08_stratification_my_solutions.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# A/B Testing Course"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Lesson 8. Stratification"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Homework"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Import Libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "executionInfo": {
     "elapsed": 580,
     "status": "ok",
     "timestamp": 1674542192205,
     "user": {
      "displayName": "Nikolay Nazarov",
      "userId": "18018785782997408667"
     },
     "user_tz": -420
    },
    "id": "agQEC38nE-72",
    "tags": []
   },
   "outputs": [],
   "source": [
    "import os\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from datetime import datetime"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import ttest_ind"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Import Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "executionInfo": {
     "elapsed": 6399,
     "status": "ok",
     "timestamp": 1674542198600,
     "user": {
      "displayName": "Nikolay Nazarov",
      "userId": "18018785782997408667"
     },
     "user_tz": -420
    },
    "id": "nQGxlqByE-73",
    "tags": []
   },
   "outputs": [],
   "source": [
    "df = pd.read_csv('stratification_task_data_public.csv')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "#### Data Description"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "df:\n",
    "- x1, ..., x10 - stratification features\n",
    "- y - metric value"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "#### Checking Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "tags": []
   },
   "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>x1</th>\n",
       "      <th>x2</th>\n",
       "      <th>x3</th>\n",
       "      <th>x4</th>\n",
       "      <th>x5</th>\n",
       "      <th>x6</th>\n",
       "      <th>x7</th>\n",
       "      <th>x8</th>\n",
       "      <th>x9</th>\n",
       "      <th>x10</th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.869</td>\n",
       "      <td>30</td>\n",
       "      <td>33.8</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0.2</td>\n",
       "      <td>1992</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1903</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.759</td>\n",
       "      <td>27</td>\n",
       "      <td>21.7</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1995</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>1313</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.456</td>\n",
       "      <td>29</td>\n",
       "      <td>37.6</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>3.1</td>\n",
       "      <td>1993</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1484</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.060</td>\n",
       "      <td>35</td>\n",
       "      <td>27.5</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>4.7</td>\n",
       "      <td>1988</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1188</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.939</td>\n",
       "      <td>19</td>\n",
       "      <td>30.7</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3.6</td>\n",
       "      <td>2003</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>842</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      x1  x2    x3  x4  x5   x6    x7  x8  x9  x10     y\n",
       "0  0.869  30  33.8   0   1  0.2  1992   1   1    1  1903\n",
       "1  0.759  27  21.7   2   0  3.5  1995   1   1    2  1313\n",
       "2  0.456  29  37.6   2   0  3.1  1993   0   0    0  1484\n",
       "3  0.060  35  27.5   2   0  4.7  1988   0   0    1  1188\n",
       "4  0.939  19  30.7   0   0  3.6  2003   1   1    2   842"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 10000 entries, 0 to 9999\n",
      "Data columns (total 11 columns):\n",
      " #   Column  Non-Null Count  Dtype  \n",
      "---  ------  --------------  -----  \n",
      " 0   x1      10000 non-null  float64\n",
      " 1   x2      10000 non-null  int64  \n",
      " 2   x3      10000 non-null  float64\n",
      " 3   x4      10000 non-null  int64  \n",
      " 4   x5      10000 non-null  int64  \n",
      " 5   x6      10000 non-null  float64\n",
      " 6   x7      10000 non-null  int64  \n",
      " 7   x8      10000 non-null  int64  \n",
      " 8   x9      10000 non-null  int64  \n",
      " 9   x10     10000 non-null  int64  \n",
      " 10  y       10000 non-null  int64  \n",
      "dtypes: float64(3), int64(8)\n",
      "memory usage: 859.5 KB\n"
     ]
    }
   ],
   "source": [
    "df.info()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Task 1. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's assume we have a set of features that are calculated independently of the experiment. Using these features, we need to divide the objects into strata so that the variance of the stratified mean is minimized and the proportion of each stratum is at least 5% of all data.\n",
    "Implement a function to divide objects into strata."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# grouping by x2 feature and calculating metrics means\n",
    "df.groupby('x2', as_index=False).agg({'y':'mean'}).plot(x='x2', y='y');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# spliting x2 feature values into categories\n",
    "df['category'] = pd.cut(df.x2, bins=[11, 23, 26, 31, 33, 36, 50], labels=['1', '2', '3', '4', '5', '6'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3    0.4112\n",
       "2    0.1490\n",
       "4    0.1447\n",
       "5    0.1358\n",
       "6    0.0825\n",
       "1    0.0768\n",
       "Name: category, dtype: float64"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# checking that none of the categories is less tha 5% size\n",
    "df.category.value_counts(normalize=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='category'>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# # grouping by category feature and calculating metrics means\n",
    "df.groupby('category', as_index=False).agg({'y':'mean'}).plot(x='category', y='y')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Perfect! Variance equal to 49850.9, that is less than our boundary 50000\n"
     ]
    }
   ],
   "source": [
    "# implementing our categroies for stratification\n",
    "def get_strats(df: pd.DataFrame):\n",
    "    \"\"\"Returns strats for our data.\n",
    "    \n",
    "    :return (list | np.array | pd.Series): list of starts.\n",
    "    \"\"\"\n",
    "    # YOUR_CODE_HERE\n",
    "    df['category'] = pd.cut(df.x2, \n",
    "                            bins=[11, 23, 26, 31, 33, 36, 50],\n",
    "                            labels=['1', '2', '3', '4', '5', '6'])\n",
    "    return df.category.to_list()\n",
    "\n",
    "\n",
    "def calculate_strat_var(df):\n",
    "    \"\"\"Calculating stratified variation of the population.\"\"\"\n",
    "    strat_vars = df.groupby('strat')['y'].var()\n",
    "    weights = df['strat'].value_counts(normalize=True)\n",
    "    stratified_var = (strat_vars * weights).sum()\n",
    "    return stratified_var\n",
    "\n",
    "\n",
    "if __name__ == \"__main__\":\n",
    "    bound = 50000\n",
    "    df = pd.read_csv('stratification_task_data_public.csv')\n",
    "    strats = get_strats(df.drop('y', axis=1))\n",
    "    assert len(strats) == len(df), \"Wrong size of strats list\"\n",
    "    min_part = pd.Series(strats).value_counts(normalize=True).min()\n",
    "    assert min_part >= 0.05, \"Minimal size of a strata is less than 5%\"\n",
    "    df['strat'] = strats\n",
    "    strat_var = calculate_strat_var(df)\n",
    "    err_msg = f\"Variance equal to {strat_var:0.1f}, and we have to lower it below {bound}\"\n",
    "    assert strat_var <= bound, err_msg\n",
    "    print(f'Perfect! Variance equal to {strat_var:0.1f}, that is less than our boundary {bound}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Task 2. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You need to write a function that will stratify the clients and distribute them among groups.\n",
    "\n",
    "We will consider the distribution among groups to be stratified if the number of clients in each stratum differs by no more than 1.\n",
    "\n",
    "Implement the function `split_stratified`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "simple test passed\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "\n",
    "def split_stratified(strats: np.array) -> np.array:\n",
    "    \"\"\"Distributes objects into groups (control and experimental).\n",
    "    \n",
    "    :param strats: an array with stratification.\n",
    "    :return: an array of 0 and 1, where 0 is the control group and 1 is the experimental group.\n",
    "    \"\"\"\n",
    "    # YOUR_CODE_HERE\n",
    "    strats_u = set(strats.tolist())\n",
    "    vals = strats.tolist()\n",
    "\n",
    "    dct = dict()\n",
    "    for strat in strats_u:\n",
    "        dct[strat] = list()\n",
    "        for i in range(len(vals)):\n",
    "            if vals[i] == strat:\n",
    "                dct[strat].append(i)\n",
    "\n",
    "    groups = [False] * len(vals)\n",
    "    for k in dct:\n",
    "        lst = dct[k]\n",
    "        np.random.shuffle(lst)\n",
    "        mid = len(lst) // 2\n",
    "        a = dct[k][:mid]\n",
    "        b = dct[k][mid:]\n",
    "        for idx in a:\n",
    "            groups[idx] = 0\n",
    "        for idx in b:\n",
    "            groups[idx] = 1\n",
    "    \n",
    "    return groups\n",
    "    \n",
    "\n",
    "def check_split(df: pd.DataFrame):\n",
    "    \"\"\"Checks the correctness of stratification.\n",
    "    \n",
    "    :param df: dataframe with two columns: ['strat', 'group'].\n",
    "    \"\"\"\n",
    "    df_agg = (\n",
    "        df\n",
    "        .groupby(['strat', 'group'])[['group']].count()\n",
    "        .rename(columns={'group': 'count'})\n",
    "        .reset_index()\n",
    "    )\n",
    "    df_pivot = df_agg.pivot(index='strat', values='count', columns='group')\n",
    "    max_delta = (df_pivot[0] - df_pivot[1]).abs().max()\n",
    "    assert max_delta <= 1, \"The sizes of strata between groups differ by more than 1.\"\n",
    "\n",
    "\n",
    "if __name__ == \"__main__\":\n",
    "    df = pd.DataFrame({'strat': [1, 2, 2, 2, 1, 1, 1, 3, 3]})\n",
    "    df['group'] = split_stratified(df['strat'].values)\n",
    "    check_split(df)\n",
    "    print('simple test passed')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Task 3. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "Implement a function to evaluate an experiment using post-stratification.\n",
    "\n",
    "Update the `_ttest_strat` method of the `ExperimentsService` class."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "simple test passed\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from pydantic import BaseModel\n",
    "from scipy import stats\n",
    "\n",
    "\n",
    "class Design(BaseModel):\n",
    "    \"\"\"Experiment class with a description of experiment parameters.\n",
    "    \n",
    "    statistical_test - type of statistical test. ['ttest', 'bootstrap']\n",
    "    effect - effect size in percentage\n",
    "    alpha - significance level\n",
    "    beta - allowable probability of type II error\n",
    "    stratification - post-stratification. 'on' - use post-stratification, 'off' - do not use.\n",
    "    \"\"\"\n",
    "    statistical_test: str = 'ttest'\n",
    "    effect: float = 3.\n",
    "    alpha: float = 0.05\n",
    "    beta: float = 0.1\n",
    "    stratification: str = 'off'\n",
    "\n",
    "\n",
    "class ExperimentsService:\n",
    "\n",
    "    def _ttest_strat(self, metrics_strat_a_group, metrics_strat_b_group):\n",
    "        \"\"\"Applies post-stratification and returns p-value.\n",
    "\n",
    "        Weights for strata are calculated using data from both groups.\n",
    "        It is assumed that the experiment is conducted on the entire population.\n",
    "        Strata weights should be calculated using data from the entire population.\n",
    "\n",
    "        :param metrics_strat_a_group (np.ndarray): metric and stratum values of group A.\n",
    "            shape = (n, 2), the first column - metrics, the second column - strata.\n",
    "        :param metrics_strat_b_group (np.ndarray): metric and stratum values of group B.\n",
    "            shape = (n, 2), the first column - metrics, the second column - strata.\n",
    "        :param design (Design): object with experiment parameters data\n",
    "        :return (float): p-value\n",
    "        \"\"\"\n",
    "        # YOUR_CODE_HERE\n",
    "        df_a = pd.DataFrame(metrics_strat_a_group, columns=['metric', 'strat'])\n",
    "        df_b = pd.DataFrame(metrics_strat_b_group, columns=['metric', 'strat'])\n",
    "        df = pd.concat([df_a, df_b]).reset_index(drop=True)\n",
    "        weights = df['strat'].value_counts(normalize=True).to_dict()\n",
    "        \n",
    "        def calculate_stratified_mean(df, weights):\n",
    "            \"\"\"Calculates the stratified mean.\n",
    "            \n",
    "            :df - a dataframe with the target metric and data for stratification\n",
    "            :weights - a dictionary - {name of the stratum: weight of the stratum}\n",
    "            :returt (float): mean_strat\n",
    "            \"\"\"\n",
    "            strat_mean = df.groupby('strat')['metric'].mean()\n",
    "            df_means_weights = pd.merge(\n",
    "                strat_mean,\n",
    "                pd.Series(weights, name='weight'),\n",
    "                how='inner',\n",
    "                left_index=True,\n",
    "                right_index=True\n",
    "            )\n",
    "            # if there were no some strata in the df data, then part of the weights will be erased and the sum of the weights will be less than 1.\n",
    "            df_means_weights['weight'] = df_means_weights['weight'] / df_means_weights['weight'].sum()\n",
    "            mean_strat = (df_means_weights['weight'] * df_means_weights['metric']).sum()\n",
    "            return mean_strat\n",
    "        \n",
    "        def calculate_strat_var(df, weights):\n",
    "            \"\"\"Calculates stratified variance.\"\"\"\n",
    "            strat_vars = df.groupby('strat')['metric'].var()\n",
    "            df_vars_weights = pd.merge(\n",
    "                strat_vars,\n",
    "                pd.Series(weights, name='weight'),\n",
    "                how='inner',\n",
    "                left_index=True,\n",
    "                right_index=True\n",
    "            )\n",
    "            # if there were no some strata in the df data, then part of the weights will be erased and the sum of the weights will be less than 1.\n",
    "            df_vars_weights['weight'] = df_vars_weights['weight'] / df_vars_weights['weight'].sum()\n",
    "            var_strat = (df_vars_weights['weight'] * df_vars_weights['metric']).sum()\n",
    "            return var_strat\n",
    "        \n",
    "        def check_stratified_test(df_control, df_pilot, weights):\n",
    "            \"\"\"Checks the hypothesis of equality of means for stratified mean.\n",
    "            \n",
    "            :return (float): p-value\n",
    "            \"\"\"\n",
    "            mean_strat_control = calculate_stratified_mean(df_control, weights)\n",
    "            mean_strat_pilot = calculate_stratified_mean(df_pilot, weights)\n",
    "            var_strat_control = calculate_strat_var(df_control, weights)\n",
    "            var_strat_pilot = calculate_strat_var(df_pilot, weights)\n",
    "            delta_mean_strat = mean_strat_pilot - mean_strat_control\n",
    "            std_mean_strat = (var_strat_pilot / len(df_pilot) + var_strat_control / len(df_control)) ** 0.5\n",
    "            t = delta_mean_strat / std_mean_strat\n",
    "            pvalue = (1 - stats.norm.cdf(np.abs(t))) * 2\n",
    "            return pvalue\n",
    "        \n",
    "        return check_stratified_test(df_a, df_b, weights)\n",
    "        \n",
    "        \n",
    "\n",
    "    def get_pvalue(self, metrics_strat_a_group, metrics_strat_b_group, design):\n",
    "        \"\"\"Applies a statistical test and returns a p-value.\n",
    "        \n",
    "        :param metrics_strat_a_group (np.ndarray): metric and stratification values for group A.\n",
    "            shape = (n, 2), first column - metrics, second column - strata.\n",
    "        :param metrics_strat_b_group (np.ndarray): metric and stratification values for group B.\n",
    "            shape = (n, 2), first column - metrics, second column - strata.\n",
    "        :param design (Design): object with data describing the experiment parameters.\n",
    "        :return (float): p-value\n",
    "        \"\"\"\n",
    "        if design.statistical_test == 'ttest':\n",
    "            if design.stratification == 'off':\n",
    "                _, pvalue = stats.ttest_ind(metrics_strat_a_group[:, 0], metrics_strat_b_group[:, 0])\n",
    "                return pvalue\n",
    "            elif design.stratification == 'on':\n",
    "                return self._ttest_strat(metrics_strat_a_group, metrics_strat_b_group)\n",
    "            else:\n",
    "                raise ValueError('Wrong design.stratification')\n",
    "        else:\n",
    "            raise ValueError('Wrong design.statistical_test')\n",
    "\n",
    "\n",
    "if __name__ == '__main__':\n",
    "    metrics_strat_a_group = np.zeros((10, 2,))\n",
    "    metrics_strat_a_group[:, 0] = np.arange(10)\n",
    "    metrics_strat_a_group[:, 1] = (np.arange(10) < 4).astype(float)\n",
    "    metrics_strat_b_group = np.zeros((10, 2,))\n",
    "    metrics_strat_b_group[:, 0] = np.arange(1, 11)\n",
    "    metrics_strat_b_group[:, 1] = (np.arange(10) < 5).astype(float)\n",
    "    design = Design(stratification='on')\n",
    "    ideal_pvalue = 0.037056\n",
    "\n",
    "    experiments_service = ExperimentsService()\n",
    "    pvalue = experiments_service.get_pvalue(metrics_strat_a_group, metrics_strat_b_group, design)\n",
    "\n",
    "    np.testing.assert_almost_equal(ideal_pvalue, pvalue, decimal=4, err_msg='Wrong pvalue')\n",
    "    print('simple test passed')"
   ]
  }
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