From 758aa33b59651b170581f204067e54a744bff83b Mon Sep 17 00:00:00 2001
From: 7f9d4a2f9f536fc2da1beb7df3382bb3
 <7f9d4a2f9f536fc2da1beb7df3382bb3@app-learninglab.inria.fr>
Date: Fri, 19 Dec 2025 19:42:13 +0000
Subject: [PATCH] Add computational document on Simpson paradox

---
 module3/exo3/exercice_en.ipynb | 317 ++++++++++++++++++++++++++++++++-
 1 file changed, 314 insertions(+), 3 deletions(-)

diff --git a/module3/exo3/exercice_en.ipynb b/module3/exo3/exercice_en.ipynb
index 0bbbe37..924d6ae 100644
--- a/module3/exo3/exercice_en.ipynb
+++ b/module3/exo3/exercice_en.ipynb
@@ -1,5 +1,317 @@
 {
- "cells": [],
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Autour du paradoxe de Simpson\n",
+    "\n",
+    "## Objectif\n",
+    "Le paradoxe de Simpson décrit une situation statistique dans laquelle une tendance observée\n",
+    "dans plusieurs sous-groupes disparaît ou s’inverse lorsque les données sont agrégées.\n",
+    "\n",
+    "L’objectif de ce document est :\n",
+    "- d’illustrer le paradoxe sur un jeu de données simple,\n",
+    "- de visualiser les tendances par sous-groupes et globalement,\n",
+    "- de discuter les implications pour l’analyse de données et la reproductibilité.\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import pandas as pd\n",
+    "import matplotlib.pyplot as plt\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>Groupe</th>\n",
+       "      <th>Succès</th>\n",
+       "      <th>Total</th>\n",
+       "      <th>Traitement</th>\n",
+       "      <th>Taux_succès</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>0</th>\n",
+       "      <td>Jeunes</td>\n",
+       "      <td>90</td>\n",
+       "      <td>100</td>\n",
+       "      <td>A</td>\n",
+       "      <td>0.9</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>1</th>\n",
+       "      <td>Âgés</td>\n",
+       "      <td>10</td>\n",
+       "      <td>100</td>\n",
+       "      <td>A</td>\n",
+       "      <td>0.1</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>2</th>\n",
+       "      <td>Jeunes</td>\n",
+       "      <td>80</td>\n",
+       "      <td>100</td>\n",
+       "      <td>B</td>\n",
+       "      <td>0.8</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>3</th>\n",
+       "      <td>Âgés</td>\n",
+       "      <td>20</td>\n",
+       "      <td>100</td>\n",
+       "      <td>B</td>\n",
+       "      <td>0.2</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "   Groupe  Succès  Total Traitement  Taux_succès\n",
+       "0  Jeunes      90    100          A          0.9\n",
+       "1    Âgés      10    100          A          0.1\n",
+       "2  Jeunes      80    100          B          0.8\n",
+       "3    Âgés      20    100          B          0.2"
+      ]
+     },
+     "execution_count": 5,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# Exemple classique du paradoxe de Simpson\n",
+    "data = pd.DataFrame({\n",
+    "    \"Traitement\": [\"A\", \"A\", \"B\", \"B\"],\n",
+    "    \"Groupe\": [\"Jeunes\", \"Âgés\", \"Jeunes\", \"Âgés\"],\n",
+    "    \"Succès\": [90, 10, 80, 20],\n",
+    "    \"Total\": [100, 100, 100, 100]\n",
+    "})\n",
+    "\n",
+    "data[\"Taux_succès\"] = data[\"Succès\"] / data[\"Total\"]\n",
+    "data\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th>Traitement</th>\n",
+       "      <th>A</th>\n",
+       "      <th>B</th>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>Groupe</th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>Jeunes</th>\n",
+       "      <td>0.9</td>\n",
+       "      <td>0.8</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>Âgés</th>\n",
+       "      <td>0.1</td>\n",
+       "      <td>0.2</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "Traitement    A    B\n",
+       "Groupe              \n",
+       "Jeunes      0.9  0.8\n",
+       "Âgés        0.1  0.2"
+      ]
+     },
+     "execution_count": 6,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "pivot = data.pivot(index=\"Groupe\", columns=\"Traitement\", values=\"Taux_succès\")\n",
+    "pivot\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>Succès</th>\n",
+       "      <th>Total</th>\n",
+       "      <th>Taux_succès</th>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>Traitement</th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>A</th>\n",
+       "      <td>100</td>\n",
+       "      <td>200</td>\n",
+       "      <td>0.5</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>B</th>\n",
+       "      <td>100</td>\n",
+       "      <td>200</td>\n",
+       "      <td>0.5</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "            Succès  Total  Taux_succès\n",
+       "Traitement                            \n",
+       "A              100    200          0.5\n",
+       "B              100    200          0.5"
+      ]
+     },
+     "execution_count": 7,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "global_data = data.groupby(\"Traitement\")[[\"Succès\", \"Total\"]].sum()\n",
+    "global_data[\"Taux_succès\"] = global_data[\"Succès\"] / global_data[\"Total\"]\n",
+    "global_data\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Discussion\n",
+    "\n",
+    "Ce paradoxe provient du fait que les groupes ne sont pas répartis de manière équilibrée\n",
+    "entre les traitements. Le poids relatif des sous-groupes influence fortement le résultat\n",
+    "agrégé.\n",
+    "\n",
+    "Ce phénomène souligne l’importance :\n",
+    "- de stratifier les données avant analyse,\n",
+    "- de comprendre les variables de confusion,\n",
+    "- de ne pas se fier uniquement aux statistiques globales.\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Reproductibilité\n",
+    "\n",
+    "- Les données sont intégrées directement dans le code.\n",
+    "- Les calculs sont déterministes (pas d’aléatoire).\n",
+    "- Les bibliothèques utilisées sont standards (pandas, matplotlib).\n",
+    "- Le document peut être réexécuté intégralement sur une autre machine.\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Conclusion\n",
+    "\n",
+    "Le paradoxe de Simpson montre que des conclusions opposées peuvent être tirées\n",
+    "selon le niveau d’agrégation des données.\n",
+    "\n",
+    "Il rappelle que l’analyse de données nécessite :\n",
+    "- une compréhension fine du contexte,\n",
+    "- une exploration multi-niveaux,\n",
+    "- une grande prudence dans l’interprétation des résultats.\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
  "metadata": {
   "kernelspec": {
    "display_name": "Python 3",
@@ -16,10 +328,9 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.6.3"
+   "version": "3.6.4"
   }
  },
  "nbformat": 4,
  "nbformat_minor": 2
 }
-
-- 
2.18.1