sem11_ab/sem11_group01.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "c92fe8df",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "7b514fce",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(90189, 5)\n"
     ]
    },
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>userid</th>\n",
       "      <th>version</th>\n",
       "      <th>sum_gamerounds</th>\n",
       "      <th>retention_1</th>\n",
       "      <th>retention_7</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>116</td>\n",
       "      <td>gate_30</td>\n",
       "      <td>3</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>337</td>\n",
       "      <td>gate_30</td>\n",
       "      <td>38</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>377</td>\n",
       "      <td>gate_40</td>\n",
       "      <td>165</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>483</td>\n",
       "      <td>gate_40</td>\n",
       "      <td>1</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>488</td>\n",
       "      <td>gate_40</td>\n",
       "      <td>179</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   userid  version  sum_gamerounds  retention_1  retention_7\n",
       "0     116  gate_30               3        False        False\n",
       "1     337  gate_30              38         True        False\n",
       "2     377  gate_40             165         True        False\n",
       "3     483  gate_40               1        False        False\n",
       "4     488  gate_40             179         True         True"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv('https://raw.githubusercontent.com/hse-econ-data-science/andan_2023/main/sem11_ab/cookie_cats.csv')\n",
    "print(df.shape)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "d38b7060",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>count</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>version</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>gate_30</th>\n",
       "      <td>0.448188</td>\n",
       "      <td>44700</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gate_40</th>\n",
       "      <td>0.442283</td>\n",
       "      <td>45489</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             mean  count\n",
       "version                 \n",
       "gate_30  0.448188  44700\n",
       "gate_40  0.442283  45489"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_agg = df.groupby('version')['retention_1'].agg(['mean', 'count'])\n",
    "df_agg"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5b24e236",
   "metadata": {},
   "source": [
    "__а)__  Постройте примерный $95\\%$-й доверительный интервал для каждой из двух долей.\n",
    "\n",
    "$$\n",
    "\\left[\\hat p - z_{crit} \\sqrt{\\frac{\\hat p \\cdot (1 - \\hat p)}{n}} ; \\quad  \\hat p + z_{crit} \\sqrt{\\frac{\\hat p \\cdot (1 - \\hat p)}{n}} \\right]\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "a133660d",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    }\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>mean</th>\n",
       "      <th>count</th>\n",
       "      <th>var</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>version</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>gate_30</th>\n",
       "      <td>0.448188</td>\n",
       "      <td>44700</td>\n",
       "      <td>0.000006</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gate_40</th>\n",
       "      <td>0.442283</td>\n",
       "      <td>45489</td>\n",
       "      <td>0.000005</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             mean  count       var\n",
       "version                           \n",
       "gate_30  0.448188  44700  0.000006\n",
       "gate_40  0.442283  45489  0.000005"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_agg['var'] = df_agg['mean'] * (1 - df_agg['mean']) / df_agg['count']\n",
    "df_agg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "5397704d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "\n",
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       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>count</th>\n",
       "      <th>var</th>\n",
       "      <th>left</th>\n",
       "      <th>right</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>version</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>gate_30</th>\n",
       "      <td>0.448188</td>\n",
       "      <td>44700</td>\n",
       "      <td>0.000006</td>\n",
       "      <td>0.443578</td>\n",
       "      <td>0.452798</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gate_40</th>\n",
       "      <td>0.442283</td>\n",
       "      <td>45489</td>\n",
       "      <td>0.000005</td>\n",
       "      <td>0.437719</td>\n",
       "      <td>0.446847</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             mean  count       var      left     right\n",
       "version                                               \n",
       "gate_30  0.448188  44700  0.000006  0.443578  0.452798\n",
       "gate_40  0.442283  45489  0.000005  0.437719  0.446847"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import scipy.stats as sts\n",
    "import numpy as np\n",
    "\n",
    "alpha = 0.05\n",
    "z_cr = sts.norm().ppf(1 - alpha/2)\n",
    "\n",
    "df_agg['left'] = df_agg['mean'] - z_cr * np.sqrt(df_agg['var'])\n",
    "df_agg['right'] = df_agg['mean'] + z_cr * np.sqrt(df_agg['var'])\n",
    "df_agg"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "76577984",
   "metadata": {},
   "source": [
    "__б)__ Постройте примерный $95\\%$-й доверительный интервал для разницы долей.\n",
    "\n",
    "$$\n",
    "\\left[\\hat p_A - \\hat p_B - z_{crit} \\sqrt{\\frac{\\hat p_A \\cdot (1 - \\hat p_A)}{n_A} + \\frac{\\hat p_B \\cdot (1 - \\hat p_B)}{n_B}} ; \\quad  \\hat p_A - \\hat p_B + z_{crit} \\sqrt{\\frac{\\hat p_A \\cdot (1 - \\hat p_A)}{n_A} + \\frac{\\hat p_B \\cdot (1 - \\hat p_B)}{n_B}} \\right]\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "c08a69af",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.0005820998747623016, 0.012392439449445217)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diff = df_agg['mean']['gate_30'] - df_agg['mean']['gate_40']\n",
    "diff_std = np.sqrt(df_agg['var']['gate_30'] + df_agg['var']['gate_40'])\n",
    "\n",
    "diff - z_cr * diff_std,  diff + z_cr * diff_std, "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "e1901fba",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.17586671271029086, 3.7440612563698172)"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diff/diff_std - z_cr, diff/diff_std + z_cr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "656d3a54",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.7840972718297632, 1.959963984540054)"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diff/diff_std, z_cr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "8f291409",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>count</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>version</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>gate_30</th>\n",
       "      <td>0.190201</td>\n",
       "      <td>44700</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gate_40</th>\n",
       "      <td>0.182000</td>\n",
       "      <td>45489</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             mean  count\n",
       "version                 \n",
       "gate_30  0.190201  44700\n",
       "gate_40  0.182000  45489"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_agg = df.groupby('version')['retention_7'].agg(['mean', 'count'])\n",
    "df_agg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "16e67234",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.008201298315205913"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diff = df_agg['mean']['gate_30'] - df_agg['mean']['gate_40']\n",
    "diff"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "a70760f6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "90189"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.shape[0] # наверное 5% от всей базы"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "1752e958",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1803780.0"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n = df.shape[0] *100/5\n",
    "n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "92303b1b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "14793.337875002122"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n * diff"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "2872cfdd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1479333.7875002122"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "100*(n * diff) # если каждый за неделю платил нам дополнительные 100 рублей, потери большие"
   ]
  }
 ],
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