Ex2.boxplot.ipynb

{
 "cells": [
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   "cell_type": "markdown",
   "id": "f01f1990",
   "metadata": {},
   "source": [
    "<img src=\"https://www.th-koeln.de/img/logo.svg\" style=\"float:right;\" width=\"200\">"
   ]
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  {
   "cell_type": "markdown",
   "id": "5466e89e",
   "metadata": {},
   "source": [
    "# 2nd exercise: <font color=\"#C70039\">Work with Boxplots for anomaly detection</font>\n",
    "* Course: AML\n",
    "* Lecturer: <a href=\"https://www.gernotheisenberg.de/\">Gernot Heisenberg</a>\n",
    "* Author of notebook: Mathis Lövenich\n",
    "* Date:   31.10.2022\n",
    "* Matr. No.: 11157363 \n",
    "\n",
    "<img src=\"https://r-graph-gallery.com/img/other/boxplot_explanation.png\" style=\"float: center;\" width=\"800\">\n",
    "<img src=\"https://i2.wp.com/upload.wikimedia.org/wikipedia/commons/thumb/1/1a/Boxplot_vs_PDF.svg/550px-Boxplot_vs_PDF.svg.png?w=578\" style=\"float: center;\" width=\"800\">\n",
    "\n",
    "\n",
    "---------------------------------\n",
    "**GENERAL NOTE 1**: \n",
    "Please make sure you are reading the entire notebook, since it contains a lot of information on your tasks (e.g. regarding the set of certain paramaters or a specific computational trick), and the written mark downs as well as comments contain a lot of information on how things work together as a whole. \n",
    "\n",
    "**GENERAL NOTE 2**: \n",
    "* Please, when commenting source code, just use English language only. \n",
    "* When describing an observation please use English language, too\n",
    "* This applies to all exercises throughout this course.  \n",
    "\n",
    "---------------------\n",
    "\n",
    "### <font color=\"ce33ff\">DESCRIPTION</font>:\n",
    "This notebook allows you for using boxplots to detect anomalies. Try to interpret the boxplot. \n",
    "\n",
    "-------------------------------------------------------------------------------------------------------------\n",
    "\n",
    "### <font color=\"FFC300\">TASKS</font>:\n",
    "The tasks that you need to work on within this notebook are always indicated below as bullet points. \n",
    "If a task is more challenging and consists of several steps, this is indicated as well. \n",
    "Make sure you have worked down the task list and commented your doings. \n",
    "This should be done by using markdown.<br> \n",
    "<font color=red>Make sure you don't forget to specify your name and your matriculation number in the notebook.</font>\n",
    "\n",
    "**YOUR TASKS in this exercise are as follows**:\n",
    "1. import the notebook to Google Colab or use your local machine.\n",
    "2. make sure you specified you name and your matriculation number in the header below my name and date. \n",
    "    * set the date too and remove mine.\n",
    "3. read the entire notebook carefully \n",
    "    * add comments whereever you feel it necessary for better understanding\n",
    "    * run the notebook for the first time. \n",
    "4. take the three data sets from exercize 1 and create a boxplot for each of them\n",
    "5. interpret the visual results and describe them\n",
    "6. how can you test your data for being normally distributed? \n",
    "-----------------------------------------------------------------------------------"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "c458a5b1",
   "metadata": {},
   "outputs": [],
   "source": [
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from numpy.random import randn\n",
    "np.random.seed(1)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "2632e190",
   "metadata": {},
   "outputs": [],
   "source": [
    "# multiply and add by random numbers to get some real values\n",
    "# randn generates samples from the normal distribution (important - see below)\n",
    "random_data = np.random.randn(50000)  * 20 + 20"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "967df330",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.boxplot(data=random_data)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "b1fc937d",
   "metadata": {},
   "outputs": [],
   "source": [
    "heights_and_weights = (\n",
    "    pd.read_csv(\"data/SOCR-HeightWeight.csv\")\n",
    ").rename(\n",
    "    columns={\n",
    "        'Height(Inches)': 'height', \n",
    "        'Weight(Pounds)': 'weight'\n",
    "    }\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "2296fd91",
   "metadata": {},
   "outputs": [],
   "source": [
    "penguins = sns.load_dataset(\"penguins\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "ae756095",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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4LqxrPvbt26eKigrl5ORow4YNmj9/vhYtWqSVK1cG9/ntb3+rkSNHKiMjQwMGDNAtt9yiF154QRMnTuzyNUtLS+X1eoMPn8/Xs58IAAD0aWEd+QgEAsrNzVVJSYkkaezYsdq9e7cqKio0Z84cSd/Ex9atW1VdXa2srCy99957WrBggdLS0nTjjTd2es3i4mI9+OCDwed+vz/iA8Tj8QS/Pv7dO6V+/V2cBgDQp3W0B4+Sn/n7I5qFFR9paWkaOXJkyLYRI0bojTfekCSdOHFCv/zlL7V27VpNmzZNknT11VfrX//6l37zm990GR8ejyfq/mVblvW/J/36Ex8AgAsS8vsjioV12iU/P1979uwJ2bZ3715lZWVJktrb29Xe3q64uNCX7devnwKBQA9HBQAA0SCsIx9LlixRXl6eSkpKVFBQoO3bt6uyslKVlZWSpKSkJE2aNEkPP/ywEhMTlZWVpc2bN2vlypV69tlnHfkBAABAZAkrPsaNG6e1a9equLhYy5cv1/Dhw1VeXq6ioqLgPmvWrFFxcbGKior03//+V1lZWfq///s/zZ8/v9eHBwAAkSes+JCkW2+9Vbfeeus511NTU0M+BwQAAOBM3NsFAAAYRXwAAACjiA8AAGAU8QEAAIwiPgAAgFHEBwAAMIr4AAAARhEfAADAKOIDAAAYRXwAAACjiA8AAGAU8QEAAIwiPgAAgFHEBwAAMIr4AAAARhEfAADAKOIDAAAYRXwAAACjiA8AAGAU8QEAAIyKd3uAaGcFTsl2ewigL7BtKXDqm6/j4iXLcnceoI+wTv+5iCHEh8Mu/tdqt0cAAKBP4bQLAAAwiiMfDkhISFBNTY3bYwB9Smtrq6ZPny5JWrt2rRISElyeCOh7YuXPBfHhAMuylJiY6PYYQJ+VkJDAnxEghnHaBQAAGEV8AAAAo4gPAABgFPEBAACMIj4AAIBRxAcAADCK+AAAAEYRHwAAwCjiAwAAGBV2fBw8eFCzZs1ScnKyBg4cqDFjxqihoSFknw8//FC33XabvF6vBg0apOuuu05NTU29NjQAAIhcYX28+tGjR5Wfn6/JkyerpqZGKSkp+uSTTzR48ODgPp988okmTpyon/3sZ/r1r38tr9erDz/8MGY+rx4AAJxfWPFRVlYmn8+nqqqq4Lbs7OyQfR577DH98Ic/1NNPPx3cdtlll/VsSgAAEDXCOu1SXV2t3NxczZgxQykpKRo7dqxefPHF4HogENDbb7+tK664QjfffLNSUlI0YcIErVu37pyv2dbWJr/fH/IAAADRK6z42LdvnyoqKpSTk6MNGzZo/vz5WrRokVauXClJOnLkiL766is99dRTuuWWW/TOO+9o+vTpuv3227V58+YuX7O0tFRerzf48Pl8Pf+pAABAn2XZtm1f6M4DBgxQbm6u6urqgtsWLVqk+vp6vf/++zp06JCGDRumn/70p3r11VeD+9x222266KKLtHr16k6v2dbWpra2tuBzv98vn8+nlpYWJSUldffnAtDHnDhxQlOnTpUk1dTUKDEx0eWJAPQmv98vr9d7Qb+/wzrykZaWppEjR4ZsGzFiRPCdLEOGDFF8fPx59zmbx+NRUlJSyAMAAESvsOIjPz9fe/bsCdm2d+9eZWVlSfrmyMi4cePOuw8AAIhtYb3bZcmSJcrLy1NJSYkKCgq0fft2VVZWqrKyMrjPww8/rJkzZ+r73/++Jk+erL/+9a9666239O677/b27AAAIAKFdeRj3LhxWrt2rVavXq3Ro0frySefVHl5uYqKioL7TJ8+Xb/73e/09NNP66qrrtIf/vAHvfHGG5o4cWKvDw8AACJPWBecmhDOBSsAIgcXnALRzbELTgEAAHqK+AAAAEYRHwAAwCjiAwAAGEV8AAAAo4gPAABgFPEBAACMIj4AAIBRxAcAADCK+AAAAEYRHwAAwCjiAwAAGEV8AAAAo4gPAABgFPEBAACMIj4AAIBRxAcAADCK+AAAAEYRHwAAwCjiAwAAGEV8AAAAo4gPAABgFPEBAACMIj4AAIBRxAcAADCK+AAAAEYRHwAAwCjiAwAAGEV8AAAAo4gPAABgFPEBAACMIj4AAIBRxAcAADCK+AAAAEaFHR8HDx7UrFmzlJycrIEDB2rMmDFqaGjoct/77rtPlmWpvLy8p3MCAIAoER/OzkePHlV+fr4mT56smpoapaSk6JNPPtHgwYM77btu3Tpt27ZN6enpvTUrAACIAmHFR1lZmXw+n6qqqoLbsrOzO+138OBBLVy4UBs2bNC0adN6PCQAAIgeYZ12qa6uVm5urmbMmKGUlBSNHTtWL774Ysg+gUBAs2fP1sMPP6xRo0Z962u2tbXJ7/eHPAAAQPQKKz727duniooK5eTkaMOGDZo/f74WLVqklStXBvcpKytTfHy8Fi1adEGvWVpaKq/XG3z4fL7wfgIAABBRwjrtEggElJubq5KSEknS2LFjtXv3blVUVGjOnDlqaGjQihUrtHPnTlmWdUGvWVxcrAcffDD43O/3EyAAAESxsI58pKWlaeTIkSHbRowYoaamJknSli1bdOTIEWVmZio+Pl7x8fFqbGzUQw891OW1IZLk8XiUlJQU8gAAANErrCMf+fn52rNnT8i2vXv3KisrS5I0e/Zs3XjjjSHrN998s2bPnq277767h6MCAIBoEFZ8LFmyRHl5eSopKVFBQYG2b9+uyspKVVZWSpKSk5OVnJwc8j39+/dXamqqrrzyyt6bGgAARKywTruMGzdOa9eu1erVqzV69Gg9+eSTKi8vV1FRkVPzAQCAKBPWkQ9JuvXWW3Xrrbde8P6ffvppuP8IAAAQxbi3CwAAMIr4AAAARhEfAADAKOIDAAAYRXwAAACjiA8AAGAU8QEAAIwiPgAAgFHEBwAAMIr4AAAARhEfAADAKOIDAAAYRXwAAACjiA8AAGAU8QEAAIwiPgAY9/LLL7s9AgAXER8AjGhpaQl+vWbNGh07dsy9YQC4Kt7tAQAn2bat1tZWt8eApGXLloU8X7p0qcrLy90ZBiESEhJkWZbbYyCGEB+Iaq2trZo6darbY6ALe/bs4b9NH1FTU6PExES3x0AM4bQLAAAwiiMfiGoJCQmqqalxe4yY9v7772v58uXnXH/88cd1/fXXG5wIZ0tISHB7BMQY4gNRzbIsDie7LC7u/AdY4+Li+G8ExBhOuwBw1IYNG3q0DiD6EB8AHPXZZ5/1aB1A9CE+ADgqPv78Z3e/bR1A9CE+ADjqsssu69E6gOhDfABwlG3bPVoHEH2IDwCOamxs7NE6gOhDfABw1KWXXtqjdQDRh/gA4KjRo0f3aB1A9CE+ADjqq6++6tE6gOhDfABw1JVXXtmjdQDRh/gA4Khhw4b1aB1A9CE+ADjq888/79E6gOgTdnwcPHhQs2bNUnJysgYOHKgxY8aooaFBktTe3q6lS5fqqquu0kUXXaT09HTNmTNHhw4d6vXBAUSG6667ThdffHGXaxdffLGuu+46wxMBcFtY8XH06FHl5+erf//+qqmp0QcffKBnnnlGgwcPliR9/fXX2rlzp5YtW6adO3fqzTff1N69e3Xbbbc5MTuACBAXF6eFCxd2ufaLX/ziW+96CyD6hHVThbKyMvl8PlVVVQW3ZWdnB7/2er3auHFjyPc899xzGj9+vJqampSZmdmzaQFEHNu29fbbb3e5tn79ek2ZMkWWZRmeCoCbwvorR3V1tXJzczVjxgylpKRo7NixevHFF8/7PS0tLbIsK3h0BEBsaWxs1K5du7pc27VrF59wCsSgsOJj3759qqioUE5OjjZs2KD58+dr0aJFWrlyZZf7t7a26tFHH1VhYaGSkpK63KetrU1+vz/kAQAAoldYp10CgYByc3NVUlIiSRo7dqx2796tiooKzZkzJ2Tf9vZ23XnnnQoEAnrhhRfO+ZqlpaX69a9/3Y3RAUQCn8+nuLg4BQKBTmtxcXHy+XwuTAXATWEd+UhLS9PIkSNDto0YMUJNTU0h29rb21VQUKD9+/dr48aN5zzqIUnFxcVqaWkJPg4cOBDOSAD6uK1bt3YZHtI3f6HZunWr4YkAuC2sIx/5+fnas2dPyLa9e/cqKysr+Px0eHz88cfatGmTkpOTz/uaHo9HHo8nnDEARBDbtnu0DiD6hBUfS5YsUV5enkpKSlRQUKDt27ersrJSlZWVkqRTp07pjjvu0M6dO7V+/Xp1dHTo8OHDkqRLLrlEAwYM6P2fAECfxiecAjhbWKddxo0bp7Vr12r16tUaPXq0nnzySZWXl6uoqEiS1NzcrOrqajU3N2vMmDFKS0sLPurq6hz5AQD0bdnZ2briiiu6XPvOd74T8nZ9ALHBsvvYMU+/3y+v16uWlpbzXisCIHI0Nzdr1qxZnba/8sorHPkAokQ4v7/5aEEAjsvIyOh0/deQIUMIDyBGER8AHLdjxw59+eWXIdu++OIL7dixw6WJALiJ+ADgqEAgoOXLl3e5tnz58nO+DRdA9CI+ADhq27Zt5/zkYr/fr23bthmeCIDbiA8AjpowYcI5Lz7zer2aMGGC4YkAuI34AOCouLg4LViwoMu1BQsWKC6O/w0BsYY/9QAcZdu2/va3v3W5VltbyyecAjGI+ADgqKamJtXX13e5Vl9f3+neUACiH/EBwFE+n++c13wkJSVxV1sgBhEfABx14MCB877bhTtZA7GH+ADgqMzMTI0bN06WZYVstyxL48ePV2ZmpkuTAXAL8QHAUZZlafHixZ3e1dKvXz8tXry4U5QAiH7EBwDHZWRkqLCwMBgalmWpsLCQe7sAMYr4AGBEUVFR8OZyQ4YMUWFhocsTAXAL8QHAiISEBI0ePVqSNGrUKCUkJLg8EQC3EB8AjDh27Jjee+89SdJ7772nY8eOuTsQANcQHwCMWLZsWfAOtoFAQI8//rjLEwFwC/EBwHE7duzQrl27Qrb9+9//1o4dO1yaCICbiA8AjgoEAlq+fHmXa8uXLw8eDQEQO4gPAI7atm3beT/hdNu2bYYnAuA24gOAo8aPH69+/fp1uRYfH6/x48cbngiA24gPAI5qbm5WR0dHl2unTp1Sc3Oz4YkAuI34AOCo0/d26Qr3dgFiE/EBwFGWZWnmzJldrs2cOZN7uwAxiPgA4CjbtvXaa691eVfbNWvWyLZtlyYD4BbiA4CjmpqaVF9f3ykybNtWfX29mpqaXJoMgFuIDwCOOn3Nx9nveOnXrx/XfAAxivgA4CjLsrR48eJzbueaDyD2EB8AHJeRkaGCgoKQbQUFBRo2bJhLEwFwE/EBAACMIj4AOK65uVmvv/56yLbXX3+dDxgDYhTxAcBRtm1rxYoV59zOW22B2EN8AHDU6bfanv0R6x0dHbzVFohRxAcAR/FWWwBnIz4AOIq32gI4W9jxcfDgQc2aNUvJyckaOHCgxowZo4aGhuC6bdt64oknlJ6ersTERN1www3avXt3rw4NILJkZGSosLAwGBqWZamwsJC32gIxKqz4OHr0qPLz89W/f3/V1NTogw8+0DPPPKPBgwcH93n66af17LPP6vnnn1d9fb1SU1N100036fjx4709O4AIUlRUpOTkZEnSkCFDVFhY6PJEANxi2WFcav7oo4/qH//4h7Zs2dLlum3bSk9P1wMPPKClS5dKktra2jR06FCVlZXpvvvu+9Z/ht/vl9frVUtLi5KSki50NAARoK6uTitWrNDixYuVl5fn9jgAelE4v7/DOvJRXV2t3NxczZgxQykpKRo7dqxefPHF4Pr+/ft1+PBhTZkyJbjN4/Fo0qRJqqur6/I129ra5Pf7Qx4AolNeXp5ee+01wgOIcWHFx759+1RRUaGcnBxt2LBB8+fP16JFi7Ry5UpJ0uHDhyVJQ4cODfm+oUOHBtfOVlpaKq/XG3z4fL7u/BwAACBChBUfgUBA11xzjUpKSjR27Fjdd999uvfee1VRURGy39lXr9u2fc4r2ouLi9XS0hJ8HDhwIMwfAQAARJKw4iMtLU0jR44M2TZixIjghwSlpqZKUqejHEeOHOl0NOQ0j8ejpKSkkAcAAIheYcVHfn6+9uzZE7Jt7969ysrKkiQNHz5cqamp2rhxY3D95MmT2rx5M+d4AQCAJCk+nJ2XLFmivLw8lZSUqKCgQNu3b1dlZaUqKyslfXO65YEHHlBJSYlycnKUk5OjkpISDRw4kLfVAQAASWHGx7hx47R27VoVFxdr+fLlGj58uMrLy1VUVBTc55FHHtGJEye0YMECHT16VBMmTNA777yjQYMG9frwAAAg8oT1OR8m8DkfAABEHsc+5wMAAKCniA8AAGBUWNd8mHD6LBCfdAoAQOQ4/Xv7Qq7m6HPxcfoGdHzSKQAAkef48ePyer3n3afPXXAaCAR06NAhDRo06JyfigogMvn9fvl8Ph04cIALyoEoY9u2jh8/rvT0dMXFnf+qjj4XHwCiF+9mAyBxwSkAADCM+AAAAEYRHwCM8Xg8+tWvfiWPx+P2KABcxDUfAADAKI58AAAAo4gPAABgFPEBAACMIj4AAIBRxAcAY1544QUNHz5cCQkJuvbaa7Vlyxa3RwLgAuIDgBGvvfaaHnjgAT322GP65z//qe9973uaOnWqmpqa3B4NgGG81RaAERMmTNA111yjioqK4LYRI0boxz/+sUpLS12cDIBpHPkA4LiTJ0+qoaFBU6ZMCdk+ZcoU1dXVuTQVALcQHwAc98UXX6ijo0NDhw4N2T506FAdPnzYpakAuIX4AGCMZVkhz23b7rQNQPQjPgA4bsiQIerXr1+noxxHjhzpdDQEQPQjPgA4bsCAAbr22mu1cePGkO0bN25UXl6eS1MBcEu82wMAiA0PPvigZs+erdzcXF1//fWqrKxUU1OT5s+f7/ZoAAwjPgAYMXPmTH355Zdavny5PvvsM40ePVp/+ctflJWV5fZoAAzjcz4AAIBRXPMBAACMIj4AAIBRxAcAADCK+AAAAEYRHwAAwCjiAwAAGEV8AAAAo4gPAABgFPEBAACMIj4AAIBRxAcAADCK+AAAAEb9f8rkX4ZhKlhUAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.boxplot(heights_and_weights.height)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "ed9b8986",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.boxplot(heights_and_weights.weight)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "30309459",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.boxplot(penguins.flipper_length_mm)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cdc3ce91",
   "metadata": {},
   "source": [
    "For human body height and weight we see a lot of outliers that are bellow or above 1.5 the IQR. This kind of anomaly detection is similar to what we have done with the normal distribution. However here we can't say that the 0.3 % holds cause a boxplot has a different mathematical definition."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b093bc41",
   "metadata": {},
   "source": [
    "We can't obeserve any outliers for the boxplot of penguins flipper length, similar to what we have observed with the anomaly detectedion from Ex1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1cfb6106",
   "metadata": {},
   "source": [
    "To 5: there are different kind of test to show or indicate that a underlying distribution is a normal distribution.\n",
    "\n",
    "One that I will present here is the Shapiro-Wilk-Test."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d52cdc86",
   "metadata": {},
   "source": [
    "The null hypothesis of the Shapiro-Wilk test, whether it is a normal distribution, \n",
    "is accepted or rejected on the basis of the value of the following estimator. \n",
    "\n",
    "\\begin{equation}\n",
    "W={\\frac  {b^{2}}{(n-1)s^{2}}}\n",
    "\\end{equation}\n",
    "\n",
    "$n$ ist the sample size, $s^{2}$ is the empirical variance and $b$ is a correction of the variance,\n",
    "measured like this:\n",
    "\n",
    "\\begin{equation}\n",
    "b=a_{{(1)}}\\left(x_{{(n)}}-x_{{(1)}}\\right)+a_{{(2)}}\\left(x_{{\\left(n-1\\right)}}-x_{{(2)}}\\right)+\\cdots \n",
    "\\end{equation}\n",
    "\n",
    "The constants $a_(i)$ can be found on a table, like: https://www.real-statistics.com/statistics-tables/shapiro-wilk-table/\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "946a498d",
   "metadata": {},
   "source": [
    "The value of $W$ is then compared to a critical value that can also be found on a table whic can finally yield a conclusion if the distribution is normal or not"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b8a453e6",
   "metadata": {},
   "source": [
    "Here I will just use the existing function of scipy:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "e5113a84",
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import shapiro"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "a30b613a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "ShapiroResult(statistic=0.999895453453064, pvalue=0.37611162662506104)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "shapiro(heights_and_weights.weight)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "63d60484",
   "metadata": {},
   "source": [
    "We cannot say that we have no normal distribution here because pvalue > 0.05"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "e47d50b5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "ShapiroResult(statistic=0.9999220371246338, pvalue=0.6875156164169312)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "shapiro(heights_and_weights.height)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "92872868",
   "metadata": {},
   "source": [
    "We cannot say that we have no normal distribution here because pvalue > 0.05"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "d7b0624f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "ShapiroResult(statistic=0.9515460133552551, pvalue=3.541138271501154e-09)"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "shapiro(penguins.flipper_length_mm.dropna())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4e14e1cf",
   "metadata": {},
   "source": [
    "First we need to get rid of nan values, as this can't be handled by the test. \\\n",
    "As a result we get a pvalues much less than 0.05, which means we can strongly assume that this data is normally distributed"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "dbbcefd3",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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