AnalyzeGoogleStoreApp.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Free or Paid, Rates of Google Play Store Users\n",
    "\n",
    "## Background\n",
    "\n",
    "Users download apps for various usage purposes. Given that paid service is usually better at offering pleasant experience, and that free apps are more accesible to everyone, what are the user opinions towards these apps? \n",
    "\n",
    "More specifically, the following questions are of interest:\n",
    "- How do the app ratings differ between paid and free apps in general?\n",
    "- How are the differences distributed across different app categories?\n",
    "- Are there any categories where the differences are statistically significant?\n",
    "\n",
    "To expore answers to the above questions, I narrawed the context to Google Play Store and conducted data analysis on the Kaggle dataset [`Google Play Store`](https://www.kaggle.com/lava18/google-play-store-apps/home),\n",
    "\n",
    "## Acknowledgement\n",
    "I would like to thank Google Play Store and [Lavanya Gupta](https://www.kaggle.com/lava18) for offering the wonderful dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import packages\n",
    "\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "import numpy as np\n",
    "import re\n",
    "from scipy.stats import mannwhitneyu\n",
    "from matplotlib import pyplot as plt\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "\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>App</th>\n",
       "      <th>Category</th>\n",
       "      <th>Rating</th>\n",
       "      <th>Reviews</th>\n",
       "      <th>Size</th>\n",
       "      <th>Installs</th>\n",
       "      <th>Type</th>\n",
       "      <th>Price</th>\n",
       "      <th>Content Rating</th>\n",
       "      <th>Genres</th>\n",
       "      <th>Last Updated</th>\n",
       "      <th>Current Ver</th>\n",
       "      <th>Android Ver</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Photo Editor &amp; Candy Camera &amp; Grid &amp; ScrapBook</td>\n",
       "      <td>ART_AND_DESIGN</td>\n",
       "      <td>4.1</td>\n",
       "      <td>159</td>\n",
       "      <td>19M</td>\n",
       "      <td>10,000+</td>\n",
       "      <td>Free</td>\n",
       "      <td>0</td>\n",
       "      <td>Everyone</td>\n",
       "      <td>Art &amp; Design</td>\n",
       "      <td>January 7, 2018</td>\n",
       "      <td>1.0.0</td>\n",
       "      <td>4.0.3 and up</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Coloring book moana</td>\n",
       "      <td>ART_AND_DESIGN</td>\n",
       "      <td>3.9</td>\n",
       "      <td>967</td>\n",
       "      <td>14M</td>\n",
       "      <td>500,000+</td>\n",
       "      <td>Free</td>\n",
       "      <td>0</td>\n",
       "      <td>Everyone</td>\n",
       "      <td>Art &amp; Design;Pretend Play</td>\n",
       "      <td>January 15, 2018</td>\n",
       "      <td>2.0.0</td>\n",
       "      <td>4.0.3 and up</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>U Launcher Lite – FREE Live Cool Themes, Hide ...</td>\n",
       "      <td>ART_AND_DESIGN</td>\n",
       "      <td>4.7</td>\n",
       "      <td>87510</td>\n",
       "      <td>8.7M</td>\n",
       "      <td>5,000,000+</td>\n",
       "      <td>Free</td>\n",
       "      <td>0</td>\n",
       "      <td>Everyone</td>\n",
       "      <td>Art &amp; Design</td>\n",
       "      <td>August 1, 2018</td>\n",
       "      <td>1.2.4</td>\n",
       "      <td>4.0.3 and up</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Sketch - Draw &amp; Paint</td>\n",
       "      <td>ART_AND_DESIGN</td>\n",
       "      <td>4.5</td>\n",
       "      <td>215644</td>\n",
       "      <td>25M</td>\n",
       "      <td>50,000,000+</td>\n",
       "      <td>Free</td>\n",
       "      <td>0</td>\n",
       "      <td>Teen</td>\n",
       "      <td>Art &amp; Design</td>\n",
       "      <td>June 8, 2018</td>\n",
       "      <td>Varies with device</td>\n",
       "      <td>4.2 and up</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Pixel Draw - Number Art Coloring Book</td>\n",
       "      <td>ART_AND_DESIGN</td>\n",
       "      <td>4.3</td>\n",
       "      <td>967</td>\n",
       "      <td>2.8M</td>\n",
       "      <td>100,000+</td>\n",
       "      <td>Free</td>\n",
       "      <td>0</td>\n",
       "      <td>Everyone</td>\n",
       "      <td>Art &amp; Design;Creativity</td>\n",
       "      <td>June 20, 2018</td>\n",
       "      <td>1.1</td>\n",
       "      <td>4.4 and up</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                 App        Category  Rating  \\\n",
       "0     Photo Editor & Candy Camera & Grid & ScrapBook  ART_AND_DESIGN     4.1   \n",
       "1                                Coloring book moana  ART_AND_DESIGN     3.9   \n",
       "2  U Launcher Lite – FREE Live Cool Themes, Hide ...  ART_AND_DESIGN     4.7   \n",
       "3                              Sketch - Draw & Paint  ART_AND_DESIGN     4.5   \n",
       "4              Pixel Draw - Number Art Coloring Book  ART_AND_DESIGN     4.3   \n",
       "\n",
       "  Reviews  Size     Installs  Type Price Content Rating  \\\n",
       "0     159   19M      10,000+  Free     0       Everyone   \n",
       "1     967   14M     500,000+  Free     0       Everyone   \n",
       "2   87510  8.7M   5,000,000+  Free     0       Everyone   \n",
       "3  215644   25M  50,000,000+  Free     0           Teen   \n",
       "4     967  2.8M     100,000+  Free     0       Everyone   \n",
       "\n",
       "                      Genres      Last Updated         Current Ver  \\\n",
       "0               Art & Design   January 7, 2018               1.0.0   \n",
       "1  Art & Design;Pretend Play  January 15, 2018               2.0.0   \n",
       "2               Art & Design    August 1, 2018               1.2.4   \n",
       "3               Art & Design      June 8, 2018  Varies with device   \n",
       "4    Art & Design;Creativity     June 20, 2018                 1.1   \n",
       "\n",
       "    Android Ver  \n",
       "0  4.0.3 and up  \n",
       "1  4.0.3 and up  \n",
       "2  4.0.3 and up  \n",
       "3    4.2 and up  \n",
       "4    4.4 and up  "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Read dataframe and display data\n",
    "df = pd.read_csv('googleplaystore.csv')\n",
    "df.head(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 0. Explore and Prepare Dataframe"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "There are 1181/10841 duplicated records.\n",
      "9660 records after dropping duplicated.\n"
     ]
    }
   ],
   "source": [
    "# check duplicates\n",
    "n_duplicated = df.duplicated(subset=['App']).sum()\n",
    "print(\"There are {}/{} duplicated records.\".format(n_duplicated, df.shape[0]))\n",
    "df_no_dup = df.drop(df.index[df.App.duplicated()], axis=0)\n",
    "print(\"{} records after dropping duplicated.\".format(df_no_dup.shape[0]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{nan, 'Free', 'Paid', '0'}\n",
      "Dropping alien Type value '0', 1 record(s) removed\n"
     ]
    }
   ],
   "source": [
    "# Check and clean type values, defer nan value processing to the next cell\n",
    "print(set(df_no_dup.Type))\n",
    "print(\"Dropping alien Type value '0', {} record(s) removed\".format(sum(df_no_dup.Type == '0')))\n",
    "df_no_dup = df_no_dup.drop(df_no_dup.index[df_no_dup.Type == '0'], axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "NaA value statistics in each column\n",
      "App                  0\n",
      "Category             0\n",
      "Rating            1463\n",
      "Reviews              0\n",
      "Size                 0\n",
      "Installs             0\n",
      "Type                 1\n",
      "Price                0\n",
      "Content Rating       0\n",
      "Genres               0\n",
      "Last Updated         0\n",
      "Current Ver          8\n",
      "Android Ver          2\n",
      "dtype: int64 \n",
      "\n",
      "Column 'Type' with NaN values are dropped, 9658 records left.\n",
      "Cleaned dataframe for 'Rating' has 8196 records.\n"
     ]
    }
   ],
   "source": [
    "# check and drop NaN values\n",
    "print(\"NaA value statistics in each column\")\n",
    "print(df_no_dup.isnull().sum(axis=0),'\\n')\n",
    "df_no_dup = df_no_dup.dropna(subset=['Type'])\n",
    "print(\"Column 'Type' with NaN values are dropped, {} records left.\".format(df_no_dup.shape[0]))\n",
    "\n",
    "# prepare rating dataframe\n",
    "df_rating = df_no_dup.dropna(subset=['Rating'])\n",
    "print(\"Cleaned dataframe for 'Rating' has {} records.\".format(df_rating.shape[0]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# we are interested in the columns Category, Rating and Type\n",
    "# Drop irrelevant columns for Rating dataframe.\n",
    "df_rating = df_rating.loc[:,['Rating', 'Type', 'Category']]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_hist(df, col, bins=10):\n",
    "    \"\"\"\n",
    "    Plot histograms for a column\n",
    "    \"\"\"\n",
    "    plt.hist(df[col], bins=bins)\n",
    "    plt.xlabel(col)\n",
    "    plt.ylabel('counts')\n",
    "    plt.title('Distribution of {}'.format(col))\n",
    "\n",
    "def compute_app_types(df):\n",
    "    \"\"\"\n",
    "    Given a dataframe, compute the number \n",
    "    of free and paid apps respectively\n",
    "    \"\"\"\n",
    "    return sum(df.Type == \"Free\"), sum(df.Type == 'Paid')\n",
    "\n",
    "def plot_app_types(df):\n",
    "    \"\"\"\n",
    "    Plot app type distributions across categories\n",
    "    \"\"\"\n",
    "    vc_rating = df.Category.value_counts()\n",
    "    cat_free_apps = []\n",
    "    cat_paid_apps = []\n",
    "    for cat in vc_rating.index:\n",
    "        n_free, n_paid = compute_app_types(df.query(\"Category == '{}'\".format(cat)))\n",
    "        cat_free_apps.append(n_free)\n",
    "        cat_paid_apps.append(n_paid)\n",
    "\n",
    "    f, ax = plt.subplots(2,1)\n",
    "    ax[0].bar(range(1, len(cat_free_apps)+1), cat_free_apps)\n",
    "    ax[1].bar(range(1, len(cat_free_apps)+1), cat_paid_apps)\n",
    "\n",
    "def drop_categories(df):\n",
    "    \"\"\"\n",
    "    Drop categories with any app type with instances fewer than 10\n",
    "    \"\"\"\n",
    "    vc_rating = df.Category.value_counts()\n",
    "    cats_to_drop = []\n",
    "    for cat in vc_rating.index:\n",
    "        n_free, n_paid = compute_app_types(df.query(\"Category == '{}'\".format(cat)))\n",
    "        if n_free < 10 or n_paid < 10:\n",
    "            cats_to_drop.append(cat)\n",
    "    for cat in cats_to_drop:\n",
    "        df.drop(df.query('Category == \"{}\"'.format(cat)).index, axis=0, inplace=True)\n",
    "    print(\"Deleted categories: {}\".format(cats_to_drop))\n",
    "    return df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Rating</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>8196.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>4.173243</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.536625</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>4.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>4.300000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>4.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>5.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            Rating\n",
       "count  8196.000000\n",
       "mean      4.173243\n",
       "std       0.536625\n",
       "min       1.000000\n",
       "25%       4.000000\n",
       "50%       4.300000\n",
       "75%       4.500000\n",
       "max       5.000000"
      ]
     },
     "execution_count": 8,
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     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAY4AAAEWCAYAAABxMXBSAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4xLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvDW2N/gAAHItJREFUeJzt3Xu0JWV95vHvw01MQIF0S6C5NDGdjOhEJC2QcTIhYBAwiknU4IraGrLIBRKNZhI0RvCCQxIvI2rMQmkBb0hUYosotqgxzkShQUAuKj2I0jaBlpabGGLjb/6o9+jmcC67us8++zT9/ay116n91ltVv13Q5zn1Vu2qVBWSJA1ru3EXIEnauhgckqReDA5JUi8GhySpF4NDktSLwSFJ6sXg0IKU5B+T/M0crWu/JPcm2b69/3ySP5iLdbf1fTLJirlaX4/tvj7Jd5P8+zxtbyyfUwtP/B6H5luSm4E9gU3AA8D1wHnAWVX1o81Y1x9U1Wd6LPN54H1V9e4+22rLngb8fFU9v++ycynJvsA3gP2r6vYp5h8OfBa4DyhgPXBGVb1nyPWfxgL4nFqYPOLQuDyjqnYF9gfOAP4KOHuuN5Jkh7le5wKxP3DHVKExYH1V7QI8Cvhz4F1JfnFeqtPDmsGhsaqqu6pqFfC7wIokTwBIck6S17fpRUkuSnJnko1J/jXJdkneC+wHfLwNRf1lkqVJKskJSb4NfHagbTBEHpvksiR3JflYkj3atg5Psm6wxiQ3J3lqkqOBVwK/27Z3dZv/46GvVterknwrye1Jzkvy6DZvoo4VSb7dhpn+erp9k+TRbfkNbX2vaut/KrAa2LvVcc4s+7iq6mJgI/BLA+t/a5Jbktyd5Iokv9rah/mcL0ryxSRvTPK9JN9McszAug9I8oUk9yT5TJJ3JHnfTHVq62FwaEGoqsuAdcCvTjH75W3eYrohrld2i9QLgG/THb3sUlV/N7DMrwGPA542zSZfCPw+sDfdkNmZQ9T4KeANwIfa9p44RbcXtdevAz8H7AK8fVKf/w78InAk8Ookj5tmk28DHt3W82ut5he3YbljaEcUVfWimepuYfNMYBGwdmDW5cBBwB7AB4B/SrLzkJ8T4FDg6229fwecnSRt3geAy4CfAU4DXjBTjdq6GBxaSNbT/RKb7IfAXnTj+T+sqn+t2U/OnVZV36+qH0wz/71VdW1VfR/4G+C5EyfPt9DvAW+uqpuq6l7gFcDxk452XlNVP6iqq4GrgYf8Ym61/C7wiqq6p6puBt5Ev1/Aeye5E/gBcCHwsqr6ysTMqnpfVd1RVZuq6k3AI+gCbVjfqqp3VdUDwLl0/432TLIf8GTg1VX1n1X1RWBVj/VqgTM4tJAsoRtOmezv6f5S/nSSm5KcMsS6bukx/1vAjnR/OW+pvdv6Bte9A92R0oTBq6DuozsqmWwRsNMU61rSo5b1VbUb3TmOM4EjBmcmeXmSG9pw3Z10Rzd99sGPP0dV3dcmd6HbBxsH2mD2/x7aihgcWhCSPJnul+IXJ89rf3G/vKp+DngG8LIkR07MnmaVsx2R7DswvR/dUc13ge8DPzVQ1/Z0Q2TDrnc93YnrwXVvAm6bZbnJvttqmryu7/RcD1V1P93FB/81ybMA2vmMvwKeC+zeAuYuYGKoaUsut7wV2CPJTw207TtdZ219DA6NVZJHJflN4Hy6S2S/OkWf30zy8238/G66S3gfaLNvozsH0NfzkxzYfrm9FvhwG3L5BrBzkqcn2RF4Fd0QzoTbgKVJpvu380Hgz9vJ4V34ybmCTX2Ka7VcAJyeZNck+wMvAzbrBHNV/SfdUNerW9OudIG2AdghyavpjkwmzPY5Z9rWt4A1wGlJdkryK3SBr4cJg0Pj8vEk99ANYfw18GbgxdP0XQZ8BrgX+DfgH6rq823e/wJe1a64+ose238vcA7dcMvOwJ9Bd5UX8CfAu+n+uv8+3Yn5Cf/Uft6R5Mop1ruyrfsLwDeB/wD+tEddg/60bf8muiOxD7T1b66VwH5JngFcAnySLii/1eocHE6a7XPO5veAXwHuAF4PfAi4fzPr1gLjFwAljVySDwFfq6pTx12LtpxHHJLmXJInJ3lsuxT4aOA44J/HXZfmxsP1W7WSxutngY/SfY9jHfDHg5cCa+vmUJUkqReHqiRJvTwsh6oWLVpUS5cuHXcZkrRVueKKK75bVYtn6/ewDI6lS5eyZs2acZchSVuVJN+avZdDVZKkngwOSVIvBockqZeRBUeSnduDcq5Ocl2S17T2c9pDX65qr4Nae5KcmWRtkmuSHDywrhVJbmwvn3ksSWM0ypPj9wNHVNW97WZxX0zyyTbvf1bVhyf1P4bunkTL6B4Q807g0HRPZjsVWE53x84rkqyqqu+NsHZJ0jRGdsTRHld5b3u7Y3vN9G3D44Dz2nJfAnZLshfdE9xWV9XGFhargaNHVbckaWYjPceRZPskVwG30/3y/3KbdXobjnpLkolbVi/hwXfnXNfapmufvK0Tk6xJsmbDhg1z/lkkSZ2RBkdVPVBVBwH7AIckeQLdozT/C92jJfege5gM/OQBMg9axQztk7d1VlUtr6rlixfP+v0VSdJmmperqqrqTuDzwNFVdWsbjrofeA9wSOu2jgc/JWwfuqepTdcuSRqDkZ0cT7IY+GFV3ZnkkcBTgb9NsldV3dqe5vYs4Nq2yCrg5CTn050cv6v1uwR4Q5LdW7+j6I5aJGlGS0/5xNi2ffMZTx/btkdtlFdV7QWc257ZvB1wQVVdlOSzLVQCXAX8Uet/MXAssBa4j/Y0uKramOR1wOWt32urauMI65YkzWBkwVFV1wBPmqL9iGn6F3DSNPNWsmWPzJQkzRG/OS5J6sXgkCT1YnBIknoxOCRJvRgckqReDA5JUi8GhySpF4NDktSLwSFJ6sXgkCT1YnBIknoxOCRJvRgckqReDA5JUi8GhySpF4NDktSLwSFJ6sXgkCT1YnBIknoxOCRJvRgckqReRhYcSXZOclmSq5Ncl+Q1rf2AJF9OcmOSDyXZqbU/or1f2+YvHVjXK1r715M8bVQ1S5JmN8ojjvuBI6rqicBBwNFJDgP+FnhLVS0Dvgec0PqfAHyvqn4eeEvrR5IDgeOBxwNHA/+QZPsR1i1JmsHIgqM697a3O7ZXAUcAH27t5wLPatPHtfe0+UcmSWs/v6rur6pvAmuBQ0ZVtyRpZiM9x5Fk+yRXAbcDq4H/B9xZVZtal3XAkja9BLgFoM2/C/iZwfYplhnc1olJ1iRZs2HDhlF8HEkSIw6Oqnqgqg4C9qE7SnjcVN3az0wzb7r2yds6q6qWV9XyxYsXb27JkqRZzMtVVVV1J/B54DBgtyQ7tFn7AOvb9DpgX4A2/9HAxsH2KZaRJM2zUV5VtTjJbm36kcBTgRuAzwHPbt1WAB9r06vae9r8z1ZVtfbj21VXBwDLgMtGVbckaWY7zN5ls+0FnNuugNoOuKCqLkpyPXB+ktcDXwHObv3PBt6bZC3dkcbxAFV1XZILgOuBTcBJVfXACOuWJM1gZMFRVdcAT5qi/SamuCqqqv4DeM406zodOH2ua5Qk9ec3xyVJvRgckqReDA5JUi8GhySpF4NDktSLwSFJ6sXgkCT1YnBIknoxOCRJvRgckqReDA5JUi8GhySpF4NDktSLwSFJ6sXgkCT1YnBIknoxOCRJvRgckqReDA5JUi8GhySpF4NDktTLyIIjyb5JPpfkhiTXJXlJaz8tyXeSXNVexw4s84oka5N8PcnTBtqPbm1rk5wyqpolSbPbYYTr3gS8vKquTLIrcEWS1W3eW6rqjYOdkxwIHA88Htgb+EySX2iz3wH8BrAOuDzJqqq6foS1S5KmMbLgqKpbgVvb9D1JbgCWzLDIccD5VXU/8M0ka4FD2ry1VXUTQJLzW1+DQ5LGYF7OcSRZCjwJ+HJrOjnJNUlWJtm9tS0BbhlYbF1rm6598jZOTLImyZoNGzbM8SeQJE0YeXAk2QX4CPDSqrobeCfwWOAguiOSN010nWLxmqH9wQ1VZ1XV8qpavnjx4jmpXZL0UKM8x0GSHelC4/1V9VGAqrptYP67gIva23XAvgOL7wOsb9PTtUuS5tkor6oKcDZwQ1W9eaB9r4FuvwVc26ZXAccneUSSA4BlwGXA5cCyJAck2YnuBPqqUdUtSZrZKI84ngK8APhqkqta2yuB5yU5iG646WbgDwGq6rokF9Cd9N4EnFRVDwAkORm4BNgeWFlV142wbknSDEZ5VdUXmfr8xMUzLHM6cPoU7RfPtJwkaf74zXFJUi8GhySpF4NDktSLwSFJ6sXgkCT1YnBIknoxOCRJvRgckqReDA5JUi8GhySpF4NDktSLwSFJ6sXgkCT1YnBIknoxOCRJvRgckqReDA5JUi8GhySpF4NDktSLwSFJ6sXgkCT1MrLgSLJvks8luSHJdUle0tr3SLI6yY3t5+6tPUnOTLI2yTVJDh5Y14rW/8YkK0ZVsyRpdkMFR5KXJHlU++V+dpIrkxw1y2KbgJdX1eOAw4CTkhwInAJcWlXLgEvbe4BjgGXtdSLwzrbtPYBTgUOBQ4BTJ8JGkjT/hj3i+P2quhs4ClgMvBg4Y6YFqurWqrqyTd8D3AAsAY4Dzm3dzgWe1aaPA86rzpeA3ZLsBTwNWF1VG6vqe8Bq4OhhP6AkaW4NGxxpP48F3lNVVw+0zb5wshR4EvBlYM+quhW6cAEe07otAW4ZWGxda5uuffI2TkyyJsmaDRs2DFuaJKmnYYPjiiSfpguOS5LsCvxomAWT7AJ8BHhpO2qZtusUbTVD+4Mbqs6qquVVtXzx4sXDlCZJ2gzDBscJdOcinlxV9wE70Q1XzSjJjnSh8f6q+mhrvq0NQdF+3t7a1wH7Diy+D7B+hnZJ0hgMGxyrq+rKqroToKruAN4y0wJJApwN3FBVbx6YtQqYuDJqBfCxgfYXthPwhwF3taGsS4CjkuzeToof1dokSWOww0wzk+wM/BSwqP3Snhg2ehSw9yzrfgrwAuCrSa5qba+kO6l+QZITgG8Dz2nzLqYbClsL3Ec7oqmqjUleB1ze+r22qjYO9/EkSXNtxuAA/hB4KV1IXMFPguNu4B0zLVhVX2T6E+hHTtG/gJOmWddKYOUstUqS5sGMwVFVbwXemuRPq+pt81STJGkBm+2IA4CqeluS/wYsHVymqs4bUV2SpAVqqOBI8l7gscBVwAOtuQCDQ5K2MUMFB7AcOLCdh5AkbcOGvRz3WuBnR1mIJGnrMOwRxyLg+iSXAfdPNFbVM0dSlSRpwRo2OE4bZRGSpK3HsFdV/cuoC5EkbR2GvarqHn5yY8GdgB2B71fVo0ZVmCRpYRr2iGPXwfdJnkX3UCVJ0jZmsx4dW1X/DBwxx7VIkrYCww5V/fbA2+3ovtfhdzokaRs07FVVzxiY3gTcTPeoV0nSFJae8omxbPfmM54+8m0Me45j1oc2SZK2DUOd40iyT5ILk9ye5LYkH0myz6iLkyQtPMOeHH8P3RP69gaWAB9vbZKkbcywwbG4qt5TVZva6xxg8QjrkiQtUMMGx3eTPD/J9u31fOCOURYmSVqYhg2O3weeC/w7cCvwbNozwSVJ25ZhL8d9HbCiqr4HkGQP4I10gSJJ2oYMe8TxSxOhAVBVG4EnjaYkSdJCNmxwbJdk94k37YhjxqOVJCvb5bvXDrSdluQ7Sa5qr2MH5r0iydokX0/ytIH2o1vb2iSnDP/RJEmjMOxQ1ZuA/5vkw3S3GnkucPosy5wDvJ2HPpf8LVX1xsGGJAcCxwOPp7vk9zNJfqHNfgfwG8A64PIkq6rq+iHrliTNsWG/OX5ekjV0NzYM8Nuz/fKuqi8kWTpkHccB51fV/cA3k6zlJ3ffXVtVNwEkOb/1NTgkaUyGPeKgBcVc/MI+OckLgTXAy9u5kyXAlwb6rGttALdMaj90qpUmORE4EWC//fabgzIlzZVx3bdJo7FZt1XfAu8EHgscRHdZ75tae6boWzO0P7Sx6qyqWl5Vyxcv9ruJkjQqQx9xzIWqum1iOsm7gIva23XAvgNd9wHWt+np2iVJYzCvRxxJ9hp4+1vAxBVXq4DjkzwiyQHAMuAy4HJgWZIDkuxEdwJ91XzWLEl6sJEdcST5IHA4sCjJOuBU4PAkB9ENN90M/CFAVV2X5AK6cyibgJOq6oG2npOBS4DtgZVVdd2oapYkzW5kwVFVz5ui+ewZ+p/OFJf4VtXFwMVzWJokaQvM98lxSdJWzuCQJPVicEiSejE4JEm9GBySpF4MDklSLwaHJKkXg0OS1IvBIUnqxeCQJPVicEiSejE4JEm9GBySpF4MDklSLwaHJKkXg0OS1IvBIUnqxeCQJPVicEiSejE4JEm9GBySpF5GFhxJVia5Pcm1A217JFmd5Mb2c/fWniRnJlmb5JokBw8ss6L1vzHJilHVK0kaziiPOM4Bjp7UdgpwaVUtAy5t7wGOAZa114nAO6ELGuBU4FDgEODUibCRJI3HyIKjqr4AbJzUfBxwbps+F3jWQPt51fkSsFuSvYCnAauramNVfQ9YzUPDSJI0j+b7HMeeVXUrQPv5mNa+BLhloN+61jZd+0MkOTHJmiRrNmzYMOeFS5I6C+XkeKZoqxnaH9pYdVZVLa+q5YsXL57T4iRJPzHfwXFbG4Ki/by9ta8D9h3otw+wfoZ2SdKYzHdwrAImroxaAXxsoP2F7eqqw4C72lDWJcBRSXZvJ8WPam2SpDHZYVQrTvJB4HBgUZJ1dFdHnQFckOQE4NvAc1r3i4FjgbXAfcCLAapqY5LXAZe3fq+tqskn3CVJ82hkwVFVz5tm1pFT9C3gpGnWsxJYOYelSZK2wEI5OS5J2koYHJKkXgwOSVIvBockqZeRnRyXtLAsPeUT4y5BDxMecUiSejE4JEm9GBySpF4MDklSLwaHJKkXg0OS1IvBIUnqxeCQJPVicEiSejE4JEm9GBySpF4MDklSLwaHJKkXg0OS1IvBIUnqxeCQJPUyluBIcnOSrya5Ksma1rZHktVJbmw/d2/tSXJmkrVJrkly8DhqliR1xnnE8etVdVBVLW/vTwEuraplwKXtPcAxwLL2OhF457xXKkn6sYU0VHUccG6bPhd41kD7edX5ErBbkr3GUaAkaXzBUcCnk1yR5MTWtmdV3QrQfj6mtS8BbhlYdl1re5AkJyZZk2TNhg0bRli6JG3bdhjTdp9SVeuTPAZYneRrM/TNFG31kIaqs4CzAJYvX/6Q+ZKkuTGWI46qWt9+3g5cCBwC3DYxBNV+3t66rwP2HVh8H2D9/FUrSRo070ccSX4a2K6q7mnTRwGvBVYBK4Az2s+PtUVWAScnOR84FLhrYkhL2hotPeUT4y5B2iLjGKraE7gwycT2P1BVn0pyOXBBkhOAbwPPaf0vBo4F1gL3AS+e/5IlSRPmPTiq6ibgiVO03wEcOUV7ASfNQ2mSpCEspMtxJUlbAYNDktSLwSFJ6sXgkCT1YnBIknoxOCRJvRgckqReDA5JUi8GhySpF4NDktSLwSFJ6sXgkCT1YnBIknoxOCRJvRgckqReDA5JUi/jeAKgNHY+vlXafB5xSJJ6MTgkSb04VKWxcshI2vp4xCFJ6mWrOeJIcjTwVmB74N1VdcaYS3pY8S9/ScPaKo44kmwPvAM4BjgQeF6SA8dblSRtm7aWI45DgLVVdRNAkvOB44DrR7Ex//qWpOltLcGxBLhl4P064NDBDklOBE5sb+9N8vUt2N4i4LtbsPyoWFc/1tWPdfWzIOvK325RXfsP02lrCY5M0VYPelN1FnDWnGwsWVNVy+diXXPJuvqxrn6sq59tua6t4hwH3RHGvgPv9wHWj6kWSdqmbS3BcTmwLMkBSXYCjgdWjbkmSdombRVDVVW1KcnJwCV0l+OurKrrRrjJORnyGgHr6se6+rGufrbZulJVs/eSJKnZWoaqJEkLhMEhSeplmw2OJCuT3J7k2mnmJ8mZSdYmuSbJwQukrsOT3JXkqvZ69TzVtW+SzyW5Icl1SV4yRZ9532dD1jXv+yzJzkkuS3J1q+s1U/R5RJIPtf315SRLF0hdL0qyYWB//cGo6xrY9vZJvpLkoinmzfv+GqKmce6rm5N8tW13zRTzR/fvsaq2yRfwP4CDgWunmX8s8Em675AcBnx5gdR1OHDRGPbXXsDBbXpX4BvAgePeZ0PWNe/7rO2DXdr0jsCXgcMm9fkT4B/b9PHAhxZIXS8C3j7f/4+1bb8M+MBU/73Gsb+GqGmc++pmYNEM80f273GbPeKoqi8AG2fochxwXnW+BOyWZK8FUNdYVNWtVXVlm74HuIHuG/2D5n2fDVnXvGv74N72dsf2mnwlynHAuW36w8CRSab6sut81zUWSfYBng68e5ou876/hqhpIRvZv8dtNjiGMNVtTsb+C6n5lTbU8Mkkj5/vjbchgifR/bU6aKz7bIa6YAz7rA1xXAXcDqyuqmn3V1VtAu4CfmYB1AXwO21448NJ9p1i/ij8b+AvgR9NM38c+2u2mmA8+wq6wP90kivS3XJpspH9ezQ4pjfrbU7G5Epg/6p6IvA24J/nc+NJdgE+Ary0qu6ePHuKReZln81S11j2WVU9UFUH0d3p4JAkT5jUZSz7a4i6Pg4srapfAj7DT/7KH5kkvwncXlVXzNRtiraR7a8ha5r3fTXgKVV1MN1dw09K8j8mzR/Z/jI4prcgb3NSVXdPDDVU1cXAjkkWzce2k+xI98v5/VX10Sm6jGWfzVbXOPdZ2+adwOeBoyfN+vH+SrID8GjmcZhyurqq6o6qur+9fRfwy/NQzlOAZya5GTgfOCLJ+yb1me/9NWtNY9pXE9te337eDlxIdxfxQSP792hwTG8V8MJ2ZcJhwF1Vdeu4i0rysxPjukkOoftveMc8bDfA2cANVfXmabrN+z4bpq5x7LMki5Ps1qYfCTwV+NqkbquAFW362cBnq53VHGddk8bBn0l33mikquoVVbVPVS2lO/H92ap6/qRu87q/hqlpHPuqbfenk+w6MQ0cBUy+EnNk/x63iluOjEKSD9JdbbMoyTrgVLoThVTVPwIX012VsBa4D3jxAqnr2cAfJ9kE/AA4ftS/bJqnAC8AvtrGxwFeCew3UNs49tkwdY1jn+0FnJvuIWTbARdU1UVJXgusqapVdIH33iRr6f5yPn7ENQ1b158leSawqdX1onmoa0oLYH/NVtO49tWewIXt76EdgA9U1aeS/BGM/t+jtxyRJPXiUJUkqReDQ5LUi8EhSerF4JAk9WJwSJJ6MTikzZDkgXZX0muTfHziuxEz9N8tyZ8MvN87yYdHX6k097wcV9oMSe6tql3a9LnAN6rq9Bn6L6W7u+rk23tIWx2POKQt92+0m8cl2SXJpUmuTPeshONanzOAx7ajlL9PsjTtmSvpnunw0SSfSnJjkr+bWHGSE5J8I8nnk7wrydvn/dNJk2yz3xyX5kL7BvaRdN9qBvgP4Leq6u52P6wvJVkFnAI8od1ccOIIZNBBdHf2vR/4epK3AQ8Af0P3fJZ7gM8CV4/0A0lDMDikzfPIdouTpcAVwOrWHuAN7U6lP6I7EtlziPVdWlV3ASS5HtgfWAT8S1VtbO3/BPzCXH4IaXM4VCVtnh+0o4f9gZ2Ak1r77wGLgV9u828Ddh5iffcPTD9A90fdSB9SJG0ug0PaAu0o4c+Av2i3d3803TMcfpjk1+mCBbqhpl17rv4y4NeS7N5uI/47c1W3tCUMDmkLVdVX6M49HA+8H1ieZA3d0cfXWp87gP/TLt/9+yHX+x3gDXRPNPwMcD3dU++ksfJyXGkBS7JLVd3bjjguBFZW1YXjrkvbNo84pIXttHYS/lrgm8zzo4KlqXjEIUnqxSMOSVIvBockqReDQ5LUi8EhSerF4JAk9fL/AdvOSrwvmHbfAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Describe Rating dataframe\n",
    "plot_hist(df_rating, 'Rating')\n",
    "df_rating.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "There are 7592 free and 604 paid apps in the the Rating dataframe \n"
     ]
    }
   ],
   "source": [
    "print(\"There are {} free and {} paid apps in the the Rating dataframe \".format(*compute_app_types(df_rating)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# explore the distributions of free and paid apps across different categories\n",
    "plot_app_types(df_rating)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Deleted categories: ['BUSINESS', 'NEWS_AND_MAGAZINES', 'SOCIAL', 'TRAVEL_AND_LOCAL', 'SHOPPING', 'BOOKS_AND_REFERENCE', 'VIDEO_PLAYERS', 'DATING', 'MAPS_AND_NAVIGATION', 'EDUCATION', 'ENTERTAINMENT', 'FOOD_AND_DRINK', 'AUTO_AND_VEHICLES', 'WEATHER', 'LIBRARIES_AND_DEMO', 'HOUSE_AND_HOME', 'ART_AND_DESIGN', 'COMICS', 'PARENTING', 'EVENTS', 'BEAUTY']\n",
      "Cleaned Rating dataframe has 5753 datapoints\n"
     ]
    }
   ],
   "source": [
    "# Exclude categories with fewer than 10 apps for any Free or Paid type\n",
    "# Otherwise the categories would contain too few data to generalize the result\n",
    "df_rating = drop_categories(df_rating)\n",
    "print(\"Cleaned Rating dataframe has {} datapoints\".format(df_rating.shape[0]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "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>Rating</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>5753.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>4.173197</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.544844</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>4.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>4.300000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>4.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>5.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            Rating\n",
       "count  5753.000000\n",
       "mean      4.173197\n",
       "std       0.544844\n",
       "min       1.000000\n",
       "25%       4.000000\n",
       "50%       4.300000\n",
       "75%       4.500000\n",
       "max       5.000000"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_rating.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Q 1. How does the ratings differ in general?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_target_by_group(df, target_col, group_col, figsize=(6,4), title=\"\"):\n",
    "    \"\"\"\n",
    "    Plot the mean of a target column (Numeric) groupped by the group column (categorical)\n",
    "    \"\"\"\n",
    "    order = sorted(list(set(df[group_col])))\n",
    "    stats = df.groupby(group_col).mean()[target_col]\n",
    "    fig, ax = plt.subplots(figsize=figsize)\n",
    "    sns.barplot(x=group_col, y=target_col, data=df, ax=ax, order=order).set_title(title)\n",
    "    ax.set(ylim=(3.8, 4.5))    \n",
    "    return stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Free app has average Rating 4.163495108382891\n",
      "Paid app has average Rating 4.266851851851849\n",
      "Mean rating: 4.173196593081873\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/chen/anaconda3/lib/python3.6/site-packages/scipy/stats/stats.py:1713: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  return np.add.reduce(sorted[indexer] * weights, axis=axis) / sumval\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "stats = plot_target_by_group(df_rating, 'Rating', 'Type', title=\"Average Rating Groupped by App Type\")\n",
    "for i, s in zip(stats.index, stats):\n",
    "    print(\"{} app has average {} {}\".format(i, 'Rating',s))\n",
    "mean_rating = df_rating.Rating.mean()\n",
    "print(\"Mean rating: {}\".format(mean_rating))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Interpretation\n",
    "In general, Free apps, with an average rating of 4.16, are lower rated than Paid apps with an average rating of 4.27. Note that the average rating for all apps is 4.17, so Free apps are rated below average, while Paid apps are rated reletively higher than the average score."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Q2 How are the differences distributed across different app categories?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "paid_stats = plot_target_by_group(df_rating.query('Type == \"Paid\"'), 'Rating', 'Category', (16, 4), \"(Paid App) Average Ratings by App Category\")\n",
    "free_stats = plot_target_by_group(df_rating.query('Type == \"Free\"'), 'Rating', 'Category', (16, 4), \"(Free App) Average Ratings by App Category\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Category\n",
       "COMMUNICATION        -0.063287\n",
       "FAMILY                0.115128\n",
       "FINANCE              -0.297604\n",
       "GAME                  0.136364\n",
       "HEALTH_AND_FITNESS    0.154858\n",
       "LIFESTYLE             0.166608\n",
       "MEDICAL               0.087344\n",
       "PERSONALIZATION       0.147692\n",
       "PHOTOGRAPHY          -0.152796\n",
       "PRODUCTIVITY          0.023577\n",
       "SPORTS                0.041940\n",
       "TOOLS                 0.142818\n",
       "Name: Rating, dtype: float64"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(16,4))\n",
    "sorted_idx = sorted(paid_stats.index)\n",
    "rating_diff = paid_stats[sorted_idx] - free_stats[sorted_idx]\n",
    "sns.barplot(x=sorted_idx, y=rating_diff, ax=ax).set_title(\"Difference of Ratings between Paid and Free Apps Across App Categories\");\n",
    "rating_diff"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Interpretation\n",
    "Although paid apps are in general more highly-rated than free apps, and so are in most app categories, there are still some app categories where free apps are likely to be favored more than the paid apps. For instance, COMMUNICATION, FINANCE and PHOTOGRAPHY are three such categories. In FINANCE category, the free apps on average are rated almost 0.3 higher than the paid apps, which is also the largest difference between app types across all the categories.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Q3 Are there any categories where the differences are statistically significant?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "General utest result: pval 4.17841444099998e-10, u 1182741.0\n"
     ]
    },
    {
     "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>Category</th>\n",
       "      <th>p_value</th>\n",
       "      <th>u_statistics</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>FAMILY</td>\n",
       "      <td>0.000036</td>\n",
       "      <td>90258.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>TOOLS</td>\n",
       "      <td>0.003025</td>\n",
       "      <td>16327.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>PERSONALIZATION</td>\n",
       "      <td>0.002357</td>\n",
       "      <td>5845.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>GAME</td>\n",
       "      <td>0.000191</td>\n",
       "      <td>24001.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           Category   p_value  u_statistics\n",
       "0            FAMILY  0.000036       90258.0\n",
       "1             TOOLS  0.003025       16327.0\n",
       "7   PERSONALIZATION  0.002357        5845.5\n",
       "11             GAME  0.000191       24001.0"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def compute_utest(df):\n",
    "    \"\"\"\n",
    "    Compute Mann-Whitney rank tests\n",
    "    for paid and free app ratings\n",
    "    \"\"\"\n",
    "    paid_rating = df.query('Type == \"Paid\"')['Rating']\n",
    "    free_rating = df.query('Type == \"Free\"')['Rating']\n",
    "    return mannwhitneyu(paid_rating, free_rating)\n",
    "\n",
    "def cat_utest(df):\n",
    "    \"\"\"\n",
    "    Iteratively compute utest for each app category\n",
    "    \"\"\"\n",
    "    cats = set(df.Category)\n",
    "    res = []\n",
    "    for cat in cats:\n",
    "        stats, pval = compute_utest(df.query('Category == \"{}\"'.format(cat)))\n",
    "        res.append({'Category':cat,\n",
    "                    'u_statistics':stats,\n",
    "                    'p_value':pval})\n",
    "    return pd.DataFrame(res)\n",
    "\n",
    "uval, pval = compute_utest(df_rating)\n",
    "\n",
    "print(\"General utest result: pval {}, u {}\".format(pval, uval))\n",
    "df_utest = cat_utest(df_rating)   \n",
    "df_utest.loc[df_utest.p_value < .05] # significant categories"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Interpretation\n",
    "As rating is not normally-distributed, Mann-Whitney's U test was applied to test the significance of rating differences, since this test is free from a normal assumption. At the 0.05 significance level, results of the u tests on different categories demonstrate that the free and paid apps in the following categories have significant rating differences: personalization, tools, family and games. Paid apps are on average higher rated than free apps in these categories."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Concluding Remarks\n",
    "\n",
    "Data analysis was conducted on the Kaggle Google Play Store dataset, the answers to the three questions were explored:\n",
    "- How do the ratings differ between paid and free apps in general?\n",
    "  In general, Paid apps are better-rated than free apps, which appears to support the argument that service quility of the paid apps is better.\n",
    "- How are the differences distributed across different app categories?\n",
    "  In most categories, Paid apps achieve higher ratings than free apps, however, in a few categories such as COMMUNICATION, FINANCE and PHOTOGRAPHY, the average ratings of free apps are higher than those of paid apps. Is this because many popular apps in these categories are free, like facebook and whatsapp in the COMMUNICATION category?\n",
    "- Are there any categories where the differences are statistically significant?\n",
    "  There are four categories (PERSONALIZATION, TOOLS, FAMILY and GAME) where paid apps are rated significantly higher than free apps.\n",
    "  \n",
    "This is only a very superficial exploration of the Google Play Store dataset. There are many other useful information including installation counts and app review texts, which might entail many more interesting facts and await further exploration.\n",
    "  \n",
    "\n",
    "  \n",
    "\n"
   ]
  },
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   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
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