The relationship between proportion and performance index

Proportions_and_PI

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The relationship between proportion and performance index"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "####Create linear spaces between 0 and 1 (actually between 0.01 and 0.99)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a = np.linspace(0.01,0.99,100)\n",
    "b = np.linspace(0.99,0.01,100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.01      ,  0.01989899,  0.02979798,  0.03969697,  0.04959596,\n",
       "        0.05949495,  0.06939394,  0.07929293,  0.08919192,  0.09909091,\n",
       "        0.1089899 ,  0.11888889,  0.12878788,  0.13868687,  0.14858586,\n",
       "        0.15848485,  0.16838384,  0.17828283,  0.18818182,  0.19808081,\n",
       "        0.2079798 ,  0.21787879,  0.22777778,  0.23767677,  0.24757576,\n",
       "        0.25747475,  0.26737374,  0.27727273,  0.28717172,  0.29707071,\n",
       "        0.3069697 ,  0.31686869,  0.32676768,  0.33666667,  0.34656566,\n",
       "        0.35646465,  0.36636364,  0.37626263,  0.38616162,  0.39606061,\n",
       "        0.4059596 ,  0.41585859,  0.42575758,  0.43565657,  0.44555556,\n",
       "        0.45545455,  0.46535354,  0.47525253,  0.48515152,  0.49505051,\n",
       "        0.50494949,  0.51484848,  0.52474747,  0.53464646,  0.54454545,\n",
       "        0.55444444,  0.56434343,  0.57424242,  0.58414141,  0.5940404 ,\n",
       "        0.60393939,  0.61383838,  0.62373737,  0.63363636,  0.64353535,\n",
       "        0.65343434,  0.66333333,  0.67323232,  0.68313131,  0.6930303 ,\n",
       "        0.70292929,  0.71282828,  0.72272727,  0.73262626,  0.74252525,\n",
       "        0.75242424,  0.76232323,  0.77222222,  0.78212121,  0.7920202 ,\n",
       "        0.80191919,  0.81181818,  0.82171717,  0.83161616,  0.84151515,\n",
       "        0.85141414,  0.86131313,  0.87121212,  0.88111111,  0.8910101 ,\n",
       "        0.90090909,  0.91080808,  0.92070707,  0.93060606,  0.94050505,\n",
       "        0.95040404,  0.96030303,  0.97020202,  0.98010101,  0.99      ])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Calculate the PI\n",
    "c = a - b/(a + b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x10621b090>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1061c9cd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(a, c)\n",
    "plt.xlabel('proportion')\n",
    "plt.ylabel('PI')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "####Calculate the proportion margin of error (MOE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x1062103d0>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ShqR/jIjz0td/FxHvzmy+h1FTSFgnSIv3c2H9cZ7/wOB2Cys7t2WUwZhtGJL2RMTZta/r\nLbeL2zAaM3om2i3Hgb3wxBW+6Kzs3JYxddyt1nKYc1mSLFaTzNOzaRpMG/bFZp0geZ/OGE6SxWqS\nr80z0/Ea1gLjNXq/UNJbSZ63XXlNZbnwyMzMrFTGSxjfA95c5zXAdwuLyArhtgvrDtm2DEi7hM9N\nZixwl/CiFToOQ9JyYBPQB1wfEVfV2WczcAHwNPDeiNiTrv848C7gOEmF+5qIeLbmWLdh5OC2C+sm\nIwed9r0SNmcHnbo9I4dC2jAknSnpJkm70q8bJb0qZ0B9wLXAcmARsErSGTX7rABeGhELgQ8An0vX\nLwDeDyyOiDNJEs47GvrNLMNtF9Y9qtOGzBhOkoXbM1plzIQhaSXwVWAQeF/69V3gNklvyXHuc4AD\nEXEwIp4DtgIra/a5kGQ2MSLiHmC2pFOBo8BzwEmSpgMnAUca+L3MzGyKjdeG8Z+ApRFxMLPuXknf\nBrYBX5/g3POBQ5nlw8C5OfaZHxG7JV0N/D/gGWB7RHxrgp9nNTxflHU3j81otfESxvSaZAFARBzM\nOdI7b+PIqHo0Sb8PXAIsAH4JfEXSOyPiljr7bswsDkbEYM6f29Wq7RbXZBoHL9mdzBd11I2D1vGS\nKUN0EXwoOzZjMaz/mp+ZMZKkAWBgsucZL2E8J+n3IuL/1vzg3yOpLprIEaA/s9xPUoIYb5/T0nUD\nwP+OiOH0Z34VeB0wKmFExMYcsfQgzxdl3c/zTOWTfpAerCxLurKZ84zX6H0l8C1J700bv8+UtAa4\nK902kZ3AQkkLJJ0IXExSlZW1DXgPgKQlwBMR8SjwALBE0kxJAs4H9jf0m5mZ2ZQas4QREV+X9FOS\n53Z+OF29H3h7RNw70Ykj4pikdSRZvg/YEhFDktam26+LiDskrZB0AHgKWJNu2yvpJpKkc5zkISpf\naPq37DEec2G9xWMzWsXPw+gyHnNhvchjMxoz5c/DkHQ7ScN1vZNGRFzY6A+zVqhtuzhzWtJ24QvG\nulf6/t6ePqN+htszijFeo/cSkkbqL5NMZw7V5NG5xRIzM2vKeNObTweWAquAM4G/B74cEfe1Lrzx\nuUpqtNGPX3WR3HqH3//5NHvvzNWGIWkGSeL4G2BjRFzbeIhTzwmjqlqHC/D4IMwZSF+70c96ysj2\njBPws+pHKyRhSHoB8CaSeZwWkHSD/VJElGKaDieMhD9VmY3ka2J8RTR6/x3wSuAO4K8iYt8k4rNC\njRqk54Y+63G+JoowXqP3O0nGRmwANiTj554XETGryMDMzKxcxhu458e3dozagUsepGe9ztdEETxw\nr8O5gc+sPl8bYyu0l1RZ9XrCcMOe2fh8jdQ35Y3e1gncsGc2Pl8jU8ntFGZmlotLGB3NDXtm4/M1\nMpXchtHhakZ4u0HPrIavkdHc6N1jfBGYNc7XTcIJo4e454dZ43zdVLmXVE9xzw+zxvm6mSz3kjIz\ns1xcwuhI7vlh1jhfN5NVaBuGpOXAJqAPuD4irqqzz2bgAuBp4L0RsSddPxu4nmTG3ADeFxE/qDm2\nJ9swwI13Zs3wdZMoXaO3pD7gAeB84AiwA1gVEUOZfVYA6yJihaRzgc9GxJJ0243AdyPiS+nT/06O\niF/W/IyeShh+s5tNjV6/lsrY6H0OcCAiDgJI2gqsBIYy+1wI3AgQEfdImi3pVODXwOsjYnW67Rgw\nIln0mmoPj2sqxenzJPVkDw+zyfC11LwiE8Z84FBm+TBwbo59TgN+Azwm6Qbg1cAuYENEPF1cuGXn\nHh5mU8PXUrOKTBh567pqi0VBEtdikuqqHZI2AR8D/sOog6WNmcXBiBhsPFQzs+4laQAYmOx5ikwY\nR4D+zHI/SQlivH1OS9cJOBwRO9L1t5IkjFEiYuNUBFt+7uFhNjV671pKP0gPVpYlXdnMeYpMGDuB\nhZIWAA8DFwOravbZBqwDtkpaAjwREY8CSDok6WUR8SBJw/l9BcZaehGxXdJFadEZONpzDXVmU8HX\nUvOK7lZ7AdVutVsi4lOS1gJExHXpPtcCy0meH74mInan619N0q32RODH6bae7iVlZjYVStetthV6\nJWH0ehdAs6L06rXlhNGlPGGaWTF6+doq4zgMmxLuAmhWDF9bjfLkg2ZmlotLGKXXe10AzVrD11aj\n3IbRAXq1Yc6saL16bbnR28zMcmn23uk2DDMzy8UJo8QkLZPm3pl8aVm74zHrZr7eJuYqqZLq5T7i\nZq3Wa9ebx2F0HfcRN2sdX295uErKzMxycQmjtNxH3Kx1fL3l4TaMEuvVPuJm7dBL15vHYZiZWS4e\nh2FmZoVywjAzs1ycMErGg4fM2svX4NjchlEivTZ4yKxseuUa9MC9ruDBQ2bt5WtwPIVWSUlaLul+\nSQ9JunyMfTan2++VdHbNtj5JeyTdXmScZmY2scJKGJL6gGuB84EjwA5J2yJiKLPPCuClEbFQ0rnA\n54AlmdNsAPYDv1VUnOXiwUNm7eVrcDxFVkmdAxyIiIMAkrYCK4GhzD4XAjcCRMQ9kmZLOjUiHpV0\nGrAC+Gvg0gLjLI2I2C7porQIDBzt6sFDZmXja3B8RSaM+cChzPJh4Nwc+8wHHgU+A3wUmFVgjKWT\nvjn9BjVrE1+DYysyYeTtflXbUi9JfwL8LCL2SBoY92BpY2ZxMCIGc0doZtYD0vvowGTPU2TCOAL0\nZ5b7SUoQ4+1zWrrubcCFaRvHC4BZkm6KiPfU/pCI2DiVQZuZdZv0g/RgZVnSlc2cp8heUjuBhZIW\nSDoRuBjYVrPPNuA9AJKWAE9ExCMRcUVE9EfE6cA7gG/XSxZmZtY6hZUwIuKYpHUkdYF9wJaIGJK0\nNt1+XUTcIWmFpAPAU8CasU5XVJxmZpaPR3qXRC9NrWzWKbr1uvT05h2sV6YjMOsk3XxdemqQjubp\nCMzKx9dlLc9Wa2ZmubiEUQqejsCsfHxd1nIbRkl0a+OaWSfr1uvSjd5mZpaLn+ltZmaFcsIwM7Nc\nnDDMzCwXJwwzM8vFCcPMzHJxwjAzs1ycMMzMLBcnjDaTtEyae2fypWXtjsfMRvN1mvDAvTbq5tkw\nzbpFN16nnq22I3k2TLPy83Va4SopMzPLxSWMtvJsmGbl5+u0ovA2DEnLgU0kz/W+PiKuqrPPZuAC\n4GngvRGxR1I/cBPwOyTP9P5CRGyuOa6j2zCge2fDNOsm3XadlnK2Wkl9wAPA+cARYAewKiKGMvus\nANZFxApJ5wKfjYglkuYB8yJir6RTgF3AW2qO7fiEYWbWamWdrfYc4EBEHIyI54CtwMqafS4EbgSI\niHuA2ZJOjYhHImJvuv5JYAh4ccHxmpnZGIpOGPOBQ5nlw+m6ifY5LbuDpAXA2cA9Ux6hmZnlUnTC\nyFvfVVs0ev64tDrqVmBDWtIwM7M2KLqX1BGgP7PcT1KCGG+f09J1SDoBuA24OSK+Xu8HSNqYWRyM\niMHJhWxm1l0kDQADkz5PwY3e00kavd8APAz8kPEbvZcAm9JGb5G0bQxHxL8f4/xu9DYza1ApR3pH\nxDFJ60hGRPYBWyJiSNLadPt1EXGHpBWSDgBPAWvSw/8AeBfwI0l70nUfj4hvFhmzmZnV57mkzMx6\nTFm71ZqZWZdwwjAzs1ycMMzMLBcnDDMzy8UJw8zMcnHCMDOzXJwwzMwsFycMMzPLxQnDzMxyccIw\nM7NcnDDMzCwXJwwzM8vFCcPMzHJxwjAzs1ycMMzMLBcnDDMzy8UJw8zMcnHCMDOzXJwwzMwsl0IT\nhqTlku6X9JCky8fYZ3O6/V5JZzdyrJmZtU5hCUNSH3AtsBxYBKySdEbNPiuAl0bEQuADwOfyHtsN\nJA20O4bJcPzt1cnxd3Ls0PnxN6vIEsY5wIGIOBgRzwFbgZU1+1wI3AgQEfcAsyXNy3lsNxhodwCT\nNNDuACZpoN0BTNJAuwOYhIF2BzBJA+0OoB2KTBjzgUOZ5cPpujz7vDjHsWZm1kJFJozIuZ8KjMHM\nzKbI9ALPfQTozyz3k5QUxtvntHSfE3IcC4CkvImplCRd2e4YJsPxt1cnx9/JsUPnx9+MIhPGTmCh\npAXAw8DFwKqafbYB64CtkpYAT0TEo5KGcxxLRLh0YmbWIoUljIg4JmkdsB3oA7ZExJCkten26yLi\nDkkrJB0AngLWjHdsUbGamdnEFNHRNTpmZtYiHTXSW9IcSXdJelDSnZJm19mnX9J3JN0n6f9IWt+O\nWGtianoAYxlMFL+kd6Zx/0jS/5L0qnbEWU/eAaCSXivpmKS3tjK+ieR87wxI2pO+3wdbHOK4crx3\nXiTpm5L2pvG/tw1h1iXpS5IelbRvnH3KfN2OG39T121EdMwX8F+Av0xfXw58us4+84Cz0tenAA8A\nZ7Qx5j7gALCApDF/b208wArgjvT1ucAP2v23bjD+fwO8MH29vCzx54k9s9+3gf8JvK3dcTf4t58N\n3Aecli6/qN1xNxj/RuBTldiBYWB6u2NP43k9cDawb4ztpb1uc8bf8HXbUSUMMgP90u9vqd0hIh6J\niL3p6yeBIZJxHe3S7ADGU1sb5pgmjD8i7o6IX6aL95D0diuDvANAPwzcCjzWyuByyBP/nwK3RcRh\ngIj4eYtjHE+e+P8JmJW+ngUMR8SxFsY4poj4PvCLcXYp83U7YfzNXLedljBOjYhH09ePAuP+c9Je\nVmeT/DHapdkBjGW56eaJP+vPgDsKjSi/CWOXNJ/kJva5dFWZGvXy/O0XAnPSatidkt7dsugmlif+\nLwKvlPQwcC+woUWxTYUyX7eNynXdFtmttimS7iKpVqr1iexCRMR4YzAknULyqXFDWtJol2YHMJbl\nxpU7Dkl/DLwP+IPiwmlIntg3AR9L30+iXANJ88R/ArAYeANwEnC3pB9ExEOFRpZPnvivAPZGxICk\n3wfukvTqiPhVwbFNlbJet7k1ct2WLmFExNKxtqUNOPMi4hFJ/xL42Rj7nQDcBtwcEV8vKNS8mh3A\neKTguPLKEz9pg9kXgeURMV4xvpXyxP4aknFAkNShXyDpuYjY1poQx5Un/kPAzyPiGeAZSd8DXg2U\nIWHkif91wF8DRMSPJf0UeDnJOK6yK/N1m0uj122nVUltA1anr1cDo5JB+ilxC7A/Ija1MLaxPD+A\nUdKJJIMQa29G24D3AGQHMLY2zDFNGL+k3wW+CrwrIg60IcaxTBh7RLwkIk6PiNNJSqR/UZJkAfne\nO98AzpPUJ+kkksbX/S2Ocyx54r8fOB8grf9/OfCTlkbZvDJftxNq6rptd0t+g63+c4BvAQ8CdwKz\n0/UvBv4+fX0ecJykR8ae9Gt5m+O+gKS31gHg4+m6tcDazD7XptvvBRa3+2/dSPzA9SS9Wyp/7x+2\nO+ZG/vaZfW8A3trumJt473yEpKfUPmB9u2Nu8L3zIuD29H2/D/jTdsecif3LJDNN/DNJSe59HXbd\njht/M9etB+6ZmVkunVYlZWZmbeKEYWZmuThhmJlZLk4YZmaWixOGmZnl4oRhZma5OGGYtYGklZLO\nyCz/R0lvaGdMZhPxOAyzMUiaFhHHCzjvdJJBU7dHxG1TfX6zoriEYT0pna7ifkk3S9ov6SuSZko6\nKOnTknYBb5e0Kn3AzD5Jn84c/6Ska9KH/nxL0ovS9WdJ+kH6YJqvKn3Il6RBSZ+RtAP4S+DNwH+V\ntFvSSyT9raS3pfu+IV3/I0lb0mk1SGPbKGlXuu3lrf67WW9zwrBe9jLgv0XEIuAo8CGS2UZ/HhGv\nAb4PfBr4Y+As4LWSKs9zOAnYERH/CvgucGW6/ibgoxHxapKpLirrAzghIl4bEZ8kmYfoIxGxOCJ+\nkm4PSS8gmaLk30XEq0gmCP2LzDkeS2P7HMmUIGYt44RhvexQRNydvr6ZZB4ygP+Rfn8t8J2IGI6I\n3wC3AH+Ybjue2e9mkgkAZ5E8wez76fobM/tnz1tROzW2SCbf+2lUJ4OrPcdX0++7SZ5kZ9YyThjW\ny7INeCJJAgBPZbarZp96jX7jrc96qma53jG162rP/Wz6/TeU8PEE1t2cMKyX/W46LTUkjzr9x5rt\nO4A/kjRXUh/wDpLqJ0iunbdnjv1+RBwFfiGpUlJ5NzCYOV82gfyK6qNJK4JkZtcF6cOEKuf4LmYl\n4IRhvezf5HFSAAAAp0lEQVQB4EOS9gMvpPqYVgAi4p+AjwHfIZkuf2dE3J5ufgo4R9I+YAD4q3T9\napLG7HuBV2XWw8iSwlbgo2kD9ksyP/NZYA3wFUk/Ao4Bn69zfNCBT3ezzuZutdaT0ue93x4RZzZ5\n/K8i4remNCizknMJw3rZZD4t+ZOW9RyXMMzMLBeXMMzMLBcnDDMzy8UJw8zMcnHCMDOzXJwwzMws\nFycMMzPL5f8Db2RtLfjhzX8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1062b6ad0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "moea = 1.96 * np.sqrt(a*b/60)\n",
    "plt.scatter(a, moea)\n",
    "plt.xlabel('proportion')\n",
    "plt.ylabel('MOE')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "####Since there is a 1:2 ratio between the proportion and PI scale, multiple the MOE by 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.05035331,  0.07067428,  0.08604684,  0.09880826,  0.10987218,\n",
       "        0.11971017,  0.1286039 ,  0.13673774,  0.14424031,  0.15120559,\n",
       "        0.15770479,  0.16379341,  0.16951569,  0.17490759,  0.1799988 ,\n",
       "        0.18481418,  0.18937476,  0.19369855,  0.19780108,  0.20169584,\n",
       "        0.20539466,  0.20890794,  0.2122449 ,  0.21541373,  0.21842175,\n",
       "        0.22127552,  0.22398094,  0.22654331,  0.22896744,  0.23125769,\n",
       "        0.23341798,  0.2354519 ,  0.2373627 ,  0.23915332,  0.24082645,\n",
       "        0.24238452,  0.24382974,  0.24516409,  0.2463894 ,  0.24750726,\n",
       "        0.24851914,  0.24942632,  0.25022994,  0.250931  ,  0.25153035,\n",
       "        0.25202872,  0.25242671,  0.25272479,  0.25292331,  0.25302251,\n",
       "        0.25302251,  0.25292331,  0.25272479,  0.25242671,  0.25202872,\n",
       "        0.25153035,  0.250931  ,  0.25022994,  0.24942632,  0.24851914,\n",
       "        0.24750726,  0.2463894 ,  0.24516409,  0.24382974,  0.24238452,\n",
       "        0.24082645,  0.23915332,  0.2373627 ,  0.2354519 ,  0.23341798,\n",
       "        0.23125769,  0.22896744,  0.22654331,  0.22398094,  0.22127552,\n",
       "        0.21842175,  0.21541373,  0.2122449 ,  0.20890794,  0.20539466,\n",
       "        0.20169584,  0.19780108,  0.19369855,  0.18937476,  0.18481418,\n",
       "        0.1799988 ,  0.17490759,  0.16951569,  0.16379341,  0.15770479,\n",
       "        0.15120559,  0.14424031,  0.13673774,  0.1286039 ,  0.11971017,\n",
       "        0.10987218,  0.09880826,  0.08604684,  0.07067428,  0.05035331])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "moePI= moea * 2\n",
    "moePI"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "####Have a look at the proportion error bars"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Container object of 3 artists>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10643a2d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.errorbar(a, c, yerr=moea)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Have a look at the PI error bars"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Container object of 3 artists>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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aKvW/ALw1u/1W4C88Pc8XnLvvBP5qyiZdfu3OrH/e127Igf94d38pu/0SMPWX\nnF0ZtJH0oEIoW4x2YoVtujJ4Vqk/7xLg7kYrms/M+s3sRNLB6PrsS106gVXl978BODqb3txlZv+i\ntepmq1L/jcA/MrPngYeB32iptmXo8mt3XjNfu42u3DWzHaTTNUVX5++4u0+7jt/Mfow0xf1GlvxD\nqDqIFC9L7crgU7kOM9sE/BrwnubKmVuV+r8MfC77ezImX2YcQpX6jwDeCfxTYA3wJ2b2PXd/otHK\nqqlS/78FHnL3xMz+IbDDzE5z979uuLZl6eprt7Kqr91GB353//lJ38tOVLzN3V80s58A9k/Y7gjg\nNuAb7n57Q6VW8RywPnd/PWkqmLbNuuxrXVClfrKTQjcCm9192n+N21al/p8Dbk3HfI4BzjWz1939\njnZKnKpK/c8AL7v73wJ/a2YPAKcBXRj4q9R/Fmk7ctz9f5vZ/yHtULurlQrr6fJrt5J5Xrshp3ru\nAC7Obl8MHDKoZ6ntPwOPuPuXW6ytzMHFaGa2mnQxWnFAuQP4GBxctXwgN50V2sz6zewk4FvAP3f3\nJwPUOM3M+t39H7j7T7r7T5L+D/Ffd2TQh2p/P78PvNfMVpnZGtKTjI+0XOckVep/DHg/QDY/fgrw\ng1arXFyXX7szzf3aDXiW+mjgu8DjwL3A2uzrJwB3ZbffS9rb/iFgd/axOWDN55JeWfQkcFX2tcuA\ny3LbfDX7/sPAO0PVukj9wH8ivRJj/Lv+H6Frnvf3n9v294APh655gb+fz5Be2bMH+GTomuf8+zkG\nuDP7298D/GromnO130LaPeD/kf7P6td69tqdWv+8r10t4BIRiYzeelFEJDIa+EVEIqOBX0QkMhr4\nRUQio4FfRCQyGvhFRCKjgV9EJDIa+EVEIvP/ATMWk+7VSiFtAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x106547f50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.errorbar(a, c, xerr=moePI)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "####The one complication is that the CI of a PI cannot extend beyond (-1, 1), so values that exceed this range must be forced to (-1, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}