Working-with-samples-ranfile.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "%pylab inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How many taxi trips are reported in the original file?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>VendorID</th>\n",
       "      <th>tpep_pickup_datetime</th>\n",
       "      <th>tpep_dropoff_datetime</th>\n",
       "      <th>passenger_count</th>\n",
       "      <th>trip_distance</th>\n",
       "      <th>RatecodeID</th>\n",
       "      <th>store_and_fwd_flag</th>\n",
       "      <th>PULocationID</th>\n",
       "      <th>DOLocationID</th>\n",
       "      <th>payment_type</th>\n",
       "      <th>fare_amount</th>\n",
       "      <th>extra</th>\n",
       "      <th>mta_tax</th>\n",
       "      <th>tip_amount</th>\n",
       "      <th>tolls_amount</th>\n",
       "      <th>improvement_surcharge</th>\n",
       "      <th>total_amount</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2</td>\n",
       "      <td>2016-12-15 12:18:37</td>\n",
       "      <td>2016-12-15 12:28:45</td>\n",
       "      <td>6</td>\n",
       "      <td>0.50</td>\n",
       "      <td>1</td>\n",
       "      <td>N</td>\n",
       "      <td>141</td>\n",
       "      <td>237</td>\n",
       "      <td>2</td>\n",
       "      <td>7.5</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.3</td>\n",
       "      <td>8.30</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>2016-12-20 22:39:23</td>\n",
       "      <td>2016-12-20 22:50:27</td>\n",
       "      <td>1</td>\n",
       "      <td>2.00</td>\n",
       "      <td>1</td>\n",
       "      <td>N</td>\n",
       "      <td>246</td>\n",
       "      <td>164</td>\n",
       "      <td>1</td>\n",
       "      <td>9.5</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.5</td>\n",
       "      <td>3.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.3</td>\n",
       "      <td>13.80</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>2016-12-09 23:02:06</td>\n",
       "      <td>2016-12-09 23:11:03</td>\n",
       "      <td>1</td>\n",
       "      <td>1.10</td>\n",
       "      <td>1</td>\n",
       "      <td>N</td>\n",
       "      <td>114</td>\n",
       "      <td>79</td>\n",
       "      <td>1</td>\n",
       "      <td>7.5</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.5</td>\n",
       "      <td>1.75</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.3</td>\n",
       "      <td>10.55</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>2016-12-11 15:40:19</td>\n",
       "      <td>2016-12-11 16:09:53</td>\n",
       "      <td>1</td>\n",
       "      <td>11.90</td>\n",
       "      <td>1</td>\n",
       "      <td>N</td>\n",
       "      <td>138</td>\n",
       "      <td>224</td>\n",
       "      <td>1</td>\n",
       "      <td>34.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.5</td>\n",
       "      <td>8.05</td>\n",
       "      <td>5.54</td>\n",
       "      <td>0.3</td>\n",
       "      <td>48.39</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2</td>\n",
       "      <td>2016-12-19 11:34:28</td>\n",
       "      <td>2016-12-19 11:47:51</td>\n",
       "      <td>1</td>\n",
       "      <td>1.96</td>\n",
       "      <td>1</td>\n",
       "      <td>N</td>\n",
       "      <td>261</td>\n",
       "      <td>144</td>\n",
       "      <td>2</td>\n",
       "      <td>10.5</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.3</td>\n",
       "      <td>11.30</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   VendorID tpep_pickup_datetime tpep_dropoff_datetime  passenger_count  \\\n",
       "0         2  2016-12-15 12:18:37   2016-12-15 12:28:45                6   \n",
       "1         1  2016-12-20 22:39:23   2016-12-20 22:50:27                1   \n",
       "2         1  2016-12-09 23:02:06   2016-12-09 23:11:03                1   \n",
       "3         1  2016-12-11 15:40:19   2016-12-11 16:09:53                1   \n",
       "4         2  2016-12-19 11:34:28   2016-12-19 11:47:51                1   \n",
       "\n",
       "   trip_distance  RatecodeID store_and_fwd_flag  PULocationID  DOLocationID  \\\n",
       "0           0.50           1                  N           141           237   \n",
       "1           2.00           1                  N           246           164   \n",
       "2           1.10           1                  N           114            79   \n",
       "3          11.90           1                  N           138           224   \n",
       "4           1.96           1                  N           261           144   \n",
       "\n",
       "   payment_type  fare_amount  extra  mta_tax  tip_amount  tolls_amount  \\\n",
       "0             2          7.5    0.0      0.5        0.00          0.00   \n",
       "1             1          9.5    0.5      0.5        3.00          0.00   \n",
       "2             1          7.5    0.5      0.5        1.75          0.00   \n",
       "3             1         34.0    0.0      0.5        8.05          5.54   \n",
       "4             2         10.5    0.0      0.5        0.00          0.00   \n",
       "\n",
       "   improvement_surcharge  total_amount  \n",
       "0                    0.3          8.30  \n",
       "1                    0.3         13.80  \n",
       "2                    0.3         10.55  \n",
       "3                    0.3         48.39  \n",
       "4                    0.3         11.30  "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sample100 = pd.read_csv('sample100.csv', parse_dates=[1,2])\n",
    "sample100.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Estimating the proportion of tippers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.66000000000000003"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "is_tipped = sample100.tip_amount>0\n",
    "is_tipped.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Standard deviation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.047370877129308042"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ph = is_tipped.mean()\n",
    "s = np.sqrt(ph * (1-ph) / len(is_tipped))\n",
    "s"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "95% confidence interval:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.56715478691048404, 0.75284521308951602)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from statsmodels.stats.proportion import proportion_confint\n",
    "proportion_confint(sum(is_tipped), len(is_tipped), alpha=0.05)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pretty wide! How big do we need a sample for the 95% confidence interval to be approximately 2% wide?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8621"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from statsmodels.stats.proportion import samplesize_confint_proportion\n",
    "int(np.ceil(samplesize_confint_proportion(ph, 0.01)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's take a bigger sample:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.61209999999999998"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sample10000 = pd.read_csv('sample10000.csv', parse_dates=[1,2])\n",
    "is_tipped = sample10000.tip_amount>0\n",
    "is_tipped.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0048727157725440952"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ph = is_tipped.mean()\n",
    "s = np.sqrt(ph * (1-ph) / len(is_tipped))\n",
    "s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.60254965257891324, 0.62165034742108671)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "proportion_confint(sum(is_tipped), len(is_tipped), alpha=0.05)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is indeed about 2% wide. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Estimating the average trip duration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sample100['duration'] = [x.total_seconds() / 60 for x in sample100.tpep_dropoff_datetime -  sample100.tpep_pickup_datetime]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "14.145500000000002"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sample100['duration'].mean() "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.2435186819673421"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s = sample100['duration'].std(ddof=1) / np.sqrt(len(sample100['duration']))\n",
    "s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(11.678089151722666, 16.612910848277338)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from statsmodels.stats.weightstats import _tconfint_generic\n",
    "_tconfint_generic(sample100['duration'].mean(), \n",
    "                  s, \n",
    "                  len(sample100['duration']) - 1, \n",
    "                  0.05, 'two-sided')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[<matplotlib.axes._subplots.AxesSubplot object at 0x7f7c95e71940>]], dtype=object)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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i6EtSQ3qFfpILkzycZDbJzjHnT05yZ3f+viSbu+NvSvJgkk92X9+4vMOXJE1i0dBPsg64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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7cc0f3df60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sample100.hist(column = 'duration', bins=30, normed=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sample10000['duration'] = [x.total_seconds() / 60 for x in sample10000.tpep_dropoff_datetime -  sample10000.tpep_pickup_datetime]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "17.032653333333332"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sample10000['duration'].mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.61104871928126259"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s = sample10000['duration'].std(ddof=1) / np.sqrt(len(sample10000['duration']))\n",
    "s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(15.834874861663989, 18.230431805002674)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "_tconfint_generic(sample10000['duration'].mean(), \n",
    "                  s, \n",
    "                  len(sample10000['duration']) - 1, \n",
    "                  0.05, 'two-sided')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[<matplotlib.axes._subplots.AxesSubplot object at 0x7f7cc0f3def0>]], dtype=object)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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VsFBI6gBuAM4BZgMXSZpdFbYI2BcRpwDXAstT+wHgM8Cnagx9I7AYmJVe81L7UuDOiJgF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\nZAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7c9e641d68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sample10000.hist(column = 'duration', bins=30, normed=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True     9980\n",
       "False      20\n",
       "Name: duration, dtype: int64"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tmp = sample10000['duration'] < 120\n",
    "tmp.value_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "14.440375751503007"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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IVX2GXiBIko5Cozx0bj1wX9/6PuDM+dpU1YEk+4ETgAdHGUSSrcBWgHXr1jE7OztKt6HW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\nSY0zCCSpcQaBJDXOIJCkxv1feuCr71eoFikAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7c965174a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sample10000[sample10000['duration'] < 120].hist(column = 'duration', bins=30, normed=True)\n",
    "sample10000['duration'][sample10000['duration'] < 120].mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10.266666666666666"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sample100['duration'].median()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "11.233333333333333"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sample10000['duration'].median()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "11.216666666666667"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sample10000['duration'][sample10000['duration'] < 120].median()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Bootstrap:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def get_bootstrap_samples(data, n_samples):\n",
    "    indices = np.random.randint(0, len(data), (n_samples, len(data)))\n",
    "    samples = data[indices]\n",
    "    return samples\n",
    "    \n",
    "def stat_intervals(stat, alpha):\n",
    "    boundaries = np.percentile(stat, [100 * alpha / 2., 100 * (1 - alpha / 2.)])\n",
    "    return boundaries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  8.58333333,  11.94166667])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "median_duration = list(map(np.median, get_bootstrap_samples(sample100['duration'].values, 1000)))\n",
    "stat_intervals(median_duration, 0.05)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 11.03291667,  11.41666667])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "median_duration = list(map(np.median, get_bootstrap_samples(sample10000['duration'].values, 1000)))\n",
    "stat_intervals(median_duration, 0.05)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.6.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}