coffee_height_bootstrapt_hypo.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 2974 entries, 0 to 2973\n",
      "Data columns (total 4 columns):\n",
      " #   Column         Non-Null Count  Dtype  \n",
      "---  ------         --------------  -----  \n",
      " 0   user_id        2974 non-null   int64  \n",
      " 1   age            2974 non-null   object \n",
      " 2   drinks_coffee  2974 non-null   bool   \n",
      " 3   height         2974 non-null   float64\n",
      "dtypes: bool(1), float64(1), int64(1), object(1)\n",
      "memory usage: 72.7+ KB\n"
     ]
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import pylab as pl\n",
    "import numpy as np\n",
    "import ssl\n",
    "from pandas import Series\n",
    "\n",
    "\n",
    "ssl._create_default_https_context = ssl._create_unverified_context\n",
    "#显示所有列\n",
    "pd.set_option('display.max_columns', None)\n",
    "#显示所有行\n",
    "pd.set_option('display.max_rows', None)\n",
    "#设置value的显示长度为100，默认为50\n",
    "pd.set_option('max_colwidth',100)\n",
    "\n",
    "#coding:utf-8\n",
    "import json\n",
    "import urllib.request\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "import time, json, requests\n",
    "# 抓取腾讯疫情实时json数据\n",
    "url = 'https://raw.githubusercontent.com/devanshmalik/Inferential-Stats-in-Python/master/confidence%20intervals%20%26%20hypothesis%20testing/coffee_dataset.csv'\n",
    "data = pd.read_csv(url)\n",
    "data.info()\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True     0.589778\n",
       "False    0.410222\n",
       "Name: drinks_coffee, dtype: float64"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# proportion of coffee drinkers in sample\n",
    "data['drinks_coffee'].value_counts(normalize=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1754"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data[data['drinks_coffee']==True]['height'].count()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "68.40021025548381"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data[data['drinks_coffee']==True]['height'].mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "66.443407762147"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data[data['drinks_coffee']==False]['height'].mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "sample=data.sample(200)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True     0.595\n",
       "False    0.405\n",
       "Name: drinks_coffee, dtype: float64"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sample['drinks_coffee'].value_counts(normalize=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-2.419430352831128"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sample[sample['drinks_coffee']==False]['height'].mean()-sample[sample['drinks_coffee']==True]['height'].mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "nocoff_means, coff_means, diff_means = [],[],[]\n",
    "\n",
    "# sampling distribution -- the distribution of sample statistics\n",
    "\n",
    "\n",
    "# bootstrap sample data\n",
    "for _ in range(10000):\n",
    "    bootsamp = sample.sample(200, replace = True)\n",
    "    nocoff_mean = bootsamp[bootsamp['drinks_coffee'] == False]['height'].mean()\n",
    "    coff_mean = bootsamp[bootsamp['drinks_coffee'] == True]['height'].mean()\n",
    "       \n",
    "    # append means    \n",
    "    nocoff_means.append(nocoff_mean)\n",
    "    coff_means.append(coff_mean)\n",
    "    diff_means.append(coff_mean - nocoff_mean)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x110969128>"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "non=plt.hist(nocoff_means, alpha = 0.5);\n",
    "drinker=plt.hist(coff_means, alpha = 0.5);\n",
    "plt.legend(['coffee_drinker','non_coffee_drinker'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([9.000e+00, 1.280e+02, 7.160e+02, 2.073e+03, 3.167e+03, 2.513e+03,\n",
       "        1.106e+03, 2.580e+02, 2.900e+01, 1.000e+00]),\n",
       " array([0.73786423, 1.09728555, 1.45670687, 1.8161282 , 2.17554952,\n",
       "        2.53497084, 2.89439217, 3.25381349, 3.61323481, 3.97265613,\n",
       "        4.33207746]),\n",
       " <a list of 10 Patch objects>)"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "plt.hist(diff_means, alpha = 0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "null_vals = np.random.normal(0, np.std(diff_means), 10000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([  13.,   83.,  504., 1524., 2753., 2800., 1626.,  578.,  109.,\n",
       "          10.]),\n",
       " array([-1.69604524, -1.35935413, -1.02266301, -0.6859719 , -0.34928079,\n",
       "        -0.01258968,  0.32410143,  0.66079254,  0.99748365,  1.33417476,\n",
       "         1.67086588]),\n",
       " <a list of 10 Patch objects>)"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "plt.hist(null_vals)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "p = np.sum(null_vals <= -2.4) / len(null_vals)\n",
    "# -2.4 is the observed results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# reject the null hypo, there is siginificant difference"
   ]
  }
 ],
 "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": "3.7.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}