{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# HIDDEN\n",
    "from datascience import *\n",
    "import numpy as np\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plots\n",
    "plots.style.use('fivethirtyeight')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The Variability of the Sample Mean ###\n",
    "By the Central Limit Theorem, the probability distribution of the mean of a large random sample is roughly normal. The bell curve is centered at the population mean. Some of the sample means are higher, and some lower, but the deviations from the population mean are roughly symmetric on either side, as we have seen repeatedly. Formally, probability theory shows that the sample mean is an *unbiased* estimate of the population mean.\n",
    "\n",
    "In our simulations, we also noticed that the means of larger samples tend to be more tightly clustered around the population mean than means of smaller samples. In this section, we will quantify the variability of the sample mean and develop a relation between the variability and the sample size."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's start with our table of flight delays. The mean delay is about 16.7 minutes, and the distribution of delays is skewed to the right."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "united = Table.read_table('united_summer2015.csv')\n",
    "delay = united.select('Delay')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "16.658155515370705"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pop_mean = np.mean(delay.column('Delay'))\n",
    "pop_mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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IcsGCBdixYwdycnLg4eGhdaw+Ju9xfJ9fABsbmybHiRlja2sLH58OuoilM3K53OjmXCxm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\nERERABYiERERABYiERERAOD/AY+gun6NOW9uAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a81d160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# HIDDEN\n",
    "delay.hist(bins=np.arange(-20, 300, 10))\n",
    "plots.scatter(pop_mean, -0.0008, marker='^', color='darkblue', s=60)\n",
    "plots.ylim(-0.004, 0.04);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's take random samples and look at the probability distribution of the sample mean. As usual, we will use simulation to get an empirical approximation to this distribution.\n",
    "\n",
    "We will define a function `simulate_sample_mean` to do this, because we are going to vary the sample size later. The arguments are the name of the table, the label of the column containing the variable, the sample size, and the number of simulations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "\"\"\"Empirical distribution of random sample means\"\"\"\n",
    "\n",
    "def simulate_sample_mean(table, label, sample_size, repetitions):\n",
    "    \n",
    "    means = make_array()\n",
    "\n",
    "    for i in range(repetitions):\n",
    "        new_sample = table.sample(sample_size)\n",
    "        new_sample_mean = np.mean(new_sample.column(label))\n",
    "        means = np.append(means, new_sample_mean)\n",
    "\n",
    "    sample_means = Table().with_column('Sample Means', means)\n",
    "    \n",
    "    # Display empirical histogram and print all relevant quantities\n",
    "    sample_means.hist(bins=20)\n",
    "    plots.xlabel('Sample Means')\n",
    "    plots.title('Sample Size ' + str(sample_size))\n",
    "    print(\"Sample size: \", sample_size)\n",
    "    print(\"Population mean:\", np.mean(table.column(label)))\n",
    "    print(\"Average of sample means: \", np.mean(means))\n",
    "    print(\"Population SD:\", np.std(table.column(label)))\n",
    "    print(\"SD of sample means:\", np.std(means))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us simulate the mean of a random sample of 100 delays, then of 400 delays, and finally of 625 delays. We will perform 10,000 repetitions of each of these process. The `xlim` and `ylim` lines set the axes consistently in all the plots for ease of comparison. You can just ignore those two lines of code in each cell."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sample size:  100\n",
      "Population mean: 16.6581555154\n",
      "Average of sample means:  16.662059\n",
      "Population SD: 39.4801998516\n",
      "SD of sample means: 3.90507237968\n"
     ]
    },
    {
     "data": {
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Y2GDp0qXYunUrSkpK0LZtW0RGRmLYsGFK1Uo1m0gsFiueS6om//jHP/DZZ5+hS5cukEql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\nx7AjIiLBY9gREZHg/T9qWoKUEEoQlQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10acb0b38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "simulate_sample_mean(delay, 'Delay', 100, 10000)\n",
    "plots.xlim(5, 35)\n",
    "plots.ylim(0, 0.25);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sample size:  400\n",
      "Population mean: 16.6581555154\n",
      "Average of sample means:  16.67117625\n",
      "Population SD: 39.4801998516\n",
      "SD of sample means: 1.98326299651\n"
     ]
    },
    {
     "data": {
      "image/png": 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KnXdrevbsGUQiEe7du4fIyEiF27KyskKnTp0AAHZ2djhz5gxWrFiBP//8E5s3b4ZUKoWp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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b14d940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "simulate_sample_mean(delay, 'Delay', 400, 10000)\n",
    "plots.xlim(5, 35)\n",
    "plots.ylim(0, 0.25);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sample size:  625\n",
      "Population mean: 16.6581555154\n",
      "Average of sample means:  16.68523712\n",
      "Population SD: 39.4801998516\n",
      "SD of sample means: 1.60089096006\n"
     ]
    },
    {
     "data": {
      "image/png": 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7IiLSOrXDLiYmpizrICIiKjNqh527u3tZ1kFERFRm1B5UTkREVFkx7IiISPQY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\nosewIyIi0WPYERGR6DHsiIhI9P4fRO1DOL3QT3kAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b2eae10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "simulate_sample_mean(delay, 'Delay', 625, 10000)\n",
    "plots.xlim(5, 35)\n",
    "plots.ylim(0, 0.25);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can see the Central Limit Theorem in action – the histograms of the sample means are roughly normal, even though the histogram of the delays themselves is far from normal.\n",
    "\n",
    "You can also see that each of the three histograms of the sample means is centered very close to the population mean. In each case, the \"average of sample means\" is very close to 16.66 minutes, the population mean. Both values are provided in the printout above each histogram. As expected, the sample mean is an unbiased estimate of the population mean."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The SD of All the Sample Means ###\n",
    "\n",
    "You can also see that the histograms get narrower, and hence taller, as the sample size increases. We have seen that before, but now we will pay closer attention to the measure of spread.\n",
    "\n",
    "The SD of the population of all delays is about 40 minutes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "39.480199851609314"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pop_sd = np.std(delay.column('Delay'))\n",
    "pop_sd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Take a look at the SDs in the sample mean histograms above. In all three of them, the SD of the population of delays is about 40 minutes, because all the samples were taken from the same population.\n",
    "\n",
    "Now look at the SD of all 10,000 sample means, when the sample size is 100. That SD is about one-tenth of the population SD. When the sample size is 400, the SD of all the sample means is about one-twentieth of the population SD. When the sample size is 625, the SD of the sample means is about one-twentyfifth of the population SD.\n",
    "\n",
    "It seems like a good idea to compare the SD of the empirical distribution of the sample means to the quantity \"population SD divided by the square root of the sample size.\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here are the numerical values. For each sample size in the first column, 10,000 random samples of that size were drawn, and the 10,000 sample means were calculated. The second column contains the SD of those 10,000 sample means. The third column contains the result of the calculation \"population SD divided by the square root of the sample size.\"\n",
    "\n",
    "The cell takes a while to run, as it's a large simulation. But you'll soon see that it's worth the wait."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "repetitions = 10000\n",
    "sample_sizes = np.arange(25, 626, 25)\n",
    "\n",
    "sd_means = make_array()\n",
    "\n",
    "for n in sample_sizes:\n",
    "    means = make_array()\n",
    "    for i in np.arange(repetitions):\n",
    "        means = np.append(means, np.mean(delay.sample(n).column('Delay')))\n",
    "    sd_means = np.append(sd_means, np.std(means))\n",
    "\n",
    "sd_comparison = Table().with_columns(\n",
    "    'Sample Size n', sample_sizes,\n",
    "    'SD of 10,000 Sample Means', sd_means,\n",
    "    'pop_sd/sqrt(n)', pop_sd/np.sqrt(sample_sizes)\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "    <thead>\n",
       "        <tr>\n",
       "            <th>Sample Size n</th> <th>SD of 10,000 Sample Means</th> <th>pop_sd/sqrt(n)</th>\n",
       "        </tr>\n",
       "    </thead>\n",
       "    <tbody>\n",
       "        <tr>\n",
       "            <td>25           </td> <td>7.95017                  </td> <td>7.89604       </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>50           </td> <td>5.53425                  </td> <td>5.58334       </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>75           </td> <td>4.54429                  </td> <td>4.55878       </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>100          </td> <td>3.96157                  </td> <td>3.94802       </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>125          </td> <td>3.51095                  </td> <td>3.53122       </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>150          </td> <td>3.23949                  </td> <td>3.22354       </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>175          </td> <td>3.00694                  </td> <td>2.98442       </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>200          </td> <td>2.74606                  </td> <td>2.79167       </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>225          </td> <td>2.63865                  </td> <td>2.63201       </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>250          </td> <td>2.51853                  </td> <td>2.49695       </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "</table>\n",
       "<p>... (15 rows omitted)</p"
      ],
      "text/plain": [
       "Sample Size n | SD of 10,000 Sample Means | pop_sd/sqrt(n)\n",
       "25            | 7.95017                   | 7.89604\n",
       "50            | 5.53425                   | 5.58334\n",
       "75            | 4.54429                   | 4.55878\n",
       "100           | 3.96157                   | 3.94802\n",
       "125           | 3.51095                   | 3.53122\n",
       "150           | 3.23949                   | 3.22354\n",
       "175           | 3.00694                   | 2.98442\n",
       "200           | 2.74606                   | 2.79167\n",
       "225           | 2.63865                   | 2.63201\n",
       "250           | 2.51853                   | 2.49695\n",
       "... (15 rows omitted)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sd_comparison"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The values in the second and third columns are very close. If we plot each of those columns with the sample size on the horizontal axis, the two graphs are essentially indistinguishable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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KWL16NSaTCQA/Pz+eeOIJduzYQfPmzW3jTCYTkZGRxe7sS/1WY5eFRIY24GTW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\nTZtwuVxkZmZSXl7ueYWHh9OnTx+2bt16yuuRnp5OQUEB11x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      "text/plain": [
       "<matplotlib.figure.Figure at 0x117c49ba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sd_comparison.plot('Sample Size n')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "There really are two curves there. But they are so close to each other that it looks as though there is just one.\n",
    "\n",
    "What we are seeing is an instance of a general result. Remember that the graph above is based on 10,000 replications for each sample size. But there are many more than 10,000 samples of each size. The probability distribution of the sample mean is based on the means of *all possible samples* of a fixed size.\n",
    "\n",
    "**Fix a sample size.** If the samples are drawn at random with replacement from the population, then\n",
    "$$\n",
    "{\\mbox{SD of all possible sample means}} ~=~\n",
    "\\frac{\\mbox{Population SD}}{\\sqrt{\\mbox{sample size}}}\n",
    "$$\n",
    "\n",
    "This is the standard deviation of the averages of all the possible samples that could be drawn. ***It measures roughly how far off the sample means are from the population mean.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The Central Limit Theorem for the Sample Mean ###\n",
    "If you draw a large random sample with replacement from a population, then, regardless of the distribution of the population, the probability distribution of the sample mean is roughly normal, centered at the population mean, with an SD equal to the population SD divided by the square root of the sample size."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The Accuracy of the Sample Mean ###\n",
    "The SD of all possible sample means measures how variable the sample mean can be. As such, it is taken as a measure of the accuracy of the sample mean as an estimate of the population mean. The smaller the SD, the more accurate the estimate.\n",
    "\n",
    "The formula shows that:\n",
    "- The population size doesn't affect the accuracy of the sample mean. The population size doesn't appear anywhere in the formula.\n",
    "- The population SD is a constant; it's the same for every sample drawn from the population. The sample size can be varied. Because the sample size appears in the denominator, the variability of the sample mean *decreases* as the sample size increases, and hence the accuracy increases."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The Square Root Law ###\n",
    "From the table of SD comparisons, you can see that the SD of the means of random samples of 25 flight delays is about 8 minutes. If you multiply the sample size by 4, you'll get samples of size 100. The SD of the means of all of those samples is about 4 minutes. That's smaller than 8 minutes, but it's not 4 times as small; it's only 2 times as small. That's because the sample size in the denominator has a square root over it. The sample size increased by a factor of 4, but the SD went down by a factor of $2 = \\sqrt{4}$. In other words, the accuracy went up by a factor of $2 = \\sqrt{4}$.\n",
    "\n",
    "In general, when you multiply the sample size by a factor, the accuracy of the sample mean goes up by the square root of that factor.\n",
    "\n",
    "So to increase accuracy by a factor of 10, you have to multiply sample size by a factor of 100. Accuracy doesn't come cheap!"
   ]
  }
 ],
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