2UGUUsoeSb6cNh1K39+S/DDts1/Tpqr4Vq31d939HjrN9mut55ZS3prkX7tFty2l7FJrHfRl/WoGP6q1TppuaLWO2/2qQ6uyTwEAsOUIGgAAsDn65csPKqXMrPI8umttmopgK3nm5Za0nPK/B4xc7585N1rS/uAsb07ztdRv++hzXMrFR64vp7z6Spq2at2y99Na64lJXpPkNaWUmbRBoJunzan9971Vr5Q27UB/MP7ULAxYHLzcx15tXb/1ze7vmaWUnZNcLy1YcecM7w9PLKW8cZFpIlg54/qTLR00GC3tvX+SH01530X71VLKfTMcMvhNkscleX9vUHCcnaZ8/LU07r27oOi3fa9Syo7TTMmSJKWU3TIcNFjqWLC1f684Mcmh3eXlTIO07Ckjutf4Y91fuuo4N07yj0lul4VB6e2SvKKUctla60pU61hOW0e/G/xmEx7vpRkOGXwlyROTfGnStBCllO0yZUCwc3QWgga7JLlVknd01+86st4kq3XcPjFtmohklfcpAABWn6kTAADYHD/uXd49rYT6VEope3WDeVuz0R98pznrf3PmEF9Ll1vGuv2Su+eknYE38OORdW8w7UZLKduVUvZZes1V038eF+/O4J/WNUeu/2wF2jONZe+j3RmZe27Og9Za52utx9ZaX1hrvW5aJYBze6vcaeQu/f3isG4++qmUUvYupWxSeepNVWs9o9b6iVrrI5IclOR1vZtn08rbs/o2pz/ZqZSy1wq04bsj16c+ziW5yhK3P7J3+ewkR9Ra37JEyCAZPs5s7nzuq2WT37skKaXs3wWa1kL/WLAuydWWcd9rZPg9GT0WXNC+Vxzbu3zVUsq0vyMu53MyVq31lFrr22ut90xyqSTf7t18SIa/i2yOvUopl5hy3dF94QfLeaBSykUzPJXBD5PcpNb6+Ukhg87oPrDoZ6OrJNV/727bPf5hSS7dLduQ5JhFNrNax+1+uy45YbqlcTZ7nwIAYOUJGgAAsDk+P3J9tPzzYt6f5G+llJNLKV8rpWyNZ2iOljyeZhD82qvRkC3g0qWUSy21UndW3e16i741cqbndzI83/GdSinTlru9V5JTSil/K6X8uJRy2ynvt1K+MHL9rmPXGu9uI9e/tJltmdam7KPXWuzGUsp+pZRXllI+W0o5sZSy5Oe6K2H9kd6ig0ZW6fcVsxmZM3qRtswm+VaSM7u2fGSp+0yxzVuWUt5SSvl2KeWUbp+eqNZ6bpJHjSwefX7bqrWuULM5x5gnJPljKeX0UsqxpZRF9/tFHJfhqgZT9UullMtk4azdcbfvlFb9Y+CTtdafT7Hdg5Ncsrdoq/xdp9Z6SoYHKm8+7YBiKeXGSU5K+9z/tJTy4NVo4yJW8ljwxZHrF7TvFZ/uXd4tbeqcadxysRtLKY8opbyvO9Z/dKmN1VpPTvLvI4tXsh++9ZTr9UNmZ2X5x/qrZbi67NFTVssYDepM87l/Q+/yLUsp69OqQwx8bDAtwwSrddz+9Mj1O0yz3SyxTwEAsDa2yv+QAgBwgfGRJKf1rj+olHLpSSsPlFJunuT63dV9k5xeaz1zFdq3uU4auX69xVbuflx9yOo1Z9U9cYp1HpLhUrf9M73TnZH3tt6ii2X4rN2xurmZn9Rd3Tlt/vEtPeXCxzJcMvtR05zBV0o5IslNe4u+UGv9/Qq3bZLT0s6EHlh0H+08bIpt3ittruwDktxlyrb0yzqfPnLb29PmnR94/JRnR94/rWTzTNeWTSlTPWqvtMHAq6UN8k0z7/To/51Hn9+2am7k+hY9w7wbXPxkb9HVSylL7o/dgPZgP98tbWD+2Mn3WLQN80le31t0/VLK301x16X60z1Gri92NnPfC0euLxqUWWP9s6V3SvLMpe7QVTEYrLdDWtn+ZZ01vgK+mxYwGbjvlN9tLpfhMMwv0wZc+y5o3yvenuFjzJOXqmpQSrlplq42cFhaaOdySW5SSplmuqLRqQNWsh9+ePc9ZKJSyhUzHLR8d611NDiylGV/7kspeyR5+sjiaT73b87CcXfPJDfM8PHu9aN3GLFax+1PJOkHHB69VIWzUsrlM2XICwCALUvQAACATVZr/WvaXLMDuyZ5fylldL7685VSDsnGP24+dxWat9m6OemP7y26e3eW6ka6wZHnJbn6FmjaarlfKeV+k27szjLtv1e/zfiyuy/I8I/T/15KueMi212X5DVppZEHjqm1/nqqVq+QbsCgvz9fLMk7u6kGxiqlXCHJWzI8APvs1Wnhxmqtc0m+2lt001LKdSetX0p5aJb4sb47g//dvUW3LqWMToUwut3Dk9y8t2jojMVa6wlpgx4DF0/ynm4AZdI2r57hQdXz0vatzfWhJH/tXX9BKWW/Je7z2JHro2dkbqtGB9F2H7vW6nrOyPVXl1KuP3bNnF8p4G0ZHtB7yWaG2f47C6/FTJJjFiu1Xkq5f5KjltjmKRl+fW+6xDbXl1JekI3P/p2m9P5aeUWSP/euP7iU8ogl7vOcJP0+7Au11q+sdMMW04VLnt9btGtaf7X/pPt033vekxaoGHhe10f3t32B+l5Ra/1Dklf2Fl0vi/TDXSDj6Ck2/dbe5e2SvLL7LjBpu9sleURv0ZkZPvZtrtK1YezvpN17/44sDPBvyKZ9dz1+5Pq9ukoD4xvVppN6V9rAfd+Sn/uuWsHHe4vun4XqGKcm+eAS91+V43b3HaP/+To0yesnvQ5dcOzt2bpDVQAAF1qCBgAAbK7nJvlm7/phSb5TSvmX/plPpZTdSykPSvKNtAHcgTfUWj+7ZZq6Sd7Su7xLkk+XUv7f4AfxUsq6UsqN0s7Qeky33l9ywfWaUsorukBIkjancCnlGUk+moVBlLkk96y1nj26gVrrTzM8MLs+yTtKKa8ppZxfKryUMtsNGH46yT166/8uyeNX7Bktz/PS9tGBGyf5binlbqWUXQYLS5s//PFJvpZ2xt7Aq2qtn9gyTT1ffx+dSfKhUsr9Sjc/cillppRyzVLK25O8rFtvqX30eUnO6T9GKeUFpZRD+yuVUvYspTww7T0cTJGxIcl/jNnmv6Wd4Ttww7S+4p6llN1629ynlPK4tLLN/ZDHs7t9a7PUWv+c5CW9RYck+UbXjqGB9FLK5Uopr0ryuN7ib2X4LPtt2WlJzu1dv9diwZvVUGv9XIYDQLsl+VQp5T/6Z5mXUrYrpdwy7TN54976x2X8/ricNvw6yVN6iy6V5Jvd5+z816OUctlSymuSvGrMZoamoeiqv7yvt2iXJJ8rpQxNN1NK2aOUcp8kX0/y6DHb3bUbkN7q1Fr/lOS+I4tfXEp5Tynl2v12l1KuWkp5d4b7/jOS/Mvqt3SsN2X4/bly2rHgQaWUvQYLSyl7lVL+Oa0Cz+V7638syasnbPuC9r3iaUl+0bv+b6WUj3SDykmSUsqu3bHga2kD0ouqtX4mw9NK3CbJZ0spNym96Wy6gM3ge0K/+sMruv1rJd0nyWdKr2JJKWWnUso90vr9/vv7/FrrjzbhMb6RpB+ivFqST3afh/N/oy2lXKI7Dv4gwxWTBnYbs2yc/vQJd83C78BvrbWeM2b9Uat13H552r4ycOckXyqlHDHoF0opO5RS7pz2f4wrjdkGAABbgYmpWQAAmEat9exSyu2TfDjJ4d3i/dLOAH1pKeWUtIGqi2XjoOunkvzzlmrrJnpBWinkwZzYl0g7u+zcUsrJac+1f5bVa9O+Z99nSzZyBXww7Yy+y6a9J/9cSvljWsnki2b4vduQ5EHdAOBYtdYXl1IuloWBsZkk90urmnB62gDmPmmDLH1/THLbWutoeektotZ6Trc/fyQL+/OhaQND55VSfp82oL5PNi4j/5aszaDY65M8OG3AImklkl+T5FWllN8luUiGz378eJJvZ5HS7rXW47ozj1/RLVqf9l4+upTy57T3b6e0/b//OswnuX+t9XtjtvnHUsqt017bwdzal0ob0NvQvbYzSfbPxq/tmzJF2fVleFbagMngzPiDuseY79pxVpK9s/Fgzq+S3KE743mbV2udK6V8Pwtl0K+e5Pdd37dDkgNHz9heJY9Om2bnbt317dMGYB9TSjktbRB2v2x8lu8Jaf3J31agDS9OG+w6qrt+0bTP2Su7fWantM/awK/S+s0Du+v9wMbAk5McmTadR9I+D+9IMtdtc+dsXGp9Pu3zO3hP1qWFnU7clCe12mqt7y2lPDzJi7JQ+v723d/fSil/SHv+o9Uyzkpy11rrD7dYY3tqrfNdwOO9WQiu7J92dv8rus9A0va70e82n05y50X6iQvU94pa65+7vvuzWZg66cgkR3bHg7+kvTaD3xjn0sJBj1hi0/dJ8pXuvknrjz+V5Jxu/0/aa7HDyP0+nummelqOHya5Ytpx4SullL8k+VPa891+ZN03J3n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      "text/plain": [
       "<Figure size 2160x1440 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(2, 1, figsize = (30,20))\n",
    "df.groupby(\"sum_gamerounds\").userid.count().plot(ax = axes[0])\n",
    "df.groupby(\"sum_gamerounds\").userid.count()[:200].plot(ax = axes[1])\n",
    "plt.suptitle(\"The number of users in the game rounds played\", fontsize = 40)\n",
    "axes[0].set_title(\"How many users are there all game rounds?\", fontsize = 25)\n",
    "axes[1].set_title(\"How many users are there first 200 game rounds?\", fontsize = 25)\n",
    "plt.tight_layout(pad=5);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "2960c98c-839b-48e0-b4bb-7ac71afce162",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "sum_gamerounds\n",
       "30    642\n",
       "40    505\n",
       "Name: userid, dtype: int64"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.groupby(\"sum_gamerounds\").userid.count().loc[[30,40]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "ac7c5d06-132f-42bf-8551-a85351f4b7a8",
   "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>count</th>\n",
       "      <th>median</th>\n",
       "      <th>mean</th>\n",
       "      <th>std</th>\n",
       "      <th>max</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>version</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>gate_30</th>\n",
       "      <td>44699</td>\n",
       "      <td>17</td>\n",
       "      <td>51.3421</td>\n",
       "      <td>102.0576</td>\n",
       "      <td>2961</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gate_40</th>\n",
       "      <td>45489</td>\n",
       "      <td>16</td>\n",
       "      <td>51.2988</td>\n",
       "      <td>103.2944</td>\n",
       "      <td>2640</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         count  median    mean      std   max\n",
       "version                                      \n",
       "gate_30  44699      17 51.3421 102.0576  2961\n",
       "gate_40  45489      16 51.2988 103.2944  2640"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.groupby(\"version\").sum_gamerounds.agg([\"count\", \"median\", \"mean\", \"std\", \"max\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f3a34a89-bc6a-4d85-95fc-0dd416d84dba",
   "metadata": {},
   "source": [
    "**Retention variables gives us player retention details.**\n",
    "\n",
    "<li><code>retention_1</code> - did the player come back and play 1 day after installing?</li>\n",
    "<li><code>retention_7</code> - did the player come back and play 7 days after installing?</li>\n",
    "\n",
    "Also players tend not to play the game! There are many players who quit the game.\n",
    "\n",
    "- 55 percent of the players didn't play the game 1 day after insalling\n",
    "- 81 percent of the players didn't play the game 7 day after insalling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "1bebed07-7c8f-415a-8b31-5b66fe18232b",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>count</th>\n",
       "      <th>median</th>\n",
       "      <th>mean</th>\n",
       "      <th>std</th>\n",
       "      <th>max</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>version</th>\n",
       "      <th>retention_1</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">gate_30</th>\n",
       "      <th>False</th>\n",
       "      <td>24665</td>\n",
       "      <td>6</td>\n",
       "      <td>16.3591</td>\n",
       "      <td>36.5284</td>\n",
       "      <td>1072</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>True</th>\n",
       "      <td>20034</td>\n",
       "      <td>48</td>\n",
       "      <td>94.4117</td>\n",
       "      <td>135.0377</td>\n",
       "      <td>2961</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">gate_40</th>\n",
       "      <th>False</th>\n",
       "      <td>25370</td>\n",
       "      <td>6</td>\n",
       "      <td>16.3404</td>\n",
       "      <td>35.9258</td>\n",
       "      <td>1241</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>True</th>\n",
       "      <td>20119</td>\n",
       "      <td>49</td>\n",
       "      <td>95.3812</td>\n",
       "      <td>137.8873</td>\n",
       "      <td>2640</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                     count  median    mean      std   max\n",
       "version retention_1                                      \n",
       "gate_30 False        24665       6 16.3591  36.5284  1072\n",
       "        True         20034      48 94.4117 135.0377  2961\n",
       "gate_40 False        25370       6 16.3404  35.9258  1241\n",
       "        True         20119      49 95.3812 137.8873  2640"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.groupby([\"version\", \"retention_1\"]).sum_gamerounds.agg([\"count\", \"median\", \"mean\", \"std\", \"max\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "cb74fa5a-3f8c-42da-bb43-4cb0d06cbfd0",
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   "outputs": [
    {
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       "      <th>median</th>\n",
       "      <th>mean</th>\n",
       "      <th>std</th>\n",
       "      <th>max</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>version</th>\n",
       "      <th>retention_7</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">gate_30</th>\n",
       "      <th>False</th>\n",
       "      <td>36198</td>\n",
       "      <td>11</td>\n",
       "      <td>25.7965</td>\n",
       "      <td>43.3162</td>\n",
       "      <td>981</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>True</th>\n",
       "      <td>8501</td>\n",
       "      <td>105</td>\n",
       "      <td>160.1175</td>\n",
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       "      <td>2961</td>\n",
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       "      <th rowspan=\"2\" valign=\"top\">gate_40</th>\n",
       "      <th>False</th>\n",
       "      <td>37210</td>\n",
       "      <td>11</td>\n",
       "      <td>25.8564</td>\n",
       "      <td>44.4061</td>\n",
       "      <td>2640</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>True</th>\n",
       "      <td>8279</td>\n",
       "      <td>111</td>\n",
       "      <td>165.6498</td>\n",
       "      <td>183.7925</td>\n",
       "      <td>2294</td>\n",
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      ],
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       "                     count  median     mean      std   max\n",
       "version retention_7                                       \n",
       "gate_30 False        36198      11  25.7965  43.3162   981\n",
       "        True          8501     105 160.1175 179.3586  2961\n",
       "gate_40 False        37210      11  25.8564  44.4061  2640\n",
       "        True          8279     111 165.6498 183.7925  2294"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.groupby([\"version\", \"retention_7\"]).sum_gamerounds.agg([\"count\", \"median\", \"mean\", \"std\", \"max\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "31d8072d-7b8c-446e-bde6-837f012a2489",
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   "outputs": [
    {
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       "      <th></th>\n",
       "      <th>version</th>\n",
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       "      <td>981</td>\n",
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       "      <th>1</th>\n",
       "      <td>gate_30</td>\n",
       "      <td>False-True</td>\n",
       "      <td>1825</td>\n",
       "      <td>43</td>\n",
       "      <td>73.1693</td>\n",
       "      <td>93.2223</td>\n",
       "      <td>1072</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>gate_30</td>\n",
       "      <td>True-False</td>\n",
       "      <td>13358</td>\n",
       "      <td>33</td>\n",
       "      <td>49.6945</td>\n",
       "      <td>58.1254</td>\n",
       "      <td>918</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>gate_30</td>\n",
       "      <td>True-True</td>\n",
       "      <td>6676</td>\n",
       "      <td>127</td>\n",
       "      <td>183.8863</td>\n",
       "      <td>189.6264</td>\n",
       "      <td>2961</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>gate_40</td>\n",
       "      <td>False-False</td>\n",
       "      <td>23597</td>\n",
       "      <td>6</td>\n",
       "      <td>11.9133</td>\n",
       "      <td>20.9010</td>\n",
       "      <td>547</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>gate_40</td>\n",
       "      <td>False-True</td>\n",
       "      <td>1773</td>\n",
       "      <td>47</td>\n",
       "      <td>75.2611</td>\n",
       "      <td>94.4780</td>\n",
       "      <td>1241</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>gate_40</td>\n",
       "      <td>True-False</td>\n",
       "      <td>13613</td>\n",
       "      <td>32</td>\n",
       "      <td>50.0255</td>\n",
       "      <td>60.9246</td>\n",
       "      <td>2640</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>gate_40</td>\n",
       "      <td>True-True</td>\n",
       "      <td>6506</td>\n",
       "      <td>133</td>\n",
       "      <td>190.2824</td>\n",
       "      <td>194.2201</td>\n",
       "      <td>2294</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   version NewRetention  count  median     mean      std   max\n",
       "0  gate_30  False-False  22840       6  11.8197  21.6426   981\n",
       "1  gate_30   False-True   1825      43  73.1693  93.2223  1072\n",
       "2  gate_30   True-False  13358      33  49.6945  58.1254   918\n",
       "3  gate_30    True-True   6676     127 183.8863 189.6264  2961\n",
       "4  gate_40  False-False  23597       6  11.9133  20.9010   547\n",
       "5  gate_40   False-True   1773      47  75.2611  94.4780  1241\n",
       "6  gate_40   True-False  13613      32  50.0255  60.9246  2640\n",
       "7  gate_40    True-True   6506     133 190.2824 194.2201  2294"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[\"NewRetention\"] = list(map(lambda x,y: str(x)+\"-\"+str(y), df.retention_1, df.retention_7))\n",
    "df.groupby([\"version\", \"NewRetention\"]).sum_gamerounds.agg([\"count\", \"median\", \"mean\", \"std\", \"max\"]).reset_index()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ce9cdb85-64da-45da-a579-7a879e29ecf3",
   "metadata": {},
   "source": [
    "<a id='ab'></a>\n",
    "<h1 style=\"color:DarkSlateBlue\" >A/B Testing</h1>\n",
    "\n",
    "### Assumptions:\n",
    "- Check normality\n",
    "- If Normal Distribution, check homogeneity\n",
    "\n",
    "### Steps:\n",
    "- Split & Define Control Group & Test Group\n",
    "- Apply Shapiro Test for normality\n",
    "- If parametric apply Levene Test for homogeneity of variances\n",
    "- If Parametric + homogeneity of variances apply T-Test\n",
    "- If Parametric - homogeneity of variances apply Welch Test\n",
    "- If Non-parametric apply Mann Whitney U Test directly"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "548afa95-bc9a-404b-8d8f-f53334b39038",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>userid</th>\n",
       "      <th>version</th>\n",
       "      <th>sum_gamerounds</th>\n",
       "      <th>retention_1</th>\n",
       "      <th>retention_7</th>\n",
       "      <th>NewRetention</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>116</td>\n",
       "      <td>A</td>\n",
       "      <td>3</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False-False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>337</td>\n",
       "      <td>A</td>\n",
       "      <td>38</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "      <td>True-False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>377</td>\n",
       "      <td>B</td>\n",
       "      <td>165</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "      <td>True-False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>483</td>\n",
       "      <td>B</td>\n",
       "      <td>1</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False-False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>488</td>\n",
       "      <td>B</td>\n",
       "      <td>179</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>True-True</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   userid version  sum_gamerounds  retention_1  retention_7 NewRetention\n",
       "0     116       A               3        False        False  False-False\n",
       "1     337       A              38         True        False   True-False\n",
       "2     377       B             165         True        False   True-False\n",
       "3     483       B               1        False        False  False-False\n",
       "4     488       B             179         True         True    True-True"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Define A/B groups\n",
    "df[\"version\"] = np.where(df.version == \"gate_30\", \"A\", \"B\")\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "afe74d41-c187-4e92-867b-a77cc497dd93",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "# A/B Testing Hypothesis\n",
      "H0: A == B\n",
      "H1: A != B \n",
      "\n"
     ]
    },
    {
     "data": {
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       "\n",
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       "    }\n",
       "\n",
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       "        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>Test Type</th>\n",
       "      <th>AB Hypothesis</th>\n",
       "      <th>p-value</th>\n",
       "      <th>Comment</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Non-Parametric</td>\n",
       "      <td>Fail to Reject H0</td>\n",
       "      <td>0.0509</td>\n",
       "      <td>A/B groups are similar!</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        Test Type      AB Hypothesis  p-value                  Comment\n",
       "0  Non-Parametric  Fail to Reject H0   0.0509  A/B groups are similar!"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# A/B Testing Function - Quick Solution\n",
    "def AB_Test(dataframe, group, target):\n",
    "    \n",
    "    # Split A/B\n",
    "    groupA = dataframe[dataframe[group] == \"A\"][target]\n",
    "    groupB = dataframe[dataframe[group] == \"B\"][target]\n",
    "    \n",
    "    # Assumption: Normality\n",
    "    ntA = shapiro(groupA)[1] < 0.05\n",
    "    ntB = shapiro(groupB)[1] < 0.05\n",
    "    # H0: Distribution is Normal! - False\n",
    "    # H1: Distribution is not Normal! - True\n",
    "    \n",
    "    \n",
    "    # \"If H0: Normal Distribution\"\n",
    "    if (ntA == False) & (ntB == False): \n",
    "        # Parametric Test\n",
    "        # Assumption: Homogeneity of variances\n",
    "        leveneTest = stats.levene(groupA, groupB)[1] < 0.05\n",
    "        # H0: Homogeneity: False\n",
    "        # H1: Heterogeneous: True\n",
    "        \n",
    "        # \"If H0: Homogeneity of variances\"\n",
    "        if leveneTest == False:\n",
    "            # Homogeneity\n",
    "            ttest = stats.ttest_ind(groupA, groupB, equal_var=True)[1]\n",
    "            # H0: M1 == M2 - False\n",
    "            # H1: M1 != M2 - True\n",
    "        else:\n",
    "            # Heterogeneous\n",
    "            ttest = stats.ttest_ind(groupA, groupB, equal_var=False)[1]\n",
    "            # H0: M1 == M2 - False\n",
    "            # H1: M1 != M2 - True\n",
    "    else:\n",
    "        # Non-Parametric Test\n",
    "        ttest = stats.mannwhitneyu(groupA, groupB)[1] \n",
    "        # H0: M1 == M2 - False\n",
    "        # H1: M1 != M2 - True\n",
    "        \n",
    "    # Put Result into a Dataframe\n",
    "    temp = pd.DataFrame({\n",
    "        \"AB Hypothesis\":[ttest < 0.05], \n",
    "        \"p-value\":[ttest]\n",
    "    })\n",
    "\n",
    "    temp[\"Test Type\"] = np.where((ntA == False) & (ntB == False), \"Parametric\", \"Non-Parametric\")\n",
    "    temp[\"AB Hypothesis\"] = np.where(temp[\"AB Hypothesis\"] == False, \"Fail to Reject H0\", \"Reject H0\")\n",
    "    temp[\"Comment\"] = np.where(temp[\"AB Hypothesis\"] == \"Fail to Reject H0\", \"A/B groups are similar!\", \"A/B groups are not similar!\")\n",
    "    \n",
    "    if (ntA == False) & (ntB == False):\n",
    "        temp[\"Homogeneity\"] = np.where(leveneTest == False, \"Yes\", \"No\")\n",
    "        temp = temp[[\"Test Type\", \"Homogeneity\",\"AB Hypothesis\", \"p-value\", \"Comment\"]]\n",
    "    else:\n",
    "        temp = temp[[\"Test Type\",\"AB Hypothesis\", \"p-value\", \"Comment\"]]\n",
    "    \n",
    "    # Print Hypothesis\n",
    "    print(\"# A/B Testing Hypothesis\")\n",
    "    print(\"H0: A == B\")\n",
    "    print(\"H1: A != B\", \"\\n\")\n",
    "    \n",
    "    return temp\n",
    "    \n",
    "    \n",
    "    \n",
    "# Apply A/B Testing\n",
    "AB_Test(dataframe=df, group = \"version\", target = \"sum_gamerounds\")"
   ]
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    "<a id='conclusion'></a>\n",
    "<h1 style=\"color:DarkSlateBlue\" >7. Conclusion</h1>\n",
    "\n",
    "### Remember business problem!\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 and game rounds.**\n",
    "\n",
    "Firstly, we investigated relationships and structures in the data. There was no missing value problem but was one outlier problem in the data. Summary stats and plots help us to understand the data and problem.\n",
    "\n",
    "Before A/B Testing, we shared some details about game, players, problems and suggestion to our customer/director/ceo etc.\n",
    "\n",
    "After applying A/B Testing, the analysis result gives us some important information. Shapiro Testing rejected H0 for Normality assumption. Therefore we needed to apply a Non-parametric test as called Mann Whitney U to compare two groups. As a result, Mann Whitney U Testing rejected H0 hypothesis and we learned A/B groups are not similar!\n",
    "\n",
    "Briefly, There are statistically significant difference between two groups about moving first gate from level 30 to level 40 for game rounds. \n",
    "\n",
    "### Which level has more advantages in terms of player retention?\n",
    "\n",
    "1-day and 7-day average retention are higher when the gate is at level 30 than when it is at level 40."
   ]
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