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    "# Two-way ANOVA\n",
    "\n",
    "ANOVA with interaction: \n",
    "\n",
    "*Measurement of fetal head circumference, by four observers in three fetuses, from a study investigating the\n",
    "reproducibility of ultrasonic fetal head circumference data.*\n",
    "\n",
    "Author:  Thomas Haslwanter, Date:    Feb-2017"
   ]
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  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
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   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import urllib\n",
    "from statsmodels.formula.api import ols\n",
    "from statsmodels.stats.anova import anova_lm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Get and format the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "slideshow": {
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   "source": [
    "inFile = 'altman_12_6.txt'\n",
    "url_base = 'https://raw.githubusercontent.com/thomas-haslwanter/statsintro_python/master/ipynb/Data/data_altman/'\n",
    "url = url_base + inFile\n",
    "data = np.genfromtxt(urllib.request.urlopen(url), delimiter=',')\n",
    "\n",
    "# Bring them in dataframe-format\n",
    "df = pd.DataFrame(data, columns=['hs', 'fetus', 'observer'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## ANOVA with interaction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
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     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                        df      sum_sq     mean_sq            F        PR(>F)\n",
      "C(fetus)               2.0  324.008889  162.004444  2113.101449  1.051039e-27\n",
      "C(observer)            3.0    1.198611    0.399537     5.211353  6.497055e-03\n",
      "C(fetus):C(observer)   6.0    0.562222    0.093704     1.222222  3.295509e-01\n",
      "Residual              24.0    1.840000    0.076667          NaN           NaN\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Programs\\WinPython-64bit-3.6.0.1Qt5\\python-3.6.0.amd64\\lib\\site-packages\\scipy\\stats\\_distn_infrastructure.py:875: RuntimeWarning: invalid value encountered in greater\n",
      "  return (self.a < x) & (x < self.b)\n",
      "C:\\Programs\\WinPython-64bit-3.6.0.1Qt5\\python-3.6.0.amd64\\lib\\site-packages\\scipy\\stats\\_distn_infrastructure.py:875: RuntimeWarning: invalid value encountered in less\n",
      "  return (self.a < x) & (x < self.b)\n",
      "C:\\Programs\\WinPython-64bit-3.6.0.1Qt5\\python-3.6.0.amd64\\lib\\site-packages\\scipy\\stats\\_distn_infrastructure.py:1814: RuntimeWarning: invalid value encountered in less_equal\n",
      "  cond2 = cond0 & (x <= self.a)\n"
     ]
    }
   ],
   "source": [
    "formula = 'hs ~ C(fetus) + C(observer) + C(fetus):C(observer)'\n",
    "lm = ols(formula, df).fit()\n",
    "print(anova_lm(lm))"
   ]
  },
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    "collapsed": true
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