{
 "metadata": {
  "name": "week2_tutorial"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Psych 216A Tutorial #2"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This matlab tutorial is intended to complement lecture #2.  \n",
      "\n",
      "It will show how to:\n",
      "\n",
      "1. Explore datasets with one variable and two conditions\n",
      "\n",
      "2. Implement nonparametric alternatives to the t-test\n",
      "\n",
      "3. Explore datasets with two variables and one condition\n",
      "     \n",
      "4. Compute the Pearson correlation coefficients\n",
      "\n",
      "5. Establish the error of the estimate, using bootstrap.\n",
      " \n",
      "6. Test hypotheses on the correlation between two variables, using\n",
      "   bootstrap.\n",
      " \n",
      "7. Use Montecarlo Methdos to test hypotheses.\n",
      "\n",
      "Written by Franco Pestilli, March 2012\n",
      "\n",
      "Translated to Python by Michael Waskom, June 2012"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%pylab inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Welcome to pylab, a matplotlib-based Python environment [backend: module://IPython.zmq.pylab.backend_inline].\n",
        "For more information, type 'help(pylab)'.\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "import utils\n",
      "import seaborn\n",
      "seaborn.set()\n",
      "colors = seaborn.color_palette()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "(1) Exploring a complex dataset: one variable, two conditions"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Motivation: \n",
      "\n",
      "   Samples from a population will show variation in their means. So, when\n",
      "   drawing two samples from a single population, there is some chance\n",
      "   that the samples will have different means, even though the underlying\n",
      "   population is the same.\n",
      "\n",
      "Suppose two samples are drawn from the same distribution. There were always\n",
      "be some non-zero likelihood of obtaining a difference in the means of these\n",
      "samples, although no difference should actually be there.\n",
      "\n",
      "The following simulation shows that given a population and finite\n",
      "sample size there will always be some probability of getting a difference\n",
      "between two random samples.\n",
      "   \n",
      "Furthermore, we will show that the probability of getting large spurious\n",
      "differences increases as the sample size decreases.\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Generate a population with mean 0 and sd of 1\n",
      "k = 10000\n",
      "N = randn(k)\n",
      "\n",
      "# Next we will simulate three samples of differnet sizes from the distribution N\n",
      "n = [8, 65, 512]\n",
      "\n",
      "# There are a variety of ways of getting random samples, we'll do it here\n",
      "# by permuting and taking the first k values in the resulting array.\n",
      "# Note that this method will sample *without* replacement, in contrast to\n",
      "# indexing with the return from randint(), as we did before.\n",
      "d_empirical = list()\n",
      "for k in n:\n",
      "    sa = permutation(N)[:k]\n",
      "    sb = permutation(N)[:k]\n",
      "    d_empirical.append(sa.mean() - sb.mean())\n",
      "\n",
      "print d_empirical"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[-0.75011551285103728, -0.16896572510913227, 0.00061757417311392171]\n"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Because the two samples were drawn from the same distribution their\n",
      "differences should be 0. But with samples of small size some spurious\n",
      "difference can be observed.\n",
      "\n",
      "Hereafter, we compute the probabilty of getting a spurious non-zero\n",
      "difference between two samples. We test how the size of the sample\n",
      "changes this probability. We will show that the smaller the sample size\n",
      "the higher the probabilty of a spurios non-zero difference. \n",
      "\n",
      "Now we compute the distribution of differences between the means of two\n",
      "random samples. We compute this distribution for each sample size and\n",
      "plot the distributions one on top of eachother (with different color)."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "To plot the distribution, we're going to use a custom function called utils.pmf_hist. This will return values to plot a histogram that behaves like a probability mass function; i.e., this sum of the bar heights will equal 1. Note that this is different than using the ``normed=True`` argument to ``hist()``, which will plot a histogram where the bars *integrate* to 1 (they will be equivalent in cases where the bars have unit width).\n",
      "\n",
      "For concise code, we're using a novel Python trick. the ``pmf_hist()`` function returns a three-tuple: x, h, w corresponding to the left x position of the bars, the height of the bars, and the width of the bars. These happen to be the three positional arguments to matplotlib's ``bar()`` function. We could do:\n",
      "\n",
      "    x, h, w = pmf_hist(d)\n",
      "    bar(x, h, w)\n",
      "\n",
      "However, Python offers us a shortcut. Within the scope of a function call, you can prepend a variable name that points at some sequence with a single asterisk, and the result will be that the variable is passed as the positional arguments to the function. In other words, this is equivalent:\n",
      "\n",
      "    args = pmf_hist(d)\n",
      "    bar(*args)\n",
      "\n",
      "Or, even less verbosely:\n",
      "\n",
      "    bar(*pmf_hist(d))\n",
      "\n",
      "Here this mostly saves us some typing, but it can be a useful usage pattern. You can see that we don't even need to know about the return values from ``pmf_hist()``, we just know that they correspond to the arguments to ``bar()``.\n",
      "\n",
      "Finally, note that you can do something similar for keyword arguments, but here you pass a dictionary of key, value pairs and prepend it with a double astrisk:\n",
      "\n",
      "    kwargs = dict(color=\"blue\", size=10)\n",
      "    bar(*args, **kwargs)\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "n_samples = 100\n",
      "for i, k in enumerate(n):\n",
      "    sa = zeros(k)\n",
      "    sb = zeros(k)\n",
      "    \n",
      "    sa, sb = [], []\n",
      "    for j in xrange(n_samples):\n",
      "        sa.append(permutation(N)[:k])\n",
      "        sb.append(permutation(N)[:k])\n",
      "    \n",
      "    # Compute the difference vector and plot a histogram\n",
      "    # Represent the histogram as a PMF\n",
      "    \n",
      "    d = mean(sa, axis=1) - mean(sb, axis=1)\n",
      "    bar(*utils.pmf_hist(d, 20), color=colors[i], alpha=0.5, label=\"sample size = %d\" % k)\n",
      "\n",
      "# Add some description to the plot\n",
      "title(\"Probability of getting a spurious\\ndifference between two random samples\\nas function of sample size.\")\n",
      "ylabel(\"Probability of occurrence\")\n",
      "xlabel(\"Difference between random samples\")\n",
      "\n",
      "# Additionally, plot the empirical diffences we obtained in the first step as vertical lines\n",
      "colors = seaborn.color_palette(\"deep\")\n",
      "for i, d in enumerate(d_empirical):\n",
      "    axvline(d, color=colors[i], linewidth=2)\n",
      "    \n",
      "legend(loc=\"best\");"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
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WBcSXFX3w4AFmzpwJPT09LFy4EC9fvuTa6+vr4/fff4etrS309PTg6+vLlaIFyqdHnTVr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\nYII=\n"
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Notice that the blue distribution, the one generated by reampling with\n",
      "the smallest sample size (8) has the largest standard deviation. This\n",
      "means that with such small sample size there is a higher chance of\n",
      "observing a spurious difference. For example the probability of\n",
      "occurrence of a difference of nearly +/-0.5 should be around 0.1 (10%,\n",
      "blue bar). The probability goes down to less then 0.01 with a larger\n",
      "sample size. \n",
      "\n",
      "If a scientific article were to report a *statistically* significant difference of 0.5 on this scale.\n",
      "\n",
      "How would you be able to tell whether their analyses and statistical tests were performed correctly?\n",
      "\n",
      "How could we relate this to a power analysis?"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "(2) Nonparametric altenatives to a t-test"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "A t-test is a statistical method to establish the likelihood of the\n",
      "difference between the means of two samples drawn from an unknown\n",
      "distribution. The shape of this distribution is assumed to be gaussian.\n",
      "\n",
      "The null-hypothesis for this test is: The two sample come from the same\n",
      "distribution. \n",
      "\n",
      "A t-test finds the probability that the two means were drawn from the\n",
      "same distribution. If that probability is small we can reject the null\n",
      "hypothesis and support the alternative hypothesis that the two samples\n",
      "did not come from the same distribution. \n",
      "\n",
      "Here after we show how to use bootstrap to generate the equivalent of a\n",
      "t-test.\n",
      "\n",
      "We first generate the distribution for a population that is not gaussian.\n",
      "\n",
      "Generate the population using mixture of a Chi-Square distribution with 6\n",
      "degrees of freedom and a standard normal.\n",
      "\n",
      "Because this population is not Gaussian, a parametric t-test would not be\n",
      "appropriate."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "k = 10000\n",
      "N = concatenate([chisquare(6, k / 2), randn(k / 2)])\n",
      "mu = mean(N)\n",
      "me = median(N)\n",
      "sd = std(N)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's take a look at the population we just generated\n",
      "\n",
      "We make a histogram of population and appreciate how well mean, median and\n",
      "standard deviation might describe the distribution."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "hist(N, 100)\n",
      "axvline(me, label=\"median\", color=colors[1], linewidth=3)\n",
      "axvline(mu, label=\"mean\", color=colors[2], linewidth=3)\n",
      "sd_y = ylim()[1] * .5\n",
      "plot([mu - sd, mu + sd], [sd_y] * 2, \"--\", color=colors[2], linewidth=3, label=\"std dev\")\n",
      "title(\"Simulated true distribution (Chisquare, 6 DOF + Gaussian)\")\n",
      "legend();"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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JlkwmU3stg5mZGX74YSvOnj2DPn0i0bGjP1JTP4EgCLCyssKHH6Zg4cIUhIV1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\nIiKSIAY0ERGRBP1/ltyX72y6RygAAAAASUVORK5CYII=\n"
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now let's set up a bootstrap test of the difference between the means of\n",
      "two samples that does not rely on the assumption that the popluation is\n",
      "gaussian. As our population is not.\n",
      "\n",
      "We simulate two empirical samples of size n and m drawn from our\n",
      "distribution.  As if we were to run two conditions of the same\n",
      "experiment.\n",
      "\n",
      "By drawing the two sampels from the same distribution we are effectively\n",
      "making the null hypothesis true."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "n = 4\n",
      "m = 8\n",
      "sa = permutation(N)[:n]\n",
      "sb = permutation(N)[:m]\n",
      "\n",
      "d_empirical = mean(sa) - mean(sb)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The first test we show is called a Randomization test (Test of the\n",
      "difference of means of two samples).\n",
      "\n",
      "So, we want to test the null hypothesis (H0) that the means of the two\n",
      "samples come from the same distribution.\n",
      "\n",
      "To do so we will first aggregate the two samples. Under the null\n",
      "hypothesis the two samples are interchanganble because they come from the\n",
      "same distribution."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sh0 = concatenate((sa, sb))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Then resample 10,000 times, effectively building 10,000 new samples from the aggregated sample"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "k = 10000\n",
      "sa_rand = zeros((n, k))\n",
      "sb_rand = zeros((m, k))\n",
      "for i in xrange(k):\n",
      "    iter_dist = permutation(sh0)\n",
      "    sa_rand[:, i] = iter_dist[:n]\n",
      "    sb_rand[:, i] = iter_dist[n:]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now compute the differences between the means of these resampled samples and plot."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "d = sa_rand.mean(axis=0) - sb_rand.mean(axis=0)\n",
      "bar(*utils.pmf_hist(d, 100))\n",
      "title(\"Distribution of the differences between the means of samples sa and sb\")\n",
      "ylabel(\"Probability of occurance\")\n",
      "xlabel(\"Difference (sa - sb)\")\n",
      "\n",
      "# Plot the actual difference we got\n",
      "plot([d_empirical, d_empirical], ylim(), color=colors[4], linewidth=2.5)\n",
      "\n",
      "# Get the probability of such a result by counting the number of larger (absolute) differences\n",
      "p = sum(abs(d) > abs(d_empirical)) / k\n",
      "text(xlim()[0], ylim()[1] * .95, \"$H_0$ is true with %.2f probability\" % p, size=12);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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Wb++BAwfBx2cSbGz64ejRU/j991/h7e2Fv/66zr1ClTEmtb2ePc2RmHgUfH4n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\n"
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The second test we show is called a Bootstrap test (Test of the\n",
      "difference of mean of two samples).\n",
      "\n",
      "This example is identical to the previous one, with one importnt\n",
      "difference. During the bootstrap proces samples are generated 'with\n",
      "replacement.'\n",
      "\n",
      "This means that on each new draw there will be equal likelihood to sample\n",
      "any element of the aggregated sample. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# First aggregate the samples\n",
      "sh0 = concatenate((sa, sb))\n",
      "\n",
      "# Resample 10,000 times with replacement\n",
      "k = 10000\n",
      "sa_rand = zeros((n, k))\n",
      "sb_rand = zeros((m, k))\n",
      "for i in xrange(k):\n",
      "    sa_rand[:, i] = sh0[randint(0, n + m, n)]\n",
      "    sb_rand[:, i] = sh0[randint(0, n + m, m)]\n",
      "    \n",
      "# Compute the difference and plot as before\n",
      "d = median(sa_rand, axis=0) - median(sb_rand, axis=0)\n",
      "\n",
      "bar(*utils.pmf_hist(d, 100), color=colors[3])\n",
      "title('Distribution of the differences between the means of samples sa and sb')\n",
      "ylabel('Probability of occurrence')\n",
      "xlabel('Difference (sa - sb)')\n",
      "\n",
      "plot([d_empirical] * 2, ylim(), color=colors[1], linewidth=2.5)\n",
      "\n",
      "p = sum(abs(d) > abs(d_empirical)) / k\n",
      "text(xlim()[0], ylim()[1] * .95, \"$H_0$ is true with %.2f probability\" % p);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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G4uLFZIwePQzDhg3G+fN/4cSJaKVpnJ374K+//sT9+wVo1qwZXF3d8eefZxEX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\nGGOM2TBu6BljjDEbxg09Y4wxZsP+ByPa9/tKUrT8AAAAAElFTkSuQmCC\n"
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**A note on Python string formatting:**\n",
      "\n",
      "MATLAB has tradtional C-style string formatting offered through the functions ``sprintf()`` and ``fprintf()``. Python's string formatting uses identical format codes, but is built into the string object itself. Thus, using the ``%`` operator between a string with format codes and a tuple (or single object) with values to plug into those codes will create a formatted string."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In case you were wondering (as you may have been in the original MATLAB tutorial, it's easy to do a parametric t-test in Python, if you are so inclined:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from scipy.stats import ttest_ind\n",
      "t, p = ttest_ind(sa, sb)\n",
      "print \"t = %.2f; p = %.3f\" % (t, p)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "t = -0.02; p = 0.988\n"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "(3) Exploring a more complex dataset: two variables, one condition"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Hereafter, we show an example of a slightly more complex data set.\n",
      "\n",
      "So suppose we have one condition and measure not just one quantity (which\n",
      "was the subject of Lecture 1) but measure two distinct quantities. For\n",
      "example, suppose we measure both the heights and weights of male adults.\n",
      "\n",
      "What can we do with the data? \n",
      "\n",
      "Let's generate two samples rapresenting two variables drawn from gaussian\n",
      "distributions. The two variables are correlated with eachother."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "n = 100\n",
      "w = 0.6\n",
      "s1 = randn(n)\n",
      "s2 = w * s1 + (1 - w) * randn(n)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 19
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "(4) Correlation"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can quantify how correlated two variables are by using the metric\n",
      "'correlation.'\n",
      "\n",
      "Correlation values lie in the range -1 to 1, where -1 indicates a perfect\n",
      "negative linear relationship, 0 indicates no relationship, and 1\n",
      "indicates a perfect positive linear relationship. (Note that we\n",
      "will use Pearson's product-moment correlation, but there are other variants of\n",
      "correlation.)\n",
      "\n",
      "Pearson's r is defined as\n",
      "\n",
      "$$r = \\frac{1}{n}\\sum ^n _{i=1}\\left[\\left(\\frac{X_i - \\bar{X}}{s_X}\\right)\\left(\\frac{Y_i - \\bar{Y}}{s_Y}\\right)\\right]$$\n",
      "\n",
      "In other words, we z-score each variable and then compute the average product of the variables.\n",
      "\n",
      "In Python, we can compute this in a variety of ways:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# First there's the longwinded arithmetic\n",
      "# (Note this isn't all that longwinded since it's a vectorized calculationg)\n",
      "r1 = mean(((s1 - s1.mean()) / s1.std()) * ((s2 - s2.mean()) / s2.std()))\n",
      "\n",
      "# We can also use functions from the scipy.stats package\n",
      "from scipy import stats\n",
      "r2 = mean(stats.zscore(s1) * stats.zscore(s2))\n",
      "\n",
      "# This package even offers a one-step function\n",
      "# Note this returns a tuple (r, p)\n",
      "r3, p3 = stats.pearsonr(s1, s2)\n",
      "\n",
      "print \"%.3f, %.3f, %.3f\" % (r1, r2, r3)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "0.823, 0.823, 0.823\n"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can also visualize the relationship with a scatterplot"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Note that scatter(s1, s2) is equivalent to plot(s1, s2, \"o\")\n",
      "plot(s1, s2, \"o\")\n",
      "xlabel(\"Values in variable 1\")\n",
      "ylabel(\"Values in variable 2\")\n",
      "\n",
      "# We can display the simulated and computed correlations\n",
      "annot = \"Correlations:\\nSimulated: %.3f\\nEstimated: %.3f\" % (w, r1)\n",
      "text(xlim()[0] + .2, ylim()[1] - 1, annot, size=12);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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EZsToBs8REZXFsYQERMfuR55CAqlEgZGBg7ihC1VqTOxEZLKOJSRg1YYdsHYN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\nlNgJIYSQAEKJnRBCCAkglNgJIYSQAPIXNDW1eWr4GCEAAAAASUVORK5CYII=\n"
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "(5) Error bars"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "- How do we obtain error bars on the correlation observed in a set of data?\n",
      "\n",
      "- How do we test whether the correlation observed in a set of data is\n",
      "  significantly different from zero? \n",
      "\n",
      "Hereafter, we compute errorbars on the correlation coefficient using\n",
      "bootstrap.\n",
      "\n",
      "We compute k bootstrap (resampling with replacement) with the same size\n",
      "of the original samples. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Number of samples\n",
      "k = 1000\n",
      "r_dist = zeros(k)\n",
      "\n",
      "# Do the bootstrap\n",
      "for i in xrange(k):\n",
      "    idx = randint(0, n, n)\n",
      "    r_dist[i] = stats.pearsonr(s1[idx], s2[idx])[0]\n",
      "\n",
      "# Compute the two-tailed 95% confidence intervals\n",
      "ci = utils.percentiles(r_dist, [2.5, 97.5])\n",
      "\n",
      "# Plot the correlation with error bars\n",
      "bar(0.5, r1, width=1)\n",
      "plot([1, 1], ci, color=colors[2], linewidth=3)\n",
      "xlim(0, 2)\n",
      "ylim(0, 1)\n",
      "xticks(())\n",
      "title(\"Estimated correlation coefficient with error\")\n",
      "ylabel(\"Correlation between s1, s2\");"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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ZWfrb3/6mgQMHatSoUd7IBgAAirG8jOnQoUPVpEkTLV26VKdOndLy5cvVunVr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\n"
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "(6) Test hypotheses"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now we want to test the hypothesis that the correlation r, was not\n",
      "obtained by chance. We want to find the probability for the null\n",
      "hypothesis to be true.\n",
      "\n",
      "If the null hypothesis were true, we would be able to shuffle the\n",
      "order of each variable and obtain datasets that are equivalent to the\n",
      "original dataset. So, to obtain a p-value, we shuffle each variable,\n",
      "calculate a correlation value for each shuffled sample. We repeat this\n",
      "process a large number of times and count the number of times that\n",
      "randomly obtained correlation values are more extreme than the actual\n",
      "observed correlation value.\n",
      "\n",
      "We create a bootstrap distribution of samples under the null hypothess\n",
      "that s1 and s2 were not correlated."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "k = 1000\n",
      "r_dist = zeros(k)\n",
      "for i in xrange(k):\n",
      "    s1_rand = s1[randint(0, n, n)]\n",
      "    s2_rand = s2[randint(0, n, n)]\n",
      "    r_dist[i] = stats.pearsonr(s1_rand, s2_rand)[0]\n",
      "\n",
      "bar(*utils.pmf_hist(r_dist, 20))\n",
      "title('Distribution of correlations between s1 and s2')\n",
      "ylabel('Likelihood of occurrence')\n",
      "xlabel('Pearson correlation coefficient')\n",
      "\n",
      "# Now plot the empirical correlation value\n",
      "axvline(r1, color=colors[3], linewidth=3)\n",
      "p = sum(abs(r1) < abs(r_dist)) / k\n",
      "text(0.2, ylim()[1] * .95, \"$H_0$ is true with %.2f probability\" % p);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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W6NGjBxo0aFDtaYmIiEg1at+ST0xMhL29vTTs6OiIs2fPIiAgQG3TGhjow8zM\nSH1F1yMGBvoAUO/6X1JSghs3rlfZJifnnlqXaWraqN6tJ2Xq6/uvDi9z3wH2X9X+6+r6Ke9/tadT\ncx1Elbpx4zqmLNgFY7PmCtvk3L6EZm0dtFgVEZFuU3vIu7m5Yc6cOdJwcnIyBg0apNZpi4tLkJf3\nuObF1kPlv1LrW/8LCp7C2Kw5TJq2UdimMC9D7cusb+tJmfr6/qvDy9x3gP1Xtf+6un7MzIzQsGH1\nI1vtx+TNzMwAlJ0ln5aWhqioKHh4eFTaVgjxwtMSERFR1TSyu37NmjUIDg5GUVERQkJCYGFhgfDw\ncABAcHAw7t+/Dzc3N+Tn50NPTw9r165FSkoKTExMKp2WiIiIqk8jIe/r64tLly7JvRYcHCz93bJl\nS9y6dUvlaYmqS5SWIj39ptJ21tY20Nd/sRNaiIjqOp54RzrpcUEWVv6YDWOzuwrbFOZlYu2cQLRv\n30GLlRERaQ9DnnSWshP9iIh0He9dT0REpKMY8kRERDqKIU9ERKSjGPJEREQ6iiFPRESkoxjyRERE\nOoohT0REpKMY8kRERDqKIU9ERKSjGPJEREQ6iiFPRESkoxjyREREOoohT0REpKMY8kRERDqKIU9E\nRKSjGPJEREQ6iiFPRESkoxjyREREOoohT0REpKMY8kRERDqKIU9ERKSjGPJEREQ6iiFPRESkowxq\nuwCq/0pKSpCWllplm/T0m1qqhoiIyjHkqcbS0lIRunw/jM2aK2yTc/sSmrV10GJVRETEkCe1MDZr\nDpOmbRSOL8zL0GI1REQE8Jg8ERGRzmLIExER6SiVdtffvn0bhw8fxrRp05CRkYG8vDx07NhR07UR\naZQoLVXphEBraxvo6+troSIiIvVSGvJbt27FmjVr8OjRI0ybNg3Pnj3DlClTcPLkSW3UR6Qxjwuy\nsPLHbBib3VXYpjAvE2vnBKJ9+w5arIyISD2UhnxERAROnz4NLy8vAMCrr76KvLw8jRdGpA3KThgk\nIqrPlB6TLyoqgrGxsTT88OFDmJiYaLQoIiIiqjmlW/L+/v7Yu3cvgLJj88uWLUNgYKDGCyMiIqKa\nUbol/8477yA2NhYZGRno3r07DAwMMG3aNG3URkRERDWgdEvewsICa9euxcqVK1FaWoqGDRtqoy4i\nIiKqIaVb8tu2bUNubi4MDAzQsGFD5ObmYvv27dqojYiIiGpAacivWLEC5ubm0rC5uTmWL1+u0aKI\niIio5pSQ57UEAAAgAElEQVSGvIGBAUpKSqTh4uJiCCE0WhQRERHVnNKQ79+/P9avX4/i4mIUFRVh\n/fr1GDhwoDZqIyIiohpQGvIzZsxAVFQUWrdujTZt2iA6OhrvvfeeNmojIiKiGlAa8jY2Nvj555+R\nnJyMixcv4ueff4a1tXWV08TFxcHBwQF2dnZYt25dpW3mzZsHW1tbuLq64vLly9LrGzduRK9eveDq\n6oqZM2dWrzdEREQkUfkpdA8fPkR2djZSUlKQkpJSZdvQ0FCEh4cjOjoa69evR3Z2ttz4hIQEnDhx\nAklJSZg9ezZmz54NAMjNzcXixYsRFRWFxMREXL16FUeOHHmBbhEREZHS6+R37dqF2bNno6ioCIaG\nhtLrqamplbYvv6+9j48PAGDgwIGIj49HQECA1CY+Ph4jR46Eubk5xowZg08//RQAYGRkBCGENI/C\nwkI0bdr0BbtGRET0clMa8osXL8bPP/+Mbt26qTTDxMRE2NvbS8OOjo44e/asXMgnJCRgwoQJ0rCl\npSWuX7+O9u3bY8OGDbC2tkajRo0QEhICd3f3ikUb6MPMzEilenSNgUHZI0/rUv9NTRvVdgkaZWra\nqM6s77r4/mvLy9x3gP1Xtf+6un7K+19dSnfXGxoawtHR8YVmrogQosJleDKZDFlZWZgxYwZSUlKQ\nlpaGM2fOIDIyUq3LJiIielko3ZJ//fXXMX36dEyePFnupjiKgt/NzQ1z5syRhpOTkzFo0CC5Nh4e\nHkhJSYG/vz8AICsrC7a2toiMjISnpyc6dCh7dvcbb7yBuLg4ub0AAFBcXIK8vMcqdlG3lP9KrUv9\nLyh4WtslaFRBwdM6s77r4vuvLS9z3wH2X9X+6+r6MTMzQsOGSiO7AqVTbNiwATKZDMeOHZN7XdEx\neTMzMwBlZ9i3a9cOUVFRCAsLk2vj4eGBjz76CBMnTsSRI0fg4OAAAPD29kZoaChyc3PRuHFjHD58\nGKGhodXuFKlPSUkJ0tIqf6/Lpaff1FI1RERUHUpDPi0trdozXbNmDYKDg1FUVISQkBBYWFggPDwc\nABAcHAx3d3d4e3ujR48eMDc3R0REBICyHwiffvopXn/9dRQWFmLQoEHo06dPtZdP6pOWlorQ5fth\nbNZcYZuc25fQrK2DFqsiIiJVqLTtf/v2bRw+fBjTpk1DRkYG8vLy0LFjR4XtfX19cenSJbnXgoOD\n5YaXLl2KpUuXVph20qRJmDRpkiplkZYYmzWHSdM2CscX5mVosRoiIlKV0hPvtm7diiFDhmDZsmUA\ngGfPnmHy5MkaL4yIiIhqRmnIR0RE4PTp0zAxMQEAvPrqq8jPz9d4YURERFQzSkO+qKgIxsbG0vDD\nhw+lwCciIqK6S+kx+YEDB2Lv3r0Ayo7NL1u2DIGBgRovjIiIiGpG6Zb89OnTERsbi4yMDHTv3h0G\nBgaYNm2aNmojIiKiGqhyS76kpAR79uzB2rVrsXLlSpSWlqJhw4baqo2IiIhqoMoteX19fXz77bcA\nAAMDAwY8ERFRPaL0mPywYcOwdu1avP3222jcuLE2aiKqM0RpqUp39LO2toG+/os9QIKISFOUhvzX\nX3+N3NxcfPzxx3jllVcAlD1MJjMzU+PFEdW2xwVZWPljNozN7ipsU5iXibVzAtG+fQctVkZEpJzS\nkI+OjkaTJk20UQtRnaTsjn9ERHVVlSFfWlqK8ePH4+LFi9qqh4iIiNSkyhPv9PT00KZNG1y7dk1b\n9RAREZGaKN1db2lpCQ8PD/j7+6NNm7JdljKZTLqXPREREdVNSkO+Q4cO+OCDDwCUhbsQAjKZTOOF\nERERUc0oDfmFCxdqoQwiIiJSN6UhP2fOnEq34Lm7noiIqG5Teu/6xo0bo3HjxjAxMcGTJ0+wc+dO\nPmqWiIioHqj27vq5c+firbfe0lQ9REREpCZKt+T/ycLCArdv39ZELURERKRGKh2TL/f06VOcPHkS\ngwYN0mhRREREVHNKQ75x48bSCXcWFhb45ptv4OHhofHCiIiIqGZ4CR0REZGOUnpMPigoCLm5udJw\ndnY2Ro0apdGiiIiIqOaUhvz169dhbm4uDVtYWODq1asaLYqIiIhqTmnIN2vWTO7Z8RkZGdJz5YmI\niKjuUnpMftSoURg7diymT58OIQTCw8Mxbtw4bdRGRERENaA05KdOnQoLCwt8//33AIAZM2YgMDBQ\n44URERFRzSgNeQMDAwQFBSEoKEgb9RAREZGaKD0m/8EHHyAnJ0cazsnJwcyZMzVaFBEREdWc0pA/\nceIEmjVrJg03a9YMMTExmqyJiIiI1EClp9A9/9S5vLw8NGrUSKNFERERUc0pDfkRI0bg3XffRVJS\nEhITE/Hee+/xZjhERET1gNIT74KDgxEeHo63334bADBhwgQEBwdrvDAiIiKqGaUhb2JiglmzZmHW\nrFnaqIeIiIjURGnICyFw4sQJ7Nq1CzKZDKNGjYK3t7f0ZDoiIiKqm5Qek9+4cSM+/vhj2NnZoX37\n9vj444+xceNGbdRGRERENaB0Sz4iIgI///wzLC0tAQDjx4/HiBEj8M4772i8OCIiInpxSrfkAcjt\nmudueiIiovpB6Zb8uHHjMGTIEIwdOxZCCPz444946623tFEbERER1YDSkH/nnXfQqVMn/PTTT5DJ\nZFiyZAl8fHy0URsRERHVgNKQl8lk8PPzg5+fnxbKISIiInVR6Zg8ERER1T8aCfm4uDg4ODjAzs4O\n69atq7TNvHnzYGtrC1dXV1y+fFl6/dGjR3jrrbfQsWNHODo64uzZs5ookYiISOcpDPnY2FgAwJMn\nT6o909DQUISHhyM6Ohrr169Hdna23PiEhAScOHECSUlJmD17NmbPni2NCwsLQ7t27fDnn3/izz//\nhIODQ7WXT0RERFWE/EcffQQA6NmzZ7VmmJeXBwDw8fGBlZUVBg4ciPj4eLk28fHxGDlyJMzNzTFm\nzBhcunRJGhcdHY358+fD0NAQBgYGMDMzq9byiYiIqIzCE+9MTEywZMkSZGdn45tvvoEQQhonk8nw\n7rvvVjpdYmIi7O3tpeHyXe4BAQHSawkJCZgwYYI0bGlpiRs3bqBhw4Z48uQJZsyYgUuXLmHEiBEI\nDQ2FoaGhfNEG+jAzM6p+b3WAgYE+AGit/6amfKywKkxNG2nlPdH2+1+XvMx9B9h/Vfuvq+unvP/V\npXBL/ptvvkFOTg4KCwuRmJiIpKQk6V9iYuILFwqU3Q//+R8N5Z48eYKrV68iKCgIMTExSE5Oxq5d\nu2q0LCIiopeVwi15JycnrFixAi1atMCcOXNUnqGbm5tc++TkZAwaNEiujYeHB1JSUuDv7w8AyMrK\ngq2tLQCgU6dOGDp0KABgzJgx2LZtGyZOnCg3fXFxCfLyHqtcky4p/5Wqrf4XFDzVynLqu4KCp1p5\nT7T9/tclL3PfAfZf1f7r6voxMzNCw4ZKr3qvQOnZ9XPmzMGTJ0+we/du7NmzR+mJeOXH0OPi4pCW\nloaoqCh4eHjItfHw8MCePXuQk5ODHTt2yJ1cZ2dnh/j4eJSWliIyMhL9+/evdqeIiIhIhZvh/Prr\nr3jrrbfg6ekJIQTef/99bNu2DQMGDFA4zZo1axAcHIyioiKEhITAwsIC4eHhAIDg4GC4u7vD29sb\nPXr0gLm5OSIiIqRpV6xYgYkTJ+LJkyfo378/3nzzTTV0k4iI6OWjNOTXr1+P6OhoODk5AQBSUlIw\nd+7cKkPe19dX7ox5oCzcn7d06VIsXbq0wrQdO3bktfFERERqoHR3/e3bt9GxY0dp2M7ODnfu3NFo\nUURERFRzSrfkhwwZgpkzZyI4OBhCCGzcuBFDhgzRRm1ERERUA0q35ENCQmBpaYmxY8di3LhxsLS0\nRGhoqDZqIyIiohpQuiXfrFkzLFy4EAsXLtRCOURERKQufAodERGRjmLIExER6SiGPBERkY5iyBMR\nEekohSfeWVpaSn/LZLIKT6HLzMzUbGVERERUIwpDvvxJczt37sTvv/+OadOmQQiBLVu2oGvXrlor\nkIiIiF6MwpC3trYGAPz44484ffo0jIzKngDk5eWFXr164V//+pdWCiQiIqIXo/SYvJGREW7evCkN\n37p1Swp8IiIiqruU3gxn7ty58PHxQe/evQEAJ0+exKZNmzReGBEREdWM0pAfNmwY/vrrLxw+fBgy\nmQybN2+WnhlPREREdZfSkAcAMzMz9O3bFzKZjAFPRERUTyg9Jn/58mX07dsXXbp0QefOndGvXz9c\nvnxZG7URERFRDSgN+dWrV2PSpEm4d+8e7t27h8mTJ2P16tXaqI2IiIhqQGnInzlzBhMnToSenh70\n9PQwbtw4nDlzRhu1ERERUQ0oDXlPT09EREQAAIQQ2LFjBzw9PTVeGBEREdWM0pCfOXMmNm3ahBYt\nWqBly5bYtGkTPvzwQ23URkRERDWg9Ox6R0dHxMTE4P79+wCAli1barwoovpElJYiPf2m0nbW1jbQ\n19fXQkVERGVUuoTuyZMnOHnyJGQyGQICAmBoaKjpuojqjccFWVj5YzaMze4qbFOYl4m1cwLRvn0H\nLVZGRC87pSH/66+/4q233oKnpyeEEHj//fexbds2DBgwQBv1kQaVlJQgLS21yjaqbKESYGzWHCZN\n29R2GUREcpSG/Pr16xEdHQ0nJycAQEpKCubOncuQ1wFpaakIXb4fxmbNFbbJuX0Jzdo6aLEqIiJS\nF6Uhf/v2bXTs2FEatrOzw507dzRaFGmPsi3QwrwMLVZDRETqpDTkhwwZgpkzZyI4OBhCCGzcuBFD\nhgzRRm1ERERUA0ovoQsJCYGlpSXGjh2LcePGwdLSEqGhodqojYiIiGpA6ZZ8s2bNsHDhQixcuFAL\n5RAREZG6qHQJ3Y0bNxATE4MnT55ACAGZTIZ3331X07URERFRDSgN+QULFmDr1q3w9vZGo0aNtFET\nERERqYHSkN+9ezdSUlJgYmKijXqIiIhITZSeeNeyZUs8e/ZMG7UQERGRGinckl+/fj0AwNnZGX36\n9MEbb7yBpk2bAgCPyRMREdUDCkM+MTERMpkMAODi4oLr169rrSgiIiKqOYUhv3XrVi2WQUREROqm\nMORPnToFLy8vREZGSlv0zxs8eLBGCyMiIqKaqXJL3svLC8uXL2fIExER1UMKQ37jxo0AgJiYGG3V\nQkRERGqkMORTUlKqnNDR0VHtxRAREZH6KAz5wYMHV7qbvlxqaqpGCiIiIiL1UBjyaWlpWiyDiIiI\n1E3pHe8A4Pbt29Ix+oyMDFy9elWjRREREVHNKQ35rVu3YsiQIVi2bBkA4NmzZ5g8eXKV08TFxcHB\nwQF2dnZYt25dpW3mzZsHW1tbuLq64vLly3LjSkpK4OLigqFDh6raDyIiIvoHpSEfERGB06dPSw+o\nefXVV5Gfn1/lNKGhoQgPD0d0dDTWr1+P7OxsufEJCQk4ceIEkpKSMHv2bMyePVtu/Nq1a+Ho6Fjl\nOQFERERUNaUhX1RUBGNjY2n44cOHVT6RLi8vDwDg4+MDKysrDBw4EPHx8XJt4uPjMXLkSJibm2PM\nmDG4dOmSNO727ds4dOgQ3n77bQghqt0hIiIiKqP0UbMDBw7E3r17AZQF8LJlyxAYGKiwfWJiIuzt\n7aVhR0dHnD17FgEBAdJrCQkJmDBhgjRsaWmJGzduwNbWFh9++CGWL19e5d4CAwN9mJkZKStdJxkY\n6AOAWvpvatqoxvMg1ZmaNqrx+6bO97++eZn7DrD/qvZfV9dPef+rS+mWfHBwMGJjY5GRkYHu3bvD\nwMAA06ZNe6GFlRNCVLqVfvDgQTRv3hwuLi7ciiciIqohpVvyz549w9q1a7Fy5UqUlpaiYcOG+OOP\nP9CsWbNK27u5uWHOnDnScHJyMgYNGiTXxsPDAykpKfD39wcAZGVlwdbWFps2bcKBAwdw6NAhPHny\nBPn5+Zg4cSK2bdsmN31xcQny8h5Xu7O6oPxXqjr6X1DwtMbzINUVFDyt8fumzve/vnmZ+w6w/6r2\nX1fXj5mZERo2VBrZFSjdkh8+fDgKCgpgYGCAhg0bIiUlBUFBQVUUYgag7Az7tLQ0REVFwcPDQ66N\nh4cH9uzZg5ycHOzYsQMODg4AgMWLF+PWrVtITU3Fzp070bdv3woBT0RERKpR+rPgo48+QlBQEA4d\nOoS0tDQMHz5cafCuWbMGwcHBKCoqQkhICCwsLBAeHg6gbPe/u7s7vL290aNHD5ibmyMiIqLS+fDs\neiIiohenNOTffPNNpKenY/To0UhOTkZ4eDh69epV5TS+vr5yZ8wDZeH+vKVLl2Lp0qVVzsPX11dZ\neURERKSAwpB//jnyTk5O+OmnnzBgwAA8fvwYhw4d4qNmiYiI6jiFIf/P58g3btwYFy9exMWLFwHw\nefJERER1ncKQ53PkiYiI6jeFIZ+amgobGxuFz5Xn8+SJiIjqNoUh//777yMyMlLhc+X5PHkiIqK6\nrcoT74DKnyv/4MEDjRVERERE6qHS8+T/qWvXruqug4iIiNTshUKe95UnIiKq+14o5ImIiKjuU3hM\nXtFZ9UIIFBcXa6wgIiIiUg+FIa/orHoAMDQ01FhBREREpB4KQ76ys+qJiIio/uAxeSIiIh3FkCci\nItJRDHkiIiIdxZAnIiLSUQx5IiIiHcWQJyIi0lEMeSIiIh3FkCciItJRCm+GQ/VbSUkJ0tJSq2yT\nnn5TS9WQKC1VaX1bW9tAX19fCxUR0cuAIa+j0tJSEbp8P4zNmitsk3P7Epq1ddBiVS+vxwVZWPlj\nNozN7ipsU5iXibVzAtG+fQctVkZEuowhr8OMzZrDpGkbheML8zK0WA0pez+IiNSNx+SJiIh0FEOe\niIhIR3F3fT1TUlKCGzeuo6DgaZXteFIdEREx5OuZGzeuY8qCXVWeUAfwpDoiImLI10uqnMDFk+qI\niIjH5ImIiHQUQ56IiEhHcXc9UR2hyl3xTE0bAQCaNWvNO+MRkVIMeaI6QpW74gG8Mx4RqY4hT1SH\n8K54RKROPCZPRESkoxjyREREOoohT0REpKMY8kRERDqKIU9ERKSjGPJEREQ6iiFPRESkoxjyRERE\nOoohT0REpKM0EvJxcXFwcHCAnZ0d1q1bV2mbefPmwdbWFq6urrh8+TIA4NatW+jTpw+cnJzg5+eH\nHTt2aKI8IiKil4JGbmsbGhqK8PBwWFlZwd/fH2PGjIGFhYU0PiEhASdOnEBSUhKOHDmC2bNn4+DB\ng2jQoAFWr14NZ2dnZGdnw93dHUOHDoWpqakmyiQiItJpat+Sz8vLAwD4+PjAysoKAwcORHx8vFyb\n+Ph4jBw5Eubm5hgzZgwuXboEAGjZsiWcnZ0BABYWFnByckJSUpK6SyQiInopqD3kExMTYW9vLw07\nOjri7Nmzcm0SEhLg6OgoDVtaWuL69etyba5du4bk5GS4u7uru0QiIqKXQq08hU4IASGE3GsymUz6\nu6CgAKNHj8bq1avRuHHjCtMbGOjDzMxI43XWRTk5fIY4lT1X/mX7P2BgUPbZf9n6XY79V63/urp+\nyvtfXWrfkndzc5NOpAOA5ORkeHp6yrXx8PBASkqKNJyVlQVbW1sAQFFREYKCgjBhwgQEBgaquzwi\nIqKXhtq35M3MzACUnWHfrl07REVFISwsTK6Nh4cHPvroI0ycOBFHjhyBg4MDgLIt/KlTp6Jz586Y\nOXOmwmUUF5cgL++xukuvF0pKSmq7BKoDCgqevnT/B8q30F62fpdj/1Xrv66uHzMzIzRsWP3I1sju\n+jVr1iA4OBhFRUUICQmBhYUFwsPDAQDBwcFwd3eHt7c3evToAXNzc0RERAAATp06hYiICHTt2hUu\nLi4AgCVLlmDQoEGaKJOIiEinaSTkfX19pTPmywUHB8sNL126FEuXLpV7zdvbG6WlpZooiYiI6KXD\nO94RERHpKIY8ERGRjmLIExER6SiGPBERkY5iyBMREekohjwREZGOYsgTERHpKIY8ERGRjmLIExER\n6SiGPBERkY5iyBMREekohjwREZGOYsgTERHpKIY8ERGRjmLIExER6SiGPBERkY5iyBMREekohjwR\nEZGOYsgTERHpKIY8ERGRjmLIExER6SiGPBERkY5iyBMREekog9ougP5PSUkJ0tJSq2yTk3NPS9VQ\nXSVKS5GeflNpO2trG+jr62uhIiKqqxjydUhaWipCl++HsVlzhW1ybl9Cs7YOWqyK6prHBVlY+WM2\njM3uKmxTmJeJtXMC0b59By1WRkR1DUO+jjE2aw6Tpm0Uji/My9BiNVRXKfucEBEBPCZPRESksxjy\nREREOoohT0REpKMY8kRERDqKJ96pgSqXvgG8pInqFn5uiXQfQ14NVLn0jZc0UV3Dzy2R7mPIqwkv\naaL6iJ9bIt3GY/JEREQ6iiFPRESkoxjyREREOorH5LVElYeKqPLQESIiIlUx5LVElYeK8OEzRESk\nTgx5LeLDZ4iISJt4TJ6IiEhHMeSJiIh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VlXZ+c+VhLpnmF187gF6vTyqOcbPXmO73ibFj\nsRgtLS3s2bPnX88zlXRjJ4rFYlgsFtrb21MeT+wLrtPpUq5Rkv40+Uxe+ivpdDr27t3LpUuXCIVC\nwMwz9ImJCX78+EEsFmPVqlVMTk7idrszxnr//j2FhYWcOnWK7du3Mzg4iE6nw2q14na7EUIwMDBA\nMBhU7+L/rX379uF2u5mYmAAgEAgAYLfb6erq4tu3bwQCAbq6uqitrVWvy1Sgli5dSmVlJS6Xi+np\naQDevXtHMBhMOi9THgwGA9FolJ8/f6Ycw2634/F4iEajjIyM8Pz5c7Zt2/bba+/o6GB8fByY2YEA\nsNls9Pb28unTJ0KhED6fT1270+nE7Xbz+fNnYKb9cmJXs7nE8zY77/GxZ8+vv7+f169fAzNF/9Wr\nV3OOsXLlSvXdBkn60+SdvPTXam5uxuPxsGXLFkKhELm5uVy/fp3i4mJOnjxJWVkZixcvZufOnQwP\nD6vXzX4r/8yZM3z48AG9Xk9RURHXrl0DoLW1lStXrmA2mykpKeH27dtpY6R707+6uppAIIDdbmdy\ncpLi4mJ1W37//v3qFnx9fb26bTw7nkaj+SV+W1sbbrebjRs3MjU1hcFgUF+Ai59rNBrT5kGv13P8\n+HE2bNhAdnY2T548SYp/7Ngx2traKC8vx2g04vP50Ov16b6KlEpLSzl9+jSHDh3i69ev5ObmMjAw\ngMlk4sKFCzQ0NBAMBrHb7epjAKvVSiAQwOl08uXLFxYsWMD58+dZvXr1L3lIlZf453R5T7wmLy8P\nr9fL5cuXGRoaQlEUamtrWbduXcax1q9fT35+PmazmYqKClwu12/lRZJ+h/wTOkmSJEmap+R2vSRJ\nkiTNU7LIS5IkSdI8JYu8JEmSJM1TsshLkiRJ0jwli7wkSZIkzVOyyEuSJEnSPPUPyrIqX5ypNx4A\nAAAASUVORK5CYII=\n"
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "(7) Monte Carlo Methods"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "While we are on the topic of p-values on correlation values, it is\n",
      "convenient to introduce here Monte Carlo methods. Monte Carlo methods are\n",
      "a very general class of methods that make use of randomly generated data\n",
      "to test various hypotheses. \n",
      "\n",
      "Monte Carlo methods are a very general class of methods that make use of\n",
      "randomly generated data to test various hypotheses.\n",
      " \n",
      "Imagine that we have obtained a correlation of r = 0.4 for a sample size\n",
      "of 10. We do not know the population or any other information.\n",
      "\n",
      "But we can assume that the true populations generating the two variables\n",
      "were normally distributed. We can then simulate a process in\n",
      "which we draw samples of size 10 from two independent Gaussian\n",
      "distributions and compute the correlation value observed in each sample.\n",
      " \n",
      "Such (Monte Carlo) simulations reveal that it is actually quite likely to\n",
      "obtain a correlation of r = 0.4 for a sample size of 10, even when the\n",
      "underlying distributions are independent. Thus, we should not believe the\n",
      "claim."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Say our acutal measured correlation was 0.4\n",
      "r_empirical = 0.4\n",
      "\n",
      "# Simulate two IID normal variables\n",
      "k = 10000 # number of sims\n",
      "n = 30 # sample size\n",
      "s1_sim = randn(k, n)\n",
      "s2_sim = randn(k, n)\n",
      "\n",
      "# Compute the correlation coefficient for each sample\n",
      "r_dist = array(map(stats.pearsonr, s1_sim, s2_sim))[:, 0] # Take first column (r values)\n",
      "\n",
      "# Plot the distribution of coefficients obtained this way\n",
      "bar(*utils.pmf_hist(r_dist, 100), color=colors[4])\n",
      "title('Distribution of the Montecarlo-simulated correlation coefficients')\n",
      "ylabel('Probability of occurrence')\n",
      "xlabel('Corr(s1,s2)')\n",
      "\n",
      "# Plot the observed correlation on this PMF\n",
      "axvline(r_empirical, color=colors[0], linewidth=3)\n",
      "\n",
      "# Obtain the probability of our observed value by counting how many\n",
      "# r's from our randomization test were more extreme\n",
      "p = sum(abs(r_empirical) > abs(r_dist)) / k\n",
      "xpos = xlim()[0] * .95\n",
      "ypos = ylim()[1] * .95\n",
      "text(xpos, ypos, \"$H_0$ is false with probability %.3f\" % p, size=12);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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XqvOECRPh4uIKOzt79Os3AKdPn1S5rK/vGMhkPdC5szNmzpyJX3/9RWGZUaNe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\n3w+KYO0TObwAAAAASUVORK5CYII=\n"
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 24
    }
   ],
   "metadata": {}
  }
 ]
}