docs/source/notebooks/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](https://twitter.com/twiecki) (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": true
   },
   "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)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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MoLQBADDC7XQARF/BnL+HbVp/nNI/bNMCADSMPW0AAIygtAEAMILSBgDACEobAAAjKG0A\nAIygtAEAMILSBgDACEobAAAjKG0AAIygtAEAMILSBgDACEobAAAjKG0AAIygtAEAMILSBgDACEob\nAAAjKG0AAIygtAEAMILSBgDACL9Ke/fu3crPz5ckHT16VKNGjdLo0aM1Y8YM1dXVRTQgAAA4r9HS\nXrJkiaZNm6Zvv/1WklRcXKzCwkK98sor8nq92rBhQ8RDAgAAP0q7TZs2Kikp8b3eu3evevfuLUnK\nzc3V1q1bI5cOAAD4uBv7gQEDBujYsWO+116vVy6XS5KUlJSkioqKRmeSnp4oScrMTAk2Z9RZyuqk\nYJaTpWVrKSuA+Ndoaf+vJk3+s3NeVVWl1NTURn+nrKxamZkpOnWq8YKPBZayOi3Q5WRp2UYzKx8O\nAPgj4LPHO3furO3bt0uSNm/erF69eoU9FIDYxsmpgDMCLu2ioiKVlJRoxIgRqq2t1YABAyKRC0CM\n4uRUwDl+HR7PysrSqlWrJElt27bVsmXLIhoKQOy6cHLqww8/LOnSk1Pfe+895eXlORkRiFsB/00b\nwJUtXCenut0JEcvYkHg9fyBexxWqWFwuoWSitAGEJNiTU51g6UTIQMTruMIh1paLP+9VQ6XObUwB\nhISTU4HoobQBhISTU4Ho4fA4gIBxcirgDPa0AQAwgtIGAMAIShsAACMobQAAjKC0AQAwgtIGAMAI\nShsAACMobQAAjKC0AQAwgtIGAMAIShsAACMobQAAjKC0AQAwgtIGAMAIShsAACMobQAAjKC0AQAw\ngtIGAMAIShsAACMobQAAjKC0AQAwgtIGAMAIShsAACMobQAAjKC0AQAwgtIGAMAIt9MBrgQFc/7u\ndAQAQBxgTxsAACMobQAAjKC0AQAwgtIGAMAIShsAACMobQAAjKC0AQAwgtIGAMAIShsAACMobQAA\njKC0AQAwgtIGAMAIShsAACN4yhcAIG6F6ymLf5zSPyzTCRV72gAAGEFpAwBgBKUNAIARlDYAAEZQ\n2gAAGBH02eM/+9nPlJKSIknKyspScXFx2EIBAIBLBVXa3377rSRp6dKlYQ0DAAAuL6jS3rdvn775\n5hsVFBTI4/HowQcfVPfu3cOdDYAhHH0DIi+o0m7evLnGjx+vO+64Q0eOHNGECRP01ltvye2uf3Lp\n6YmSpMzMlOCTRpmlrE4KZjlZWraWsjqJo29AdARV2m3btlV2drZcLpfatm2rtLQ0nTp1SldffXW9\nP19WVq3MzBSdOlURUthosZTVaYEuJ0vLNppZrX844OgbEB1BlfaaNWt04MABzZw5U1988YUqKyuV\nmZkZ7mwAjAjm6JvbnRDllOdZ/4B0ObEwrtsfet3pCBETzuUbyrSCKu1hw4bpkUce0ahRo+RyuTR7\n9uzLrpwA4l8wR9+cYOlITyDidVyxJFzL15/3qqFSD6ppmzVrpnnz5gXzqwDiEEffgOhg9xhAyDj6\nBkQHaxWAkHH0DYgObmMKAIARlDYAAEZQ2gAAGEFpAwBgBKUNAIARlDYAAEZQ2gAAGEFpAwBgBKUN\nAIARlDYAAEZQ2gAAGEFpAwBgBKUNAIARlDYAAEZQ2gAAGEFpAwBgBKUNAIARlDYAAEa4nQ4AAECs\nK5jz97BM5415g0P6ffa0AQAwgtIGAMAIShsAACMobQAAjKC0AQAwgtIGAMAIShsAACMobQAAjKC0\nAQAwgjuiAfUI192PJOmPU/qHbVoArmyUNgBc4cL5IRWRxeFxAACMoLQBADCC0gYAwAhKGwAAIyht\nAACMoLQBADCC0gYAwAhKGwAAIyhtAACMoLQBADAiZm5jyr2ebQrX+8Z7BgCNi5nSBoD/xgdC4FIc\nHgcAwAhKGwAAIyhtAACMoLQBADCC0gYAwAhKGwAAIyhtAACMCOo67bq6Os2cOVP79+9Xs2bN9OST\nTyo7Ozvc2QAYwTYBiI6g9rTXr1+vmpoarVy5Ug899JDmzJkT7lwADGGbAERHUKW9c+dO3XzzzZKk\n7t27a8+ePWENBcAWtglAdAR1eLyyslLJycm+1wkJCfJ4PHK7659cZmbKRf9fnzfmDQ4mSsQ0lDVQ\nsTY2NI73LDDBbhMaEqn3IJzrdiwJZVz8e4+uUN6roPa0k5OTVVVV5XtdV1d32ZUTQPxjmwBER1Cl\n3aNHD23evFmStGvXLnXo0CGsoQDYwjYBiA6X1+v1BvpLF84UPXDggLxer2bPnq127dpFIh8AA9gm\nANERVGkDAIDo4+YqAAAYQWkDAGAEpQ0AgBGUNgAARkTsQsr169dr27ZtqqioUGpqqnr27KmBAwfK\n5XJFapZB++STTy7J2rVrV6djAQhRPK7bH374oXr16qW6ujotX75cn3zyibp06aLhw4crISHB6XiI\nsIicPf7444+rrq5Oubm5SkpKUlVVlTZv3iyPx6P/+7//C/fsQjJ//nyVlpbqpptu8mXdsmWLOnfu\nrMLCQqfjXVZZWZkqKyuVkpKitLQ0p+NcVm1trfbv3+/baLZv317NmjVzOtZlWcuLy7O6bjfm5z//\nuV566SU99dRTqqqq0i233KL3339fZ8+e1YwZM5yOFzIr27ZgnDlzRocPH1a7du2CHltE9rQ//fRT\nLVu27KKv3XLLLRo5cmQkZheSrVu36pVXXrnoa/n5+Ro+fHhMrtilpaV64oknVFdXp8TERFVVVcnr\n9Wr69Onq0aOH0/EusnHjRs2bN085OTm+rIcOHdKDDz6oW2+91el4l7CWFw2ztm4HqrS0VC+//LIk\nqV+/fsrPz3c4UWgsbdsC8ctf/lKLFy/Wxo0bVVxcrE6dOungwYN68MEH1b9//4CnF5HSrqur8x3C\nuWDHjh1q2rRpJGYXEo/Ho2PHjikrK8v3tWPHjqlJk9j8c39xcbFKSkp09dVX+7524sQJPfDAA1q9\nerWDyS61aNEiLV++/KJ7UldUVGjs2LExWYLW8qJh1tZtf508eVLvvPOOkpOTfeP74osvdPbsWaej\nhcTSti0QF96XJUuWaPny5WrVqpWqqqr0i1/8InZKe86cOSouLtZDDz0kr9er2tpade7cWU8++WQk\nZheSRx99VPfdd59qamqUmJiob775Rk2bNtXjjz/udLR6eTyei/5RS9LVV18dk+cK1NbWqnnz5hd9\n7Tvf+U5MZpXs5UXDrK3b/nr44Yf18ccfy+v1av369Ro2bJhGjRoVk9vXQFjatgXC4/FI0kWH+5OS\nklRXVxfU9CJS2ufOnVPTpk3Vs2dP5efnq6ioSIcPH9bevXuVnZ0diVkGLS0tTa1atdKePXtUUVGh\njh07Kicn55J/PLGiX79+Gjt2rPr27auUlBRVVlbqvffeU25urtPRLjFixAgNGTJEPXv29GXduXNn\nzB7Gs5YXDbO2bvurQ4cOWrFihQ4dOqQtW7bozTffVLdu3dS+fXuno4XE0rYtEC1bttRPf/pTlZeX\n66WXXtKIESNUWFio7t27BzW9iJyINmbMGN1zzz2qqKjQ9OnTtXbtWqWkpGjcuHFauXJluGcXkvHj\nx+uxxx5TTk6Odu3apY0bN+rWW2/V73//ey1evNjpePX6+OOPtXPnTlVVVSk5OVnXX3+9unTp4nSs\nep0+fVqlpaW+Rzd27dpVGRkZTse6LGt5cXkW121/xOu4JFvbtkB99dVX8ng8ysjICOnDSET+uOPx\neHTjjTfqxz/+sdLS0vS9731PiYmJMfmovsrKSuXk5EiSunfvro8++kjXXXedysvLnQ3WgBMnTujw\n4cP65z//qSNHjuizzz5TrN5CPiMjQ/3799egQYPUv3//mC7AM2fO6IUXXtDu3bt18803+/LOnz/f\n6WgIgsV12x/xOi7J1rYtEOvXr9eCBQs0b948FRcX+06yC0ZEWrR169b69a9/rXPnzikpKUnPPvus\nkpOTlZmZGYnZhSQrK0vTp09Xbm6uNm7cqE6dOuntt99WixYtnI5Wr8tdTrdly5aYu5yuoaMqI0aM\niGIS/zz88MPKy8uTx+PRmDFjtHjxYrVu3Vo7duxwOhqCYG3d9le8jsvSti0Q4R5XRA6Pezwebdq0\nSTk5OUpKStKLL76oli1b6q677lJiYmK4ZxeSmpoarV69WgcPHlSnTp00dOhQ/eMf/1B2drbS09Od\njneJMWPGXHI5nSSNHDlSK1ascCDR5RUXF+vdd9/VoEGDLvnevffe60Cihl24/lWSPvroIz3++ONa\nunSpJk2apKVLlzqcDoGytm77K17HZWnbFohwjysie9put1u33HKL7/WUKVMiMZuwaNasme68886L\nvhbsCQLRUN/ldB988EFMXk73yCOP6NChQ8rNzTVxF6pz585p//79uvbaa9WjRw/96le/0sSJE1Vd\nXe10NATB2rrtr3gdl6VtWyDCPS6ep23MZ599puLiYu3du1der1dNmjRR586dVVRU5Ps7Vyw5c+aM\nqqurL7pWNlZ98sknmj17tp599lnf395ff/11zZ49W9u3b3c4HRDfrG3b/BXucVHaQCPq6urM35AD\nQHyIvdO50aD8/HzV1tbW+71Y+7tPfVm9Xq9cLlfMZZVsLVsg3sTr+hfucbGnbczu3bs1bdo0Pf/8\n85c80ad169YOpaqfpaySvbxAPInX9S/c40qYOXPmzDBlQxRcddVVqq6ulsfjUffu3ZWamur7X6yx\nlFWylxeIJ/G6/oV7XOxpAwBgBGfXAABgBKUNAIARlDYAAEZQ2gAAGEFpAwBgxP8D+QNg21wuTLwA\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3b7f246358>"
      ]
     },
     "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",
    "$$f(x|\\mu,\\lambda,\\nu) = \\frac{\\Gamma(\\frac{\\nu + 1}{2})}{\\Gamma(\\frac{\\nu}{2})} \\left(\\frac{\\lambda}{\\pi\\nu}\\right)^{\\frac{1}{2}} \\left[1+\\frac{\\lambda(x-\\mu)^2}{\\nu}\\right]^{-\\frac{\\nu+1}{2}}$$\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",
    "    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": true
   },
   "outputs": [],
   "source": [
    "σ_low = 1\n",
    "σ_high = 10\n",
    "\n",
    "with model:\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 $\\nu$ 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": {},
   "outputs": [
    {
     "data": {
      "image/png": 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L+9I3AAAYHxQ1AAAGo6gBADAYRQ0AgMEoagAADEZRAwBgMIoaAACDUdQAABiMogYAwGAU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\nAQAwGEUNAIDB/heDQao3Jbh1EgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3b7b6aff60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with model:\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",
    "    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": true
   },
   "outputs": [],
   "source": [
    "with model:\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 / np.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": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using ADVI...\n",
      "Average Loss = 231.07:   8%|▊         | 15144/200000 [00:03<00:44, 4112.61it/s]\n",
      "Convergence archived at 15400\n",
      "Interrupted at 15,400 [7%]: Average Loss = 243.61\n",
      "100%|██████████| 2500/2500 [00:10<00:00, 236.95it/s]\n"
     ]
    }
   ],
   "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": {},
   "outputs": [
    {
     "data": {
      "image/png": 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+2RPAmz2RyTBa0uXsbAsLC+2L693cHIy1SZNVHPsM5GO/I6LzZz1kFBIALi72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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3b5c2767f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.plot_posterior(trace, 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, 99.4% 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": {},
   "outputs": [
    {
     "data": {
      "image/png": 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TsCvlxrYvBpMYfvOB752amsKYMR8SGRlh9JrkghCPlpyhEg9No9EQFPQzS5Ys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\nF1REREREREQycUFFREREREQk038B4a/ayfHDed0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3b55046c18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.plot_posterior(trace, 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": {},
   "outputs": [
    {
     "data": {
      "image/png": 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7tmzZoo4dOyojI0NHjhxRt27dNG7cOM2aNUupqamy2Wzq3LmzJk+eLC8vL7Vu3VqJiYkK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\nRhEjAADAKGIEAAAY9f8wRy/zd1WGfQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3b551581d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.forestplot(trace, varnames=['group1_mean',\n",
    "                               'group2_mean']);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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HxCBffvmFwsICVaVKLbNLAQDAcgggBhk+fAh3wwUAwAUCiEG6deuhkBB/s8sAPEZGhpe2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\nvBo0aKAffvhBkjRo0CCNHTt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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3b5512b588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.forestplot(trace, varnames=['group1_std',\n",
    "                               'group2_std',\n",
    "                               'ν_minus_one']);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>mc_error</th>\n",
       "      <th>hpd_2.5</th>\n",
       "      <th>hpd_97.5</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>difference of means</th>\n",
       "      <td>1.016574</td>\n",
       "      <td>0.435722</td>\n",
       "      <td>0.005570</td>\n",
       "      <td>0.152392</td>\n",
       "      <td>1.870192</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>difference of stds</th>\n",
       "      <td>0.922935</td>\n",
       "      <td>0.441076</td>\n",
       "      <td>0.007856</td>\n",
       "      <td>0.079557</td>\n",
       "      <td>1.782849</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>effect size</th>\n",
       "      <td>0.604915</td>\n",
       "      <td>0.272488</td>\n",
       "      <td>0.004162</td>\n",
       "      <td>0.083181</td>\n",
       "      <td>1.151870</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                         mean        sd  mc_error   hpd_2.5  hpd_97.5\n",
       "difference of means  1.016574  0.435722  0.005570  0.152392  1.870192\n",
       "difference of stds   0.922935  0.441076  0.007856  0.079557  1.782849\n",
       "effect size          0.604915  0.272488  0.004162  0.083181  1.151870"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pm.df_summary(trace,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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