{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Are the scores not really normally distributed?\n",
    "\n",
    "I am trying to apply a statistical normalization on some scores. The normalization scheme require the  scores to be normally distributed. \n",
    "I'am the scipy.stats.normaltest found here:\n",
    "https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.normaltest.html\n",
    "According to the test, the scores are not normally distributed.\n",
    "But watching the qqplot, they seems normally distributed.\n",
    "\n",
    "More the paper applying the normalization scheme shows a qqplot of normally distributed scores which seems visually less incordance with the theoritical values: right plot here: https://pubs.acs.org/appl/literatum/publisher/achs/journals/content/jmcmar/2004/jmcmar.2004.47.issue-1/jm030161o/production/images/large/jm030161of00002.jpeg \n",
    "\n",
    "Interestingly I tried a transmation to normalize the scores:\n",
    "x = x - 2*x  # to transform scores into positive value to apply the log function\n",
    "log_data = np.log(x)\n",
    "Still the scores are not normally distributed according to the test.\n",
    "Am I using the wrong test?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "15.707656653124452 0.0003882627229176248\n",
      "p = 0.000388263\n",
      "The null hypothesis (x comes from a normal distribution) can be rejected.\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from scipy import stats\n",
    "from statsmodels.graphics.gofplots import qqplot\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "scores = [-11.4, -9.2, -11.2, -7.8, -7.8, -7.8, -9.3, -8.6, -8.7, -9.6, -7.4, -8.9, -7.8, -8.0, -7.5, -8.6, -9.2, -9.0, -8.6, -6.8, -9.1, -8.8, -7.7, -9.3, -7.6, -7.4, -8.3, -8.5, -10.0, -8.8, -8.1, -9.5, -8.5, -9.4, -7.7, -8.9, -6.5, -6.5, -6.2, -9.4, -8.2, -7.6, -7.2, -6.2, -8.2, -7.4, -7.5, -8.3, -7.3, -7.9, -6.5, -7.5, -7.2, -7.5, -7.3, -7.9, -7.5, -7.0, -6.9, -7.9, -9.1, -7.4, -8.1, -6.2, -7.2, -7.1, -7.0, -7.4, -6.9, -6.8, -7.2, -8.0, -6.9, -7.2, -7.0, -6.0, -7.5, -8.8, -11.6, -7.6, -7.7, -7.0, -8.7, -8.5, -8.8, -8.9, -6.7, -8.6, -7.5, -7.7, -7.3, -8.5, -8.1, -8.2, -8.3, -7.0, -7.8, -8.0, -6.9, -8.6, -8.8, -7.4, -7.7, -7.7, -8.9, -8.6, -8.6, -8.5, -8.4, -9.5, -7.5, -8.7, -6.2, -6.3, -6.6, -7.1, -7.7, -7.7, -6.7, -6.2, -7.4, -6.7, -6.6, -7.0, -7.0, -6.7, -5.9, -6.5, -6.3, -7.3, -7.1, -7.5, -7.3, -5.8, -7.1, -7.3, -6.1, -7.2, -7.2, -6.0, -6.9, -6.2, -6.7, -7.7, -6.8, -6.7, -6.5, -7.5, -6.1, -6.4, -5.9, -5.9, -5.3, -6.3, -6.3, -5.7, -5.7, -4.8, -5.8, -5.6, -5.5, -6.4, -6.1, -6.0, -5.1, -5.5, -5.7, -6.0, -5.5, -6.1, -5.9, -5.2, -5.4, -5.9, -6.6, -5.4, -5.8, -4.9, -5.5, -5.3, -5.8, -6.2, -5.3, -5.6, -5.5, -6.1, -6.4, -5.9, -5.5, -5.3, -7.6, -8.3, -8.4, -7.2, -6.7, -6.3, -8.5, -7.5, -8.3, -8.6, -8.2, -7.8, -6.7, -7.2, -7.0, -8.0, -6.8, -9.1, -7.5, -6.8, -7.7, -9.1, -7.6, -7.6, -8.6, -6.2, -7.1, -7.5, -7.5, -7.9, -7.0, -7.9, -7.9, -7.9, -8.3, -7.3, -7.0, -5.5, -8.3, -10.8, -10.6, -9.8, -8.7, -8.4, -12.1, -9.8, -8.9, -10.9, -8.1, -9.3, -7.8, -9.6, -9.3, -8.2, -9.1, -9.8, -10.3, -8.8, -10.9, -9.7, -9.4, -9.9, -9.4, -8.3, -8.6, -9.6, -8.5, -7.8, -8.9, -9.0, -9.0, -9.9, -9.7, -9.9, -9.1, -7.9, -6.3, -7.2, -7.1, -6.2, -5.9, -5.1, -6.8, -6.2, -6.7, -7.1, -7.1, -6.6, -5.9, -6.6, -6.2, -6.9, -6.3, -7.6, -7.0, -5.5, -6.5, -6.8, -6.9, -6.4, -6.8, -5.6, -6.2, -6.5, -6.7, -6.9, -5.9, -6.2, -7.0, -6.8, -7.5, -6.4, -6.1, -5.2, -8.0, -7.7, -8.3, -7.4, -6.3, -6.6, -8.0, -7.5, -7.2, -8.1, -6.8, -7.7, -6.4, -7.0, -6.7, -8.4, -7.6, -6.5, -8.1, -6.6, -7.8, -7.1, -6.8, -7.0, -7.8, -6.4, -7.6, -6.8, -7.8, -7.2, -6.8, -8.1, -8.3, -8.5, -6.7, -7.4, -6.3, -5.6, -6.8, -9.8, -9.5, -8.4, -8.2, -7.6, -9.6, -8.8, -8.6, -9.8, -9.6, -9.3, -7.4, -8.1, -8.3, -7.6, -8.0, -10.1, -8.9, -8.4, -9.1, -10.1, -8.5, -8.5, -9.2, -6.7, -8.2, -8.6, -7.8, -8.1, -8.0, -7.3, -9.0, -8.4, -8.2, -9.3, -7.6, -6.9, -6.6, -10.0, -7.8, -9.3, -7.7, -8.2, -9.2, -9.1, -9.9, -9.4, -12.1, -10.6, -8.1, -10.3, -9.9, -7.6, -9.8, -9.9, -9.9, -9.1, -10.1, -9.9, -9.0, -10.1, -9.7, -7.8, -10.8, -8.9, -8.8, -9.3, -9.7, -8.1, -9.7, -9.4, -10.0, -9.0, -8.4, -7.9, -9.0, -9.3, -9.3, -8.9, -8.3, -8.2, -9.3, -7.7, -8.4, -9.4, -7.8, -8.8, -6.9, -8.8, -7.7, -8.1, -8.6, -9.0, -8.4, -7.7, -8.0, -9.1, -8.0, -9.1, -7.5, -7.2, -8.2, -7.6, -7.6, -10.0, -8.3, -8.8, -9.0, -9.3, -7.6, -8.8, -7.5, -7.0, -8.1, -8.4, -8.3, -7.4, -6.9, -6.8, -7.7, -7.7, -7.7, -8.4, -6.5, -7.8, -8.7, -7.4, -6.7, -9.4, -7.7, -8.0, -8.2, -6.4, -8.1, -7.6, -7.1, -8.2, -7.6, -6.7, -7.2, -7.4, -8.1, -9.8, -7.2, -7.7, -8.0, -9.0, -7.8, -8.1, -6.7, -5.6, -10.8, -9.8, -9.8, -8.6, -8.1, -7.6, -9.5, -9.3, -8.8, -10.1, -6.9, -8.4, -7.6, -8.0, -7.7, -7.6, -9.5, -9.4, -8.5, -7.1, -9.3, -9.0, -8.3, -10.3, -7.9, -7.7, -9.1, -8.1, -9.3, -9.7, -7.9, -9.7, -9.2, -9.8, -8.4, -9.5, -6.6, -6.4, -7.1, -9.0, -8.2, -7.9, -7.1, -7.2, -9.4, -7.5, -7.2, -9.0, -8.2, -8.7, -6.8, -8.1, -8.2, -6.8, -7.6, -8.6, -9.5, -6.7, -8.5, -9.5, -7.5, -7.4, -9.2, -6.7, -7.9, -7.6, -7.9, -8.0, -8.0, -7.5, -7.5, -8.6, -7.6, -8.1, -7.4, -6.4, -6.0, -7.8, -8.2, -6.9, -6.2, -7.0, -7.3, -7.8, -7.0, -8.0, -6.1, -7.5, -7.6, -6.6, -6.7, -9.6, -7.4, -7.0, -7.4, -6.2, -6.9, -7.0, -6.5, -7.6, -6.9, -6.3, -7.2, -6.6, -7.1, -8.8, -6.9, -7.6, -7.4, -8.6, -7.1, -7.7, -6.3, -5.4, -8.6, -11.5, -8.1, -9.1, -7.9, -8.2, -9.0, -10.7, -9.5, -11.7, -7.5, -9.3, -8.4, -9.9, -8.7, -8.5, -10.4, -8.9, -10.0, -7.1, -9.2, -9.9, -8.0, -10.4, -7.8, -7.7, -10.4, -8.4, -10.6, -9.3, -9.1, -9.3, -12.0, -11.1, -8.9, -10.0, -7.6, -6.9, -9.3, -10.4, -10.4, -9.8, -8.2, -8.5, -8.6, -9.6, -9.8, -10.5, -8.7, -9.8, -9.5, -8.4, -8.4, -8.2, -9.4, -9.5, -8.9, -8.6, -8.9, -8.6, -9.4, -9.3, -9.0, -7.4, -8.7, -9.2, -9.5, -10.8, -8.6, -8.1, -9.7, -10.5, -8.3, -9.7, -7.8, -7.1, -5.5, -4.0, -5.0, -4.5, -4.2, -3.9, -4.1, -4.2, -4.5, -4.2, -3.8, -4.8, -4.0, -4.3, -4.3, -4.5, -5.2, -4.5, -4.6, -3.6, -4.3, -3.8, -4.3, -4.3, -4.3, -4.0, -4.2, -4.6, -5.6, -5.1, -4.1, -4.8, -4.3, -4.8, -4.9, -4.4, -4.2, -3.6, -7.8, -10.9, -8.0, -8.6, -8.8, -8.3, -7.5, -7.8, -8.6, -10.4, -9.8, -10.1, -7.6, -9.1, -8.7, -7.7, -8.8, -10.2, -9.9, -9.0, -8.7, -10.9, -8.3, -9.0, -7.6, -7.5, -9.9, -8.3, -9.6, -7.9, -9.5, -7.9, -9.9, -8.5, -9.2, -8.1, -8.0, -8.0, -8.4, -11.6, -10.5, -9.2, -8.5, -9.2, -10.6, -10.4, -9.5, -11.5, -8.6, -10.2, -8.2, -10.3, -9.7, -8.1, -9.6, -9.9, -9.6, -7.4, -11.6, -9.6, -8.1, -10.6, -7.8, -7.8, -10.1, -9.0, -10.0, -10.4, -9.4, -9.0, -9.9, -12.7, -9.3, -9.8, -7.2, -7.5, -9.0, -9.8, -9.5, -8.6, -8.3, -7.7, -9.7, -9.1, -8.7, -9.8, -7.4, -8.9, -8.1, -8.3, -7.6, -8.0, -9.8, -9.3, -9.2, -7.2, -9.3, -9.1, -8.1, -10.5, -7.9, -7.7, -9.0, -8.1, -10.4, -9.6, -7.9, -9.5, -9.0, -9.7, -8.3, -9.8, -6.5, -6.5, -6.8, -10.0, -8.1, -7.6, -7.0, -6.5, -8.7, -7.7, -7.4, -9.3, -7.4, -7.8, -6.3, -7.8, -6.9, -7.8, -7.3, -7.8, -7.8, -6.9, -7.2, -8.0, -9.4, -7.6, -8.2, -6.4, -7.2, -7.3, -6.8, -7.3, -6.9, -7.6, -7.3, -8.3, -7.3, -7.0, -7.0, -5.9, -10.6, -9.1, -6.8, -8.7, -8.0, -7.2, -9.1, -8.8, -8.6, -9.2, -7.0, -8.4, -7.8, -7.8, -7.2, -8.1, -9.6, -9.5, -8.5, -6.9, -9.4, -9.0, -8.2, -10.4, -7.9, -7.7, -9.0, -8.3, -10.0, -9.4, -8.0, -9.9, -8.9, -9.7, -8.4, -9.8, -7.1, -6.3, -7.2, -9.4, -9.7, -8.5, -7.7, -7.3, -8.8, -8.9, -8.1, -9.4, -7.9, -9.2, -7.5, -7.7, -8.1, -8.5, -8.2, -8.4, -8.8, -7.6, -8.2, -8.4, -8.7, -8.8, -11.1, -7.5, -8.2, -8.1, -8.0, -9.0, -7.8, -7.7, -8.2, -9.8, -8.4, -8.2, -8.1, -6.9, -6.0, -8.3, -6.6, -7.9, -6.4, -6.6, -7.2, -7.3, -6.8, -8.4, -6.5, -7.7, -7.4, -7.5, -7.1, -5.7, -7.1, -7.6, -8.0, -6.5, -7.5, -8.4, -6.8, -7.6, -6.3, -7.8, -7.2, -7.1, -6.6, -7.1, -7.0, -7.3, -7.2, -7.5, -6.9, -6.5, -6.7, -6.0, -7.3, -11.3, -7.6, -8.3, -8.7, -8.2, -7.8, -8.5, -8.1, -11.7, -9.5, -9.3, -8.1, -9.3, -8.4, -7.3, -8.1, -9.2, -9.1, -8.7, -9.2, -9.6, -8.5, -9.2, -7.7, -7.5, -9.4, -8.2, -7.4, -8.6, -9.6, -8.2, -8.9, -7.8, -8.5, -8.9, -8.1, -7.7, -7.6, -10.4, -9.0, -9.3, -8.8, -8.7, -10.3, -9.2, -9.6, -10.0, -9.3, -9.2, -8.8, -9.2, -9.1, -9.1, -9.1, -9.4, -10.3, -8.6, -9.2, -10.0, -9.5, -9.2, -8.3, -8.3, -8.8, -8.2, -8.7, -8.9, -9.8, -8.5, -9.3, -9.5, -8.9, -9.2, -8.2, -7.6, -10.6, -9.1, -7.1, -7.9, -7.5, -7.4, -9.0, -8.8, -8.1, -9.4, -7.1, -8.9, -7.4, -7.9, -7.4, -9.1, -8.9, -8.5, -8.9, -7.0, -8.9, -8.6, -7.3, -9.1, -8.0, -7.4, -8.8, -8.5, -10.6, -8.9, -7.9, -9.3, -8.3, -9.8, -7.4, -8.4, -6.6, -6.1, -8.6, -8.8, -9.2, -7.9, -7.8, -7.0, -8.0, -8.3, -8.1, -8.8, -7.4, -8.5, -8.8, -7.4, -7.6, -9.7, -8.6, -8.4, -8.4, -6.9, -8.3, -7.9, -7.7, -8.1, -8.1, -6.5, -8.0, -7.5, -8.8, -10.4, -7.5, -8.8, -8.1, -10.0, -8.0, -8.1, -7.1, -5.6, -9.9, -8.1, -10.4, -8.1, -7.5, -7.9, -8.5, -8.1, -8.5, -9.0, -7.3, -8.7, -8.0, -7.8, -7.1, -9.6, -8.5, -7.9, -8.4, -6.9, -8.7, -8.2, -7.0, -8.7, -8.4, -7.2, -8.3, -7.6, -9.0, -8.4, -8.3, -9.4, -8.9, -9.2, -7.6, -8.3, -6.6, -5.8, -6.8, -7.6, -7.9, -6.7, -6.4, -5.7, -7.3, -6.2, -6.9, -7.4, -6.9, -7.1, -6.0, -7.0, -6.7, -7.0, -6.3, -7.1, -7.2, -6.0, -6.6, -7.2, -7.5, -6.4, -7.3, -5.3, -6.5, -6.3, -7.1, -6.8, -6.0, -6.8, -7.0, -7.1, -7.1, -6.6, -6.1, -5.7, -9.0, -11.4, -11.1, -9.1, -8.0, -8.8, -8.6, -9.2, -9.7, -11.9, -8.2, -10.0, -9.0, -10.1, -8.7, -8.7, -10.5, -9.8, -10.5, -7.3, -9.9, -9.1, -7.6, -10.1, -8.0, -8.6, -9.3, -9.0, -9.3, -9.7, -9.1, -9.3, -12.6, -11.5, -9.3, -9.7, -7.1, -7.4, -8.0, -11.3, -9.1, -9.0, -8.0, -9.0, -11.0, -11.3, -9.5, -11.2, -8.5, -10.5, -8.2, -10.7, -9.5, -8.5, -10.2, -10.0, -9.4, -7.3, -11.6, -9.2, -8.8, -10.8, -8.3, -7.0, -10.2, -10.2, -10.8, -8.7, -9.5, -9.5, -10.8, -13.5, -9.4, -10.1, -7.9, -7.3, -8.1, -9.5, -7.4, -8.1, -8.2, -8.2, -10.4, -9.2, -8.4, -9.1, -8.0, -9.4, -7.6, -9.4, -8.9, -8.0, -8.6, -8.5, -9.3, -8.5, -10.3, -9.3, -9.2, -9.2, -7.0, -7.3, -8.6, -8.8, -7.8, -7.8, -9.3, -7.3, -8.4, -8.6, -10.9, -9.6, -8.3, -7.0, -7.0, -9.9, -9.4, -8.9, -7.9, -7.9, -8.9, -9.6, -9.7, -10.1, -8.7, -9.2, -8.3, -8.7, -8.0, -7.7, -8.5, -9.5, -9.1, -8.2, -9.4, -9.1, -8.5, -10.0, -7.8, -7.7, -8.6, -8.6, -8.7, -8.0, -8.5, -8.5, -9.3, -10.0, -8.4, -10.5, -7.9, -7.1, -6.2, -8.9, -6.6, -7.9, -7.9, -7.3, -8.3, -8.0, -8.2, -9.0, -7.7, -8.7, -6.9, -8.1, -8.1, -7.0, -8.5, -8.7, -9.2, -7.3, -7.9, -8.7, -7.6, -8.3, -7.0, -7.5, -8.2, -8.1, -6.7, -7.3, -7.8, -7.9, -8.2, -7.3, -8.0, -7.9, -7.4, -6.7, -6.5, -7.7, -6.9, -7.3, -7.0, -7.6, -7.2, -8.8, -7.0, -7.6, -7.8, -7.9, -6.7, -7.2, -7.4, -7.3, -8.8, -7.7, -7.2, -7.5, -7.7, -6.7, -7.1, -8.2, -7.1, -6.5, -7.6, -7.2, -6.7, -6.3, -9.3, -7.1, -8.3, -8.7, -7.8, -7.6, -6.4, -8.6]\n",
    "x = np.array(scores)\n",
    "k2, p = stats.normaltest(x); alpha = 1e-3\n",
    "print(k2, p)\n",
    "print(\"p = {:g}\".format(p))\n",
    "if p < alpha:  # null hypothesis: x comes from a normal distribution\n",
    "    print(\"The null hypothesis (x comes from a normal distribution) can be rejected.\")\n",
    "else:\n",
    "    print(\"The null hypothesis (is not normal) cannot be rejected.\")\n",
    "\n",
    "qqplot(x, line='s') \n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}