{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# HIDDEN\n",
    "from datascience import *\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "plt.style.use('fivethirtyeight')\n",
    "import math\n",
    "from scipy import stats\n",
    "import numpy as np\n",
    "np.random.seed(0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Whenever we analyze a random sample of a population, our goal is to draw robust conclusions about the whole population, despite the fact that we can measure only part of it. We must guard against being misled by the inevitable random variations in a sample. It is possible that a sample has very different characteristics than the population itself, but those samples are unlikely. It is much more typical that a random sample, especially a large simple random sample, is representative of the population. More importantly, the chance that a sample resembles the population is something that we know in advance, based on how we selected our random sample. Statistical inference is the practice of using this information to make precise statements about a population based on a random sample."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Statistics and Parameters\n",
    "\n",
    "The [Bay Area Bike Share](http://www.bayareabikeshare.com/) service published a [dataset](http://www.bayareabikeshare.com/open-data) describing every bicycle rental from September 2014 to August 2015 in their system. This set of all trips is a population, and fortunately we have the data for each and every trip rather than just a sample. We'll focus only on the *free trips*, which are trips that last less than 1800 seconds (half an hour)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "    <thead>\n",
       "        <tr>\n",
       "            <th>Start Station</th> <th>End Station</th> <th>Duration</th>\n",
       "        </tr>\n",
       "    </thead>\n",
       "    <tbody>\n",
       "        <tr>\n",
       "            <td>Harry Bridges Plaza (Ferry Building)         </td> <td>San Francisco Caltrain (Townsend at 4th)     </td> <td>765     </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>San Antonio Shopping Center                  </td> <td>Mountain View City Hall                      </td> <td>1036    </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>Post at Kearny                               </td> <td>2nd at South Park                            </td> <td>307     </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>San Jose City Hall                           </td> <td>San Salvador at 1st                          </td> <td>409     </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>Embarcadero at Folsom                        </td> <td>Embarcadero at Sansome                       </td> <td>789     </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>Yerba Buena Center of the Arts (3rd @ Howard)</td> <td>San Francisco Caltrain (Townsend at 4th)     </td> <td>293     </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>Embarcadero at Folsom                        </td> <td>Embarcadero at Sansome                       </td> <td>896     </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>Embarcadero at Sansome                       </td> <td>Steuart at Market                            </td> <td>255     </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>Beale at Market                              </td> <td>Temporary Transbay Terminal (Howard at Beale)</td> <td>126     </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>Post at Kearny                               </td> <td>South Van Ness at Market                     </td> <td>932     </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "</table>\n",
       "<p>... (338333 rows omitted)</p"
      ],
      "text/plain": [
       "Start Station                                 | End Station                                   | Duration\n",
       "Harry Bridges Plaza (Ferry Building)          | San Francisco Caltrain (Townsend at 4th)      | 765\n",
       "San Antonio Shopping Center                   | Mountain View City Hall                       | 1036\n",
       "Post at Kearny                                | 2nd at South Park                             | 307\n",
       "San Jose City Hall                            | San Salvador at 1st                           | 409\n",
       "Embarcadero at Folsom                         | Embarcadero at Sansome                        | 789\n",
       "Yerba Buena Center of the Arts (3rd @ Howard) | San Francisco Caltrain (Townsend at 4th)      | 293\n",
       "Embarcadero at Folsom                         | Embarcadero at Sansome                        | 896\n",
       "Embarcadero at Sansome                        | Steuart at Market                             | 255\n",
       "Beale at Market                               | Temporary Transbay Terminal (Howard at Beale) | 126\n",
       "Post at Kearny                                | South Van Ness at Market                      | 932\n",
       "... (338333 rows omitted)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "free_trips = Table.read_table(\"trip.csv\").where('Duration', are.below(1800)).select([3, 6, 1])\n",
    "free_trips"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A quantity measured for a whole population is called a *parameter*. For example, the average duration for any free trip between September 2014 to August 2015 can be computed exactly from these data: 550.00."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "550.00143345658103"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.average(free_trips.column('Duration'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Although we have information for the full population, we will investigate what we can learn from a simple random sample. Below, we sample 100 trips without replacement from `free_trips` not just once, but 40 different times. All 4000 trips are stored in a table called `samples`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "    <thead>\n",
       "        <tr>\n",
       "            <th>Sample #</th> <th>Duration</th>\n",
       "        </tr>\n",
       "    </thead>\n",
       "    <tbody>\n",
       "        <tr>\n",
       "            <td>0       </td> <td>557     </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>0       </td> <td>491     </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>0       </td> <td>877     </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>0       </td> <td>279     </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>0       </td> <td>339     </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>0       </td> <td>542     </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>0       </td> <td>715     </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>0       </td> <td>255     </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>0       </td> <td>1543    </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>0       </td> <td>194     </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "</table>\n",
       "<p>... (3990 rows omitted)</p"
      ],
      "text/plain": [
       "Sample # | Duration\n",
       "0        | 557\n",
       "0        | 491\n",
       "0        | 877\n",
       "0        | 279\n",
       "0        | 339\n",
       "0        | 542\n",
       "0        | 715\n",
       "0        | 255\n",
       "0        | 1543\n",
       "0        | 194\n",
       "... (3990 rows omitted)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n = 100\n",
    "samples = Table(['Sample #', 'Duration'])\n",
    "for i in np.arange(40):\n",
    "    for trip in free_trips.sample(n).rows:\n",
    "        samples.append([i, trip.item('Duration')])\n",
    "samples"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A quantity measured for a sample is called a *statistic*. For example, the average duration of a free trip in a sample is a statistic, and we find that there is some variation across samples."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average duration in sample 0 is 547.29\n",
      "Average duration in sample 1 is 500.6\n",
      "Average duration in sample 2 is 660.16\n"
     ]
    }
   ],
   "source": [
    "for i in np.arange(3):\n",
    "    sample_average = np.average(samples.where('Sample #', i).column('Duration'))\n",
    "    print(\"Average duration in sample\", i, \"is\", sample_average)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Often, the goal of analysis is to estimate parameters from statistics. Proper statistical inference involves more than just picking an estimate: we should also say something about how confident we should be in that estimate. A single guess is rarely sufficient to make a robust conclusion about a population. We also need to quantify in some way how precise we believe that guess to be. \n",
    "\n",
    "Already we can see from the example above that the average duration of a sample is around 550, the parameter. Our goal is to quantify this notion of *around*, and one way to do so is to state a range of values."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Error in Estimates"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can learn a great deal about the behavior of a statistic by computing it for many samples. In the scatter diagram below, the order in which the statistic was computed appears on the horizontal axis, and the value of the average duration for a sample of `n` trips appears on the vertical axis. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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Xit08+qeffuJf//pXme5n0KdPH7ufO3ToQHR0NBs2bGDy5MkMGzbMtu5m7yEq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\n/w/VY87kqC71yQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d67b780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "samples.group(0, np.average).scatter(0, 1, s=50)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The sample number doesn't tell us anything beyond when the sample was selected, and we can see from this unstructured cloud of points that one sample does not affect the next in any consistent way. The sample averages are indeed all around 550. Some are above, and some are below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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hwh8rbuDAgcyaNYtJkyZZzTtw4AB9+vShdevWAPTp04fFixfz7bff0rt3by5e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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10beb5e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "samples.group(0, np.average).hist(1, bins=np.arange(480, 641, 10))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are 40 averages for 40 samples. If we find an interval that contains the middle 38 out of 40, it will contain 95% of the samples. One such interval is bounded by the second smallest and the second largest sample averages among the 40 samples."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Empirically, 95% of sample averages fell within the interval 502.38 to 620.04\n"
     ]
    }
   ],
   "source": [
    "averages = np.sort(samples.group(0, np.average).column(1))\n",
    "lower = averages.item(1)\n",
    "upper = averages.item(38)\n",
    "print('Empirically, 95% of sample averages fell within the interval', lower, 'to', upper)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This statement gives us our first notion of a margin of error. If this statement were to hold up not just for our 40 samples, but for all samples, then a reasonable strategy for estimating the true population average would be to draw a 100-trip sample, compute its sample average, and guess that the true average was within `max_deviation` of this quantity. We would be right at least 95% of the time.\n",
    "\n",
    "The problem with this approach is that finding the `max_deviation` required drawing many different samples, and we would like to be able to say something similar after having collected only one 100-trip sample."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Variability Within Samples \n",
    "\n",
    "By contrast, The individual durations in the samples themselves are not closely clustered around 550. Instead, they span the whole range from 0 to 1800. The durations for the first three 100-item samples are visualized below. All have somewhat similar shapes; they were drawn from the same population. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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GjF1FZ1ft/vvf/4aJSfs2Z2ZmBk9PT5WpB7OysrS+KCgjIwMrVqzAjh074O/vr9W2iIiI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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d67b898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Cxtoi+fQXY7G0tISPjw/S09O1ph85cgQBAQHGCUVERPT/KX6NFAAiIiIQHh4OX19fBAQE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\nfKwhiQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10487fd68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Wr18PqVSK4OBgAEB0dDROnjyJ9PR0+TyFhYV4+PAhysrKUFlZiYKCAgBAv379dLINRETU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\nGvg/x6eAaMUag/4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x104a25860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in np.arange(3):\n",
    "    samples.where('Sample #', i).hist(1, bins=np.arange(0, 1801, 200))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have now observed two different ways in which the variation of a random sample can be observed: the statistics computed from those samples vary in magnitude, and the sampled quantities themselves vary in distribution. That is, there is variability *across samples*, which we see by comparing sample averages, and there is variability *within each sample*, which we see in the duration histograms above."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Percentiles\n",
    "\n",
    "The 80th percentile of a collection of values is the smallest value in the collection that is at least as large as 80% of the values in the collection. Likewise, the 40th percentile is at least as large as 40% of the values. \n",
    "\n",
    "For example, let's consider the sizes of the five largest continents: Africa, Antarctica, Asia, North America, and South America, rounded to the nearest million square miles."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sizes = [12, 17, 6, 9, 7]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The 20th percentile is the smallest value that is at least as large as 20% or one fifth of the elements."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "percentile(20, sizes)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The 60th percentile is at least as large as 60% or three fifths of the elements."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "percentile(60, sizes)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To find the element corresponding to a percentile $p$, sort the elements and take the $k$th element, where $k=\\frac{p}{100} \\times n$ where $n$ is the size of the collection. In general, any percentile from 0 to 100 can be computed for a collection of values, and it is always an element of the collection. If $k$ is not an integer, round it up to find the percentile element. For example, the 90th percentile of a five element set is the fifth element, because $\\frac{90}{100} \\times 5$ is 4.5, which rounds up to 5."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "17"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "percentile(90, sizes)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When the `percentile` function is called with a single argument, it returns a function that computes percentiles of collections."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tenth = percentile(10)\n",
    "tenth(sizes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tenth(np.arange(50))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "499"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tenth(np.arange(5000))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Confidence Intervals\n",
    "\n",
    "Inference begins with a population: a collection that you can describe but often cannot measure directly. One thing we can often do with a populuation is to draw a simple random sample. By measuring a statistic of the sample, we may hope to estimate a parameter of the population. In this process, the population is not random, nor are its parameters. The sample is random, and so is its statistic. The whole process of estimation therefore gives a random result. It starts from a population (fixed), draws a sample (random), computes a statistic (random), and then estimates the parameter from the statistic (random). By calling the process random, we mean that the final estimate could have been different because the sample could have been different.\n",
    "\n",
    "A confidence interval is one notion of a margin of error around an estimate. The margin of error acknowledges that the estimation process could have been misleading because of the variation in the sample. It gives a range that might contain the original parameter, along with a percentage of confidence. For example, a 95% confidence interval is one in which we would expect the interval to contain the true parameter for 95% of random samples. For any particular sample, any particular estimate, and any particular interval, the parameter is either contained or not; we never know for sure. The purpose of the confidence interval is to quantify how often our estimation process gives us a range containing the truth.\n",
    "\n",
    "There are many different ways to compute a confidence interval. The challenge in computing a confidence interval from a single sample is that we don't know the population, and so we don't know how its samples will vary. One way to make progress despite this limited information is to assume that the variability *within the sample* is similar to the variability within the population."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Resampling from a Sample\n",
    "\n",
    "Even though we happen to have the whole population of `free_trips`, let's imagine for a moment that we have only a single 100-trip sample from this population. That sample has 100 durations. Our goal now is to learn what we can about the population using just this sample."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "    <thead>\n",
       "        <tr>\n",
       "            <th>Start Station</th> <th>End Station</th> <th>Duration</th>\n",
       "        </tr>\n",
       "    </thead>\n",
       "    <tbody>\n",
       "        <tr>\n",
       "            <td>Grant Avenue at Columbus Avenue    </td> <td>San Francisco Caltrain 2 (330 Townsend) </td> <td>877     </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>Embarcadero at Folsom              </td> <td>San Francisco Caltrain (Townsend at 4th)</td> <td>597     </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>Beale at Market                    </td> <td>Beale at Market                         </td> <td>67      </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2nd at Folsom                      </td> <td>Washington at Kearny                    </td> <td>714     </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>Clay at Battery                    </td> <td>Embarcadero at Sansome                  </td> <td>510     </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>South Van Ness at Market           </td> <td>Powell Street BART                      </td> <td>494     </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>San Jose Diridon Caltrain Station  </td> <td>MLK Library                             </td> <td>530     </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>Mechanics Plaza (Market at Battery)</td> <td>Clay at Battery                         </td> <td>286     </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>South Van Ness at Market           </td> <td>Civic Center BART (7th at Market)       </td> <td>172     </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>Broadway St at Battery St          </td> <td>5th at Howard                           </td> <td>551     </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "</table>\n",
       "<p>... (90 rows omitted)</p"
      ],
      "text/plain": [
       "Start Station                       | End Station                              | Duration\n",
       "Grant Avenue at Columbus Avenue     | San Francisco Caltrain 2 (330 Townsend)  | 877\n",
       "Embarcadero at Folsom               | San Francisco Caltrain (Townsend at 4th) | 597\n",
       "Beale at Market                     | Beale at Market                          | 67\n",
       "2nd at Folsom                       | Washington at Kearny                     | 714\n",
       "Clay at Battery                     | Embarcadero at Sansome                   | 510\n",
       "South Van Ness at Market            | Powell Street BART                       | 494\n",
       "San Jose Diridon Caltrain Station   | MLK Library                              | 530\n",
       "Mechanics Plaza (Market at Battery) | Clay at Battery                          | 286\n",
       "South Van Ness at Market            | Civic Center BART (7th at Market)        | 172\n",
       "Broadway St at Battery St           | 5th at Howard                            | 551\n",
       "... (90 rows omitted)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sample = free_trips.sample(n)\n",
    "sample"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "518.55999999999995"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "average = np.average(sample.column('Duration'))\n",
    "average"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A technique called *bootstrap resampling* uses the variability of the sample as a proxy for the variability of the population. Instead of drawing many samples from the population, we will draw many samples from the sample. Since the original sample and the re-sampled sample have the same size, we must draw with replacement in order to see any variability at all."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "    <thead>\n",
       "        <tr>\n",
       "            <th>Resample #</th> <th>Duration</th>\n",
       "        </tr>\n",
       "    </thead>\n",
       "    <tbody>\n",
       "        <tr>\n",
       "            <td>0         </td> <td>329     </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>0         </td> <td>252     </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>0         </td> <td>252     </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>0         </td> <td>685     </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>0         </td> <td>434     </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>0         </td> <td>396     </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>0         </td> <td>434     </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>0         </td> <td>585     </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>0         </td> <td>394     </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>0         </td> <td>202     </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "</table>\n",
       "<p>... (3990 rows omitted)</p"
      ],
      "text/plain": [
       "Resample # | Duration\n",
       "0          | 329\n",
       "0          | 252\n",
       "0          | 252\n",
       "0          | 685\n",
       "0          | 434\n",
       "0          | 396\n",
       "0          | 434\n",
       "0          | 585\n",
       "0          | 394\n",
       "0          | 202\n",
       "... (3990 rows omitted)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "resamples = Table(['Resample #', 'Duration'])\n",
    "for i in np.arange(40):\n",
    "    resample = sample.sample(n, with_replacement=True)\n",
    "    for trip in resample.rows:\n",
    "        resamples.append([i, trip.item('Duration')])\n",
    "resamples"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using the `resamples`, we can investigate the variability of the corresponding sample averages."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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FhdA2/rw8I8HWoYhIBay6z6Bp06akpqby1FNPUVJSQuvWrSkpKSEhIYGtW7dy223lvwFU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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108664080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "resamples.group(0, np.average).scatter(0, 1, s=50)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These sample averages are not necessarily clustered around the true average 550. Instead, they will be clustered around the average of the sample from which they were re-sampled."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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4ODBp0iQjs4qIiBjG6kJs0qQJW7ZsYfLkyURHR5Obm2t5ek3nzp2JjY3F19fXsKB/VXJy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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1090d3080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "resamples.group(0, np.average).hist(1, bins=np.arange(480, 641, 10))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Although the center of this distribution is not the same as the true population average, its variability is similar. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Bootstrap Confidence Interval\n",
    "\n",
    "A technique called *bootstrap resampling* estimates a confidence interval using resampling. To find a confidence interval, we must estimate how much the sample statistic deviates from the population parameter. The boostrap assumes that a resampled statistic will deviate from the sample statistic in approximately the same way that the sample statistic deviates from the parameter. \n",
    "\n",
    "To carry out the technique, we first compute the deviations from the sample statistic (in this case, the sample average) for many resampled samples. The number is arbitrary, and it doesn't require any collecting of new data; 1000 or more is typical."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "    <thead>\n",
       "        <tr>\n",
       "            <th>Resample #</th> <th>Deviation</th>\n",
       "        </tr>\n",
       "    </thead>\n",
       "    <tbody>\n",
       "        <tr>\n",
       "            <td>0         </td> <td>30.95    </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>1         </td> <td>41.16    </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2         </td> <td>3.37     </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>3         </td> <td>2.54     </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>4         </td> <td>-22.87   </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>5         </td> <td>27.63    </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>6         </td> <td>49.93    </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>7         </td> <td>11.91    </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>8         </td> <td>26.32    </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>9         </td> <td>-5.97    </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "</table>\n",
       "<p>... (990 rows omitted)</p"
      ],
      "text/plain": [
       "Resample # | Deviation\n",
       "0          | 30.95\n",
       "1          | 41.16\n",
       "2          | 3.37\n",
       "3          | 2.54\n",
       "4          | -22.87\n",
       "5          | 27.63\n",
       "6          | 49.93\n",
       "7          | 11.91\n",
       "8          | 26.32\n",
       "9          | -5.97\n",
       "... (990 rows omitted)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "deviations = Table(['Resample #', 'Deviation'])\n",
    "for i in np.arange(1000):\n",
    "    resample = sample.sample(n, with_replacement=True)\n",
    "    dev = average - np.average(resample.column(2))\n",
    "    deviations.append([i, dev])\n",
    "deviations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A deviation of zero indicates that the resampled statistic is the same as the sampled statistic. That's evidence that the sample statistic is perhaps the same as the population parameter. A positive deviation is evidence that the sample statistic may be greater than the parameter. As we can see, for averages, the distribution of deviations is roughly symmetric."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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LPEZYq1YtPQpKREQqLIsDcciQIaxevZrLly8Xmnbx4kVWr17N0KFDb6mIFStWEBQUhLe3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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x109302a20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "deviations.hist(1, bins=np.arange(-100, 101, 10))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A 95% confidence interval is computed based on the middle 95% of this distribution of deviations. The max and min devations are computed by the 97.5th percentile and 2.5th percentile respectively, because the span between these contains 95% of the distribution. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "461.93000000000001"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lower = average - percentile(97.5, deviations.column(1))\n",
    "lower"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "576.29999999999995"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "upper = average - percentile(2.5, deviations.column(1))\n",
    "upper"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we have not only an estimate, but an interval around it that expresses our uncertainty about the value of the parameter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A 95% confidence interval around 518.56 is 461.93 to 576.3\n"
     ]
    }
   ],
   "source": [
    "print('A 95% confidence interval around', average, 'is', lower, 'to', upper)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And behold, the interval happens to contain the true parameter 550. Normally, after generating a confidence interval, there is no way to check that it is correct, because to do so requires access to the entire population. In this case, we started with the whole population in a single table, and so we are able to check.\n",
    "\n",
    "The following function encapsulates the entire process of producing a confidence interval for the population average using a single sample.  Each time it is run, even for the same sample, the interval will be slightly different because of the random variation of resampling. However, the upper and lower bounds generated by 2000 samples for this problem are typically quite similar for multiple calls."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(457.43999999999994, 572.63999999999987)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def average_ci(sample, label):\n",
    "    deviations = Table(['Resample #', 'Deviation'])\n",
    "    n = sample.num_rows\n",
    "    average = np.average(sample.column(label))\n",
    "    for i in np.arange(1000):\n",
    "        resample = sample.sample(n, with_replacement=True)\n",
    "        dev = np.average(resample.column(label)) - average\n",
    "        deviations.append([i, dev])\n",
    "    return (average - percentile(97.5, deviations.column(1)),\n",
    "            average - percentile(2.5, deviations.column(1)))\n",
    "\n",
    "average_ci(sample, 'Duration')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(458.7399999999999, 575.50999999999988)"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "average_ci(sample, 'Duration')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "However, if we draw an entirely new sample, then the confidence interval will change."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(530.18000000000006, 661.21000000000004)"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "average_ci(free_trips.sample(n), 'Duration')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The interval is about the same width, and that's typical of multiple samples of the same size drawn from the same population. However, if a much larger sample is drawn, then the confidence interval that results is typically going to be much smaller. We're not losing confidence in this case; we're just using more evidence to perform inference, and so we have less uncertainty about the full population."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(527.18937499999993, 555.11437499999988)"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "average_ci(free_trips.sample(16 * n), 'Duration')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Evaluating Confidence Intervals\n",
    "\n",
    "When given only a sample, it is not possible to check whether the parameter was estimated correctly. However, in the case of the Bay Area Bike Share, we have not only the sample, but many samples and the whole population. Therefore, we can check how often the confidence intervals we compute in this way do in fact contain the true parameter.\n",
    "\n",
    "Before measuring the accuracy of our technique, we can visualize the result of resampling each sample. The following scatter diagram has 6 vertical lines for 6 samples, and each line consists of 100 points that represent the statistics from resamples for that sample."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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aNP7617964pKTk+nfvz+zZ8/m0Ucf9RzPz89n5syZ3HHHHV55PfPMM17vP8Bl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\n/we0qCxBYwi1zwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10932dc18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "samples = Table(['Sample #', 'Resample average', 'Sample Average'])\n",
    "for i in np.arange(6):\n",
    "    sample = free_trips.sample(n)\n",
    "    average = np.average(sample.column('Duration'))\n",
    "    for j in np.arange(100):\n",
    "        resample = sample.sample(n, with_replacement=True)\n",
    "        resample_average = np.average(resample.column('Duration'))\n",
    "        samples.append([i, resample_average, average])\n",
    "samples.scatter(0, s=80)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see from the plot above that for almost every sample, there are some resampled averages above 550 and some below. When we use these resampled averages to compute confidence intervals, many of those intervals contain 550 as a result. \n",
    "\n",
    "Below, we draw 100 more samples and show the upper and lower bounds of the confidence intervals computed from each one."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "intervals = Table(['Sample #', 'Lower', 'Estimate', 'Upper'])\n",
    "for i in np.arange(100):\n",
    "    sample = free_trips.sample(n)\n",
    "    average = np.average(sample.column('Duration'))\n",
    "    lower, upper = average_ci(sample, 'Duration')\n",
    "    intervals.append([i, lower, average, upper])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can compute precisely which intervals contain the truth, and we should find that about 95 of them do. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "97"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "correct = np.logical_and(intervals.column('Lower') <= 550, intervals.column('Upper') >= 550)\n",
    "np.count_nonzero(correct)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Each confidence interval is generated from only a single sample of 100 trips. As a result, the width of the interval varies quite a bit as well. Compared to the interval width we computed originally (which required multiple samples), we see that some of these intervals are much more narrow and some are much wider. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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BdHS00byvvvoKCQkJSE5Oxvbt200ekoiIyNxE7yEWFBRgxowZjcoQAJ5//nm8+eabUKvV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\nFiIREREAFiIREREA4P8AMkUIMT9dYDYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1099b6550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Table().with_column('Width', intervals.column('Upper')-intervals.column('Lower')).hist(0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Given a single sample, it is impossible to know whether you have correctly estimated the parameter or not. However, you can infer a precise notion of confidence by following a process based on random sampling."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}