A_B_test/statistics_A_B_test.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "899a4829",
   "metadata": {},
   "source": [
    "# Imports\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "id": "056a6944",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd \n",
    "import numpy as np\n",
    "\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.dates as mdates\n",
    "\n",
    "import seaborn as sns\n",
    "\n",
    "from scipy import stats as st\n",
    "\n",
    "from scipy.stats import ttest_ind\n",
    "\n",
    "import warnings\n",
    "warnings.filterwarnings( 'ignore' )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "id": "f0c4ec89",
   "metadata": {},
   "outputs": [],
   "source": [
    "def lift(a,b):\n",
    "    # Calcuate the mean of a and b\n",
    "    a_mean = np.mean(a)\n",
    "    b_mean = np.mean(b)\n",
    "    \n",
    "    # Calculate the lift using a_mean and b_mean\n",
    "    lift = (b_mean - a_mean) / a_mean\n",
    "  \n",
    "    return str(round(lift*100, 2)) + '%'\n",
    "  \n",
    "\n",
    "def ab_segmentation(segment):\n",
    "  # Build a for loop for each subsegment in marketing\n",
    "  for subsegment in np.unique(marketing[segment].values):\n",
    "      print(subsegment)\n",
    "      \n",
    "      # Limit marketing to email and subsegment\n",
    "      email = marketing[(marketing['marketing_channel'] == 'Email') & (marketing[segment] == subsegment)]\n",
    "\n",
    "      subscribers = email.groupby(['user_id', 'variant'])['converted'].max()\n",
    "      subscribers = pd.DataFrame(subscribers.unstack(level=1)) \n",
    "      control = subscribers['control'].dropna()\n",
    "      personalization = subscribers['personalization'].dropna()\n",
    "      static, p = ttest_ind(control, personalization)\n",
    "    \n",
    "      print('lift:', lift(control,personalization )) \n",
    "      print('stat=%.3f, p=%.3f' % (stat, p))\n",
    "      [print('Acepted' if p < 0.05 else print('Rejected'))]\n",
    "      print('\\n\\n')\n",
    "      \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "id": "6fecd881",
   "metadata": {},
   "outputs": [],
   "source": [
    "marketing = pd.read_csv('../KPIs_and_Exploratory/data/marketing_new.csv', parse_dates=['date_served', 'date_subscribed', 'date_canceled'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "id": "b95bee05",
   "metadata": {},
   "outputs": [
    {
     "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": [
    "# Subset the DataFrame\n",
    "email = marketing[marketing.marketing_channel == 'Email']\n",
    "\n",
    "# Group the email DataFrame by variant \n",
    "alloc = email.groupby('variant')['user_id'].nunique()\n",
    "\n",
    "# Plot a bar chart of the test allocation\n",
    "alloc.plot(kind= 'bar')\n",
    "plt.title('Personalization test allocation')\n",
    "plt.ylabel('# participants')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "id": "03283550",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "personalization    0.515044\n",
       "control            0.484956\n",
       "Name: variant, dtype: float64"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "marketing[marketing.marketing_channel == 'Email']['variant'].value_counts(normalize=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "id": "37aa3af4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Control conversion rate: 0.2814814814814815\n",
      "Personalization conversion rate: 0.3908450704225352\n"
     ]
    }
   ],
   "source": [
    "# Group marketing by user_id and variant\n",
    "subscribers = email.groupby(['user_id', \n",
    "                             'variant'])['converted'].max()\n",
    "subscribers_df = pd.DataFrame(subscribers.unstack(level=1)) \n",
    "\n",
    "# Drop missing values from the control column\n",
    "control = subscribers_df.control.dropna()\n",
    "\n",
    "# Drop missing values from the personalization column\n",
    "personalization = subscribers_df.personalization.dropna()\n",
    "\n",
    "print('Control conversion rate:', np.mean(control))\n",
    "print('Personalization conversion rate:', np.mean(personalization))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dc8b488a",
   "metadata": {},
   "source": [
    "**Evaluating statistical significance**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "id": "55f46b47",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "stat=-2.734, p=0.006\n",
      "The p value obtained from the t-test is not significant (p > 0.05)- Rejeitamos h0, the results are not the same. There are differences\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[None]"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stat, p = ttest_ind(control, personalization)\n",
    "print('stat=%.3f, p=%.3f' % (stat, p))\n",
    "[print('The p value obtained from the t-test is not significant (p > 0.05)- Rejeitamos h0, the results are not the same. There are differences') if p < 0.05 else print('Aceitamos H0')  ]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3651c974",
   "metadata": {},
   "source": [
    "**LIFT**\n",
    "\n",
    "Lift is a measure of the effectiveness of a marketing campaign or other intervention in increasing a desired outcome"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "id": "9dbc64f9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "38.85%\n"
     ]
    }
   ],
   "source": [
    "# Print lift() with control and personalization as inputs\n",
    "print(lift(control, personalization))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "id": "5c6d18bc",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Arabic\n",
      "lift: 50.0%\n",
      "stat=-2.734, p=0.580\n",
      "Rejected\n",
      "None\n",
      "\n",
      "\n",
      "\n",
      "English\n",
      "lift: 39.0%\n",
      "stat=-2.734, p=0.027\n",
      "Acepted\n",
      "\n",
      "\n",
      "\n",
      "German\n",
      "lift: -1.62%\n",
      "stat=-2.734, p=0.849\n",
      "Rejected\n",
      "None\n",
      "\n",
      "\n",
      "\n",
      "Spanish\n",
      "lift: 166.67%\n",
      "stat=-2.734, p=0.040\n",
      "Acepted\n",
      "\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "ab_segmentation('language_displayed')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "id": "0cb54000",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0-18 years\n",
      "lift: 121.4%\n",
      "stat=-2.734, p=0.004\n",
      "Acepted\n",
      "\n",
      "\n",
      "\n",
      "19-24 years\n",
      "lift: 106.24%\n",
      "stat=-2.734, p=0.003\n",
      "Acepted\n",
      "\n",
      "\n",
      "\n",
      "24-30 years\n",
      "lift: 161.19%\n",
      "stat=-2.734, p=0.000\n",
      "Acepted\n",
      "\n",
      "\n",
      "\n",
      "30-36 years\n",
      "lift: -100.0%\n",
      "stat=-2.734, p=0.002\n",
      "Acepted\n",
      "\n",
      "\n",
      "\n",
      "36-45 years\n",
      "lift: -85.23%\n",
      "stat=-2.734, p=0.018\n",
      "Acepted\n",
      "\n",
      "\n",
      "\n",
      "45-55 years\n",
      "lift: -72.22%\n",
      "stat=-2.734, p=0.043\n",
      "Acepted\n",
      "\n",
      "\n",
      "\n",
      "55+ years\n",
      "lift: -100.0%\n",
      "stat=-2.734, p=0.002\n",
      "Acepted\n",
      "\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Use ab_segmentation on age group\n",
    "ab_segmentation('age_group')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0cf0cda2",
   "metadata": {},
   "source": [
    "You found that personalization was extremely effective for younger groups but less effective than the control for older groups. One explanation might be that younger users understand how their data might be used online and think personalization is cool because it gives them more insight into themselves while older people might feel that this is a violation of their privacy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "11e4baea",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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