ChiSquare.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Performing Chi$^2$ analysis to see whether the frequency distribution of a dataset matches the expected distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "from scipy.stats import chi2_contingency"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Unnamed: 0</th>\n",
       "      <th>Clothing ID</th>\n",
       "      <th>Age</th>\n",
       "      <th>Title</th>\n",
       "      <th>Review Text</th>\n",
       "      <th>Rating</th>\n",
       "      <th>Recommended IND</th>\n",
       "      <th>Positive Feedback Count</th>\n",
       "      <th>Division Name</th>\n",
       "      <th>Department Name</th>\n",
       "      <th>Class Name</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>767</td>\n",
       "      <td>33</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Absolutely wonderful - silky and sexy and comf...</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>Initmates</td>\n",
       "      <td>Intimate</td>\n",
       "      <td>Intimates</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>1080</td>\n",
       "      <td>34</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Love this dress!  it's sooo pretty.  i happene...</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>General</td>\n",
       "      <td>Dresses</td>\n",
       "      <td>Dresses</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>1077</td>\n",
       "      <td>60</td>\n",
       "      <td>Some major design flaws</td>\n",
       "      <td>I had such high hopes for this dress and reall...</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>General</td>\n",
       "      <td>Dresses</td>\n",
       "      <td>Dresses</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>1049</td>\n",
       "      <td>50</td>\n",
       "      <td>My favorite buy!</td>\n",
       "      <td>I love, love, love this jumpsuit. it's fun, fl...</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>General Petite</td>\n",
       "      <td>Bottoms</td>\n",
       "      <td>Pants</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>847</td>\n",
       "      <td>47</td>\n",
       "      <td>Flattering shirt</td>\n",
       "      <td>This shirt is very flattering to all due to th...</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>6</td>\n",
       "      <td>General</td>\n",
       "      <td>Tops</td>\n",
       "      <td>Blouses</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Unnamed: 0  Clothing ID  Age                    Title  \\\n",
       "0           0          767   33                      NaN   \n",
       "1           1         1080   34                      NaN   \n",
       "2           2         1077   60  Some major design flaws   \n",
       "3           3         1049   50         My favorite buy!   \n",
       "4           4          847   47         Flattering shirt   \n",
       "\n",
       "                                         Review Text  Rating  Recommended IND  \\\n",
       "0  Absolutely wonderful - silky and sexy and comf...       4                1   \n",
       "1  Love this dress!  it's sooo pretty.  i happene...       5                1   \n",
       "2  I had such high hopes for this dress and reall...       3                0   \n",
       "3  I love, love, love this jumpsuit. it's fun, fl...       5                1   \n",
       "4  This shirt is very flattering to all due to th...       5                1   \n",
       "\n",
       "   Positive Feedback Count   Division Name Department Name Class Name  \n",
       "0                        0       Initmates        Intimate  Intimates  \n",
       "1                        4         General         Dresses    Dresses  \n",
       "2                        0         General         Dresses    Dresses  \n",
       "3                        0  General Petite         Bottoms      Pants  \n",
       "4                        6         General            Tops    Blouses  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "e_comm_data = pd.read_csv('datasets/Womens Clothing E-Commerce Reviews.csv')\n",
    "e_comm_data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['Unnamed: 0', 'Clothing ID', 'Age', 'Title', 'Review Text', 'Rating',\n",
       "       'Recommended IND', 'Positive Feedback Count', 'Division Name',\n",
       "       'Department Name', 'Class Name'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "e_comm_data.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "columns_to_keep = ['Clothing ID', 'Age', 'Rating',\n",
    "       'Recommended IND', 'Positive Feedback Count', 'Division Name',\n",
    "       'Department Name', 'Class Name']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "new_e_comm_data = e_comm_data[columns_to_keep]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Clothing ID</th>\n",
       "      <th>Age</th>\n",
       "      <th>Rating</th>\n",
       "      <th>Recommended IND</th>\n",
       "      <th>Positive Feedback Count</th>\n",
       "      <th>Division Name</th>\n",
       "      <th>Department Name</th>\n",
       "      <th>Class Name</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>14394</th>\n",
       "      <td>1078</td>\n",
       "      <td>36</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>General Petite</td>\n",
       "      <td>Dresses</td>\n",
       "      <td>Dresses</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3607</th>\n",
       "      <td>881</td>\n",
       "      <td>47</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>General</td>\n",
       "      <td>Tops</td>\n",
       "      <td>Knits</td>\n",
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       "    <tr>\n",
       "      <th>4025</th>\n",
       "      <td>1094</td>\n",
       "      <td>38</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>General Petite</td>\n",
       "      <td>Dresses</td>\n",
       "      <td>Dresses</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19504</th>\n",
       "      <td>875</td>\n",
       "      <td>57</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>8</td>\n",
       "      <td>General</td>\n",
       "      <td>Tops</td>\n",
       "      <td>Knits</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9909</th>\n",
       "      <td>961</td>\n",
       "      <td>21</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>General</td>\n",
       "      <td>Jackets</td>\n",
       "      <td>Jackets</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22405</th>\n",
       "      <td>877</td>\n",
       "      <td>42</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>General Petite</td>\n",
       "      <td>Tops</td>\n",
       "      <td>Knits</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12774</th>\n",
       "      <td>215</td>\n",
       "      <td>42</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>Initmates</td>\n",
       "      <td>Intimate</td>\n",
       "      <td>Legwear</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5532</th>\n",
       "      <td>861</td>\n",
       "      <td>41</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>General</td>\n",
       "      <td>Tops</td>\n",
       "      <td>Knits</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12443</th>\n",
       "      <td>936</td>\n",
       "      <td>75</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>General Petite</td>\n",
       "      <td>Tops</td>\n",
       "      <td>Sweaters</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8925</th>\n",
       "      <td>1110</td>\n",
       "      <td>61</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>General</td>\n",
       "      <td>Dresses</td>\n",
       "      <td>Dresses</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Clothing ID  Age  Rating  Recommended IND  Positive Feedback Count  \\\n",
       "14394         1078   36       4                1                        0   \n",
       "3607           881   47       5                1                        0   \n",
       "4025          1094   38       5                1                        0   \n",
       "19504          875   57       4                1                        8   \n",
       "9909           961   21       5                1                        0   \n",
       "22405          877   42       5                1                        1   \n",
       "12774          215   42       4                1                        1   \n",
       "5532           861   41       5                1                        0   \n",
       "12443          936   75       5                1                        2   \n",
       "8925          1110   61       4                1                        1   \n",
       "\n",
       "        Division Name Department Name Class Name  \n",
       "14394  General Petite         Dresses    Dresses  \n",
       "3607          General            Tops      Knits  \n",
       "4025   General Petite         Dresses    Dresses  \n",
       "19504         General            Tops      Knits  \n",
       "9909          General         Jackets    Jackets  \n",
       "22405  General Petite            Tops      Knits  \n",
       "12774       Initmates        Intimate    Legwear  \n",
       "5532          General            Tops      Knits  \n",
       "12443  General Petite            Tops   Sweaters  \n",
       "8925          General         Dresses    Dresses  "
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new_e_comm_data.sample(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(23486, 8)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new_e_comm_data.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Recommended IND</th>\n",
       "      <th>Rating</th>\n",
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       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
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       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>5</td>\n",
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       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>5</td>\n",
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      ],
      "text/plain": [
       "   Recommended IND  Rating\n",
       "0                1       4\n",
       "1                1       5\n",
       "2                0       3\n",
       "3                1       5\n",
       "4                1       5"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "working_data = new_e_comm_data[['Recommended IND', 'Rating']]\n",
    "working_data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[<AxesSubplot:title={'center':'Rating'}>]], dtype=object)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "new_e_comm_data[['Rating']].hist(figsize=(12, 8))"
   ]
  },
  {
   "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>Rating</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Recommended IND</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>0</th>\n",
       "      <td>826</td>\n",
       "      <td>1471</td>\n",
       "      <td>1682</td>\n",
       "      <td>168</td>\n",
       "      <td>25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>16</td>\n",
       "      <td>94</td>\n",
       "      <td>1189</td>\n",
       "      <td>4909</td>\n",
       "      <td>13106</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Rating             1     2     3     4      5\n",
       "Recommended IND                              \n",
       "0                826  1471  1682   168     25\n",
       "1                 16    94  1189  4909  13106"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_for_obs = pd.crosstab(new_e_comm_data['Recommended IND'], new_e_comm_data['Rating'])\n",
    "df_for_obs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4> Using Pearson's Chi$2$ statistic to test for the independence of two categorical variables<h4>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "chi2, p_value, degrees_of_freedom, expected_values = chi2_contingency(df_for_obs.values)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Objective </h3>\n",
    "\n",
    "Are recommendations **independent** of ratings? Are the observed frequencies of ratings different across these categories?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Chi2 stats: 16722.503\n"
     ]
    }
   ],
   "source": [
    "print('Chi2 stats: {}'.format(round(chi2, 3)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Checking p-values if Chi$2$ is significant or not"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The p-values: 0.0\n"
     ]
    }
   ],
   "source": [
    "print(\"The p-values: {}\".format(p_value))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This tells us that the Chi$2$ test is significant"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The degree of freedom: 4\n"
     ]
    }
   ],
   "source": [
    "print(\"The degree of freedom: {}\".format(degrees_of_freedom))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The degree of freedom <br>\n",
    "= (the number of categories we're working with - 1) <br>\n",
    "= 5 - 1 <br>\n",
    "= 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  149.57097846,   278.00306566,   509.99795623,   901.86681427,\n",
       "         2332.56118539],\n",
       "       [  692.42902154,  1286.99693434,  2361.00204377,  4175.13318573,\n",
       "        10798.43881461]])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "expected_values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Expected values are the values that Chi$2$ expected the values to be distributed for both recommended and not recommended product. <br>\n",
    "First row: Expected distribution for not recommended product <br>\n",
    "Second row: Expected distribution for recommended product\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "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>0</th>\n",
       "      <th>1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>149.570978</td>\n",
       "      <td>692.429022</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>278.003066</td>\n",
       "      <td>1286.996934</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>509.997956</td>\n",
       "      <td>2361.002044</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>901.866814</td>\n",
       "      <td>4175.133186</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2332.561185</td>\n",
       "      <td>10798.438815</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             0             1\n",
       "0   149.570978    692.429022\n",
       "1   278.003066   1286.996934\n",
       "2   509.997956   2361.002044\n",
       "3   901.866814   4175.133186\n",
       "4  2332.561185  10798.438815"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "expected_df = pd.DataFrame({\n",
    "    '0': expected_values[0],\n",
    "    '1': expected_values[1]\n",
    "})\n",
    "expected_df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Barplot visualization of the expected values for 'Ratings' product**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f8f1077e1f0>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12, 8 ))\n",
    "\n",
    "plt.bar(expected_df.index, expected_df['1'], label='Recommended')\n",
    "plt.bar(expected_df.index, expected_df['0'], label='Not recommended')\n",
    "\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "ratings_recommended = new_e_comm_data[new_e_comm_data['Recommended IND'] == 1]\n",
    "ratings_not_recommended = new_e_comm_data[new_e_comm_data['Recommended IND'] == 0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((19314, 8), (4172, 8))"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ratings_recommended.shape, ratings_not_recommended.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "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>Clothing ID</th>\n",
       "      <th>Age</th>\n",
       "      <th>Rating</th>\n",
       "      <th>Recommended IND</th>\n",
       "      <th>Positive Feedback Count</th>\n",
       "      <th>Division Name</th>\n",
       "      <th>Department Name</th>\n",
       "      <th>Class Name</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>22500</th>\n",
       "      <td>1098</td>\n",
       "      <td>57</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>General</td>\n",
       "      <td>Dresses</td>\n",
       "      <td>Dresses</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3021</th>\n",
       "      <td>999</td>\n",
       "      <td>33</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>General</td>\n",
       "      <td>Bottoms</td>\n",
       "      <td>Skirts</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14885</th>\n",
       "      <td>940</td>\n",
       "      <td>74</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>General</td>\n",
       "      <td>Tops</td>\n",
       "      <td>Sweaters</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5280</th>\n",
       "      <td>895</td>\n",
       "      <td>36</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>General</td>\n",
       "      <td>Tops</td>\n",
       "      <td>Fine gauge</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14005</th>\n",
       "      <td>939</td>\n",
       "      <td>44</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>General Petite</td>\n",
       "      <td>Tops</td>\n",
       "      <td>Sweaters</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10782</th>\n",
       "      <td>1110</td>\n",
       "      <td>43</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>General Petite</td>\n",
       "      <td>Dresses</td>\n",
       "      <td>Dresses</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3553</th>\n",
       "      <td>1077</td>\n",
       "      <td>46</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>5</td>\n",
       "      <td>General</td>\n",
       "      <td>Dresses</td>\n",
       "      <td>Dresses</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9986</th>\n",
       "      <td>1110</td>\n",
       "      <td>55</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>General</td>\n",
       "      <td>Dresses</td>\n",
       "      <td>Dresses</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11392</th>\n",
       "      <td>1094</td>\n",
       "      <td>52</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>General Petite</td>\n",
       "      <td>Dresses</td>\n",
       "      <td>Dresses</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10833</th>\n",
       "      <td>1110</td>\n",
       "      <td>30</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>General</td>\n",
       "      <td>Dresses</td>\n",
       "      <td>Dresses</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Clothing ID  Age  Rating  Recommended IND  Positive Feedback Count  \\\n",
       "22500         1098   57       5                1                        1   \n",
       "3021           999   33       5                1                        0   \n",
       "14885          940   74       3                1                        0   \n",
       "5280           895   36       4                1                        0   \n",
       "14005          939   44       4                1                        0   \n",
       "10782         1110   43       5                1                        0   \n",
       "3553          1077   46       4                1                        5   \n",
       "9986          1110   55       5                1                        2   \n",
       "11392         1094   52       5                1                        0   \n",
       "10833         1110   30       5                1                        1   \n",
       "\n",
       "        Division Name Department Name  Class Name  \n",
       "22500         General         Dresses     Dresses  \n",
       "3021          General         Bottoms      Skirts  \n",
       "14885         General            Tops    Sweaters  \n",
       "5280          General            Tops  Fine gauge  \n",
       "14005  General Petite            Tops    Sweaters  \n",
       "10782  General Petite         Dresses     Dresses  \n",
       "3553          General         Dresses     Dresses  \n",
       "9986          General         Dresses     Dresses  \n",
       "11392  General Petite         Dresses     Dresses  \n",
       "10833         General         Dresses     Dresses  "
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ratings_recommended.sample(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "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>Clothing ID</th>\n",
       "      <th>Age</th>\n",
       "      <th>Rating</th>\n",
       "      <th>Recommended IND</th>\n",
       "      <th>Positive Feedback Count</th>\n",
       "      <th>Division Name</th>\n",
       "      <th>Department Name</th>\n",
       "      <th>Class Name</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2459</th>\n",
       "      <td>1116</td>\n",
       "      <td>63</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>General</td>\n",
       "      <td>Jackets</td>\n",
       "      <td>Outerwear</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20344</th>\n",
       "      <td>872</td>\n",
       "      <td>54</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>General</td>\n",
       "      <td>Tops</td>\n",
       "      <td>Knits</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9693</th>\n",
       "      <td>865</td>\n",
       "      <td>23</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>General</td>\n",
       "      <td>Tops</td>\n",
       "      <td>Knits</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9338</th>\n",
       "      <td>868</td>\n",
       "      <td>38</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>General Petite</td>\n",
       "      <td>Tops</td>\n",
       "      <td>Knits</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14599</th>\n",
       "      <td>1084</td>\n",
       "      <td>40</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>11</td>\n",
       "      <td>General</td>\n",
       "      <td>Dresses</td>\n",
       "      <td>Dresses</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12990</th>\n",
       "      <td>661</td>\n",
       "      <td>43</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>General Petite</td>\n",
       "      <td>Intimate</td>\n",
       "      <td>Lounge</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19885</th>\n",
       "      <td>1080</td>\n",
       "      <td>39</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>General Petite</td>\n",
       "      <td>Dresses</td>\n",
       "      <td>Dresses</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18818</th>\n",
       "      <td>857</td>\n",
       "      <td>39</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>12</td>\n",
       "      <td>General Petite</td>\n",
       "      <td>Tops</td>\n",
       "      <td>Knits</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17971</th>\n",
       "      <td>1146</td>\n",
       "      <td>44</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>General Petite</td>\n",
       "      <td>Trend</td>\n",
       "      <td>Trend</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17521</th>\n",
       "      <td>450</td>\n",
       "      <td>36</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>11</td>\n",
       "      <td>General</td>\n",
       "      <td>Bottoms</td>\n",
       "      <td>Shorts</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Clothing ID  Age  Rating  Recommended IND  Positive Feedback Count  \\\n",
       "2459          1116   63       2                0                        5   \n",
       "20344          872   54       3                0                        2   \n",
       "9693           865   23       2                0                        1   \n",
       "9338           868   38       2                0                        1   \n",
       "14599         1084   40       1                0                       11   \n",
       "12990          661   43       1                0                        0   \n",
       "19885         1080   39       3                0                        0   \n",
       "18818          857   39       3                0                       12   \n",
       "17971         1146   44       3                0                        4   \n",
       "17521          450   36       1                0                       11   \n",
       "\n",
       "        Division Name Department Name Class Name  \n",
       "2459          General         Jackets  Outerwear  \n",
       "20344         General            Tops      Knits  \n",
       "9693          General            Tops      Knits  \n",
       "9338   General Petite            Tops      Knits  \n",
       "14599         General         Dresses    Dresses  \n",
       "12990  General Petite        Intimate     Lounge  \n",
       "19885  General Petite         Dresses    Dresses  \n",
       "18818  General Petite            Tops      Knits  \n",
       "17971  General Petite           Trend      Trend  \n",
       "17521         General         Bottoms     Shorts  "
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ratings_not_recommended.sample(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[<AxesSubplot:title={'center':'Rating'}>]], dtype=object)"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ratings_recommended[['Rating']].hist(figsize=(12, 8))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This shows that only the product with ratings greater than 3 are recommended."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[<AxesSubplot:title={'center':'Rating'}>]], dtype=object)"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Visualizing not recommended products\n",
    "ratings_not_recommended[['Rating']].hist(figsize=(12, 8))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This actually proves that our Chi$2$ analysis got it right"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f8f107fac70>"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12, 8))\n",
    "\n",
    "plt.hist(ratings_recommended['Rating'], label='Recommended ')\n",
    "plt.hist(ratings_not_recommended['Rating'], label='Not Recommended')\n",
    "\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Conclusion**<br>\n",
    "This shows that the recommendations of e-commerce sites are not indpendent of the ratings of the products."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}