{
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  "name": ""
 },
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 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import matplotlib.pyplot as plt\n",
      "import numpy as np\n",
      "import scipy.stats"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Define the test statistics and test them on examples from the lectures."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def pearson(counts):\n",
      "    counts = np.asarray(counts)\n",
      "    expected = scipy.stats.contingency.expected_freq(counts)\n",
      "    return np.sum((counts - expected)**2 / expected)\n",
      "\n",
      "assert np.allclose(pearson([[17066, 14464, 788, 126, 37], [48, 38, 5, 1, 1]]),\n",
      "                   12.0821, atol=0.0001)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# TODO: Oops, this is 2x2 only... but the segment has a 3x3 table... ???\n",
      "\n",
      "def wald_2x2(counts):\n",
      "    counts = np.asarray(counts)\n",
      "    m, n = counts[0, 0], counts[0, 1]\n",
      "    M, N = counts.sum(axis=0)\n",
      "\n",
      "    p1_hat = m / float(M)\n",
      "    p2_hat = n / float(N)\n",
      "    p_hat = (m + n) / float(M + N)\n",
      "\n",
      "    numerator = p1_hat - p2_hat\n",
      "    denominator = np.sqrt(p_hat * (1 - p_hat) * ((1.0 / M) + (1.0 / N)))\n",
      "    return numerator / denominator\n",
      "\n",
      "assert np.allclose(wald_2x2([[8, 3], [16, 26]]), 2.0542, atol=0.0001)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Code for permuting tables and collecting test statistics from the permutations."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def expand(table):\n",
      "    items = []\n",
      "    for row in xrange(table.shape[0]):\n",
      "        for col in xrange(table.shape[1]):\n",
      "            items.extend([[row, col]] * table[row, col])\n",
      "    expanded = np.array(items)\n",
      "    assert expanded.shape == (table.sum(), 2)\n",
      "    return expanded\n",
      "\n",
      "def shuffle(expanded_table):\n",
      "    expanded_table[:, 1] = np.random.permutation(expanded_table[:, 1])\n",
      "    return expanded_table\n",
      "\n",
      "def rebuild(expanded_table):\n",
      "    table = np.zeros(np.max(expanded_table, axis=0) + 1, dtype=int)\n",
      "    for item in expanded_table:\n",
      "        table[tuple(item)] += 1\n",
      "    assert expanded_table.shape == (table.sum(), 2)\n",
      "    return table\n",
      "\n",
      "def permute(table):\n",
      "    return rebuild(shuffle(expand(table)))\n",
      "\n",
      "def sanity_check():\n",
      "    table = np.arange(9).reshape(3, 3)\n",
      "    \n",
      "    # Expand and rebuild the same table.\n",
      "    assert np.all(rebuild(expand(table)) == table)\n",
      "\n",
      "    # Verify marginals are the same after shuffling.\n",
      "    marginals_before = np.array([table.sum(axis=0), table.sum(axis=1)])\n",
      "    permutation = permute(table)\n",
      "    marginals_after = np.array([permutation.sum(axis=0), permutation.sum(axis=1)])\n",
      "    assert np.all(marginals_before == marginals_after)\n",
      "\n",
      "sanity_check()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def permutation_stats(table, num_permutations=100000, statistic_func=pearson):\n",
      "    stats = [statistic_func(permute(table)) for _ in xrange(num_permutations)]\n",
      "    return np.array(stats)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Problem 1"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "table = np.array([[5, 3, 2],\n",
      "                  [2, 3, 6],\n",
      "                  [0, 2, 3]])\n",
      "table"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "array([[5, 3, 2],\n",
        "       [2, 3, 6],\n",
        "       [0, 2, 3]])"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pearson(table)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "5.7559917355371892"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "stats = permutation_stats(table, statistic_func=pearson)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.hist(stats, bins=np.arange(20), histtype='step', fill=True, normed=True)\n",
      "plt.axvline(x=pearson(table), color='red', label='Pearson statistic for the table')\n",
      "plt.title('Permutation Stats')\n",
      "plt.legend()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 9,
       "text": [
        "<matplotlib.legend.Legend at 0xab0aaac>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
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mqF+/fvLz89OAAQPUr18/+fv76+6779bjjz+ugoICvffee8VOT+jUqZPS09M1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\n",
       "text": [
        "<matplotlib.figure.Figure at 0xa95070c>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pval = np.mean(stats >= pearson(table))\n",
      "pval"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 10,
       "text": [
        "0.22777"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Not significant!"
     ]
    }
   ],
   "metadata": {}
  }
 ]
}