normality_test.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy.random import seed\n",
    "from numpy.random import randn\n",
    "from scipy.stats import shapiro\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.stats import normaltest\n",
    "from scipy.stats import anderson"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "seed(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# data = [1, 2, 3, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6,\n",
    "#        6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 9, 9]\n",
    "data = [1, 2, 3, 4, 4, 4, 4, 4, 4, 4, 5, 6, 7, 7, 8, 8, 8, 8, 8, 8, 8, 9, 9]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([1., 1., 1., 7., 0., 1., 1., 2., 7., 2.]),\n",
       " array([1. , 1.8, 2.6, 3.4, 4.2, 5. , 5.8, 6.6, 7.4, 8.2, 9. ]),\n",
       " <a list of 10 Patch objects>)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "plt.hist(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Statistics=0.890, p=0.016\n"
     ]
    }
   ],
   "source": [
    "stat, p = shapiro(data)\n",
    "print('Statistics=%.3f, p=%.3f' % (stat, p))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sample does not look Gaussian (reject H0)\n"
     ]
    }
   ],
   "source": [
    "alpha = 0.05\n",
    "if p > alpha:\n",
    "    print('Sample looks Gaussian (fail to reject H0)')\n",
    "else:\n",
    "    print('Sample does not look Gaussian (reject H0)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Statistic: 1.167\n"
     ]
    }
   ],
   "source": [
    "result = anderson(data)\n",
    "print('Statistic: %.3f' % result.statistic)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "15.000: 0.511, data does not look normal (reject H0)\n",
      "10.000: 0.582, data does not look normal (reject H0)\n",
      "5.000: 0.699, data does not look normal (reject H0)\n",
      "2.500: 0.815, data does not look normal (reject H0)\n",
      "1.000: 0.969, data does not look normal (reject H0)\n"
     ]
    }
   ],
   "source": [
    "for i in range(len(result.critical_values)):\n",
    "    sl, cv = result.significance_level[i], result.critical_values[i]\n",
    "    if result.statistic < result.critical_values[i]:\n",
    "        print('%.3f: %.3f, data looks normal (fail to reject H0)' % (sl, cv))\n",
    "    else:\n",
    "        print('%.3f: %.3f, data does not look normal (reject H0)' % (sl, cv))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "normal = []\n",
    "for i in range(len(result.critical_values)):\n",
    "    sl, cv = result.significance_level[i], result.critical_values[i]\n",
    "    if result.statistic < result.critical_values[i]:\n",
    "        normal.append(1)\n",
    "    else:\n",
    "        normal.append(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Não é normal\n"
     ]
    }
   ],
   "source": [
    "if normal.count(1) >= 3:\n",
    "    print('É normal')\n",
    "else:\n",
    "    print('Não é normal')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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