{
 "metadata": {
  "name": "",
  "signature": "sha256:b5b3610940305d9961f99e776cb37b0c2b260f3edad089531da65c7feb4f289f"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%load_ext watermark"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%watermark -a 'Sebastian Raschka' -d -v -p matplotlib,numpy"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Sebastian Raschka 11/10/2014 \n",
        "\n",
        "CPython 3.4.1\n",
        "IPython 2.2.0\n",
        "\n",
        "matplotlib 1.4.0\n",
        "numpy 1.9.0\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example Data"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "ary = np.array([[ 0.76223776,  0.71328671,  0.87412587,  0.77408175,  0.79020979,\n",
      "         0.67132867,  0.70629371],\n",
      "       [ 0.69230769,  0.29772375,  0.79020979,  0.55789817,  0.51748252,\n",
      "         0.69230769,  0.58741259],\n",
      "       [ 0.32167832,  0.2253577 ,  0.36363636,  0.55944056, -0.3006993 ,\n",
      "         0.07692308,  0.37062937],\n",
      "       [ 0.57142857,        0,  0.57142857,  0.81084372,  0.85714286,\n",
      "         0.53571429,  0.42857143],\n",
      "       [ 0.38461538,  0.35164835,  0.7032967 ,  0.64835165,  0.52747253,\n",
      "         0.52747253,  0.54395604],\n",
      "       [ 0.42892157,  0.58840274,  0.83823529,  0.81054583,  0.88480392,\n",
      "         0.56127451,  0.79901961],\n",
      "       [ 0.78571429,  0.28571429,  0.57142857,  0.32142857,  0.53571429,\n",
      "         0.67857143,  0.71428571],\n",
      "       [ 0.51648352,  0.86813187,  0.85714286,  0.81818492,  0.73626374,\n",
      "         0.5989011 ,  0.48901099],\n",
      "       [ 0.59803922, -0.01470588,  0.56617647,  0.91911765,  0.72303922,\n",
      "         0.3995098 ,  0.37254902],\n",
      "       [ 0.69090909,  0.22779102,  0.43636364,  0.44545455, -0.27272727,\n",
      "         0.13636364,  0.02727273],\n",
      "       [ 0.40970072,  0.55343322,  0.51702786,  0.8121775 ,  0.8369453 ,\n",
      "         0.78534572,  0.72342621]])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Boxplot Notch problem"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "It appears that the notches are incorrectly drawn..."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import matplotlib.pyplot as plt\n",
      "\n",
      "def boxplot1(data):\n",
      "\n",
      "    fig = plt.figure(figsize=(8,6))\n",
      "    ax = plt.subplot(111) \n",
      "\n",
      "    bplot = plt.boxplot(data, \n",
      "            notch=True,          # notch shape \n",
      "            vert=True,           # vertical box aligmnent\n",
      "            )   \n",
      "\n",
      "    plt.show()\n",
      "boxplot1(ary)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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UhWUqOB85Ys7o4lpvDjRrZuZg1a5fgkLAUqv0S11zDYJzltadKd2CDWBc8Dm1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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1054a89e8>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Boxplot without Notch"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This problem does not occur in the regular rectangular shape."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def boxplot2(data):\n",
      "\n",
      "    fig = plt.figure(figsize=(8,6))\n",
      "    ax = plt.subplot(111) \n",
      "\n",
      "    bplot = plt.boxplot(data, \n",
      "            #notch=True,          # notch shape \n",
      "            vert=True,           # vertical box aligmnent\n",
      "            )   \n",
      "\n",
      "    plt.show()\n",
      "boxplot2(ary)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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S8XBEnFrWbAAA+ouTkAAAmtTnYW0AADBlhDPmuloRALLIfKQKw9qoPrQDAC1iWBsAgA4h\nnAEASIZwBgAgGcIZAIBkCGekXrEIALOS+UgVVmsDQMOGQ6nVawzVPlKF1doAgCWt8iJJmDPCGQCA\nZEqv5wwA6Jjh8FCPeefOQz8fDNod4s6GcAaAxkyGcOaFUa1iWBu8MAE0KfORKqzWRvUViwDqaXm1\ndm0rrdYmnEE4A0AFHEoFAECHEM4AACRDOAMAkAzhjNQrFgFgVjIfqcKCMABAk2ovhmVBGAAAHUI4\nA0DDuPBFToQzADSMcM6JcAYAIBkufAEtLORetQhgurgq1aLMR6qwWhvVVywCqIcP5/WwWhsAgA4h\nnAGgYS0NY3cJw9pgWBsAKmBYGwCADiGckXrFIgDMSuaFcAxrAwCaVHtKj2FtAAA6hHAGACAZwhkA\ngGQIZwAAkiGckXrFIgCsle0Vv6SVf7+4TaW2l66Qtr1N0sWS1kn6SERctMQ2H5J0uqSHJL01Im5Z\nYhtWa1dSe8UiALRoZqu1ba+T9GFJ2yS9QNJ228+f2OYMSc+OiJMkvV3SJSU1AQDou9Jh7VMl3RMR\n90bEw5KuknTWxDZnStolSRFxg6QNtjcX1gUAoLdKw/l4SXvGbu8d/exw25xQWBcAgN4qDefVzlRO\njqkzwwkAwDLWF/79Pklbxm5v0WLPeKVtThj97AkWxpYNDwYDDbiW2Vxwbm0AmL3hcKjhcLiqbYtW\na9teL+kuSa+WdJ+kGyVtj4jdY9ucIenciDjD9lZJF0fE1iXui9XaAIBmrLRau6jnHBGP2D5X0he0\neCjV5RGx2/Y5o99fGhGft32G7Xsk/UzS2SU1AQDoO65KBQBABTPrOaM7Ss90wwcnAJgfwrkRhCsA\ndAfn1gYAIBnCGQCAZAhnAACSIZwBAEiGcAYAIBnCGQCAZAhnAACSIZwBAEiGcAYAIBnCGQCAZAhn\nAACSIZwBAEiGcAYAIBnCGQCAZAhnAACSIZwBAEiGcAYAIBnCGQCAZAhnAACSIZwBAEiGcAYAIBnC\nGQCAZAhnAACSIZwBAEiGcAYAIBnCGQCAZAhnAACSIZwBAEiGcAYAIBnCGQCAZAhnAACSIZwBAEiG\ncAYAIBnCGQCAZAhnAACSIZwBAEiGcAYAIJmicLa9yfZ1tr9r+4u2NyyxzRbb19v+ju3bbb+zpCYA\nAH1X2nM+X9J1EfEcSV8a3Z70sKR3R8RvSNoq6R22n19YFwCA3ioN5zMl7Rp9v0vS6yc3iIj7I+LW\n0fc/lbRb0nGFdQEA6K3ScN4cEftH3++XtHmljW2fKOkUSTcU1gUAoLfWH24D29dJOnaJX71v/EZE\nhO1Y4X6eJulqSe8a9aABAMASDhvOEfGa5X5ne7/tYyPiftvPkPTDZbY7UtI1kj4WEZ9e7v4WFhYe\n/34wGGgwGByueQAAdMJwONRwOFzVto5YtrN7+D+2PyjpgYi4yPb5kjZExPkT21iL89EPRMS7V7iv\nKGkLAABdYlsR4SV/VxjOmyT9q6RnSrpX0hsi4ie2j5N0WUT8oe3flfQVSbdJeqzYBRFx7cR9Ec4A\ngGbMLJyniXAGALRkpXDmDGEAACRDOAMAkAzhDABAMoQzAADJEM4AACRDOAMAkAzhDABAMoQzAADJ\nEM4AACRDOAMAkAzhDKBpq7xIEDBXhDOAphHOyIhwBgAgmfW1GwAA8zYcHuox79x56OeDweIXUBvh\nDKA5kyG8sFCpIcAyGNYGACAZwhlA0xjGRkaEMwAAyRDOAJrGoVTIiHAGACAZVmsDaA6HUiE7whlA\ncziUCtkxrA0AQDKEM4CmMYyNjBwRtdsgSbIdWdoCAMCs2VZEeKnf0XMGACAZwhkAgGQIZwAAkiGc\nAQBIhnAGACAZwhkAgGQIZwAAkiGcAQBIhnAGACAZwhkAgGQIZwAAkiGcAQBIhnAGACAZwhkAgGTW\nHM62N9m+zvZ3bX/R9oYVtl1n+xbbn11rPQAAWlHScz5f0nUR8RxJXxrdXs67JN0hKe0Fm4fDYe0m\nVNPyvkvsP/s/rN2Eqlre/8z7XhLOZ0raNfp+l6TXL7WR7RMknSHpI5KWvKh0BpkfpFlred8l9p/9\nH9ZuQlUt73/mfS8J580RsX/0/X5Jm5fZ7h8k/Y2kRwtqAQDQjPUr/dL2dZKOXeJX7xu/ERFh+wlD\n1rb/SNIPI+IW24OShgIA0ApHrG0a2PadkgYRcb/tZ0i6PiKeN7HN30l6s6RHJD1F0tMlXRMRb1ni\n/tLORwMAMAsRseR0b0k4f1DSAxFxke3zJW2IiGUXhdl+paT3RMTr1lQQAIBGlMw5f0DSa2x/V9Kr\nRrdl+zjbn1vmb+gdAwBwGGvuOQMAgNlo/gxhtq+wvd/2t2u3Zd5sb7F9ve3v2L7d9jtrt2mebD/F\n9g22b7V9h+0La7dp3lo+QZDte23fNtr/G2u3Z95sb7B9te3do+f/1tptmhfbzx097o99PZjt/a/5\nnrPtV0j6qaSPRsRv1m7PPNk+VtKxEXGr7adJ+qak10fE7spNmxvbR0XEQ7bXS/qaFtdFfK12u+bF\n9l9LerGkoyPizNrtmSfb35f04og4ULstNdjeJem/IuKK0fP/qRHxYO12zZvtIyTtk3RqROyp3Z7H\nNN9zjoivSjpYux01RMT9EXHr6PufStot6bi6rZqviHho9O2TJK2T1MwbdVdOEDRjTe637V+V9IqI\nuEKSIuKRFoN55DRJ38sUzBLhjBHbJ0o6RdINdVsyX7aPsH2rFk+kc31E3FG7TXPU+gmCQtJ/2r7Z\n9ttqN2bOniXpR7avtP0/ti+zfVTtRlXyJ5I+UbsRkwhnaDSkfbWkd4160M2IiEcj4oWSTpD0e62c\nLGf8BEFqtPco6eURcYqk0yW9YzTF1Yr1kl4k6Z8i4kWSfqaVr4/QS7afJOl1kv6tdlsmEc6Ns32k\npGskfSwiPl27PbWMhvQ+J+m3a7dlTl4m6czRvOsnJb3K9kcrt2muIuIHo///SNKnJJ1at0VztVfS\n3oi4aXT7ai2GdWtOl/TN0XMgFcK5YbYt6XJJd0TExbXbM2+2j3nsUqe2f0XSayTdUrdV8xER742I\nLRHxLC0O6315qTP39ZXto2wfPfr+qZL+QFIzR2xExP2S9th+zuhHp0n6TsUm1bJdix9O01nx3Not\nsP1JSa+U9Gu290h6f0RcWblZ8/JySW+SdJvtx0Lpgoi4tmKb5ukZknaNVmseIemfI+JLldtUS2uH\nbWyW9KnFz6daL+njEfHFuk2au7+U9PHR0O73JJ1duT1zNfpQdpqklOsNmj+UCgCAbBjWBgAgGcIZ\nAIBkCGcAAJIhnAEASIZwBgAgGcIZAIBkCGcAAJIhnAEASOb/Acqv3YLbRgEcAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1054a88d0>"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "This behavior is correct!"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "From [Wikipedia](http://en.wikipedia.org/wiki/Box_plot):\n",
      "\n",
      "> Notched box plots apply a \"notch\" or narrowing of the box around the median. Notches are useful in offering a rough guide to significance of difference of medians; if the notches of two boxes do not overlap, this offers evidence of a statistically significant difference between the medians. The width of the notches is proportional to the interquartile range of the sample and inversely proportional to the square root of the size of the sample. However, there is uncertainty about the most appropriate multiplier (as this may vary depending on the similarity of the variances of the samples). One convention is to use +/-1.58*IQR/sqrt(n)."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This was also discussed in an [issue on GitHub](https://github.com/matplotlib/matplotlib/issues/3631#issuecomment-58684973); R produces a similar output as evidence that this behaviour is \"correct.\""
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Thus, if we have this weird \"flipped\" appearance in the notched box plots, it simply means that the 1st quartile has a lower value than the confidence of the mean and vice versa for the 3rd quartile. Although it looks ugly, it's actually useful information that about the (un)confidence of the median. We can do a bootstrapping (random sampling with replacement to estimate parameters of a sampling distribution, here: confidence intervals).\n",
      "\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "From the `plt.boxplot` documentation:\n",
      "\n",
      "> bootstrap : None (default) or integer\n",
      "    Specifies whether to bootstrap the confidence intervals\n",
      "    around the median for notched boxplots. If bootstrap==None,\n",
      "    no bootstrapping is performed, and notches are calculated\n",
      "    using a Gaussian-based asymptotic approximation  (see McGill, R.,\n",
      "    Tukey, J.W., and Larsen, W.A., 1978, and Kendall and Stuart,\n",
      "    1967). Otherwise, bootstrap specifies the number of times to\n",
      "    bootstrap the median to determine it's 95% confidence intervals.\n",
      "    Values between 1000 and 10000 are recommended."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def boxplot3(data):\n",
      "\n",
      "    fig = plt.figure(figsize=(8,6))\n",
      "    ax = plt.subplot(111) \n",
      "\n",
      "    bplot = plt.boxplot(data, \n",
      "            notch=True,          # notch shape \n",
      "            vert=True,           # vertical box aligmnent\n",
      "            bootstrap=5000\n",
      "            )   \n",
      "\n",
      "    plt.show()\n",
      "boxplot3(ary)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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SueWW9QczhGBN+tGZF19MNukoC5WGSZq/m7U27pzW5iENDaH1PGNG8rK6XXf+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\njMJZREQkMv8fpDVPb0XPoAkAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x105e61978>"
       ]
      }
     ],
     "prompt_number": 12
    }
   ],
   "metadata": {}
  }
 ]
}