{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Autour du Paradoxe de Simpson \"réalisé par Wahb ZOUHRI\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Importation des librairies et des données" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "import pandas as pd\n", "import numpy as np\n", "import warnings\n", "warnings.filterwarnings('ignore')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Les données sont disponibles dans ce [fichier CSV](https://gitlab.inria.fr/learninglab/mooc-rr/mooc-rr-ressources/blob/master/module3/Practical_session/Subject6_smoking.csv). Vous trouverez sur chaque ligne si la personne fume ou non, si elle est vivante ou décédée au moment de la seconde étude, et son âge lors du premier sondage." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "url = \"https://filebin.net/ldwl9zcu2wjz0rv9/module3_Practical_session_Subject6_smoking.csv?t=t2k6oqq8\"\n", "raw_data = pd.read_csv(url, skiprows=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Analyse 1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Représentez dans un tableau le nombre total de femmes vivantes et décédées sur la période en fonction de leur habitude de tabagisme." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
AliveDead
Smoker1329.0417.0
Non_Smoker1506.0690.0
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" ], "text/plain": [ " Alive Dead\n", "Smoker 1329.0 417.0\n", "Non_Smoker 1506.0 690.0" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Smokers = raw_data['Smoker'] == \"Yes\"\n", "Non_smokers = raw_data['Smoker'] == \"No\"\n", "dead = raw_data['Status'] == \"Dead\"\n", "alive = raw_data['Status'] == \"Alive\"\n", "\n", "SA = raw_data[Smokers & alive]\n", "SD = raw_data[Smokers & dead]\n", "NSA = raw_data[Non_smokers & alive]\n", "NSD = raw_data[Non_smokers & dead]\n", "\n", "Totals = np.zeros((2,2))\n", "\n", "Totals[0,0]= SA.size\n", "Totals[0,1]= SD.size\n", "Totals[1,0]= NSA.size\n", "Totals[1,1]= NSD.size\n", "\n", "Table = pd.DataFrame(data=Totals, index=[\"Smoker\", \"Non_Smoker\"], columns=[\"Alive\", \"Dead\"])\n", "Table" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Calculez dans chaque groupe (fumeuses / non fumeuses) le taux de mortalité (le rapport entre le nombre de femmes décédées dans un groupe et le nombre total de femmes dans ce groupe). " ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Taux_mortalité_fumeuses: 0.23883161512027493\n", "Taux_mortalité_NON_fumeuses: 0.31420765027322406\n" ] } ], "source": [ "Taux_mortalité_fumeuses = (Totals[0,1])/(Totals[0,0]+Totals[0,1]) \n", "Taux_mortalité_NON_fumeuses = (Totals[1,1])/(Totals[1,0]+Totals[1,1])\n", "\n", "print(\"Taux_mortalité_fumeuses: \"+str(Taux_mortalité_fumeuses))\n", "print(\"Taux_mortalité_NON_fumeuses: \"+str(Taux_mortalité_NON_fumeuses))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Représentation graphique de ces résultas" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.bar([\"Taux_mortalité_fumeuses\",\"Taux_mortalité_NON_fumeuses\"],[Taux_mortalité_fumeuses,Taux_mortalité_NON_fumeuses])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Remarque : le taux de mortalité des femmes fumeuses est moins élevé." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Analyse 2\n", "la même analyse qu'auparavant, en tenant compte cette fois du paramètre \"Age\"." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " Smoker Age class Alive Dead\n", "0 Yes Age_1 546 663\n", "1 Yes Age_2 588 540\n", "2 Yes Age_3 192 243\n", "3 Yes Age_4 21 84\n", "4 No Age_1 21 18\n", "5 No Age_2 123 57\n", "6 No Age_3 153 120\n", "7 No Age_4 126 495" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Age_1 = raw_data['Age'] < 35 # Age_1 = 18-34 ans\n", "Age_2 = (raw_data['Age'] < 55) & (raw_data['Age'] > 34) # Age_2 = 35-54 ans\n", "Age_3 = (raw_data['Age'] < 65) & (raw_data['Age'] > 54) # Age_3 = 55-64 ans\n", "Age_4 = raw_data['Age'] > 64 # Age_4 = plus de 65 ans\n", "\n", "Totals_2 = [[0]*4]\n", "for row in range(0,7):\n", " Totals_2.append([0]*4)\n", " \n", "for i in range(0,4):\n", " AGE = \"Age_\"+str(int(i+1))\n", " Totals_2[i][0] = \"Yes\"; Totals_2[i+4][0] = \"No\"\n", " Totals_2[i][1] = AGE; Totals_2[i+4][1] = AGE\n", " \n", "\"\"\" Alive smokers\"\"\" \n", "Totals_2[0][2] = SA[Age_1].size; Totals_2[1][2] = SA[Age_2].size\n", "Totals_2[2][2] = SA[Age_3].size; Totals_2[3][2] = SA[Age_4].size\n", "\n", "\"\"\" Dead smokers\"\"\" \n", "Totals_2[4][2] = SD[Age_1].size; Totals_2[5][2] = SD[Age_2].size\n", "Totals_2[6][2] = SD[Age_3].size; Totals_2[7][2] = SD[Age_4].size\n", "\n", "\"\"\" Alive NON_smokers\"\"\" \n", "Totals_2[0][3] = NSA[Age_1].size; Totals_2[1][3] = NSA[Age_2].size\n", "Totals_2[2][3] = NSA[Age_3].size; Totals_2[3][3] = NSA[Age_4].size\n", "\n", "\"\"\" Dead NON_smokers\"\"\" \n", "Totals_2[4][3] = NSD[Age_1].size; Totals_2[5][3] = NSD[Age_2].size\n", "Totals_2[6][3] = NSD[Age_3].size; Totals_2[7][3] = NSD[Age_4].size\n", "\n", "Table_2 = pd.DataFrame(data=Totals_2, columns=[\"Smoker\",\"Age class\",\"Alive\", \"Dead\"])\n", "\n", "Table_2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Remarque : \n", "* Age_1 = 18-34 ans\n", "* Age_2 = 35-54 ans\n", "* Age_3 = 55-64 ans\n", "* Age_4 = plus de 65 ans.\n", "\n", "Calcul de taux de mortalité." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SmokerAge classTaux_Mortalité
0YesAge_10.548387
4NoAge_10.461538
1YesAge_20.478723
5NoAge_20.316667
2YesAge_30.558621
6NoAge_30.439560
3YesAge_40.800000
7NoAge_40.797101
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" ], "text/plain": [ " Smoker Age class Taux_Mortalité\n", "0 Yes Age_1 0.548387\n", "4 No Age_1 0.461538\n", "1 Yes Age_2 0.478723\n", "5 No Age_2 0.316667\n", "2 Yes Age_3 0.558621\n", "6 No Age_3 0.439560\n", "3 Yes Age_4 0.800000\n", "7 No Age_4 0.797101" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Taux_Mortalité = np.zeros((8,1))\n", "for i in range(0,8):\n", " Taux_Mortalité[i,0]= (Totals_2[i][3])/(Totals_2[i][3]+Totals_2[i][2])\n", "\n", "Table_21 = Table_2[[\"Smoker\",\"Age class\"]]\n", "\n", "Table_3 = pd.DataFrame(data=Taux_Mortalité, columns=[\"Taux_Mortalité\"])\n", "Table_3 = Table_21.join(Table_3)\n", "Table_3 = Table_3.sort_values(by=[\"Age class\"])\n", "Table_3" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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E4PvAQ411FBFTIqI6IqorKiqaV6mZmaWWJtxrgZ55y5XAhvwGEfF2RGzJvZ4LdJbUvWBVmplZs6QJ9yXA0ZL6StofuAyYld9A0mGSlHs9MNfv5kIXa2Zm6TR5tUxE1EsaCzwGlAFTI2K1pDG57ZOBTwH/W1I98A/gsohoeOrGzMz2kVTzuedOtcxtsG5y3uu7gbsLW5qZmbWU71DtoEr9NKlS798s69rlk5is9fw0K7Ns85G7mVkGOdzNzDLI4d4S2+o69v7NrM3zOfeW6FwOEw8q3f4nvlW6fZtZu+AjdzOzDHK4m5llkMPdzCyDHO5mZhnkcDdrj0p9xVSp929N8tUyZu2Rr9iyJvjI3cwsgxzuZmYZ5HA3M8sgh7uZWQY53M3MMihVuEsaJmmNpHWSJuyl3amStkv6VOFKNDOz5moy3CWVAfcAw4F+wChJ/fbQ7uskz1o1M7MSSnPkPhBYFxHrI2IrMAMY0Ui7ccADwBsFrM/MzFogTbgfCbyWt1ybW7eLpCOBi4DJ7IWkGklLJS3duHFjc2s1M7OU0oS7GlkXDZa/C9wSEXt96nFETImI6oiorqioSFujmZk1U5rpB2qBnnnLlcCGBm2qgRmSALoD/yKpPiIeKkiVZmbWLGnCfQlwtKS+wJ+Ay4DL8xtERN+dryVNA2Y72M3MSqfJcI+IekljSa6CKQOmRsRqSWNy2/d6nt3MzPa9VLNCRsRcYG6DdY2GekRc1fqyzMysNXyHqplZBjnczcwyyOFuZpZBDnczswxyuJuZZZDD3cwsgxzuZmYZ5HA3M8sgh7uZWQY53M3MMsjhbmaWQQ53M7MMcribmWWQw93MLIMc7mZmGeRwNzPLoFThLmmYpDWS1kma0Mj2EZJWSlohaamkMwtfqmXKtrqOvX+zImvySUySyoB7gHNJHpa9RNKsiHghr9mvgVkREZKqgPuA44pRsGVE53KYeFDp9j/xrdLt22wfSHPkPhBYFxHrI2IrMAMYkd8gIrZEROQWDwACMzMrmTThfiTwWt5ybW7dbiRdJOklYA5wTWHKMzOzlkgT7mpk3fuOzCNiZkQcB1wI3NFoR1JN7pz80o0bNzavUjMzSy1NuNcCPfOWK4ENe2ocEU8CH5HUvZFtUyKiOiKqKyoqml2smZmlkybclwBHS+oraX/gMmBWfgNJH5Wk3OuTgf2BzYUu1szM0mnyapmIqJc0FngMKAOmRsRqSWNy2ycDFwOjJW0D/gGMzPsDq5mZ7WNNhjtARMwF5jZYNznv9deBrxe2NDMzaynfoWpmlkEOdzOzDHK4m5llkMPdzCyDHO5mZhnkcDczyyCHu5lZBjnczcwyyOFuZpZBDnczswxyuJuZZZDD3cwsgxzuZmYZ5HA3M8sgh7uZWQY53M3MMsjhbmaWQanCXdIwSWskrZM0oZHtV0hamfv6raQTC1+qmZml1WS4SyoD7gGGA/2AUZL6NWj2B+DsiKgC7gCmFLpQMzNLL82R+0BgXUSsj4itwAxgRH6DiPhtRPwtt/g7oLKwZZqZWXOkCfcjgdfylmtz6/bkM8CjrSnKzMxap1OKNmpkXTTaUPpnknA/cw/ba4AagF69eqUs0czMmivNkXst0DNvuRLY0LCRpCrgh8CIiNjcWEcRMSUiqiOiuqKioiX1mplZCmnCfQlwtKS+kvYHLgNm5TeQ1At4ELgyItYWvkwzM2uOJk/LRES9pLHAY0AZMDUiVksak9s+GbgdOBT4gSSA+oioLl7ZZma2N2nOuRMRc4G5DdZNznt9LXBtYUszM7OW8h2qZmYZ5HA3M8sgh7uZWQY53M3MMsjhbmaWQQ53M7MMcribmWWQw93MLIMc7mZmGeRwNzPLIIe7mVkGOdzNzDLI4W5mlkEOdzOzDHK4m5llkMPdzCyDHO5mZhmUKtwlDZO0RtI6SRMa2X6cpEWS/p+kLxS+TDMza44mH7MnqQy4BzgXqAWWSJoVES/kNfsrcB1wYVGqNDOzZklz5D4QWBcR6yNiKzADGJHfICLeiIglwLYi1GhmZs2UJtyPBF7LW67NrTMzszYqTbirkXXRkp1JqpG0VNLSjRs3tqQLMzNLIU241wI985YrgQ0t2VlETImI6oiorqioaEkXZmaWQppwXwIcLamvpP2By4BZxS3LzMxao8mrZSKiXtJY4DGgDJgaEasljcltnyzpMGAp0A3YIWk80C8i3i5i7WZmtgdNhjtARMwF5jZYNznv9Z9JTteYmVkb4DtUzcwyyOFuZpZBDnczswxyuJuZZZDD3cwsgxzuZmYZ5HA3M8sgh7uZWQY53M3MMsjhbmaWQQ53M7MMcribmWWQw93MLIMc7mZmGeRwNzPLIIe7mVkGOdzNzDIoVbhLGiZpjaR1kiY0sl2S7sptXynp5MKXamZmaTUZ7pLKgHuA4UA/YJSkfg2aDQeOzn3VAP+3wHWamVkzpDlyHwisi4j1EbEVmAGMaNBmBPBfkfgdcLCkwwtcq5mZpZQm3I8EXstbrs2ta24bMzPbRzqlaKNG1kUL2iCphuS0DcAWSWtS7L/N0dfpDmwqWQH/3thwty8ew9bx+LVOOx+/3mkapQn3WqBn3nIlsKEFbYiIKcCUNIW1ZZKWRkR1qetozzyGrePxa52OMH5pTsssAY6W1FfS/sBlwKwGbWYBo3NXzfwT8FZEvF7gWs3MLKUmj9wjol7SWOAxoAyYGhGrJY3JbZ8MzAX+BVgH/B24unglm5lZU9KcliEi5pIEeP66yXmvA/hcYUtr09r9qaU2wGPYOh6/1sn8+CnJZTMzyxJPP2BmlkEOdzOzDOrw4S7pIkkh6bgC93uJpNWSdkjK7CVXRRy/b0p6KTdX0UxJBxey/7aiiON3R27sVkiaJ+mIQvbfVhRr/PL6/0Ku/+7F6L+YOny4A6OAhSSXeBbS88C/Ak8WuN+2pljj9zhwQkRUAWuBLxa4/7aiWOP3zYioioiTgNnA7QXuv60o1vghqSdwLvBqofveFzp0uEs6EDgD+Ay5/xyS9pP0g9xR92xJcyV9KrftFEm/kbRM0mN7mz8nIl6MiHZ5B25aRR6/eRFRn1v8HcmNcZlS5PF7O2/xABq5Y7y9K+b45XwHuJl2OnapLoXMsAuBX0bEWkl/zU1VfBTQBxgAfBh4EZgqqTPwfWBERGyUNBL4GnBNaUpvE/bV+F0D3FuMN1BiRR0/SV8DRgNvAf9c1HdSGkUbP0kXAH+KiOek9jnVQkcP91HAd3OvZ+SWOwP3R8QO4M+SFuS2HwucADye+2GXAR39Ltyij5+kLwH1wPTClt4mFHX8IuJLwJckfREYC3yl4O+gtIoyfpI+CHwJGFq80ouvw4a7pEOBc4ATJAXJDzuAmXv6FmB1RJy2j0ps0/bF+En6NHA+MDgydkPGPv7/9zNgDhkK9yKP30eAvsDOo/ZKYLmkgRHx51YXv4905HPunyKZg753RPSJiJ7AH0hmirs4d+6uBzAo134NUCHpNABJnSX1L0XhbURRx0/SMOAW4IKI+Hsx30iJFHv8js5bvAB4qRhvooSKNn4RsSoiPpzrtw/JxIgnt6dgh44d7qN4/2/5B4AjSH6YzwP/CSwmmQhtK8l/qK9Leg5YAZy+p85zl2jVAqcBcyQ9Vvi3UFJFHT/gbqArycfoFZIm76Vte1Ts8Zsk6XlJK0lOL1xf4PpLrdjj1+55+oFGSDowIrbkPvo9A5zR3n5rl5LHr3U8fq3j8Ut02HPuTZit5KaZ/YE7OuJ/jFby+LWOx691PH74yL3VJN1Dcq1tvu9FxI9LUU974/FrHY9f62R5/BzuZmYZ1JH/oGpmllkOd7OMkTRG0tmlrsNKy+FuBSXpFSWz6DX8eqUEtUzO7fvMZn7fwtz3vZS37py89/JvLajlQEkTJY1O2f6/c/s6SdJHc68fym07P9dXr0a+76tAf5LJtKwD89UyVmjjSCaqOh+4ApgM/AZ4t5RFtdCxks6IiKdpxRxCkjoBB5LcIfpr4L+a2cWfSa7rrs0tnw/8L+BXNJixMCKyOvujNZOP3K2gIuKRiJhBcpMIwOKImBERj0g6TNKzkrZIekfJDH3HAUj6j9zR6YW55Zck1edefzu3bYikj0j6u6RfNty3Et+V9LfcnCJHNNg+Qskc5+/mbow6p4m3sx64RtJBJNM3v9ygv7MkPZN7P7+X9Jnc+p1H2gslzScJ4KW5bxuc23abpPMkvSypTtImST9TMtNhQ4cBPwe+IOlakmAHeCpvjM6UtDhXy9qWfLqwbHG42760neQuwuuBbwCnkEyr2pQvkdw+Phn4IbAVuLaRdv+a63tFbj+7ZkKUdDxwP7AFuINkMrKHJH14L/v9MXBp3r7uy+uvAphFMu/IjcBm4IeSzsr7/jNIpiv+CnBrbt3zJEfhDwLvkNyJex3JrJejaPpB8/NJjtgBJgKXK3mQxCNAOfAF4PfATyR9rIm+LMN8Wsb2pS7AJ4CPk0zkBMnUrHsVEf+QdBXwNMmkTtdERG0jTQfl/p0YEb+RdAbvPcRhKMmMgaflvnb6J5KQbsx04DaSqWHvB/LnSD8DOIjkmuj/lPQqMBcYDvwo12ZJRNwKIOmw3Lq/5D7ZIGkIyWmsvnn97nU8ImK9pJeBIcCvI2KhpBHAwUA3kl8WIjlwOxt4dm/9WXY53G1fGk8SpneRzFI4jeRoE5Kjenjv/2TDx+r14L1Pmk09ZGEnNfL6/5Ac/e70wl6+/2/AQ8BIkqP4gY202duNIhuaaDcJ6E1ymuUdktkbyxtp19Q+d763H5DMp7LTX1P0ZRnlcLd9aWcIHUByVHk4yekMgFdy/14i6RiSMN8OIOkQklMyK0jOg39F0qyIeL5B/wtI5i2fKOkBkk8JOz0GbAMuJpk98EMkoT2iiZr/g+R8+QJ2D/enSR6C8T8lbQCuzq1/dA/9vEUSysdIugJ4iveOsLsB5zVRR76/5f69RFI3kitj3iQ5hbSG5Lb7T5E8RWhDoz1Y5vmcu+1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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# set width of bar\n", "barWidth = 0.4\n", " \n", "# set height of bar\n", "bars1=np.zeros((4,))\n", "bars2=np.zeros((4,))\n", "\n", "for i in range(0,4):\n", " bars1[i] = Table_3.iat[2*i,-1]\n", " bars2[i] = Table_3.iat[2*i+1,-1]\n", " \n", "# Set position of bar on X axis\n", "r1 = np.arange(len(bars1))\n", "r2 = [x + barWidth for x in r1]\n", "r3 = [x + barWidth for x in r2]\n", " \n", "# Make the plot\n", "plt.bar(r2, bars1, width=barWidth, edgecolor='white')\n", "plt.bar(r3, bars2, width=barWidth, edgecolor='white')\n", " \n", "# Add xticks on the middle of the group bars\n", "plt.xlabel('Taux de Mortalité', fontweight='bold')\n", "plt.xticks([r + barWidth*1.5 for r in range(len(bars1))], ['Age_1', 'Age_2', 'Age_3', 'Age_4'])\n", " \n", "# Create legend & Show graphic\n", "plt.legend(['Smoker','Non_Smoker'])\n", "plt.show()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Remarque:\n", "\n", "En tenant compte du paramètre \"AGE\", on constate que le tabagisme augmente le taux de mortalité des femmes. Cependant, nous ne pouvons pas voir cet impact des cigarettes pour les personnes âgées de 65 ans et plus. Cette étude montre que le fait de négliger un paramètre dans une étude peut biaiser l'analyse." ] } ], "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": "3.6.4" } }, "nbformat": 4, "nbformat_minor": 2 }