BEST.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Bayesian Estimation Supersedes the T-Test"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This model replicates the example used in:\n",
    "Kruschke, John. (2012) **Bayesian estimation supersedes the t-test**. *Journal of Experimental Psychology*: General.\n",
    "\n",
    "The original pymc2 implementation was written by Andrew Straw and can be found here: https://github.com/strawlab/best\n",
    "\n",
    "Ported to PyMC3 by Thomas Wiecki (c) 2015, updated by Chris Fonnesbeck."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The Problem\n",
    "\n",
    "Several statistical inference procedures involve the comparison of two groups. We may be interested in whether one group is larger than another, or simply different from the other. We require a statistical model for this because true differences are usually accompanied by measurement or stochastic noise that prevent us from drawing conclusions simply from differences calculated from the observed data. \n",
    "\n",
    "The *de facto* standard for statistically comparing two (or more) samples is to use a statistical test. This involves expressing a null hypothesis, which typically claims that there is no difference between the groups, and using a chosen test statistic to determine whether the distribution of the observed data is plausible under the hypothesis. This rejection occurs when the calculated test statistic is higher than some pre-specified threshold value.\n",
    "\n",
    "Unfortunately, it is not easy to conduct hypothesis tests correctly, and their results are very easy to misinterpret. Setting up a statistical test involves several subjective choices (*e.g.* statistical test to use, null hypothesis to test, significance level) by the user that are rarely justified based on the problem or decision at hand, but rather, are usually based on traditional choices that are entirely arbitrary (Johnson 1999). The evidence that it provides to the user is indirect, incomplete, and typically overstates the evidence against the null hypothesis (Goodman 1999). \n",
    "\n",
    "A more informative and effective approach for comparing groups is one based on **estimation** rather than **testing**, and is driven by Bayesian probability rather than frequentist. That is, rather than testing whether two groups are different, we instead pursue an estimate of how different they are, which is fundamentally more informative. Moreover, we include an estimate of uncertainty associated with that difference which includes uncertainty due to our lack of knowledge of the model parameters (epistemic uncertainty) and uncertainty due to the inherent stochasticity of the system (aleatory uncertainty)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: Drug trial evaluation\n",
    "\n",
    "To illustrate how this Bayesian estimation approach works in practice, we will use a fictitious example from Kruschke (2012) concerning the evaluation of a clinical trial for drug evaluation. The trial aims to evaluate the efficacy of a \"smart drug\" that is supposed to increase intelligence by comparing IQ scores of individuals in a treatment arm (those receiving the drug) to those in a control arm (those recieving a placebo). There are 47 individuals and 42 individuals in the treatment and control arms, respectively."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import pymc3 as pm\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "sns.set(color_codes=True)\n",
    "\n",
    "np.random.seed(20090425)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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gKEocAABDUeIAABiKEgcAwFCUOAAAhqLEAQAwFCUOAIChKHEAAAxFiQMAYChKHAAAQ1Wo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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11549c2b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "drug = (101,100,102,104,102,97,105,105,98,101,100,123,105,103,100,95,102,106,\n",
    "        109,102,82,102,100,102,102,101,102,102,103,103,97,97,103,101,97,104,\n",
    "        96,103,124,101,101,100,101,101,104,100,101)\n",
    "placebo = (99,101,100,101,102,100,97,101,104,101,102,102,100,105,88,101,100,\n",
    "           104,100,100,100,101,102,103,97,101,101,100,101,99,101,100,100,\n",
    "           101,100,99,101,100,102,99,100,99)\n",
    "\n",
    "y1 = np.array(drug)\n",
    "y2 = np.array(placebo)\n",
    "y = pd.DataFrame(dict(value=np.r_[y1, y2], group=np.r_[['drug']*len(drug), ['placebo']*len(placebo)]))\n",
    "\n",
    "y.hist('value', by='group');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first step in a Bayesian approach to inference is to specify the full probability model that corresponds to the problem. For this example, Kruschke chooses a Student-t distribution to describe the distributions of the scores in each group. This choice adds robustness to the analysis, as a T distribution is less sensitive to outlier observations, relative to a normal distribution. The three-parameter Student-t distribution allows for the specification of a mean $\\mu$, a precision (inverse-variance) $\\lambda$ and a degrees-of-freedom parameter $\\nu$:\n",
    "\n",
    "$$ f(x|\\mu,\\lambda,\\nu) =\n",
    "           \\frac{\\Gamma(\\frac{\\nu + 1}{2})}{\\Gamma(\\frac{\\nu}{2})}\n",
    "           \\left(\\frac{\\lambda}{\\pi\\nu}\\right)^{\\frac{1}{2}}\n",
    "           \\left[1+\\frac{\\lambda(x-\\mu)^2}{\\nu}\\right]^{-\\frac{\\nu+1}{2}}$$\n",
    "           \n",
    "the degrees-of-freedom parameter essentially specifies the \"normality\" of the data, since larger values of $\\nu$ make the distribution converge to a normal distribution, while small values (close to zero) result in heavier tails.\n",
    "\n",
    "Thus, the likelihood functions of our model are specified as follows:\n",
    "\n",
    "$$y^{(treat)}_i \\sim T(\\nu, \\mu_1, \\sigma_1)$$\n",
    "\n",
    "$$y^{(placebo)}_i \\sim T(\\nu, \\mu_2, \\sigma_2)$$\n",
    "\n",
    "As a simplifying assumption, we will assume that the degree of normality $\\nu$ is the same for both groups. We will, of course, have separate parameters for the means $\\mu_k, k=1,2$ and standard deviations $\\sigma_k$.\n",
    "\n",
    "Since the means are real-valued, we will apply normal priors on them, and arbitrarily set the hyperparameters to the pooled empirical mean of the data and twice the pooled empirical standard deviation, which applies very diffuse information to these quantities (and importantly, does not favor one or the other *a priori*).\n",
    "\n",
    "$$\\mu_k \\sim N(\\bar{x}, 2s)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "μ_m = y.value.mean()\n",
    "μ_s = y.value.std() * 2\n",
    "\n",
    "with pm.Model() as model:\n",
    "    \n",
    "    group1_mean = pm.Normal('group1_mean', μ_m, sd=μ_s)\n",
    "    group2_mean = pm.Normal('group2_mean', μ_m, sd=μ_s)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The group standard deviations will be given a uniform prior over a plausible range of values for the variability of the outcome variable, IQ.\n",
    "\n",
    "In Kruschke's original model, he uses a very wide uniform prior for the group standard deviations, from the pooled empirical standard deviation divided by 1000 to the pooled standard deviation multiplied by 1000. This is a poor choice of prior, because very basic prior knowledge about measures of human coginition dictate that the variation cannot ever be as high as this upper bound. IQ is a standardized measure, and hence this constrains how variable a given population's IQ values can be. When you place such a wide uniform prior on these values, you are essentially giving a lot of prior weight on inadmissable values. In this example, there is little practical difference, but in general it is best to apply as much prior information that you have available to the parameterization of prior distributions. \n",
    "\n",
    "We will instead set the group standard deviations to have a $\\text{Uniform}(1,10)$ prior:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Applied interval-transform to group1_std and added transformed group1_std_interval to model.\n",
      "Applied interval-transform to group2_std and added transformed group2_std_interval to model.\n"
     ]
    }
   ],
   "source": [
    "σ_low = 1\n",
    "σ_high = 10\n",
    "\n",
    "with model:\n",
    "    \n",
    "    group1_std = pm.Uniform('group1_std', lower=σ_low, upper=σ_high)\n",
    "    group2_std = pm.Uniform('group2_std', lower=σ_low, upper=σ_high)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We follow Kruschke by making the prior for $\\mu$ exponentially distributed with a mean of 30; this allocates high prior probability over the regions of the parameter that describe the range from normal to heavy-tailed data under the Student-T distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Applied log-transform to ν_minus_one and added transformed ν_minus_one_log to model.\n"
     ]
    },
    {
     "data": {
      "image/png": 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V7FfnycsqmFM4xv4BPb6kZMSfCwAAUzWlkBcXF2v+/PnDHxcWFurs2bPD+xOJhAoKCuQ4\nzohHpze2T0bciYy6/dpAROFoRNHY6PsHByIK5uSM+fUzsT8ej2nuv9wz6v7+hKt77nFUUDB2yIuK\n/B155md+P/Pz/H6e/W5MKeSHDx/WX//6V7W0tOjzzz+X67patmyZPvzwQz366KPq7OzU0qVLVVZW\npr1792pwcFCpVErnz59XaWnppH5Gn5scc3uel9Q1b/SlJ/qTCgRDCoVH//pM7x/oT6q311UqNfqp\n9aKiuC5ezO6zFuNhfuZnfn/O7+fZpbu7EzOlkD/zzDPatGmTampqFAwG1draqsLCQjU3N2toaEgl\nJSVauXKlAoGAamtrVVNTI8/z1NDQoHA4POXFAgCAkaYU8tzcXO3evfu27W1tbbdtW7NmjdasWTOV\nHwMAACbABWEAADCMkAMAYBghBwDAsClfohVTM9EFY/LyPPX1uVw0BgAwKYR8hk10wRgnFtGlS19w\n0RgAwKQQ8gzIi+QrP+qMui8ai8hNjP4edAAAbsVz5AAAGEbIAQAwjJADAGAYIQcAwDBCDgCAYYQc\nAADDCDkAAIYRcgAADCPkAAAYRsgBADCMkAMAYBghBwDAMEIOAIBhhBwAAMMIOQAAhvH7yGchz/Pk\nuu64t3EcR4FAYIZWBACYrQj5LJRK9qvz5GUVzCkcY/+AHl9Song8PsMrAwDMNoR8lsqL5Cs/6mR6\nGQCAWY7nyAEAMIxH5AbxHDoA4AZCbhDPoQMAbiDkRvEcOgBA4jlyAABMI+QAABhGyAEAMIyQAwBg\nGCEHAMAwQg4AgGGEHAAAwwg5AACGcUGYLMQlXAHAPwh5FuISrgDgH4Q8S3EJVwDwB54jBwDAMEIO\nAIBhhBwAAMMIOQAAhvFiNx/i7WkAkD0IuQ/x9jQAyB6E3Kd4exoAZAeeIwcAwDBCDgCAYYQcAADD\nCDkAAIYRcgAADCPkAAAYxtvPcBsuGAMAdhBy3IYLxgCAHYQcoxrvgjE8YgeA2YOQ447xiB0AZg9C\njinhETsAzA6EHNOOR+wAMHMIOdKCX8oCADOD95EDAGAYIQcAwDBOrWPWmcyL5SReMAcAEiFHBowX\n6rw8T//4xz/0wdnPlZefP+b34AVzAPAVQo4ZN96r2p1YRBf+/wVFos64L5bjLW4A8BVCjowY61Xt\n0VhEeZHIhF8/0VvckgP9Wrrw/8pxxr4zQOgBZANCDrPGe4tbciChzpOf8l52AFmPkCNrcfU5AH5A\nyOFLnJoHkC0IOXyLU/MAskHaQ+55nrZt26Zz584pHA7r1Vdf1bx589L9Y4G7djen5j3Pk6RxH7Hz\niB7AdEh7yI8eParBwUH99re/1alTp7Rr1y7t378/3T8WSKuJTs1f/uKSAsGcOz51n5fnqa/P5Y4A\ngElLe8i7u7v12GOPSZIWLVqkjz76KN0/EpgRE52aDwRDd3zq3olF5CaSU74jcMNk7ghMdJtM7L9x\nR2Y6vr80/p0dC1cQ5EWZmIy0h9x13RHPI4ZCIV2/fl3B4NiXeU+5l5Ryk6Pu8wb7lcoZ+33GqWRS\ngWCOBvpH/8s/2/fnBK5mfA2Z3D+Z+TO9xuncP1Wp5IDe+68exQvmjLr/8uX/UTCQM+b+ydwmE/tj\n0Twl+lPT8v1TqaT+ffHXxryz47quOv78N+XljfPvyQTfY7rdfEdGmniNM72+dLp19umU7a9lSXvI\nHcdRIpEY/nyiiEvSUyvK072sWe6hTC8gw/w+P2bKww8vyPQSblNQUDDi89m4xnS5dXZMTtp/+9k3\nv/lNdXR0SJJOnjypBQv885cSAIB0C3g3nmhKk5tftS5Ju3bt0te+9rV0/kgAAHwj7SEHAADpk/ZT\n6wAAIH0IOQAAhhFyAAAMI+QAABg2a35pil+vyf70008PX8zhvvvuU319vZqamhQMBlVaWqqWlpYM\nrzA9Tp06pd27d6utrU2ffvrpqDO3t7fr0KFDys3NVX19vaqqqjK76Gl08/wff/yxXnzxRRUXF0uS\nqqur9cQTT2Tl/FevXtXmzZt14cIFDQ0Nqb6+Xvfff78vjv9os997772+OfbXr19Xc3Oz/va3vykY\nDOrnP/+5wuGwL469NPr8Q0ND03P8vVnij3/8o9fU1OR5nuedPHnSW7duXYZXlH6pVMpbvXr1iG31\n9fXeiRMnPM/zvFdeecV77733MrG0tPrlL3/prVq1yvve977ned7oM1+8eNFbtWqVNzQ05PX19Xmr\nVq3yBgcHM7nsaXPr/O3t7d6vf/3rEbfJ1vkPHz7svfbaa57ned7ly5e9qqoq3xz/m2f/8ssvvaqq\nKu93v/udb479e++9523evNnzPM/74IMPvHXr1vnm2Hve6PNP1//7s+bUuh+vyd7T06P+/n7V1dXp\nhRde0KlTp3T27FlVVFRIkiorK9XV1ZXhVU6/+fPna9++fcOfnzlzZsTMx48f1+nTp1VeXq5QKCTH\ncVRcXDx8LQLrRpv/2LFjWrt2rZqbm5VIJLJ2/ieeeELr16+XJF27dk05OTm3/Z3P1uN/8+zXr19X\nKBTSmTNn9Kc//ckXx3758uXasWOHJOnvf/+75syZ45tjL42c/8KFC5ozZ860Hf9ZE/KxrsmezSKR\niOrq6vSrX/1K27Zt089+9rPhXwQhSbFYTH19fRlcYXqsWLFCOTn/vM74rTO7rqtEIjHi70M0Gs2a\nP4tb51+0aJFefvllHTx4UPPmzdPrr79+2/8P2TJ/fn6+otGoXNfV+vXrtWHDBt8c/1tn/+lPf6qH\nH35YjY2Nvjj2khQMBtXU1KSdO3dq1apVvjn2N9yY/9VXX9W3v/1tLVq0aFqO/6wJ+VSuyW5dcXGx\nvvOd7wx/XFhYqEuXLg3vTyQSvrj28M3H+cbMjuOM+K1P2fxnsXz5ci1cuHD4456eHsXj8ayd/7PP\nPtPzzz+v1atX68knn/TV8b91dr8de0lqbW3VH/7wBzU3NyuVSg1vz/Zjf8PN8y9btmxajv+sKaUf\nr8l++PBhtba2SpI+//xzua6rZcuW6cMPP5QkdXZ2qrw8+3+BzMKFC3XixAlJ/5y5rKxM3d3dGhwc\nVF9fn86fP6/S0tIMrzQ96urq9Je//EWS1NXVpQcffDBr5+/t7VVdXZ02btyo1atXS5IeeOABXxz/\n0Wb307F/55139Itf/EKSlJeXp2AwqIceeui2f+/8Mn8gENCPf/xjnT59WtLdHf9Z86r1FStW6P33\n39ezzz4r6atrsme7Z555Rps2bVJNTY2CwaBaW1tVWFio5uZmDQ0NqaSkRCtXrsz0MtOusbFRW7du\nHTFzIBBQbW2tampq5HmeGhoaFA6HM73UtNi2bZt27Nih3NxcFRUVafv27YrFYlk5/xtvvKErV65o\n//792rdvnwKBgLZs2aKdO3dm/fEfbfZNmzbptdde88Wx/9a3vqVNmzZp7dq1unr1qpqbm/X1r3/9\ntn/vsvHYS7fPv2XLFt17773avn37XR9/rrUOAIBhs+bUOgAAuHOEHAAAwwg5AACGEXIAAAwj5AAA\nGEbIAQAwjJADAGDY/wJocKLh1pUoWgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x129219128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with model:\n",
    "    \n",
    "    ν = pm.Exponential('ν_minus_one', 1/29.) + 1\n",
    "\n",
    "sns.distplot(np.random.exponential(30, size=10000), kde=False);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since PyMC3 parameterizes the Student-T in terms of precision, rather than standard deviation, we must transform the standard deviations before specifying our likelihoods."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "with model:\n",
    "    \n",
    "    λ1 = group1_std**-2\n",
    "    λ2 = group2_std**-2\n",
    "\n",
    "    group1 = pm.StudentT('drug', nu=ν, mu=group1_mean, lam=λ1, observed=y1)\n",
    "    group2 = pm.StudentT('placebo', nu=ν, mu=group2_mean, lam=λ2, observed=y2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Having fully specified our probabilistic model, we can turn our attention to calculating the comparisons of interest in order to evaluate the effect of the drug. To this end, we can specify deterministic nodes in our model for the difference between the group means and the difference between the group standard deviations. Wrapping them in named `Deterministic` objects signals to PyMC that we wish to record the sampled values as part of the output.\n",
    "\n",
    "As a joint measure of the groups, we will also estimate the \"effect size\", which is the difference in means scaled by the pooled estimates of standard deviation. This quantity can be harder to interpret, since it is no longer in the same units as our data, but the quantity is a function of all four estimated parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "with model:\n",
    "\n",
    "    diff_of_means = pm.Deterministic('difference of means', group1_mean - group2_mean)\n",
    "    diff_of_stds = pm.Deterministic('difference of stds', group1_std - group2_std)\n",
    "    effect_size = pm.Deterministic('effect size', \n",
    "                                   diff_of_means / pm.sqrt((group1_std**2 + group2_std**2) / 2))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we can fit the model and evaluate its output."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Assigned NUTS to group1_mean\n",
      "Assigned NUTS to group2_mean\n",
      "Assigned NUTS to group1_std_interval\n",
      "Assigned NUTS to group2_std_interval\n",
      "Assigned NUTS to ν_minus_one_log\n",
      " [-----------------100%-----------------] 2000 of 2000 complete in 22.8 sec"
     ]
    }
   ],
   "source": [
    "with model:\n",
    "    trace = pm.sample(2000, njobs=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can plot the stochastic parameters of the model. PyMC's `plot_posterior` function replicates the informative histograms portrayed in Kruschke (2012). These summarize the posterior distributions of the parameters, and present a 95% credible interval and the posterior mean. The plots below are constructed with the final 1000 samples from each of the 2 chains, pooled together."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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DmJhoPv74I5588jEWLvyCcuV8OXLkEBkZ6Xh6evL66+8QHn6K2bNnMHz448yb9xlOTtk/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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11c283b00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.plot_posterior(trace[1000:], \n",
    "                  varnames=['group1_mean', 'group2_mean', 'group1_std', 'group2_std', 'ν_minus_one'],\n",
    "                  color='#87ceeb');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Looking at the group differences, we can conclude that there are meaningful differences between the two groups for all three measures. For these comparisons, it is useful to use zero as a reference value (`ref_val`); providing this reference value yields cumulative probabilities for the posterior distribution on either side of the value. Thus, for the difference in means, 98.9% of the posterior probability is greater than zero, which suggests the group means are credibly different. The effect size and differences in standard deviation are similarly positive.\n",
    "\n",
    "These estimates suggest that the \"smart drug\" increased both the expected scores, but also the  variability in scores across the sample. So, this does not rule out the possibility that some recipients may be adversely affected by the drug at the same time others benefit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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vvtmLL7/8H+3bv86HH77HrVs3AdiyZROOjk70+mwdgZfOEHDuuGHfS7s2UbPr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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12caa4d68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.plot_posterior(trace[1000:], \n",
    "                  varnames=['difference of means', 'difference of stds', 'effect size'],\n",
    "                  ref_val=0,\n",
    "                  color='#87ceeb');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When `forestplot` is called on a trace with more than one chain, it also plots the potential scale reduction parameter, which is used to reveal evidence for lack of convergence; values near one, as we have here, suggest that the model has converged."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.gridspec.GridSpec at 0x129d48be0>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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O4ODgCw7cv39/lixZwpAhQ6hTpw6jRo0qdfmePXvo3r27a3wvrwv/rN2ZHE2b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\nyCA+Pp7k5GSef/55Nm3aREl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      "text/plain": [
       "<matplotlib.figure.Figure at 0x131542b70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.forestplot(trace[1000:], varnames=[v.name for v in model.vars])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "difference of means:\n",
      "\n",
      "  Mean             SD               MC Error         95% HPD interval\n",
      "  -------------------------------------------------------------------\n",
      "  \n",
      "  1.023            0.449            0.009            [0.188, 1.938]\n",
      "\n",
      "  Posterior quantiles:\n",
      "  2.5            25             50             75             97.5\n",
      "  |--------------|==============|==============|--------------|\n",
      "  \n",
      "  0.128          0.726          1.032          1.333          1.892\n",
      "\n",
      "\n",
      "difference of stds:\n",
      "\n",
      "  Mean             SD               MC Error         95% HPD interval\n",
      "  -------------------------------------------------------------------\n",
      "  \n",
      "  0.897            0.453            0.019            [0.024, 1.775]\n",
      "\n",
      "  Posterior quantiles:\n",
      "  2.5            25             50             75             97.5\n",
      "  |--------------|==============|==============|--------------|\n",
      "  \n",
      "  0.097          0.586          0.868          1.195          1.859\n",
      "\n",
      "\n",
      "effect size:\n",
      "\n",
      "  Mean             SD               MC Error         95% HPD interval\n",
      "  -------------------------------------------------------------------\n",
      "  \n",
      "  0.618            0.288            0.008            [0.024, 1.165]\n",
      "\n",
      "  Posterior quantiles:\n",
      "  2.5            25             50             75             97.5\n",
      "  |--------------|==============|==============|--------------|\n",
      "  \n",
      "  0.067          0.419          0.609          0.813          1.218\n",
      "\n"
     ]
    }
   ],
   "source": [
    "pm.plots.summary(trace[1000:], \n",
    "                 varnames=['difference of means', 'difference of stds', 'effect size'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References\n",
    "\n",
    "1.\tGoodman SN. Toward evidence-based medical statistics. 1: The P value fallacy. Annals of Internal Medicine. 1999;130(12):995-1004. doi:10.7326/0003-4819-130-12-199906150-00008.\n",
    "2.\tJohnson D. The insignificance of statistical significance testing. Journal of Wildlife Management. 1999;63(3):763-772.\n",
    "3.\tKruschke JK. Bayesian estimation supersedes the t test. J Exp Psychol Gen. 2013;142(2):573-603. doi:10.1037/a0029146."
   ]
  }
 ],
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