Week+4.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "_You are currently looking at **version 1.0** of this notebook. To download notebooks and datafiles, as well as get help on Jupyter notebooks in the Coursera platform, visit the [Jupyter Notebook FAQ](https://www.coursera.org/learn/python-data-analysis/resources/0dhYG) course resource._\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Distributions in Pandas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.binomial(1, 0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.496"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.binomial(1000, 0.5)/1000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "14"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "chance_of_tornado = 0.01/100\n",
    "np.random.binomial(100000, chance_of_tornado)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "101 tornadoes back to back in 2739.72602739726 years\n"
     ]
    }
   ],
   "source": [
    "chance_of_tornado = 0.01\n",
    "\n",
    "tornado_events = np.random.binomial(1, chance_of_tornado, 1000000)\n",
    "    \n",
    "two_days_in_a_row = 0\n",
    "for j in range(1,len(tornado_events)-1):\n",
    "    if tornado_events[j]==1 and tornado_events[j-1]==1:\n",
    "        two_days_in_a_row+=1\n",
    "\n",
    "print('{} tornadoes back to back in {} years'.format(two_days_in_a_row, 1000000/365))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.25158715,  0.27346771,  0.26127781,  0.6568407 ,  0.87522234,\n",
       "        0.65242526,  0.15149743,  0.55887019,  0.77719986,  0.53984175])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.uniform(0, 1,10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6201105629835879"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.normal(0.75)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Formula for standard deviation\n",
    "$$\\sqrt{\\frac{1}{N} \\sum_{i=1}^N (x_i - \\overline{x})^2}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0177959320133663"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "distribution = np.random.normal(0.75,size=1000)\n",
    "\n",
    "np.sqrt(np.sum((np.mean(distribution)-distribution)**2)/len(distribution))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0177959320133663"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.std(distribution)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.05984850674748454"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import scipy.stats as stats\n",
    "stats.kurtosis(distribution)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.05887961927922374"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.skew(distribution)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.126905704273622"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "chi_squared_df2 = np.random.chisquare(2, size=10000)\n",
    "stats.skew(chi_squared_df2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.34915934905776"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "chi_squared_df5 = np.random.chisquare(5, size=10000)\n",
    "stats.skew(chi_squared_df5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f2e1fe84240>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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vNmhV4gjkggNUW7RoUWx+gwYNANi1a1epvVaHCgcLC/4UTQT+5u6fFhl6E5gN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\nFb3SiKcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f2e616b9e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "output = plt.hist([chi_squared_df2,chi_squared_df5], bins=50, histtype='step', \n",
    "                  label=['2 degrees of freedom','5 degrees of freedom'])\n",
    "plt.legend(loc='upper right')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Hypothesis Testing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "df = pd.read_csv('grades.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>student_id</th>\n",
       "      <th>assignment1_grade</th>\n",
       "      <th>assignment1_submission</th>\n",
       "      <th>assignment2_grade</th>\n",
       "      <th>assignment2_submission</th>\n",
       "      <th>assignment3_grade</th>\n",
       "      <th>assignment3_submission</th>\n",
       "      <th>assignment4_grade</th>\n",
       "      <th>assignment4_submission</th>\n",
       "      <th>assignment5_grade</th>\n",
       "      <th>assignment5_submission</th>\n",
       "      <th>assignment6_grade</th>\n",
       "      <th>assignment6_submission</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>B73F2C11-70F0-E37D-8B10-1D20AFED50B1</td>\n",
       "      <td>92.733946</td>\n",
       "      <td>2015-11-02 06:55:34.282000000</td>\n",
       "      <td>83.030552</td>\n",
       "      <td>2015-11-09 02:22:58.938000000</td>\n",
       "      <td>67.164441</td>\n",
       "      <td>2015-11-12 08:58:33.998000000</td>\n",
       "      <td>53.011553</td>\n",
       "      <td>2015-11-16 01:21:24.663000000</td>\n",
       "      <td>47.710398</td>\n",
       "      <td>2015-11-20 13:24:59.692000000</td>\n",
       "      <td>38.168318</td>\n",
       "      <td>2015-11-22 18:31:15.934000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>98A0FAE0-A19A-13D2-4BB5-CFBFD94031D1</td>\n",
       "      <td>86.790821</td>\n",
       "      <td>2015-11-29 14:57:44.429000000</td>\n",
       "      <td>86.290821</td>\n",
       "      <td>2015-12-06 17:41:18.449000000</td>\n",
       "      <td>69.772657</td>\n",
       "      <td>2015-12-10 08:54:55.904000000</td>\n",
       "      <td>55.098125</td>\n",
       "      <td>2015-12-13 17:32:30.941000000</td>\n",
       "      <td>49.588313</td>\n",
       "      <td>2015-12-19 23:26:39.285000000</td>\n",
       "      <td>44.629482</td>\n",
       "      <td>2015-12-21 17:07:24.275000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>D0F62040-CEB0-904C-F563-2F8620916C4E</td>\n",
       "      <td>85.512541</td>\n",
       "      <td>2016-01-09 05:36:02.389000000</td>\n",
       "      <td>85.512541</td>\n",
       "      <td>2016-01-09 06:39:44.416000000</td>\n",
       "      <td>68.410033</td>\n",
       "      <td>2016-01-15 20:22:45.882000000</td>\n",
       "      <td>54.728026</td>\n",
       "      <td>2016-01-11 12:41:50.749000000</td>\n",
       "      <td>49.255224</td>\n",
       "      <td>2016-01-11 17:31:12.489000000</td>\n",
       "      <td>44.329701</td>\n",
       "      <td>2016-01-17 16:24:42.765000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>FFDF2B2C-F514-EF7F-6538-A6A53518E9DC</td>\n",
       "      <td>86.030665</td>\n",
       "      <td>2016-04-30 06:50:39.801000000</td>\n",
       "      <td>68.824532</td>\n",
       "      <td>2016-04-30 17:20:38.727000000</td>\n",
       "      <td>61.942079</td>\n",
       "      <td>2016-05-12 07:47:16.326000000</td>\n",
       "      <td>49.553663</td>\n",
       "      <td>2016-05-07 16:09:20.485000000</td>\n",
       "      <td>49.553663</td>\n",
       "      <td>2016-05-24 12:51:18.016000000</td>\n",
       "      <td>44.598297</td>\n",
       "      <td>2016-05-26 08:09:12.058000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5ECBEEB6-F1CE-80AE-3164-E45E99473FB4</td>\n",
       "      <td>64.813800</td>\n",
       "      <td>2015-12-13 17:06:10.750000000</td>\n",
       "      <td>51.491040</td>\n",
       "      <td>2015-12-14 12:25:12.056000000</td>\n",
       "      <td>41.932832</td>\n",
       "      <td>2015-12-29 14:25:22.594000000</td>\n",
       "      <td>36.929549</td>\n",
       "      <td>2015-12-28 01:29:55.901000000</td>\n",
       "      <td>33.236594</td>\n",
       "      <td>2015-12-29 14:46:06.628000000</td>\n",
       "      <td>33.236594</td>\n",
       "      <td>2016-01-05 01:06:59.546000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                             student_id  assignment1_grade  \\\n",
       "0  B73F2C11-70F0-E37D-8B10-1D20AFED50B1          92.733946   \n",
       "1  98A0FAE0-A19A-13D2-4BB5-CFBFD94031D1          86.790821   \n",
       "2  D0F62040-CEB0-904C-F563-2F8620916C4E          85.512541   \n",
       "3  FFDF2B2C-F514-EF7F-6538-A6A53518E9DC          86.030665   \n",
       "4  5ECBEEB6-F1CE-80AE-3164-E45E99473FB4          64.813800   \n",
       "\n",
       "          assignment1_submission  assignment2_grade  \\\n",
       "0  2015-11-02 06:55:34.282000000          83.030552   \n",
       "1  2015-11-29 14:57:44.429000000          86.290821   \n",
       "2  2016-01-09 05:36:02.389000000          85.512541   \n",
       "3  2016-04-30 06:50:39.801000000          68.824532   \n",
       "4  2015-12-13 17:06:10.750000000          51.491040   \n",
       "\n",
       "          assignment2_submission  assignment3_grade  \\\n",
       "0  2015-11-09 02:22:58.938000000          67.164441   \n",
       "1  2015-12-06 17:41:18.449000000          69.772657   \n",
       "2  2016-01-09 06:39:44.416000000          68.410033   \n",
       "3  2016-04-30 17:20:38.727000000          61.942079   \n",
       "4  2015-12-14 12:25:12.056000000          41.932832   \n",
       "\n",
       "          assignment3_submission  assignment4_grade  \\\n",
       "0  2015-11-12 08:58:33.998000000          53.011553   \n",
       "1  2015-12-10 08:54:55.904000000          55.098125   \n",
       "2  2016-01-15 20:22:45.882000000          54.728026   \n",
       "3  2016-05-12 07:47:16.326000000          49.553663   \n",
       "4  2015-12-29 14:25:22.594000000          36.929549   \n",
       "\n",
       "          assignment4_submission  assignment5_grade  \\\n",
       "0  2015-11-16 01:21:24.663000000          47.710398   \n",
       "1  2015-12-13 17:32:30.941000000          49.588313   \n",
       "2  2016-01-11 12:41:50.749000000          49.255224   \n",
       "3  2016-05-07 16:09:20.485000000          49.553663   \n",
       "4  2015-12-28 01:29:55.901000000          33.236594   \n",
       "\n",
       "          assignment5_submission  assignment6_grade  \\\n",
       "0  2015-11-20 13:24:59.692000000          38.168318   \n",
       "1  2015-12-19 23:26:39.285000000          44.629482   \n",
       "2  2016-01-11 17:31:12.489000000          44.329701   \n",
       "3  2016-05-24 12:51:18.016000000          44.598297   \n",
       "4  2015-12-29 14:46:06.628000000          33.236594   \n",
       "\n",
       "          assignment6_submission  \n",
       "0  2015-11-22 18:31:15.934000000  \n",
       "1  2015-12-21 17:07:24.275000000  \n",
       "2  2016-01-17 16:24:42.765000000  \n",
       "3  2016-05-26 08:09:12.058000000  \n",
       "4  2016-01-05 01:06:59.546000000  "
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2315"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "early = df[df['assignment1_submission'] <= '2015-12-31']\n",
    "late = df[df['assignment1_submission'] > '2015-12-31']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "assignment1_grade    74.972741\n",
       "assignment2_grade    67.252190\n",
       "assignment3_grade    61.129050\n",
       "assignment4_grade    54.157620\n",
       "assignment5_grade    48.634643\n",
       "assignment6_grade    43.838980\n",
       "dtype: float64"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "early.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "assignment1_grade    74.017429\n",
       "assignment2_grade    66.370822\n",
       "assignment3_grade    60.023244\n",
       "assignment4_grade    54.058138\n",
       "assignment5_grade    48.599402\n",
       "assignment6_grade    43.844384\n",
       "dtype: float64"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "late.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from scipy import stats\n",
    "stats.ttest_ind?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ttest_indResult(statistic=1.400549944897566, pvalue=0.16148283016060577)"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.ttest_ind(early['assignment1_grade'], late['assignment1_grade'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ttest_indResult(statistic=1.3239868220912567, pvalue=0.18563824610067967)"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.ttest_ind(early['assignment2_grade'], late['assignment2_grade'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ttest_indResult(statistic=1.7116160037010733, pvalue=0.087101516341556676)"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.ttest_ind(early['assignment3_grade'], late['assignment3_grade'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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