05_bootstrap_my_solutions.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# A/B Testing Course"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Lesson 5. Bootstrap & Confidence Intervals"
   ]
  },
  {
   "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 scipy.stats import norm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Import Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "executionInfo": {
     "elapsed": 6,
     "status": "ok",
     "timestamp": 1674542192206,
     "user": {
      "displayName": "Nikolay Nazarov",
      "userId": "18018785782997408667"
     },
     "user_tz": -420
    },
    "id": "xxFeCfFuFKng",
    "tags": []
   },
   "outputs": [],
   "source": [
    "df_exp_users = pd.read_csv('experiment_users.csv')"
   ]
  },
  {
   "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_web_logs = pd.read_csv('2022-04-13T12_df_web_logs.csv')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "#### Data Description"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "df_exp_users - users split in the experiment:\n",
    "- user_id - user identifier;\n",
    "- pilot - test group flag."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "nNRTGF6aBHrZ"
   },
   "source": [
    "df_web_logs - web logs information:\n",
    "- user_id - user identifier;\n",
    "- page - visited page;\n",
    "- date - date and time of a page visit;\n",
    "- load_time - page load time."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "#### Checking Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 204
    },
    "executionInfo": {
     "elapsed": 53,
     "status": "ok",
     "timestamp": 1674542198602,
     "user": {
      "displayName": "Nikolay Nazarov",
      "userId": "18018785782997408667"
     },
     "user_tz": -420
    },
    "id": "0dZkzMMTE-73",
    "outputId": "44f7566a-b32d-4479-b963-7c5977351149",
    "tags": []
   },
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>user_id</th>\n",
       "      <th>pilot</th>\n",
       "    </tr>\n",
       "  </thead>\n",
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      "text/plain": [
       "  user_id  pilot\n",
       "0  c36b2e      0\n",
       "1  20336e      0\n",
       "2  034652      0\n",
       "3  e98e3b      0\n",
       "4  3f1105      0"
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     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_exp_users.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 5456 entries, 0 to 5455\n",
      "Data columns (total 2 columns):\n",
      " #   Column   Non-Null Count  Dtype \n",
      "---  ------   --------------  ----- \n",
      " 0   user_id  5456 non-null   object\n",
      " 1   pilot    5456 non-null   int64 \n",
      "dtypes: int64(1), object(1)\n",
      "memory usage: 85.4+ KB\n"
     ]
    }
   ],
   "source": [
    "df_exp_users.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
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       "<div>\n",
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>user_id</th>\n",
       "      <th>page</th>\n",
       "      <th>date</th>\n",
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       "      <td>f25239</td>\n",
       "      <td>m</td>\n",
       "      <td>2022-02-03 23:45:37</td>\n",
       "      <td>80.8</td>\n",
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      "text/plain": [
       "  user_id page                 date  load_time\n",
       "0  f25239    m  2022-02-03 23:45:37       80.8\n",
       "1  06d6df    m  2022-02-03 23:49:56       70.5\n",
       "2  06d6df    m  2022-02-03 23:51:16       89.7\n",
       "3  f25239    m  2022-02-03 23:51:43       74.4\n",
       "4  697870    m  2022-02-03 23:53:12       66.8"
      ]
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     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "df_web_logs.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 2401709 entries, 0 to 2401708\n",
      "Data columns (total 4 columns):\n",
      " #   Column     Dtype  \n",
      "---  ------     -----  \n",
      " 0   user_id    object \n",
      " 1   page       object \n",
      " 2   date       object \n",
      " 3   load_time  float64\n",
      "dtypes: float64(1), object(3)\n",
      "memory usage: 73.3+ MB\n"
     ]
    }
   ],
   "source": [
    "df_web_logs.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
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     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "df_web_logs.load_time.isna().sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Task 1. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Experiment was held from 2022-04-05 to 2022-04-12.  \n",
    "Check the significance of differences of other quantiles: 0.7; 0.74; 0.78; 0.82; 0.86; 0.90; 0.95; 0.99; 0.999; 0.9999  \n",
    "When checking, use a normal confidence interval."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# filtering data by date\n",
    "logs_filt = df_web_logs[(df_web_logs['date'] >= '2022-04-05') & \\\n",
    "                      (df_web_logs['date'] < '2022-04-12')]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# merging web logs and experiment groups data\n",
    "df_groups = pd.merge(logs_filt, df_exp_users, how='inner', on='user_id')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# control and test groups data\n",
    "load_time_a = df_groups[df_groups['pilot'] == 0]['load_time'].values\n",
    "load_time_b = df_groups[df_groups['pilot'] == 1]['load_time'].values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# function to get normal confidence interval with help of bootstrap\n",
    "def get_ci_bootstrap_normal(boot_metrics: np.array, pe_metric: float, alpha: float=0.05):\n",
    "    c = norm.ppf(1 - alpha / 2)\n",
    "    se = np.std(boot_metrics)\n",
    "    left, right = pe_metric - c * se, pe_metric + c * se\n",
    "    return left, right"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# function to run bootstrap\n",
    "def bootstrap(group_a, group_b, quantile, iterations=1000):\n",
    "    # helper function to get point estimate\n",
    "    def get_point_estimate(a_group, b_group, quantile=0.95):\n",
    "        return np.quantile(b_group, quantile) - np.quantile(a_group, quantile)\n",
    "    \n",
    "    # getting point estimate\n",
    "    point_estimate = get_point_estimate(group_a, group_b, quantile=quantile)\n",
    "\n",
    "    # bootstrapping data\n",
    "    bs_point_estimates = []\n",
    "    for _ in range(iterations):\n",
    "        bs_a = np.random.choice(group_a, size=len(group_a), replace=True)\n",
    "        bs_b = np.random.choice(group_b, size=len(group_b), replace=True)\n",
    "        bs_point_estimate = get_point_estimate(bs_a, bs_b, quantile=quantile)\n",
    "        bs_point_estimates.append(bs_point_estimate)\n",
    "        \n",
    "    return bs_point_estimates, point_estimate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "There is a significant difference!\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "There is a significant difference!\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "There is no significant effect here.\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "There is a significant difference!\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "There is a significant difference!\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "There is a significant difference!\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "There is a significant difference!\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "There is a significant difference!\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "There is no significant effect here.\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "There is no significant effect here.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# lets check significance of difference for given percentiles\n",
    "percentiles = [0.7, 0.74, 0.78, 0.82, 0.86, 0.90, 0.95, 0.99, 0.999, 0.9999]\n",
    "\n",
    "\n",
    "for perc in percentiles:\n",
    "    bs_data, pe = bootstrap(load_time_a, load_time_b, quantile=perc, iterations=5000)\n",
    "    normal_ci = get_ci_bootstrap_normal(bs_data, pe)\n",
    "    \n",
    "    plt.title(f'{perc*100}% percentile difference')\n",
    "    plt.hist(bs_data, bins=20);\n",
    "    plt.vlines(normal_ci, 0, 1000, label='normal CI', color='red')\n",
    "    plt.legend()\n",
    "    plt.show()\n",
    "    \n",
    "    if normal_ci[0] > 0 or normal_ci[1] < 0:\n",
    "        print('There is a significant difference!\\n')\n",
    "    else:\n",
    "        print('There is no significant effect here.\\n')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Task 2. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "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",
    "    \"\"\"Date class with 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",
    "    bootstrap_iter - number of bootstrap iterations\n",
    "    bootstrap_ci_type - method of constructing a confidence interval. ['normal', 'percentile', 'pivotal']\n",
    "    bootstrap_agg_func - experiment metric. ['mean', 'quantile 95']\n",
    "    \"\"\"\n",
    "    statistical_test: str\n",
    "    effect: float\n",
    "    alpha: float = 0.05\n",
    "    beta: float = 0.1\n",
    "    bootstrap_iter: int = 1000\n",
    "    bootstrap_ci_type: str\n",
    "    bootstrap_agg_func: str\n",
    "\n",
    "\n",
    "class ExperimentsService:\n",
    "\n",
    "    def _generate_bootstrap_metrics(self, data_one, data_two, design):\n",
    "        \"\"\"Generates metric values obtained using bootstrap.\n",
    "        \n",
    "        :param data_one, data_two (np.array): metric values in the groups.\n",
    "        :param design (Design): an object with data describing the experiment parameters.\n",
    "        :return bootstrap_metrics, pe_metric:\n",
    "            bootstrap_metrics (np.array) - test statistic values calculated on bootstrap subsamples\n",
    "            pe_metric (float) - test statistic value calculated on the original data.\n",
    "        \"\"\"\n",
    "        bootstrap_data_one = np.random.choice(data_one, (len(data_one), design.bootstrap_iter))\n",
    "        bootstrap_data_two = np.random.choice(data_two, (len(data_two), design.bootstrap_iter))\n",
    "        if design.bootstrap_agg_func == 'mean':\n",
    "            bootstrap_metrics = bootstrap_data_two.mean(axis=0) - bootstrap_data_one.mean(axis=0)\n",
    "            pe_metric = data_two.mean() - data_one.mean()\n",
    "            return bootstrap_metrics, pe_metric\n",
    "        elif design.bootstrap_agg_func == 'quantile 95':\n",
    "            bootstrap_metrics = (\n",
    "                np.quantile(bootstrap_data_two, 0.95, axis=0)\n",
    "                - np.quantile(bootstrap_data_one, 0.95, axis=0)\n",
    "            )\n",
    "            pe_metric = np.quantile(data_two, 0.95) - np.quantile(data_one, 0.95)\n",
    "            return bootstrap_metrics, pe_metric\n",
    "        else:\n",
    "            raise ValueError('Wrong value: design.bootstrap_agg_func')\n",
    "\n",
    "    def _run_bootstrap(self, bootstrap_metrics, pe_metric, design):\n",
    "        \"\"\"Builds a confidence interval and tests for significance of differences using bootstrap.\n",
    "        \n",
    "        :param bootstrap_metrics (np.array): test statistic calculated on bootstrap samples.\n",
    "        :param pe_metric (float): test statistic calculated on the original data.\n",
    "        :return ci, pvalue:\n",
    "            ci [float, float] - confidence interval boundaries.\n",
    "            pvalue (float) - 0 if there is a statistically significant difference, otherwise 1.\n",
    "                It is not trivial to compute the true p-value for an arbitrary bootstrap confidence interval. \n",
    "                Therefore, we will use the boundary values of 0 and 1.\n",
    "        \"\"\"\n",
    "        # YOUR_CODE_HERE\n",
    "        alpha = design.alpha   \n",
    "        bootstrap_ci_type = design.bootstrap_ci_type \n",
    "\n",
    "        def get_ci_bootstrap_normal(boot_metrics: np.array, pe_metric: float, alpha: float=0.05):\n",
    "            c = stats.norm.ppf(1 - alpha / 2)\n",
    "            se = np.std(boot_metrics)\n",
    "            left, right = pe_metric - c * se, pe_metric + c * se\n",
    "            return left, right\n",
    "\n",
    "        def get_ci_bootstrap_percentile(boot_metrics: np.array, pe_metric: float, alpha: float=0.05):\n",
    "            left, right = np.quantile(boot_metrics, [alpha / 2, 1 - alpha / 2])\n",
    "            return left, right\n",
    "\n",
    "        def get_ci_bootstrap_pivotal(boot_metrics: np.array, pe_metric: float, alpha: float=0.05):\n",
    "            right, left = 2 * pe_metric - np.quantile(boot_metrics, [alpha / 2, 1 - alpha / 2])\n",
    "            return left, right\n",
    "        \n",
    "        if bootstrap_ci_type == 'normal':\n",
    "            ci = get_ci_bootstrap_normal(bootstrap_metrics, pe_metric, alpha)\n",
    "        elif bootstrap_ci_type == 'percentile':\n",
    "            ci = get_ci_bootstrap_percentile(bootstrap_metrics, pe_metric, alpha)\n",
    "        elif bootstrap_ci_type == 'pivotal':\n",
    "            ci = get_ci_bootstrap_pivotal(bootstrap_metrics, pe_metric, alpha)\n",
    "        \n",
    "        p_value = 0 if ci[0] > 0 or ci[1] < 0 else 1\n",
    "        \n",
    "        return ci, p_value\n",
    "\n",
    "\n",
    "    def get_pvalue(self, metrics_a_group, metrics_b_group, design):\n",
    "        \"\"\"Applies a statistical test and returns the p-value.\n",
    "        \n",
    "        :param metrics_a_group (np.array): array of metric values for group A\n",
    "        :param metrics_b_group (np.array): array of metric values for group B\n",
    "        :param design (Design): object with experiment parameters description\n",
    "        :return (float): p-value\n",
    "        \"\"\"\n",
    "        if design.statistical_test == 'ttest':\n",
    "            _, pvalue = stats.ttest_ind(metrics_a_group, metrics_b_group)\n",
    "            return pvalue\n",
    "        elif design.statistical_test == 'bootstrap':\n",
    "            bootstrap_metrics, pe_metric = self._generate_bootstrap_metrics(metrics_a_group, metrics_b_group, design)\n",
    "            _, pvalue = self._run_bootstrap(bootstrap_metrics, pe_metric, design)\n",
    "        else:\n",
    "            raise ValueError('Wrong design.statistical_test')\n",
    "\n",
    "\n",
    "if __name__ == '__main__':\n",
    "    bootstrap_metrics = np.arange(-490, 510)\n",
    "    pe_metric = 5.\n",
    "    design = Design(\n",
    "        statistical_test='bootstrap',\n",
    "        effect=5,\n",
    "        bootstrap_ci_type='normal',\n",
    "        bootstrap_agg_func='mean'\n",
    "    )\n",
    "    ideal_ci = (-560.79258, 570.79258)\n",
    "    ideal_pvalue = 1.\n",
    "\n",
    "    experiments_service = ExperimentsService()\n",
    "    ci, pvalue = experiments_service._run_bootstrap(bootstrap_metrics, pe_metric, design)\n",
    "    np.testing.assert_almost_equal(ideal_ci, ci, decimal=4, err_msg='Wrong confidence interval!')\n",
    "    assert ideal_pvalue == pvalue, 'Wrong pvalue!'\n",
    "    print('simple test passed')"
   ]
  }
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