notebooks/06_Anscombes_Quartet.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Anscombe's Quartet"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In a 1973 paper, *Graphs in Statistical Analysis*, published in *The American Statistician*, Vol. 27, No. 1. (Feb., 1973), pp. 17-21, statistician Francis Anscombe provided the briefiest of abstracts: *\"Graphs are essential to good statistical analysis\"*.\n",
    "\n",
    "His paper opened with a brief meditation on *the usefulness of graphs*:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<em>\"Most textbooks on statistical methods, and most statistical computer programs, pay too little attention to graphs. Few of us escape being indoctrinated with these notions:\n",
    "\n",
    "\n",
    "1. numerical calculations are exact, but graphs are rough; \n",
    "2. for any particular kind of statistical data there is just one set of calculations constituting a correct statistical analysis; \n",
    "3. performing intricate calculations is virtuous, whereas actually looking at the data is cheating. \n",
    "\n",
    "\n",
    "A computer should make both calculations and graphs. Both sorts of output should be studied; each will contribute to understanding. \n",
    "\n",
    "Graphs can have various purposes, such as: (i) to help us perceive and appreciate some broad features of the data, (ii) to let us look behind those broad features and see what else is there. Most kinds of statistical calculation rest on assumptions about the behavior of the data. Those assumptions may be false, and then the calculations may be misleading. We ought always to try to check whether the assumptions are reasonably correct; and if they are wrong we ought to be able to perceive in what ways they are wrong. Graphs are very valuable for these purposes.\n",
    "\n",
    "Good statistical analysis is not a purely routine matter, and generally calls for more than one pass through the computer. The analysis should be sensitive both to peculiar features in the given numbers and also to whatever background information is available about the variables. The latter is particularly helpful in suggesting alternative ways of setting up the analysis. Thought and ingenuity devoted to devising good graphs are likely to pay off. Many ideas can be gleaned from the literature...\"</em>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean=7.50, std=1.94, r=0.82\n",
      "mean=7.50, std=1.94, r=0.82\n",
      "mean=7.50, std=1.94, r=0.82\n",
      "mean=7.50, std=1.94, r=0.82\n"
     ]
    },
    {
     "data": {
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ALB0s1opV3AEyt8hUtaqE77YBsvRwURTFJu4AmVtkuihKtUr7d9sAWfzcIlOJ\n2749fyZ97LH5Qj19Onz96/Ctb00s6e0WmapWaf5uu4VlOjkMrgkxQCZVBwNk6Wax1l4pxwpkLS0t\n1Nfnt8gcOlToFpmqdAPf7Vwux7Zt2wCYOnVqIt9tA2SVwUENjcvQLSyXLs0HyG68ER59NP6lQjOZ\nDB0dHYBbZKq6ZDIZ5s+fz5o1a9ixYwc7duxgzZo1zJ8/v6zf7cItLE86Kb+F5dVXW6jTxoCZipbU\nCmSVcHlLqRgwq05JB8wMkJWfu26p5JJegSyTyXDccceV/o2kMhkImDU0NAzeF0Igm83S3d1d0u+7\nK5BVpliOoUIImRDCNSGEZ0MIO/r/e00IwWO0Cved78Ds2XDddbBrVz5A9sQT8KEPjV6oc7kcXV1d\ndHV1kcvlyttgSSPavDk/MnbSSflC3dQE3/8+3HuvhboSxHVmfSUwHzgXeAw4BrgH6AWujek9VEZ7\nGyCrhIUepKSVMzxpgKw6xDJnHUL4FvD7KIrOH3Lf3cD+URR9YITnO8+VUhNZgSzpebhq5Jx19So8\nsN1vv/24+eabYz2wdQWy9EjLnPWPgfkhhDdGUfRUCOEtwBw8q64oEw2QJTkPJ1Wa5uZmvv/977Nk\nyRIA5s6dS11Mm7oXBshe97r8bQNklSuWb0YURdeFEOqBVSGEXcAk4Nooiu6M4/VVWsUGyGo5lS3F\nrfDM+q677oplymikANmNN8JBB020xUpSXMPgc4HrgE8Dq4Bm4Bbg01EUfXWE5zt0lhKFK5BdcsnI\nK5AVMxftMHj8HAavTqXoK65Alm5pGQa/Hrg+iqIH+28/HkKYASwAdivWAO3t7YN/bm1tpbW1Naam\nqBjjCZDlcjna2toABoe4oyiira1t2C+WgUVM2trayGazwKvzcBbq4nR2dtLZ2Zl0M8bFvjx+3d3d\nbN26lWnTpg3eF0Jgy5Yt454yMkCWTnH35bjOrH8PfC6Koi8NuW8BcGEURU0jPN+j8YTsTYCsq6uL\nefPmDZuLhvyqYosWLdrtF4vD5fHxzLo6/epXv+K8887joIKx6Y0bN3L33Xfzx3/8x0W9jgGyypGW\nM+tvAVeGENYCjwPHApcBd8f0+opBuVYgcxETaWybNm3iwAMPHDYMvmnTpqL+rgGy2hNXsf5r4Brg\nduAgYANwZ/99StieAmRRlKOra89nwW6oIcUrk8nwute9jtWrVw8OhW/ZsoXXve51Y45EGSCrTa4N\nXuX2FCBvkHvZAAALS0lEQVQbzwIm5bgmVLtzGLw6DQTMoigatutWCGHUgJkBsso20b5ssa5SYwXI\n9iaN6lx0+Vmsq1exB8AGyKqDxVrDFBsgG29oTMmwWFe3sQ6ADZBVj7QEzJQChQGyE0/cwhVXPM/7\n3z/bs2AphUYLYxogUyHPrKtAYYDsgANe4aCDrmHfff+TEFzApJJ5Zl3d+vr6dltu1ABZdXIYvMYV\nBsjmz49YseJPqKvbNmYRNjSWfhbr6rV06VIuv/xyGvuXC9yypYc3v/lefvCDVsAAWbWxWNeowgDZ\nMcfk56rr6lzApJpYrKtTX18fM2bMoKmpadhB9fLlsG3bD1iwYJIBsioz0b7sb+YK09eXY8GCdcya\n1cfSpfkA2Q03wKOPwvHHj//1BubMjjvuOAu1VCZLliyhsbFxsFBD/pf59Olb+cIX/o2rr7ZQazgD\nZhXkwQef5MILd9HTMxuA/ff/Gf/yLw28//2zB5/jAiZS+uVyOUYakQjhf5g+vTeBFintPJWqANu3\nwxVXRJx1VhM9PbPZZ5/fM3v23/PWty7g+usvJZfLDT53YDMNyA99Z7NZoiiio6PDM2cpJd74xjey\nadOmYQV7YLnRN77xjQm2TGnlmXXKvRogC0CGQw/9Jkcd9WXq6rYBgWw2u9suPc3NzSxbtsy5aCml\n6urqmDZt2m7LjU6bNo260XbUUU3zW5FSGzZAWxs88ED+9syZ28lk5jN9+m+K+vtupiGlV0tLC42N\njRx88MGDy40effTR9Pb2Ol2lEXm6lRK5XI6uri5+9asubr89x5velC/UAwGylSuncMgh63YbNnMu\nWqpMuVyONWvW0NvbS29vL6tXrx42pSUNZbFOgeXLlzNnzhzOOed6TjllMn/91xmy2fwWlqtWwac/\nDfvu61y0VC26u7vJ5XI0NTUxZcoUpkyZwsyZM4ddSikN5TB4wnK5HJ/85BWsWzePF174CFFUxz77\n/J6mplt46KF2Jk16tRA7Fy1VlxAC9fX1STdDFcBinbDbblvDL3/5FXbuPAzIDQbItm/fwPLlf7bb\nvLNz0VLl8xJLjZenZSU2MBfd1dU1bD5qwwY46yz41KdmsnPnYUyduoZjj/1rZs26pT/pLalaeYml\nxsvlRkuocO3t+vp6brqpg1/8opkrr4RsFl772ohDDrmDww77OpMm5Yu5G2pogMuNVjeX+60drg2e\nUiPtatXTM4Onn/704ApkZ54Jt98Omze7oYZGZrGWqoP7WadUd3c3PT09NDQ0sGvXvqxde+5ggOyA\nA3Zyxx378MEP5nfKOuIIg2OSpNFZrPdSscNXL7/8Dp55po3e3ulAjgMPXMqDD87i5JOHh0gMjkm1\nx2FwFcth8L0w0lx0R0fHsGHr9etztLR08rvf5YfCp05dw6xZN9LQ8IRz0Sqaw+DVq5jfI6oezlmX\n2Uhz0UMDYZDhzjsZDJBlMjuYPv1ODjrofurrpzgXrXGxWFensX6PeDBffZyzLrOhc9EDQshvqPHg\ng0/Q0TGbn/88f/+ZZ8Ktt+7Lpk0nASc5zCUJePX3SH19/bBgaU9Pz24b80hgsY7Frl37sn79J/nY\nx97Crl0wfTrceiv9AbIMRx5px5M03I4dO3jppZcGd9168cUXh50ESEM5DF5grMBH4fDV0ABZCBGX\nXBK49lpobCx701WFHAavTn19fcyYMYOmpqZhw+CrV69m7dq1bpNZhRwGj1ExgY+BlYfmz7+aJ5/8\nK7ZseQ8AM2fu4F/+5TUcf3wiTZdUQVasWMGBBx44WKgh/8v8wAMPZMWKFQ6DazdOoPbL5XK0tbUB\n0NDQMDgc1dbWNmyZ0FwOfvazZlat+je2bHkPU6bs4vrrczz+uIVaUvFGyq+YadFo/Gb0Gwh8FB7p\nDgQ+AFauhBNOgEsugWw2cOaZ8OSTk/i//zfD5MlJtVxSpWlpaaGurm63/enr6urcyEMjchi8CL29\ngSuvhIULoa+vMECWdOskVaJcLsfq1asHA2abN2/m0EMPTbhVSivPrPsNbFmXy+Xo6emhp6eHXC7H\nzp2ncvbZLVx3HezaBZdeCk88AR/6kIVa0t7p7u4ml8vR1NTElClTmDJlCjNnzhwWcJWG8sy6XyaT\nYf78+Vx++eU0NjYCgbVr4eWXPwoEjjkGFi3CeWlJsQkhUF9fn3QzVAG8dKvfaCsK/frXcOWVy7js\nMuelVX5eulWdXMGs9ky0L/uN6DdawGzGjB5OPbXbQi0pNgOXgAJks1my2SxRFNHR0WGh1ogcBh+D\n89KSSqG52a1xVTyHwfs5LKU0chhcqg4Og8fEYSlJUlp5Zl3AzeCVJp5ZS9XB/aylKmaxlqqDw+CS\nJFU5i7UkSSlXkmIdQlgQQsiFEG4pxetLklRLYi/WIYR3AhcDK+J+bUmSalGsxTqE0AjcB5wPbInz\ntSVJqlVxn1kvAh6IouiHMb+uJEk1K7blRkMIFwNHAX8Z12tKkqSYinUIYRZwLXBCFEW5Yv5Oe3v7\n4J9bW1tpbW2NoylSRevs7KSzszPpZoyLfVnaXdx9OZZFUUIIHwe+Agwt1JOACNgFTI2i6JUhz3ch\nBakILooiVYdUrGAWQmgA/qjg7ruBp4Froyh6ouD5dnCpCBZrqTpMtC/HMgweRVEWWDX0vhDCNmBT\nYaGWJEnjU8oVzDzcliQpBm7kIaWYw+BSdXAjD0mSqpzFWpKklLNYS5KUchZrSZJSzmItSVLKWawl\nSUo5i7UkSSlnsZYkKeUs1pIkpZzFWpKklLNYS5KUchZrSZJSzmItSVLKWawlSUo5i7UkSSlnsZYk\nKeUs1gKgs7Mz6SZIion9ufpYrAXYuaVqYn+uPhZrSZJSzmItSVLKhSiKyv+mIZT/TaUKFUVRSLoN\no7EvS8WbSF9OpFhLkqTiOQwuSVLKWawlSUo5i7UkSSlX1mIdQrgkhPBsCGFHCOHREMKJ5Xz/WhdC\nOCmE8FAI4YUQQi6EcO4Iz2kPIawPIWwPITwSQnhLEm2tFSGEBSGEX4YQtoYQNoYQ/iOEMHuE56Xu\nc7E/J8v+nC6l7stlK9YhhLOADuALQDPwU+A7IYQ/KlcbxH7ASuBvgO2FD4YQrgAuAy4F/hewEfiv\nEMLUcjayxrwbuA14F3AK0Ad8P4QwbeAJafxc7M+pYH9Ol9L25SiKyvID/By4o+C+p4Fry9UGf4b9\n2/cA5xbc91vgyiG3pwBZ4OKk21srP8DU/k5+Zpo/F/tzun7sz+n7ibsvl+XMOoQwGTgO+K+Chx4G\n/nc52qA9CyEcCRzCkM8oiqJe4Ef4GZVTA/kRr82Qzs/F/px+afze1KBY+3K5hsEPACYBLxXc/xL5\nxit5hwARfkZJuxn4b+Bn/bfT+LnYn9Mvjd+bWhNrX66LtWmS9loI4SbyR9gnRP1jZJIqTyn6crnO\nrH8P7AIOLrj/YODFMrVBe/YiEPAzSkQI4Z+As4BToihaN+ShNH4u9uf0S+P3piaUqi+XpVhHUfQK\n0AWcXvDQ6cBPytEG7VkURc+R/8IMfkYhhCnASfgZlVQI4WZe7dzPDH0sjZ+L/Tn90vi9qQWl7Mvl\nHAa/Cbg3hPAr8g2bD0wH7ix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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10873e350>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "####!/usr/bin/env python\n",
    "# -*- coding: utf-8 -*-\n",
    "\"\"\"\n",
    "Created on Sat Nov 28 13:41:39 2015\n",
    "\n",
    "@author: jim_byers\n",
    "# Heavily leveraged from matplotlib example with slight changes:\n",
    "# http://matplotlib.org/examples/pylab_examples/anscombe.html\n",
    "# Description and Anscrombe quote are from:\n",
    "#    http://nbviewer.ipython.org/github/psychemedia/ou-tm351/blob/master/notebooks-RFC/Anscombe's%20Quartet%20%5Bopen%5D.ipynb\n",
    "\n",
    "\"\"\"\n",
    "\n",
    "from __future__ import print_function\n",
    "\"\"\"\n",
    "Edward Tufte uses this example from Anscombe to show 4 datasets of x\n",
    "and y that have the same mean, standard deviation, and regression\n",
    "line, but which are qualitatively different.\n",
    "\n",
    "matplotlib fun for a rainy day\n",
    "\"\"\"\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "%matplotlib inline\n",
    "plt.rcParams['figure.figsize'] = (8, 6)\n",
    "plt.rcParams['font.size'] = 14\n",
    "\n",
    "# Implement Anscombe dataset values into arrays\n",
    "x = np.array([10, 8, 13, 9, 11, 14, 6, 4, 12, 7, 5])\n",
    "y1 = np.array([8.04, 6.95, 7.58, 8.81, 8.33, 9.96, 7.24, 4.26, 10.84, 4.82, 5.68])\n",
    "y2 = np.array([9.14, 8.14, 8.74, 8.77, 9.26, 8.10, 6.13, 3.10, 9.13, 7.26, 4.74])\n",
    "y3 = np.array([7.46, 6.77, 12.74, 7.11, 7.81, 8.84, 6.08, 5.39, 8.15, 6.42, 5.73])\n",
    "x4 = np.array([8, 8, 8, 8, 8, 8, 8, 19, 8, 8, 8])\n",
    "y4 = np.array([6.58, 5.76, 7.71, 8.84, 8.47, 7.04, 5.25, 12.50, 5.56, 7.91, 6.89])\n",
    "\n",
    "\n",
    "def fit(x):\n",
    "    return 3 + 0.5*x\n",
    "\n",
    "# plt.set_marker('circle')\n",
    "xfit = np.array([np.amin(x), np.amax(x)])\n",
    "\n",
    "plt.subplot(221)\n",
    "plt.plot(x, y1, 'ks', xfit, fit(xfit), 'r-', lw=2, marker='o', markerfacecolor = '.25', markeredgecolor = '0', color='b')\n",
    "plt.axis([2, 20, 2, 14])\n",
    "plt.setp(plt.gca(), xticklabels=[], yticks=(4, 8, 12), xticks=(0, 10, 20))\n",
    "plt.text(3, 12, 'I', fontsize=20)\n",
    "\n",
    "plt.subplot(222)\n",
    "plt.plot(x, y2, 'ks', xfit, fit(xfit), 'r-', lw=2, marker='o', markerfacecolor = '.25', markeredgecolor = '0', color='b')\n",
    "plt.axis([2, 20, 2, 14])\n",
    "plt.setp(plt.gca(), xticklabels=[], yticks=(4, 8, 12), yticklabels=[], xticks=(0, 10, 20))\n",
    "plt.text(3, 12, 'II', fontsize=20)\n",
    "\n",
    "plt.subplot(223)\n",
    "plt.plot(x, y3, 'ks', xfit, fit(xfit), 'r-', lw=2, marker='o', markerfacecolor = '.25', markeredgecolor = '0', color='b')\n",
    "plt.axis([2, 20, 2, 14])\n",
    "plt.text(3, 12, 'III', fontsize=20)\n",
    "plt.setp(plt.gca(), yticks=(4, 8, 12), xticks=(0, 10, 20))\n",
    "\n",
    "plt.subplot(224)\n",
    "\n",
    "xfit = np.array([np.amin(x4), np.amax(x4)])\n",
    "plt.plot(x4, y4, 'ks', xfit, fit(xfit), 'r-', lw=2, marker='o', markerfacecolor = '.25', markeredgecolor = '0', color='b')\n",
    "plt.axis([2, 20, 2, 14])\n",
    "plt.setp(plt.gca(), yticklabels=[], yticks=(4, 8, 12), xticks=(0, 10, 20))\n",
    "plt.text(3, 12, 'IV', fontsize=20)\n",
    "\n",
    "# verify the stats\n",
    "pairs = (x, y1), (x, y2), (x, y3), (x4, y4)\n",
    "for x, y in pairs:\n",
    "    print('mean=%1.2f, std=%1.2f, r=%1.2f' % (np.mean(y), np.std(y), np.corrcoef(x, y)[0][1]))\n",
    "\n",
    "plt.show()"
   ]
  },
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   "execution_count": null,
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   "source": []
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  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
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   },
   "outputs": [],
   "source": []
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