{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "9bad8ced-d99e-4417-bb97-386bf8f09435",
   "metadata": {
    "tags": [
     "remove-cell"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "---------------------------------\n",
      "Working on the host: Joachims-MacBook-Pro.local\n",
      "\n",
      "---------------------------------\n",
      "Python version: 3.10.2 | packaged by conda-forge | (main, Feb  1 2022, 19:30:18) [Clang 11.1.0 ]\n",
      "\n",
      "---------------------------------\n",
      "Python interpreter: /opt/miniconda3/envs/srh/bin/python\n"
     ]
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "# Load the \"autoreload\" extension\n",
    "%load_ext autoreload\n",
    "# always reload modules\n",
    "%autoreload 2\n",
    "# black formatter for jupyter notebooks\n",
    "#%load_ext nb_black\n",
    "# black formatter for jupyter lab\n",
    "%load_ext lab_black\n",
    "\n",
    "%run ../../src/notebook_env.py"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "82bad07a-11ad-441f-99fa-377005e6a312",
   "metadata": {},
   "source": [
    "# Varianzanalyse - ANOVA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "64930077-9a2b-49e4-bfbf-8357338fb3b9",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from scipy.stats import f, f_oneway, ttest_ind\n",
    "import statsmodels.api as smi\n",
    "from statsmodels.stats.multicomp import pairwise_tukeyhsd"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cfd2f4eb-de37-4173-9bbf-0785916d352f",
   "metadata": {},
   "source": [
    "In diesem Abschnitt wird eine Methode namens <a href=\"https://de.wikipedia.org/wiki/Varianzanalyse\">Varianzanalyse</a> (englisch analysis of variance, kurz ANOVA) erörtert, mit der mehrere Mittelwerte einer Grundgesamtheit verglichen werden können.\n",
    "\n",
    "Genauer gesagt geht es um die sogenannte einfaktorielle Varianzanalyse ({cite:t}`fahrmeirstatistik` s.478). Bei dieser Art der ANOVA werden die Mittelwerte einer Variablen verglichen, die sich aus der Klassifizierung durch *eine* andere Variable, dem sogenannten **Faktor**, ergeben. Um das Konzept zu veranschaulichen, wollen wir ein einfaches Beispiel entwerfen. Angenommen, wir vergleichen die mittleren Jahresgehälter der in Deutschland lebenden Personen, gruppiert nach Bundesländern, dann erhalten wir $16$ Mittelwerte der Jahresgehälter, einen für jedes Bundesland. In diesem Beispiel ist die Bundeslandvariable also eine Klassifikationsvariable, der so genannte Faktor.\n",
    "\n",
    "Bitte beachten Sie, dass die einfaktorielle Varianzanalyse die Verallgemeinerung des $2$-Stichproben $t$-Tests auf mehr als zwei Grundgesamtheiten ist."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "167f023d-d0dc-4117-9abc-f443c289782b",
   "metadata": {},
   "source": [
    "## Einfaktorielle ANOVA"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4e637344-eb20-4d44-a920-ad47aade6f8c",
   "metadata": {},
   "source": [
    "Die grundlegende Logik einer einfaktoriellen ANOVA besteht darin, aus jeder Gruppe unabhängige Zufallsstichproben zu ziehen, dann die Stichprobenmittelwerte für jede Gruppe zu berechnen und anschließend die Variation der Stichprobenmittelwerte zwischen den Gruppen mit der Variation innerhalb der Gruppen zu vergleichen. Schließlich wird auf der Grundlage einer Teststatistik entschieden, ob die Mittelwerte der Gruppen gleich sind oder nicht.\n",
    "\n",
    "Auf der Grundlage dieser Logik benötigen wir quantitative **Maße für die Variabilität**. Daher teilen wir die Gesamtvariabilität in zwei Segmente auf: Eines, das die **Variabilität zwischen den Gruppen** berücksichtigt, und das andere, das die **Variabilität innerhalb der Gruppen** berücksichtigt."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "02f9a1a6-7976-4465-a2a4-838a6849ce31",
   "metadata": {},
   "source": [
    "### Maße der Variabilität"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b5224692-d5c7-448e-830a-7016842582df",
   "metadata": {},
   "source": [
    "Wir führen drei quantitative Maße für die Variation ein:\n",
    "\n",
    "- Summe der Gesamtquadrate (SST)\n",
    "- Summe der Gruppenquadrate (SSG)\n",
    "- Summe der Fehlerquadrate (SSE)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bf44d7a8-e02d-441e-82da-ab24a278f4a7",
   "metadata": {},
   "source": [
    "Die **Summe der Gesamtquadrate (SST)** ist ein Maß für die Gesamtvariabilität der Variablen. Sie ist gegeben durch"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a2fbff1f-d7c7-4633-a9a1-98ca9e17a48c",
   "metadata": {},
   "source": [
    "$$SST = \\sum_{i=1}^n(x_i-\\bar x)^2\\text{,}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d9bcd349-e944-444b-ac4c-8cc2c574ec94",
   "metadata": {},
   "source": [
    "wobei $x_i$ den Beobachtungen in den Stichproben entspricht und $\\bar x$ für den Gesamtmittelwert aller Stichproben steht.\n",
    "\n",
    "Die **Summe der Gruppenquadrate (SSG)** ist ein Maß für die Variabilität zwischen Gruppen und entspricht der quadrierten Abweichung der Gruppenmittelwerte vom Gesamtmittelwert, gewichtet mit dem Stichprobenumfang."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8a312c0a-7610-4370-9699-49f4c9a55389",
   "metadata": {},
   "source": [
    "$$SSG = \\sum_{i=1}^n n_j(\\bar x_i-\\bar x)^2$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c9c18f0a-4643-4c8a-a293-823823965ff7",
   "metadata": {},
   "source": [
    "Dabei steht $n_j$ für den Stichprobenumfang der Gruppe $j$, $\\bar{x}_i$ für den Mittelwert der Gruppe $j$ und $\\bar{x}$ für den Gesamtmittelwert der Stichprobe."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b7bd2ec7-d13c-4722-8f70-b7e495e50ada",
   "metadata": {},
   "source": [
    "Die **Summe der Fehlerquadrate ($SSE$)** schließlich ist ein Maß für die Variabilität innerhalb der Gruppen. Sie steht im Zusammenhang mit der unerklärten Variabilität, d. h. der Variabilität, die nicht durch die Gruppenvariable erklärt werden kann. Die Summe der Fehlerquadrate ist gegeben durch"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0241ab4d-60a6-4e11-9830-697cb81c5163",
   "metadata": {},
   "source": [
    "$$SSE = \\sum_{i=1}^n (n_j-1)s_j^2\\text{,}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "388112ed-56ba-404b-9dd9-8c75f8498df5",
   "metadata": {},
   "source": [
    "wobei $n_j$ den Stichprobenumfang für Gruppe $j$ und $s^2_{j}$ die Varianz von Gruppe $j$ bezeichnet. Alternativ kann man $SSE$ sowie die Differenz von $SST$ und $SSG$ berechnen"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "58e6ef07-931b-48c0-a386-73f384308cd1",
   "metadata": {},
   "source": [
    "$$SSE = SST-SSG\\text{.}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "34b9adeb-78a6-4166-ad29-56a24f26e22f",
   "metadata": {},
   "source": [
    "### Maße der mittleren Variabilität"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8db5b37b-33a4-4bac-b2e4-eb6c9fffea8e",
   "metadata": {},
   "source": [
    "Bisher haben wir Maße für die Gesamtvariabilität ($SST$), die Variabilität zwischen Gruppen ($SSG$) und die Variabilität innerhalb von Gruppen ($SSE$) berechnet. Um eine durchschnittliche Variabilität zu erhalten, skalieren wir im nächsten Schritt diese Variabilitätsmaße mit dem Stichprobenumfang (genauer gesagt mit den Freiheitsgraden, $df$).\n",
    "\n",
    "Die **Freiheitsgrade** werden für jede Unterteilung der Variabilität (Gesamtvariabilität, Variabilität zwischen Gruppen und Variabilität innerhalb von Gruppen) definiert.\n",
    "\n",
    "-    Gesamtvariabilität"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "15ff3495-8e46-4c2a-9a2a-942aef17d97a",
   "metadata": {},
   "source": [
    "$$df_T = n-1\\text{,}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d4d7a2e9-5348-45c3-9e26-0e67e7d4d89a",
   "metadata": {},
   "source": [
    "wobei $n$ den Gesamtumfang der Stichprobe bezeichnet. den Gesamtumfang der Stichprobe bezeichnet.\n",
    "\n",
    "- Variabilität zwischen den Gruppen"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d0b18266-f8d9-4527-8a03-0d9fc7c2bc85",
   "metadata": {},
   "source": [
    "$$df_G=k-1\\text{,}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c9af7014-448e-4ff7-b4b8-83e5b8aaaff0",
   "metadata": {},
   "source": [
    "wobei $k$ die Anzahl der Gruppen bezeichnet.\n",
    "den Gesamtumfang der Stichprobe bezeichnet.\n",
    "\n",
    "- Variabilität innerhalb der Gruppe"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "44351466-1ecb-4a6b-bf50-7f7adc17543e",
   "metadata": {},
   "source": [
    "$$df_E = n-k\\text{.}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "712accff-a333-48e6-94e4-79747626a1d9",
   "metadata": {},
   "source": [
    "Nun können wir die **mittleren Quadrate** für die Variabilität zwischen den Gruppen und die Variabilität innerhalb der Gruppen berechnen. Die durchschnittliche Variabilität zwischen und innerhalb der Gruppen wird als die Gesamtvariabilität, skaliert mit den zugehörigen Freiheitsgraden, berechnet.\n",
    "\n",
    "- Mittlere Variabilität zwischen den Gruppen"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d0cddd16-9323-49a0-aa5a-cd114c46bda7",
   "metadata": {},
   "source": [
    "$$MSG = \\frac{SSG}{df_G}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e7dee819-f45f-4024-b084-5c1aaae7aadb",
   "metadata": {},
   "source": [
    "- Mittlere Variabilität innerhalb der Gruppe"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "071aa68d-ed8d-4975-8681-e0c7ad75d711",
   "metadata": {},
   "source": [
    "$$MSE = \\frac{SSE}{df_E}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7e9d69cc-e48c-456a-9a71-f5dfb22872a5",
   "metadata": {},
   "source": [
    "### Teststatistik und $p$-Wert"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c21dbcf8-1ac0-4031-bdd4-3c6961080097",
   "metadata": {},
   "source": [
    "Schließlich vergleichen wir die mittlere Variation zwischen den Gruppen, $MSG$, mit der Variation innerhalb der Gruppe, $MSE$. Daher berechnen wir das Verhältnis zwischen der durchschnittlichen Variation zwischen den Gruppen ($MSG$) und der Variation innerhalb der Gruppen ($MSE$), das mit $F$ bezeichnet wird."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d632d30a-b0c0-4761-9a82-5aed6075143b",
   "metadata": {},
   "source": [
    "$$F= \\frac{MSG}{MSE}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3721fa25-b2e1-46d2-a7f8-962130960a41",
   "metadata": {},
   "source": [
    "Die $F$-Statistik hat die $F$-Verteilung (benannt nach <a href=\"https://de.wikipedia.org/wiki/Ronald_Aylmer_Fisher\">Sir Ronald A. Fisher</a>) mit"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "39867d8d-a2ae-4c39-a758-ff4d619f47d8",
   "metadata": {},
   "source": [
    "$$df = (k-1, n-k)\\text{,}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "19472d0c-108e-41fb-9d21-4f057ebb1e3a",
   "metadata": {},
   "source": [
    "wobei $k$ für die Anzahl der Gruppen und $n$ für den Stichprobenumfang steht. Große Werte der $F$-Werte zeigen an, dass die Variation zwischen den Stichprobenmittelwerten der Gruppen im Verhältnis zur Variation innerhalb der Gruppe groß ist. Darüber hinaus können wir den $p$-Wert für jeden gegebenen $F$-Wert berechnen. Wenn der $p$-Wert klein ist, liefern die Daten überzeugende Beweise dafür, dass sich mindestens ein Paar von Gruppenmittelwerten voneinander unterscheidet. Ist der $p$-Wert groß, liefern die Daten keinen überzeugenden Beweis dafür, dass sich zumindest ein Paar von Gruppenmittelwerten voneinander unterscheidet, und die beobachteten Unterschiede in den Stichprobenmittelwerten sind somit auf Stichprobenvariabilität (oder Zufall) zurückzuführen."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ac22694d-4a7d-42b9-8a07-03033625cf97",
   "metadata": {},
   "source": [
    "### Einfaktorielle ANOVA-Tabellen"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "de80e04e-2745-4812-8051-5e4a1d9ea279",
   "metadata": {},
   "source": [
    "Wie oben dargestellt, umfasst die einfache Varianzanalyse mehrere Analyseschritte. Dabei ist eine gängige Methode zur Darstellung einer einfachen ANOVA die so genannte **einfaktorielle ANOVA-Tabelle**. Der allgemeine Aufbau einer solchen Tabelle ist unten dargestellt."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d8eac7f2-1658-416a-84cc-f07732c6dc7e",
   "metadata": {},
   "source": [
    "|Quelle|$df$|Summe der Quadrate (SS)| Mittlere Quadrate (MS)|$F$-Statistik|$p$-Wert|\n",
    "|---|---|---|---|---|---|\n",
    "|Gruppe/Klasse|$k-1$|$SSG$|$MSG = \\frac{SSG}{k-1}$ | $F=\\frac{MSG}{MSE}$ | $p$|\n",
    "|Fehler/Residuen|$n-k$|$SSE$|$MSE=\\frac{SSE}{n-k}$||\n",
    "|Insgesamt|$n-1$|$SST$|||"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c35667d6-dfc8-4a31-a1b6-faa5c8d0304d",
   "metadata": {},
   "source": [
    "## Einfaktorieller ANOVA-Hypothesentest"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eb58a399-fefb-406a-b52e-0b37c508fb02",
   "metadata": {},
   "source": [
    "Der Zweck eines **einfaktoriellen ANOVA-Hypothesentests** ist der Vergleich von $k$ Grundgesamtheits-/Gruppenmittelwerten, $\\mu_1, \\mu_2,...,\\mu_k$. \n",
    "Die folgenden Annahmen müssen erfüllt sein, damit eine einseitige ANOVA angewendet werden kann ({cite:t}`fahrmeirstatistik` s.485):\n",
    "\n",
    "- Zufällige Stichproben\n",
    "- Unabhängige Stichproben\n",
    "- Für jede Grundgesamtheit ist die betrachtete Variable normalverteilt.\n",
    "- Die Standardabweichungen der betrachteten Variable sind für alle Grundgesamtheiten gleich.\n",
    "\n",
    "Ein einfaktorieller ANOVA-Hypothesentest folgt demselben schrittweisen Verfahren wie andere Hypothesentests. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "18dac56a",
   "metadata": {},
   "source": [
    "|||\n",
    "|---|---|\n",
    "|Schritt 1| Geben Sie die Nullhypothese $H_0$ und alternative Hypothese $H_A$ an|\n",
    "|Schritt 2|Legen Sie das Signifikanzniveau,$\\alpha$ fest|\n",
    "|Schritt 3|Berechnen Sie den Wert der Teststatistik|\n",
    "|Schritt 4|Bestimmen Sie den p-Wert|\n",
    "|Schritt 5| Wenn $p \\le \\alpha$, $H_0$ ablehnen; ansonsten $H_0$ nicht ablehnen|\n",
    "|Schritt 6|Interpretieren Sie das Ergebnis des Hypothesentests|"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1e1aa8da-2ea6-420e-82ac-f5a1e0e53e18",
   "metadata": {},
   "source": [
    "### Einfaktorieller ANOVA-Hypothesentest: Ein Beispiel"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "70c5e165-6dd8-4b92-bdc2-b10c520be7cb",
   "metadata": {},
   "source": [
    "Um praktische Erfahrungen zu sammeln, wenden wir den **einfaktoriellen ANOVA-Hypothesentest** in einer Übung an. Dazu laden wir den `students` Datensatz. Sie können die Datei `students.csv` <a href=\"https://userpage.fu-berlin.de/soga/200/2010_data_sets/students.csv\">hier</a> herunterladen. Importieren Sie den Datensatz und geben Sie ihm einen passenden Namen."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "17627746-49ca-4557-a442-ac3d22c7d773",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Lese Datei students.csv als Dataframe ein\n",
    "students = pd.read_csv(\"../../data/students.csv\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cd20ceaf-4ceb-43fa-bbfc-f4d88d03146a",
   "metadata": {},
   "source": [
    "Der `students` Datensatz besteht aus $8239$ Zeilen, von denen jede einen bestimmten Studenten repräsentiert, und $16$ Spalten, von denen jede einer Variable/einem Merkmal entspricht, das sich auf diesen bestimmten Studenten bezieht. Diese selbsterklärenden Variablen sind: *stud_id, name, gender, age, height, weight, religion, nc_score, semester, major, minor, score1, score2, online_tutorial, graduated, salary.*"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d31cc806-0629-4eef-9206-e333323c2f3e",
   "metadata": {},
   "source": [
    "Um den **einfaktoriellen ANOVA-Hypothesentest** zu veranschaulichen, untersuchen wir das mittlere Jahresgehalt der Absolventen, gruppiert nach ihrem Hauptstudienfach. Zur Verdeutlichung: In diesem Beispiel erfolgt die Klassifizierung/Gruppierung durch eine Variable, die Hauptvariable, den so genannten Faktor, wir führen also eine einfaktorielle ANOVA durch. In dieser Übung **wollen wir testen, ob sich das mittlere Jahresgehalt der Absolventen zwischen den Absolventen verschiedener Studienfächer unterscheidet.**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "900352a2-936e-49f5-8f88-b8f6c6a06e3e",
   "metadata": {},
   "source": [
    "### Datenexploration und Aufbereitung"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aa1ed41b-60f0-48fd-b552-78c9f871d3b4",
   "metadata": {},
   "source": [
    "Wir beginnen unsere Datenanalyse mit dem Zufallsstichprobenverfahren. Wir ziehen eine Zufallsstichprobe von $275$ Studenten aus dem Datensatz mit Hilfe der `sample()` Methode in Python. Wir wollen sicherstellen, dass wir nur Studenten mit abgeschlossenem Studium in die Stichprobe aufnehmen, deshalb unterteilen wir die Daten des Dataframes zuvor in Python. Des Weiteren reduzieren wir unseren Datensatz auf die zwei Variablen von Interesse, die kategoriale Variable `major` und die numerische Variable `salary`. Dann zeigen wir die ersten $10$ Zeilen des Datensatzes an."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "41c9f204-fcaa-418d-b68e-8bba9301748d",
   "metadata": {},
   "outputs": [
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       "      <th>2489</th>\n",
       "      <td>Economics and Finance</td>\n",
       "      <td>59920.480581</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1194</th>\n",
       "      <td>Mathematics and Statistics</td>\n",
       "      <td>46116.221731</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>242</th>\n",
       "      <td>Social Sciences</td>\n",
       "      <td>35881.736200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2969</th>\n",
       "      <td>Economics and Finance</td>\n",
       "      <td>48456.787464</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1476</th>\n",
       "      <td>Mathematics and Statistics</td>\n",
       "      <td>61384.549346</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6765</th>\n",
       "      <td>Biology</td>\n",
       "      <td>61819.845923</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                           major        salary\n",
       "5019                     Biology  49976.937146\n",
       "4477           Political Science  27821.990115\n",
       "241       Environmental Sciences  37668.890265\n",
       "7166                     Biology  60958.213489\n",
       "2489       Economics and Finance  59920.480581\n",
       "1194  Mathematics and Statistics  46116.221731\n",
       "242              Social Sciences  35881.736200\n",
       "2969       Economics and Finance  48456.787464\n",
       "1476  Mathematics and Statistics  61384.549346\n",
       "6765                     Biology  61819.845923"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n = 275\n",
    "data = students.loc[students[\"graduated\"] == 1, [\"major\", \"salary\"]].sample(\n",
    "    n, random_state=1\n",
    ")\n",
    "data.head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "94c1748f-e157-4ef2-aebe-5282facfeef8",
   "metadata": {},
   "source": [
    "Aus reinem Interesse visualisieren wir die Zählungen für jede der $6$ verschiedenen Studienteilnehmer in unserer Stichprobe, indem wir ein Balkendiagramm erstellen. Wir verwenden die `barh()` Funktion aus der `mathplotlib` Bibliothek für die Darstellung."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "dfc21929-ffd0-4673-9599-6f3d25f22743",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'Anzahl')"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "data.groupby(\"major\")[\"salary\"].count().plot.barh(ax=ax)\n",
    "ax.set_ylabel(\"\")\n",
    "ax.set_xlabel(\"Anzahl\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e270927b-3ea8-48d9-a79f-9fd682544bcc",
   "metadata": {},
   "source": [
    "Wir sehen, dass die verschiedenen Studienteilnehmer in unserer Stichprobe nicht gleich verteilt sind, aber das ist in Ordnung.\n",
    "\n",
    "Bevor wir mit dem Hypothesentest beginnen, überprüfen wir, ob die Annahmen für den einfaktoriellen ANOVA-Hypothesentest erfüllt sind. Die Stichproben sind Zufallsstichproben und unabhängig. Das ist in Ordnung. Wir überprüfen die Normalitätsannahme, indem wir für jede gruppierte Variable ein Normalwahrscheinlichkeitsdiagramm (<a href=\"https://de.wikipedia.org/wiki/Quantil-Quantil-Diagramm\">Q-Q-Diagramm</a>) erstellen."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "8b783c69-7abc-4916-9107-4b14e76dd4f1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Erzeuge Q-Q Plot\n",
    "for _major in data.major.unique():\n",
    "    _ = smi.qqplot(data.loc[data[\"major\"] == _major, \"salary\"], line=\"r\")\n",
    "    ax = plt.gca()\n",
    "    ax.set_title(_major)\n",
    "    ax.set_xlabel(\"Theoretische Quantile\")\n",
    "    ax.set_ylabel(\"Stichproben Quantile\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d28fc8ff-1d22-4ad4-bf1b-75ab0fdf2a93",
   "metadata": {},
   "source": [
    "Als nächstes testen wir die Annahme gleicher Standardabweichungen. Dazu berechnen wir die Standardabweichung für jede Gruppe. Die Programmiersprache Python bietet einige ausgezeichnete Funktionen zur Berechnung statistischer Parameter für verschiedene Gruppierungen eines Datensatzes. Für unser Beispiel verwenden wir die Funktion `pivot_table()`, um die Standardabweichungen für jede Gruppe zu berechnen."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "f1830e68-e1ed-4c12-a6d2-7248b31363fb",
   "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>major</th>\n",
       "      <th>salary</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>5019</th>\n",
       "      <td>Biology</td>\n",
       "      <td>49976.937146</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4477</th>\n",
       "      <td>Political Science</td>\n",
       "      <td>27821.990115</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>241</th>\n",
       "      <td>Environmental Sciences</td>\n",
       "      <td>37668.890265</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7166</th>\n",
       "      <td>Biology</td>\n",
       "      <td>60958.213489</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2489</th>\n",
       "      <td>Economics and Finance</td>\n",
       "      <td>59920.480581</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                       major        salary\n",
       "5019                 Biology  49976.937146\n",
       "4477       Political Science  27821.990115\n",
       "241   Environmental Sciences  37668.890265\n",
       "7166                 Biology  60958.213489\n",
       "2489   Economics and Finance  59920.480581"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "768c52a2-4ce0-4c2a-931a-27f129cb7d32",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "major\n",
       "Biology                        8470.016077\n",
       "Economics and Finance          7175.592532\n",
       "Environmental Sciences         6460.464096\n",
       "Mathematics and Statistics     8384.559216\n",
       "Political Science             10273.903367\n",
       "Social Sciences                7227.381892\n",
       "Name: salary, dtype: float64"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "table = data.groupby(\"major\")[\"salary\"].std()\n",
    "table"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7db4e5be-c2d5-41ed-a4cb-3b5b970bf0c6",
   "metadata": {},
   "source": [
    "Als Faustregel gilt die Annahme gleicher Standardabweichungen als erfüllt, wenn das Verhältnis der größten zur kleinsten Standardabweichung der Stichprobe kleiner als $2$ ist."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "e033c0c3-3891-478b-bb6a-fc85a10700fa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.5902732705830243"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ratio = table.max() / table.min()\n",
    "ratio"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c9318331-86d4-42c2-8964-897e42701fcb",
   "metadata": {},
   "source": [
    "Das Verhältnis zwischen der größten und der kleinsten Standardabweichung der Stichprobe beträgt $1,59$. Das liegt nahe am Schwellenwert von $2$, ist aber für unser Musterbeispiel noch akzeptabel. Daraus können wir schließen, dass die Annahmen erfüllt sind.\n",
    "\n",
    "Beachten Sie, dass die einseitige ANOVA robust gegenüber moderaten Verstößen gegen die Normalitätsannahme und die Annahme gleicher Standardabweichungen ist ({cite:t}`fahrmeirstatistik` s.486)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "beff4e78-3e59-4f27-82fa-b2331ec2eb6b",
   "metadata": {
    "tags": []
   },
   "source": [
    "### Überprüfung der Hypothesen"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f3f1d15c-2408-4847-8a86-1021b4eca0ad",
   "metadata": {},
   "source": [
    "Um den **einfaktoriellen ANOVA-Hypothesentest** durchzuführen, folgen wir dem schrittweisen Durchführungsverfahren für Hypothesentests."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ee32c7b9-1e03-4e57-8fcc-c5df0fb21d3c",
   "metadata": {},
   "source": [
    "**Schritt 1 : Geben Sie die Nullhypothese $H_0$ und alternative Hypothese $H_A$ an**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ed155539-6de7-4003-94df-4f295bdca8d8",
   "metadata": {},
   "source": [
    "Die Nullhypothese besagt, dass das mittlere Jahresgehalt bei allen Gruppen von Absolventen gleich ist."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1bed1841-c421-40a8-a792-7e8f58213293",
   "metadata": {},
   "source": [
    "$$H_0: \\quad \\mu_1=\\mu_2=\\mu_3=\\mu_4=\\mu_5=\\mu_6$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "16c3c394-458d-400f-ae9d-47c472f266b0",
   "metadata": {},
   "source": [
    "**Alternative Hypothese**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6f2eab79-9dc9-4b56-b0e1-93efc214f7d3",
   "metadata": {},
   "source": [
    "$$H_A: \\quad \\text{Nicht alle Mittelwerte sind gleich}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e753611d-9467-489a-b5ed-aeb33909745c",
   "metadata": {},
   "source": [
    "**Schritt 2: Legen Sie das Signifikanzniveau,$\\alpha$ fest**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0788b846-5b36-4a9b-8834-17939a7c6645",
   "metadata": {},
   "source": [
    "$$\\alpha = 0,01$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "d9b6b426-3361-4592-963f-664a6a819fe1",
   "metadata": {},
   "outputs": [],
   "source": [
    "alpha = 0.01"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3cfdcb51-daa5-4f30-9839-760250182748",
   "metadata": {},
   "source": [
    "**Schritt 3 und 4: Berechnen Sie den Wert der Teststatistik und den $p$-Wert**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "25d990c7-c7a2-4ce4-a3b6-c04ed6024e24",
   "metadata": {
    "tags": []
   },
   "source": [
    "Um die $F$-Test-Statistik zu berechnen, müssen wir zuvor mehrere Größen bestimmen. Zur Veranschaulichung berechnen wir die $F$-Teststatistik manuell in Python. Schritt für Schritt füllen wir die ANOVA-Tabelle aus, bis wir schließlich die $F$-Teststatistik und folglich den $p$-Wert erhalten."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "756f7ab4",
   "metadata": {},
   "source": [
    "|Quelle|$df$|Summe der Quadrate (SS)| Mittlere Quadrate (MS)|$F$-Statistik|$p$-Wert|\n",
    "|---|---|---|---|---|---|\n",
    "|Gruppe/Klasse|$k-1$|$SSG$|$MSG = \\frac{SSG}{k-1}$|$F=\\frac{MSG}{MSE}$| $p$|\n",
    "|Fehler/Residuen|$n-k$|$SSE$|$MSE=\\frac{SSE}{n-k}$||\n",
    "|Insgesamt|$n-1$|$SST$|||"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "70a20bef-9d59-4523-a35c-a597bb6e4031",
   "metadata": {},
   "source": [
    "Wir beginnen mit der ersten Spalte und berechnen die Freiheitsgrade."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "6d82de82-ef8f-41c3-8b98-fc2e95048c68",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k = data[\"major\"].nunique()\n",
    "n = data.shape[0]\n",
    "\n",
    "df_G = k - 1\n",
    "df_G"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "30362ec4-3b70-4aca-9074-e80257818ede",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "269"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_E = n - k\n",
    "df_E"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "2e018888-bbae-4b93-8af4-afcb2ab32d75",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "274"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_T = n - 1\n",
    "df_T"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "67ac3872",
   "metadata": {},
   "source": [
    "|Quelle|$df$|Summe der Quadrate (SS)| Mittlere Quadrate (MS)|$F$-Statistik|$p$-Wert|\n",
    "|---|---|---|---|---|---|\n",
    "|Gruppe/Klasse|$5$|$SSG$|$MSG = \\frac{SSG}{k-1}$|$F=\\frac{MSG}{MSE}$| $p$|\n",
    "|Fehler/Residuen|$269$|$SSE$|$MSE=\\frac{SSE}{n-k}$||\n",
    "|Insgesamt|$274$|$SST$|||"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "33e3999f-39f6-4291-b4dd-e859f113c11a",
   "metadata": {},
   "source": [
    "Außerdem berechnen wir die drei Summen der Quadrate, $SST$, $SSG$ und $SSE$. Erinnern Sie sich an die Gleichungen von oben."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "68fbfc3a-1ac4-468a-92a7-b6a61d29f9a4",
   "metadata": {},
   "source": [
    "$$SST = \\sum_{i=1}^n(x_i-\\bar x)^2\\text{,}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "97080283-d55f-4ad0-8640-94535b230ea8",
   "metadata": {},
   "source": [
    "wobei $x_i$den Beobachtungen in den Stichproben und $\\bar x$ dem Gesamtmittelwert aller Stichproben entspricht."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "99d49062-627f-4dcd-89ee-27cc4dbb6dbd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "33169011167.80223"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Berechne Gesamtmittelwert\n",
    "x_bar = data[\"salary\"].mean()\n",
    "\n",
    "# Beobachtungen\n",
    "xi = data[\"salary\"]\n",
    "\n",
    "# Berechne SST\n",
    "SST = np.sum((xi - x_bar) ** 2)\n",
    "SST"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a4671f95-e95d-43ce-b5ff-fa025b9bfec7",
   "metadata": {},
   "source": [
    "$$SSG = \\sum_{i=1}^n n_j(\\bar x_i-\\bar x)^2$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1dc9432e-2089-4c19-8e2a-049582ffaa3a",
   "metadata": {},
   "source": [
    "Dabei steht $n_j$ für den Stichprobenumfang der Gruppe $j, \\bar{x}_i$ für den Mittelwert der Gruppe $j$ und $\\bar x$ für den Gesamtmittelwert aller Stichproben."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "a00ac31e-7c85-4952-a130-0b0b95610243",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "major\n",
       "Biology                       50\n",
       "Economics and Finance         48\n",
       "Environmental Sciences        53\n",
       "Mathematics and Statistics    40\n",
       "Political Science             50\n",
       "Social Sciences               34\n",
       "Name: salary, dtype: int64"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n_j = data.groupby(\"major\")[\"salary\"].count()\n",
    "n_j"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "08950881-e69d-4c68-8687-196df3a175a4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "15425759144.907019"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Berechne Stichprobengrösse für alle Gruppen\n",
    "n_j = data.groupby(\"major\")[\"salary\"].count()\n",
    "\n",
    "# Berechne Mittelwert für alle Gruppen\n",
    "xi_bar = data.groupby(\"major\")[\"salary\"].mean()\n",
    "\n",
    "# Berechne SSG\n",
    "SSG = np.sum(n_j * (xi_bar - x_bar) ** 2)\n",
    "SSG"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1e88b45e-7820-4d6b-90c0-230d1aba934b",
   "metadata": {
    "tags": []
   },
   "source": [
    "$$SSE = \\sum_{i=1}^n (n_j-1)s_j^2\\text{,}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "197a7efe-584d-4ab6-9bc9-6593e64e9e64",
   "metadata": {},
   "source": [
    "wobei $n_j$ den Stichprobenumfang für die Gruppe $j$ und $s^2_j$ die Varianz der Gruppe $j$ bezeichnet."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "279e0943-7927-49c1-9899-59cd1784ddd0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "17743252022.895218"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Berechne Standardabweichung für die einzelnen Gruppen\n",
    "s2_j = data.groupby(\"major\")[\"salary\"].std()\n",
    "\n",
    "# Berechne SSE\n",
    "SSE = np.sum((n_j - 1.0) * s2_j**2.0)\n",
    "SSE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "211ad60c-ea06-4f56-bb74-a761f006acef",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "17743252022.89521"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# alternativ kann SSE auch so berechnet werden\n",
    "SSE2 = SST - SSG\n",
    "SSE2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "92f95249",
   "metadata": {},
   "source": [
    "|Quelle|$df$|Summe der Quadrate (SS)| Mittlere Quadrate (MS)|$F$-Statistik|$p$-Wert|\n",
    "|---|---|---|---|---|---|\n",
    "|Gruppe/Klasse|$5$|$1,542576 \\cdot 10^{10}$|$MSG = \\frac{SSG}{k-1}$|$F=\\frac{MSG}{MSE}$| $p$|\n",
    "|Fehler/Residuen|$269$|$1,774325 \\cdot 10^{10}$|$MSE=\\frac{SSE}{n-k}$||\n",
    "|Insgesamt|$274$|$3,316901 \\cdot 10^{10}$|||"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "26322c99-8443-4bec-8164-6c3b1dbd411d",
   "metadata": {},
   "source": [
    "Nun berechnen wir die beiden Maße für die mittlere Variabilität, $MSG$ und $MSE$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "05a5e272-c76f-4bab-9b17-e662aa957849",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3085151828.981404"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Berechne MSG\n",
    "MSG = SSG / (k - 1)\n",
    "MSG"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "c2f4604e-4267-40d1-905c-354ebaf0719a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "65960044.694777764"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Berechne MSE\n",
    "MSE = SSE / (n - k)\n",
    "MSE"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d1df3fa6",
   "metadata": {},
   "source": [
    "|Quelle|$df$|Summe der Quadrate (SS)| Mittlere Quadrate (MS)|$F$-Statistik|$p$-Wert|\n",
    "|---|---|---|---|---|---|\n",
    "|Gruppe/Klasse|$5$|$1,542576 \\cdot 10^{10}$|$3,085152 \\cdot 10^{9}$|$F=\\frac{MSG}{MSE}$| $p$|\n",
    "|Fehler/Residuen|$269$|$1,774325 \\cdot 10^{10}$|$6,596004 \\cdot 10^{7}$||\n",
    "|Insgesamt|$274$|$3,316901 \\cdot 10^{10}$|||"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5a6c290d-fd99-418e-a4a4-9ee1d4a4198e",
   "metadata": {},
   "source": [
    "Schließlich erhalten wir die $F$-Statistiken durch das Verhältnis von $MSG$ und $MSE$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "a09a2c4a-bd55-4606-8c7c-a96f3085afde",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "46.77304030428687"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Berechne Teststatistik\n",
    "Fstat = MSG / MSE\n",
    "Fstat"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3ee294b9",
   "metadata": {},
   "source": [
    "|Quelle|$df$|Summe der Quadrate (SS)| Mittlere Quadrate (MS)|$F$-Statistik|$p$-Wert|\n",
    "|---|---|---|---|---|---|\n",
    "|Gruppe/Klasse|$5$|$1,542576 \\cdot 10^{10}$|$3,085152 \\cdot 10^{9}$|$46,77304$| $p$|\n",
    "|Fehler/Residuen|$269$|$1,774325 \\cdot 10^{10}$|$6,596004 \\cdot 10^{7}$||\n",
    "|Insgesamt|$274$|$3,316901 \\cdot 10^{10}$|||"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9ded2806-ce16-46d2-a00f-3ecca6534dfd",
   "metadata": {},
   "source": [
    "Im letzten Schritt berechnen wir den $p$-Wert durch Aufruf der Funktion `f.cdf()` in Python. Erinnern Sie sich, wie man die Freiheitsgrade berechnet."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b0f2a6db-d482-4571-aa4a-f32ae9553b7e",
   "metadata": {},
   "source": [
    "$$df = (k-1, n-k)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "01807a4f-987f-4b5c-aadd-acf132e15d19",
   "metadata": {},
   "source": [
    "Da die Nullhypothese nur dann abgelehnt wird, wenn die Teststatistik $F$ zu groß ist, ist ein einfaktorieller ANOVA-Test immer rechtsschief."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "5a63d46c-a1d3-4953-a91d-3afe24d3a490",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0932120917246151e-34"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1 = k - 1\n",
    "df2 = n - k\n",
    "\n",
    "p_value = f.sf(Fstat, dfn=df1, dfd=df2)\n",
    "p_value"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "295d16cc",
   "metadata": {},
   "source": [
    "|Quelle|$df$|Summe der Quadrate (SS)| Mittlere Quadrate (MS)|$F$-Statistik|$p$-Wert|\n",
    "|---|---|---|---|---|---|\n",
    "|Gruppe/Klasse|$5$|$1,542576 \\cdot 10^{10}$|$3,085152 \\cdot 10^{9}$|$46,77304$| $1,093212 \\cdot 10^{-34}$|\n",
    "|Fehler/Residuen|$269$|$1,774325 \\cdot 10^{10}$|$6,596004 \\cdot 10^{7}$||\n",
    "|Insgesamt|$274$|$3,316901 \\cdot 10^{10}$|||"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6750b98f-0005-488e-b82c-3db98491902f",
   "metadata": {},
   "source": [
    "**Schritt 5: Wenn $p \\le \\alpha , H_0$ ablehnen; ansonsten $H_0$ nicht ablehnen**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "bbcc6a0e-e9f0-438e-a36e-8b7db2da6dcd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p_value <= alpha"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b4a7f429-6279-4203-b9e1-b74081059fe5",
   "metadata": {},
   "source": [
    "Der $p$-Wert ist kleiner als das angegebene Signifikanzniveau von $0,01$; wir verwerfen $H_0$. Die Testergebnisse sind statistisch signifikant auf dem $1 \\%$-Niveau und liefern einen sehr starken Beweis gegen die Nullhypothese."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "868f87e1-c750-4238-8ac0-f4bc6549a027",
   "metadata": {},
   "source": [
    "**Schritt 6: Interpretieren Sie das Ergebnis des Hypothesentests**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "339a5ad5-afb1-4b45-b406-5a3cc4f685dd",
   "metadata": {},
   "source": [
    "$p=1,093212 \\cdot 10^{-34}$. Bei einem Signifikanzniveau von $1 \\%$ liefern die Daten sehr starke Hinweise darauf, dass sich mindestens ein Paar von Gruppenmittelwerten voneinander unterscheidet."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "113352fa-0e0f-470c-92be-4a081b9cffc4",
   "metadata": {},
   "source": [
    "### Hypothesentests in Python"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "90429755-b662-49f5-83d9-bfa6e503886b",
   "metadata": {},
   "source": [
    "Wir haben gerade einen einfaktoriellen ANOVA-Hypothesentest in Python manuell durchgeführt. Toll, aber jetzt wiederholen wir das Beispiel und nutzen die Möglichkeiten von Python, um das gleiche Ergebnis wie oben mit nur wenigen Zeilen Code zu erhalten!\n",
    "\n",
    "Um einen einseitigen ANOVA-Hypothesentest in Python durchzuführen, verwenden wir die Funktion `f_oneway()`. Die `f_oneway()`-Funktion erwartet die Eingabe der zu vergleichenden Untergruppen. Hierfür verwenden wir eine `list-comprehension`. Außerdem lesen wir die $F$-Teststatistik `statistics` und $p$-Wert `p_value` aus."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "670c2d14-9989-43ae-927f-c123c2042404",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Wert der F-Statistik: 46.773040304286866\n",
      "p-Wert: 1.0932120917246455e-34\n"
     ]
    }
   ],
   "source": [
    "dat = [\n",
    "    data.loc[data[\"major\"] == major, \"salary\"].values\n",
    "    for major in data[\"major\"].unique()\n",
    "]\n",
    "statistics, pvalue = f_oneway(*dat)\n",
    "\n",
    "print(f\"Wert der F-Statistik: {statistics}\")\n",
    "print(f\"p-Wert: {pvalue}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "65987448-de82-4f81-b4ec-9b51e070dd80",
   "metadata": {},
   "source": [
    "Es hat gut funktioniert! Vergleichen Sie die Ausgabe der Funktion `f_oneway()` mit unserem Ergebnis von oben. Auch hier können wir zu dem Schluss kommen, dass die Daten bei einem Signifikanzniveau von $1 \\%$ sehr starke Hinweise darauf liefern, dass sich mindestens ein Paar von Gruppenmitteln voneinander unterscheidet."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d30d803a-2706-4d8f-b96d-0b545376f733",
   "metadata": {
    "tags": []
   },
   "source": [
    "## Multiples Testproblem"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "05877db9-f9a7-455c-8102-173d8630ee09",
   "metadata": {},
   "source": [
    "Eine Einschränkung der ANOVA besteht darin, dass wir, wenn wir die Nullhypothese ablehnen, feststellen, dass die Mittelwerte der betrachteten Populationen nicht alle gleich sind. Wir können jedoch weder entscheiden, welche Mittelwerte unterschiedlich sind, noch, in welchem Verhältnis die Mittelwerte zueinander stehen.\n",
    "\n",
    "Um diese Frage zu klären, wenden wir Methoden an, die als **multiples Testen** oder **Mehrfachvergleiche** bezeichnet werden. Das Problem bei Mehrfachvergleichen ist, dass je mehr Hypothesen für einen bestimmten Datensatz getestet werden, desto wahrscheinlicher ist es, dass die Nullhypothese fälschlicherweise zurückgewiesen wird. Daher erfordern die Methoden des Mehrfachvergleichs eine höhere Signifikanzschwelle ($\\alpha$) für einzelne Vergleiche, um die Anzahl der gezogenen Schlüsse zu kompensieren."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "acf0bc3c-6d7a-4b02-8906-904fcfeb40ac",
   "metadata": {},
   "source": [
    "### Alphafehler-Kumulierung (engl. Family Wise Error Rate - FWER)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6b234a1c-1b59-4244-846b-d5a5e6cdf775",
   "metadata": {},
   "source": [
    "Eine **Testfamilie** ist der Fachbegriff für eine Reihe von Tests, die an einem Datensatz durchgeführt werden. Die <a href=\"https://de.wikipedia.org/wiki/Alphafehler-Kumulierung\">Alphafehler-Kumulierung</a> (engl. Family Wise Error Rate) ist die Wahrscheinlichkeit, dass bei der Durchführung von Mehrfachhypothesentests ein oder mehrere falsche Zurückweisungen der Null-Hypothese oder Fehler vom <a href=\"https://de.wikipedia.org/wiki/Fehler_1._und_2._Art\">Typ I</a> gemacht werden.\n",
    "\n",
    "Es sei daran erinnert, dass bei einem Signifikanzniveau von $\\alpha=0,05$ die Wahrscheinlichkeit, einen Fehler vom Typ I zu machen, $0,05$ oder $5 \\%$ beträgt. Folglich ist die Wahrscheinlichkeit, keinen Fehler vom Typ I zu machen, $1-\\alpha=1-0,05=0,95$. Außerdem ist die Wahrscheinlichkeit, zwei unabhängige Ereignisse zu beobachten, das Produkt ihrer Wahrscheinlichkeiten. Wenn wir also zwei unabhängige Tests durchführen, ist die Wahrscheinlichkeit, beim ersten und beim zweiten Test keinen Fehler vom Typ I zu machen"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "17383fa0-330c-4ca0-a3ec-bfde8f0125b9",
   "metadata": {},
   "source": [
    "$$(1-\\alpha) \\times (1-\\alpha) = (1-\\alpha)^2$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9eee4182-dd78-4a36-b6b7-55e847b38fe3",
   "metadata": {},
   "source": [
    "Wenn $\\alpha=0,05$ ist, ergibt sich eine Wahrscheinlichkeit, dass beim ersten und zweiten Test kein Fehler vom Typ I auftritt, von"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f364e082-ca01-426b-a892-28c1279e8e7b",
   "metadata": {},
   "source": [
    "$$(1 - \\alpha)^2 = (1-0,05)^2 = 0,95^2 \\approx 0,902$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a5257da5-0f03-44cc-a7be-e7b08f695d31",
   "metadata": {},
   "source": [
    "Für eine Familie von $C$-Tests ist die Wahrscheinlichkeit, dass kein Fehler vom Typ I für die gesamte Familie auftritt, formal ausgedrückt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7ff7a527-ba1a-41b8-ae36-2d502975811f",
   "metadata": {},
   "source": [
    "$$(1-\\alpha)^C\\text{.}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5d44e298-bba0-41c6-9079-24d1f2ca2c1e",
   "metadata": {},
   "source": [
    "Betrachten wir nun $C=10$ und $\\alpha=0,05$. Wir führen also $10$ Mehrfachvergleiche mit einem Datensatz durch. Die Wahrscheinlichkeit, keinen Fehler vom Typ I in der Familie zu machen, ist dann"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ce65cab2-0e60-48a9-9c66-dc89b36b14d6",
   "metadata": {},
   "source": [
    "$$(1-\\alpha)^C=(1-0,05)^{10} \\approx 0,599$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "be1feef6-7343-49e0-ace2-2037a453e9ec",
   "metadata": {},
   "source": [
    "Folglich ist die Wahrscheinlichkeit, dass **ein oder mehrere Fehler vom Typ I** in der Testfamilie auftreten"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0c978519-109d-44cd-b8b9-0a238fdf1967",
   "metadata": {},
   "source": [
    "$$1 - (1-\\alpha)^C$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "000d8e09-b0e4-4d60-b712-51ca3518c7f6",
   "metadata": {},
   "source": [
    "Für unser Beispiel finden wir"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "23428c8a-dad4-4086-ac4f-c342a8da33ee",
   "metadata": {},
   "source": [
    "$$1 - (1-\\alpha)^C = 1 - (1-0,05)^{10} \\approx 0,401$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "720e034d-9797-439f-a20f-bfaeeaa29357",
   "metadata": {},
   "source": [
    "Somit ist bei $\\alpha=0,05$ für jeden der $10$ Mehrfachvergleiche die Wahrscheinlichkeit, dass die Nullhypothese falsch zurückgewiesen wird, $0,401$ oder $40,1 \\%$.\n",
    "\n",
    "Um diesem Problem Rechnung zu tragen, gibt es <a href=\"https://de.wikipedia.org/wiki/Alphafehler-Kumulierung#Adjustierung_des_globalen_%CE%B1-Niveaus\">mehrere statistische Methoden</a>. In diesem Abschnitt werden die <a href=\"https://de.wikipedia.org/wiki/Bonferroni-Korrektur\">Bonferroni-Korrektur</a> und die <a href=\"https://de.wikipedia.org/wiki/Post-hoc-Test#Tukey-Test\">Tukey-Test</a>, auch bekannt als **Tukeys HSD-Test (hoenstly significant difference)**, behandelt."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fbef8cd4-718b-4626-87b4-07786845243f",
   "metadata": {},
   "source": [
    "### Beispiel-Daten"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4308a978-9fc0-4b7b-bfcd-1a982b462de9",
   "metadata": {},
   "source": [
    "In diesem Abschnitt wiederholen wir das Beispiel aus dem vorherigen Abschnitt. Dort haben wir eine einfaktorielle ANOVA angewandt, um zu **testen, ob sich das mittlere Jahresgehalt der Absolventen zwischen den Absolventen verschiedener Studienfächer unterscheidet**. Dieses Mal werden wir jedoch mehrere Vergleiche durchführen, um die Beziehung zwischen allen Gruppenmittelwerten zu analysieren.\n",
    "\n",
    "Laden Sie den `students` Datensatz erneut (Sie können die Datei `students.csv` <a href=\"https://userpage.fu-berlin.de/soga/200/2010_data_sets/students.csv\">hier</a> herunterladen)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "874e4d96-3426-4546-9b2a-b06436c7c301",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Lese Datei students.csv als Dataframe ein\n",
    "students = pd.read_csv(\"../../data/students.csv\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "33f64541-0024-444b-892c-04bc3e4bef98",
   "metadata": {},
   "source": [
    "Der `students` Datensatz besteht aus $8239$ Zeilen, von denen jede einen bestimmten Studenten repräsentiert, und $16$ Spalten, von denen jede einer Variable/einem Merkmal entspricht, das sich auf diesen bestimmten Studenten bezieht. Diese selbsterklärenden Variablen sind: *stud_id, name, gender, age, height, weight, religion, nc_score, semester, major, minor, score1, score2, online_tutorial, graduated, salary.*"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fb63fe9a-0f3b-49d9-9a21-225615a8d494",
   "metadata": {},
   "source": [
    "Aus dem Datensatz der Studierenden ziehen wir eine Zufallsstichprobe von $275$ Absolventen und reduzieren den Datensatz auf die beiden interessierenden Variablen, die kategoriale Variable `major` und die numerische Variable `salary`. Für eine bessere Lesbarkeit in der folgenden Analyse ersetzen wir die Namen der Studienfächer durch entsprechende Abkürzungen."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "b24dd642-58b2-4f3a-ad34-8b44260f5dd3",
   "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>major</th>\n",
       "      <th>salary</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>3826</th>\n",
       "      <td>MaSt</td>\n",
       "      <td>57849.343490</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>795</th>\n",
       "      <td>MaSt</td>\n",
       "      <td>56558.160738</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2127</th>\n",
       "      <td>PoS</td>\n",
       "      <td>46945.174104</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1292</th>\n",
       "      <td>Bio</td>\n",
       "      <td>40093.455971</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5913</th>\n",
       "      <td>EnS</td>\n",
       "      <td>35106.961865</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1871</th>\n",
       "      <td>EnS</td>\n",
       "      <td>33216.118981</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1853</th>\n",
       "      <td>EnS</td>\n",
       "      <td>30606.198317</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1484</th>\n",
       "      <td>PoS</td>\n",
       "      <td>37240.113342</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5619</th>\n",
       "      <td>MaSt</td>\n",
       "      <td>50913.038493</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2299</th>\n",
       "      <td>EcFi</td>\n",
       "      <td>50365.098269</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     major        salary\n",
       "3826  MaSt  57849.343490\n",
       "795   MaSt  56558.160738\n",
       "2127   PoS  46945.174104\n",
       "1292   Bio  40093.455971\n",
       "5913   EnS  35106.961865\n",
       "1871   EnS  33216.118981\n",
       "1853   EnS  30606.198317\n",
       "1484   PoS  37240.113342\n",
       "5619  MaSt  50913.038493\n",
       "2299  EcFi  50365.098269"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n = 275\n",
    "data = students.loc[students[\"graduated\"] == 1, [\"major\", \"salary\"]].sample(\n",
    "    n, random_state=300\n",
    ")\n",
    "\n",
    "lookup = {\n",
    "    \"Biology\": \"Bio\",\n",
    "    \"Political Science\": \"PoS\",\n",
    "    \"Economics and Finance\": \"EcFi\",\n",
    "    \"Environmental Sciences\": \"EnS\",\n",
    "    \"Mathematics and Statistics\": \"MaSt\",\n",
    "    \"Social Sciences\": \"SoS\",\n",
    "}\n",
    "data[\"major\"] = data[\"major\"].apply(lambda x: lookup[x])\n",
    "\n",
    "data.head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fad39d75-4b71-4c02-aaaf-4c3f13602b4a",
   "metadata": {},
   "source": [
    "Des Weiteren führen wir einen einfaktoriellen ANOVA-Hypothesentest in Python durch, indem wir die Funktion `f_oneway()` anwenden."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "763bdf06-78e8-4b98-ba8b-8f808ba197e3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Wert der F-Statistik: 41.14261241723518\n",
      "p-Wert: 2.283897894495435e-31\n"
     ]
    }
   ],
   "source": [
    "dat = [\n",
    "    data.loc[data[\"major\"] == major, \"salary\"].values\n",
    "    for major in data[\"major\"].unique()\n",
    "]\n",
    "statistics, pvalue = f_oneway(*dat)\n",
    "\n",
    "print(f\"Wert der F-Statistik: {statistics}\")\n",
    "print(f\"p-Wert: {pvalue}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f8375608-c4c0-4ef5-b505-cbc3cd2e3331",
   "metadata": {},
   "source": [
    "### Bonferroni-Korrektur"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1777a6b2-c34f-4331-b04d-66bd994ebd3a",
   "metadata": {},
   "source": [
    "Die Bonferroni-Korrektur kompensiert die erhöhte Wahrscheinlichkeit, dass eine Nullhypothese aufgrund von Mehrfachvergleichen fälschlicherweise abgelehnt wird (Fehler vom Typ I), indem das Signifikanzniveau $\\alpha$ in folgender Form angepasst wird"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "632f9f96-1ff8-4ded-9e49-7727c1b66c41",
   "metadata": {},
   "source": [
    "$$\\alpha = \\frac{\\alpha}{m}\\text{,}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6a698c86-8b72-4454-9f6e-f868ac7636f0",
   "metadata": {},
   "source": [
    "wobei $m$ der Anzahl der Vergleiche entspricht, die gegeben ist durch"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6169c6fd-1493-4521-97e8-6de1ae96b753",
   "metadata": {},
   "source": [
    "$$m=\\frac{k(k-1)}{2}\\text{,}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d57c69a5-f6ce-45a7-bb64-59ac565829ad",
   "metadata": {},
   "source": [
    "wobei $k$ den Ebenen des Faktors entspricht, der die kategoriale Klassifikationsvariable ist."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "e9466fd6-f534-487a-a10c-b07c92f516dc",
   "metadata": {},
   "outputs": [],
   "source": [
    "def bonferroni(alpha, k):\n",
    "    \"\"\"Computes the boferroni correction\"\"\"\n",
    "    m = k * (k - 1) / 2\n",
    "    bonf = alpha / m\n",
    "    return bonf"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cd7e6795-11fb-4515-bbeb-7265cd2c92fe",
   "metadata": {},
   "source": [
    "### Der paarweiser $t$-Test in Python: Bonferroni-Korrektur"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "010701b8-cbe8-49af-bb5d-ccf0ada19162",
   "metadata": {},
   "source": [
    "Wie im vorigen Abschnitt erwähnt, ist eine einfaktorielle Varianzanalyse die Verallgemeinerung des $2$-Stichproben $t$-Tests auf mehr als zwei Grundgesamtheiten. Die Python-Funktion zur Durchführung von Mehrfachvergleichen ist `ttest_ind()`. Die Funktion `ttest_ind()` vergleicht die jeweiligen Gehaltsverteilungen (`salary`) nach Studienfächer gruppiert (`major`) miteinander."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1af46981-44ba-40cd-a91a-3442d58ec13b",
   "metadata": {},
   "source": [
    "Zunächst führen wir einen paarweisen $t$-Test ohne Anpassung durch, wodurch sich die Wahrscheinlichkeit erhöht, dass die Nullhypothese falsch zurückgewiesen wird."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "b70dc8ed-be28-4128-ba6c-fec41db50f2a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('MaSt', 'PoS'),\n",
       " ('MaSt', 'Bio'),\n",
       " ('MaSt', 'EnS'),\n",
       " ('MaSt', 'EcFi'),\n",
       " ('MaSt', 'SoS'),\n",
       " ('PoS', 'Bio'),\n",
       " ('PoS', 'EnS'),\n",
       " ('PoS', 'EcFi'),\n",
       " ('PoS', 'SoS'),\n",
       " ('Bio', 'EnS'),\n",
       " ('Bio', 'EcFi'),\n",
       " ('Bio', 'SoS'),\n",
       " ('EnS', 'EcFi'),\n",
       " ('EnS', 'SoS'),\n",
       " ('EcFi', 'SoS')]"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from itertools import combinations\n",
    "\n",
    "major = list(combinations(data.major.unique(), 2))\n",
    "major"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "532c5b58-8b87-4b29-bf81-6e74938a8219",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MaSt vs. PoS\n",
      "p-value:   5.2857708581268477e-11\n",
      "Reject H0 (p-value <= 0.05): True\n",
      "\n",
      "MaSt vs. Bio\n",
      "p-value:   0.23955813674375898\n",
      "Reject H0 (p-value <= 0.05): False\n",
      "\n",
      "MaSt vs. EnS\n",
      "p-value:   2.8739133454494936e-10\n",
      "Reject H0 (p-value <= 0.05): True\n",
      "\n",
      "MaSt vs. EcFi\n",
      "p-value:   0.6139629263411384\n",
      "Reject H0 (p-value <= 0.05): False\n",
      "\n",
      "MaSt vs. SoS\n",
      "p-value:   1.0518783466253219e-10\n",
      "Reject H0 (p-value <= 0.05): True\n",
      "\n",
      "PoS vs. Bio\n",
      "p-value:   4.8406849116995696e-15\n",
      "Reject H0 (p-value <= 0.05): True\n",
      "\n",
      "PoS vs. EnS\n",
      "p-value:   0.120165093300726\n",
      "Reject H0 (p-value <= 0.05): False\n",
      "\n",
      "PoS vs. EcFi\n",
      "p-value:   2.649042688427034e-12\n",
      "Reject H0 (p-value <= 0.05): True\n",
      "\n",
      "PoS vs. SoS\n",
      "p-value:   0.23097741142110123\n",
      "Reject H0 (p-value <= 0.05): False\n",
      "\n",
      "Bio vs. EnS\n",
      "p-value:   1.790220430001192e-14\n",
      "Reject H0 (p-value <= 0.05): True\n",
      "\n",
      "Bio vs. EcFi\n",
      "p-value:   0.5127682352930607\n",
      "Reject H0 (p-value <= 0.05): False\n",
      "\n",
      "Bio vs. SoS\n",
      "p-value:   6.474671293237731e-14\n",
      "Reject H0 (p-value <= 0.05): True\n",
      "\n",
      "EnS vs. EcFi\n",
      "p-value:   8.151876693739742e-12\n",
      "Reject H0 (p-value <= 0.05): True\n",
      "\n",
      "EnS vs. SoS\n",
      "p-value:   0.00557583127097583\n",
      "Reject H0 (p-value <= 0.05): True\n",
      "\n",
      "EcFi vs. SoS\n",
      "p-value:   7.1456783247184506e-12\n",
      "Reject H0 (p-value <= 0.05): True\n",
      "\n"
     ]
    }
   ],
   "source": [
    "alpha = 0.05\n",
    "\n",
    "for major1, major2 in major:\n",
    "    _, p_value = ttest_ind(\n",
    "        data.loc[data[\"major\"] == major1, \"salary\"],\n",
    "        data.loc[data[\"major\"] == major2, \"salary\"],\n",
    "    )\n",
    "    print(f\"{major1} vs. {major2}\")\n",
    "    print(f\"p-value:   {p_value}\")\n",
    "    print(f\"Reject H0 (p-value <= {alpha}): {p_value <= alpha}\\n\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4f5431ad-2f8d-41bb-95cc-fe349d07cc7d",
   "metadata": {},
   "source": [
    "Der paarweise $t$-Test zeigt, dass bei einem Signifikanzniveau von $5 \\%$ die Mittelwerte für $5$ Kombinationen **nicht** statistisch signifikant unterschiedlich sind. Diese Kombinationen sind Bio-EcFi, Bio-MaSt, EcFi-MaSt, EnS-PoS, PoS-SoS mit $p$-Werten von $0,5128$, $0,2396$, $0,61396$ , $0,1202$ , $0,635057$ bzw. $0,230977$. Für die restlichen $10$ Kombinationen verwerfen wir $H_0$; d. h. für $10$ Kombinationen sind die Mittelwerte bei einem Signifikanzniveau von $5 \\%$ unterschiedlich!\n",
    "\n",
    "Zweitens führen wir einen **paarweisen $t$-Test mit der Bonferroni-Anpassung** durch."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "abd4801e-5f4c-45d8-96e8-96b2dd89d8e9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0033333333333333335"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bonf = bonferroni(alpha=0.05, k=data.major.nunique())\n",
    "bonf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "f98bbd3c-4d43-4c00-8920-3e066de8533d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MaSt vs. PoS\n",
      "p-value:   5.2857708581268477e-11\n",
      "Reject H0 (p-value <= 0.00333): True\n",
      "\n",
      "MaSt vs. Bio\n",
      "p-value:   0.23955813674375898\n",
      "Reject H0 (p-value <= 0.00333): False\n",
      "\n",
      "MaSt vs. EnS\n",
      "p-value:   2.8739133454494936e-10\n",
      "Reject H0 (p-value <= 0.00333): True\n",
      "\n",
      "MaSt vs. EcFi\n",
      "p-value:   0.6139629263411384\n",
      "Reject H0 (p-value <= 0.00333): False\n",
      "\n",
      "MaSt vs. SoS\n",
      "p-value:   1.0518783466253219e-10\n",
      "Reject H0 (p-value <= 0.00333): True\n",
      "\n",
      "PoS vs. Bio\n",
      "p-value:   4.8406849116995696e-15\n",
      "Reject H0 (p-value <= 0.00333): True\n",
      "\n",
      "PoS vs. EnS\n",
      "p-value:   0.120165093300726\n",
      "Reject H0 (p-value <= 0.00333): False\n",
      "\n",
      "PoS vs. EcFi\n",
      "p-value:   2.649042688427034e-12\n",
      "Reject H0 (p-value <= 0.00333): True\n",
      "\n",
      "PoS vs. SoS\n",
      "p-value:   0.23097741142110123\n",
      "Reject H0 (p-value <= 0.00333): False\n",
      "\n",
      "Bio vs. EnS\n",
      "p-value:   1.790220430001192e-14\n",
      "Reject H0 (p-value <= 0.00333): True\n",
      "\n",
      "Bio vs. EcFi\n",
      "p-value:   0.5127682352930607\n",
      "Reject H0 (p-value <= 0.00333): False\n",
      "\n",
      "Bio vs. SoS\n",
      "p-value:   6.474671293237731e-14\n",
      "Reject H0 (p-value <= 0.00333): True\n",
      "\n",
      "EnS vs. EcFi\n",
      "p-value:   8.151876693739742e-12\n",
      "Reject H0 (p-value <= 0.00333): True\n",
      "\n",
      "EnS vs. SoS\n",
      "p-value:   0.00557583127097583\n",
      "Reject H0 (p-value <= 0.00333): False\n",
      "\n",
      "EcFi vs. SoS\n",
      "p-value:   7.1456783247184506e-12\n",
      "Reject H0 (p-value <= 0.00333): True\n",
      "\n"
     ]
    }
   ],
   "source": [
    "for major1, major2 in major:\n",
    "    _, p_value = ttest_ind(\n",
    "        data.loc[data[\"major\"] == major1, \"salary\"],\n",
    "        data.loc[data[\"major\"] == major2, \"salary\"],\n",
    "    )\n",
    "    print(f\"{major1} vs. {major2}\")\n",
    "    print(f\"p-value:   {p_value}\")\n",
    "    print(f\"Reject H0 (p-value <= {np.round(bonf,5)}): {p_value <= bonf}\\n\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3ea2a00d-fc0e-45c9-bc68-e966f8a73924",
   "metadata": {},
   "source": [
    "Der paarweise $t$-Test mit der Bonferroni-Anpassung zeigt, dass bei einem Signifikanzniveau von $5 \\%$ die Mittelwerte für $6$ Kombinationen nicht statistisch signifikant unterschiedlich sind. Bei diesen Kombinationen handelt es sich um Bio-EcFi, Bio-MaSt, EcFi-MaSt, EnS-PoS, PoS-SoS, EnS-SoS mit $p$-Werten von $0,5128$, $0,2396$, $0,61397$, $0,1202$, $0,230978$ bzw. $0,00558$. (beim Bonferroni-Verfahren wird $\\alpha$ durch die Anzahl der Tests geteilt bzw. der $p$-Wert mit dieser Anzahl multipliziert und auf $1$ gekürzt, wenn das Ergebnis über $1$ liegt und somit keine Wahrscheinlichkeit darstellt). Für die verbleibenden $9$ Kombinationen haben wir $H_0$ abgelehnt, d. h. für $9$ Kombinationen sind die Mittelwerte bei einem Signifikanzniveau von $\\approx 0,0067 \\%$ unterschiedlich!"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "411b92a8-cfd6-45f1-8cb0-dd287c839019",
   "metadata": {},
   "source": [
    "### Tukey-Mehrfach-Vergleichsmethode"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "23559814-3cd2-488c-a812-cdf574da18ec",
   "metadata": {},
   "source": [
    "Der <a href=\"https://de.wikipedia.org/wiki/Post-hoc-Test#Tukey-Test\">Tukey-Test</a>, auch bekannt als **Tukey's HSD-Test (honest significant difference)**, basiert auf der <a href=\"https://de.wikipedia.org/wiki/Studentisierung\">studentized range-Verteilung</a>, die manchmal auch als $q$-Verteilung bezeichnet wird. Die **$q$-Verteilung** ist eine rechtsschiefe Wahrscheinlichkeitsdichtekurve mit zwei Parametern, $\\kappa$ und $\\nu$, die ihre Form beschreiben. Diese Parameter sind gegeben durch"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e792fed9-141f-47b3-a7d5-f986a2afde63",
   "metadata": {},
   "source": [
    "$$\\kappa = k$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "28d642fc-a5da-4e6f-b9d2-ac8fd002e6b9",
   "metadata": {},
   "source": [
    "und"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8446e77b-1070-4b2e-8455-14715b06379d",
   "metadata": {},
   "source": [
    "$$\\nu = n-k\\text{,}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cc039e9f-cbed-41c5-b162-9e8a3722bd8f",
   "metadata": {},
   "source": [
    "wobei $n$ die Gesamtzahl der Beobachtungen ist und $k$ die Anzahl der Gruppen/Klassen.\n",
    "\n",
    "Der Tukey-Test vergleicht die Mittelwerte jeder Gruppe mit den Mittelwerten jeder anderen Gruppe. Er liefert das Konfidenzintervall für jedes"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "570b5c27-1f44-49dd-930d-12f405cf2c45",
   "metadata": {},
   "source": [
    "$$\\mu_i-\\mu_j\\text{.}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a48d3b79-73c5-4089-826f-de5a2a2e77ab",
   "metadata": {},
   "source": [
    "Wenn das Konfidenzintervall für einen paarweisen Vergleich $0$ einschließt, wird $H_0$ nicht verworfen, es wird nicht angenommen, dass sie signifikant unterschiedlich sind. Alle anderen Paare, für die das Konfidenzintervall nicht $0$ einschließt, sind signifikant unterschiedlich, $H_0$ wird also verworfen."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c1e611f6-7493-4396-9233-e1c0343c673f",
   "metadata": {},
   "source": [
    "### Tukey's Test in Python"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b2f8b5db-de1c-4ad0-8135-6c5150333066",
   "metadata": {},
   "source": [
    "In Python werden Tukey's HSD Tests durch die `pairwise_tukeyhsd()` Funktion berechnet. Die `pairwise_tukeyhsd()`-Funktion erwartet als Eingabe `endog`, die zu vergleichende Größe und `groups` die Aufteilung der Gruppen. Um die Breite der Konfidenzintervalle festzulegen, geben wir der Funktion das Konfidenzniveau mit dem Argument `alpha` an."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "50a8c5c2-9357-4a97-86d5-f51ba60c74b1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>Multiple Comparison of Means - Tukey HSD, FWER=0.05</caption>\n",
       "<tr>\n",
       "  <th>group1</th> <th>group2</th>  <th>meandiff</th>    <th>p-adj</th>    <th>lower</th>       <th>upper</th>    <th>reject</th>\n",
       "</tr>\n",
       "<tr>\n",
       "    <td>Bio</td>   <td>EcFi</td>  <td>-1012.3086</td>   <td>0.983</td>  <td>-5228.585</td>   <td>3203.9678</td>   <td>False</td>\n",
       "</tr>\n",
       "<tr>\n",
       "    <td>Bio</td>    <td>EnS</td>  <td>-11777.6601</td>  <td>-0.0</td>  <td>-15810.772</td>  <td>-7744.5482</td>   <td>True</td> \n",
       "</tr>\n",
       "<tr>\n",
       "    <td>Bio</td>   <td>MaSt</td>  <td>-1846.3679</td>  <td>0.8039</td> <td>-6036.7581</td>   <td>2344.0223</td>   <td>False</td>\n",
       "</tr>\n",
       "<tr>\n",
       "    <td>Bio</td>    <td>PoS</td>  <td>-13913.133</td>   <td>-0.0</td>  <td>-18078.5879</td> <td>-9747.6782</td>   <td>True</td> \n",
       "</tr>\n",
       "<tr>\n",
       "    <td>Bio</td>    <td>SoS</td>  <td>-16091.4853</td>  <td>-0.0</td>  <td>-21100.7005</td> <td>-11082.2702</td>  <td>True</td> \n",
       "</tr>\n",
       "<tr>\n",
       "   <td>EcFi</td>    <td>EnS</td>  <td>-10765.3515</td>   <td>0.0</td>  <td>-15067.6403</td> <td>-6463.0628</td>   <td>True</td> \n",
       "</tr>\n",
       "<tr>\n",
       "   <td>EcFi</td>   <td>MaSt</td>   <td>-834.0593</td>  <td>0.9946</td> <td>-5284.1231</td>   <td>3616.0045</td>   <td>False</td>\n",
       "</tr>\n",
       "<tr>\n",
       "   <td>EcFi</td>    <td>PoS</td>  <td>-12900.8245</td>  <td>-0.0</td>  <td>-17327.4159</td>  <td>-8474.233</td>   <td>True</td> \n",
       "</tr>\n",
       "<tr>\n",
       "   <td>EcFi</td>    <td>SoS</td>  <td>-15079.1768</td>  <td>-0.0</td>  <td>-20307.5545</td>  <td>-9850.799</td>   <td>True</td> \n",
       "</tr>\n",
       "<tr>\n",
       "    <td>EnS</td>   <td>MaSt</td>   <td>9931.2922</td>    <td>0.0</td>   <td>5654.369</td>   <td>14208.2155</td>   <td>True</td> \n",
       "</tr>\n",
       "<tr>\n",
       "    <td>EnS</td>    <td>PoS</td>  <td>-2135.4729</td>  <td>0.7016</td> <td>-6387.9683</td>   <td>2117.0224</td>   <td>False</td>\n",
       "</tr>\n",
       "<tr>\n",
       "    <td>EnS</td>    <td>SoS</td>  <td>-4313.8252</td>  <td>0.1475</td> <td>-9395.6496</td>   <td>767.9991</td>    <td>False</td>\n",
       "</tr>\n",
       "<tr>\n",
       "   <td>MaSt</td>    <td>PoS</td>  <td>-12066.7651</td>   <td>0.0</td>  <td>-16468.7074</td> <td>-7664.8229</td>   <td>True</td> \n",
       "</tr>\n",
       "<tr>\n",
       "   <td>MaSt</td>    <td>SoS</td>  <td>-14245.1174</td>   <td>0.0</td>  <td>-19452.6425</td> <td>-9037.5924</td>   <td>True</td> \n",
       "</tr>\n",
       "<tr>\n",
       "    <td>PoS</td>    <td>SoS</td>  <td>-2178.3523</td>   <td>0.834</td> <td>-7365.8335</td>   <td>3009.1289</td>   <td>False</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.table.SimpleTable'>"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Tukey's test ausführen\n",
    "tukey = pairwise_tukeyhsd(endog=data[\"salary\"], groups=data[\"major\"], alpha=0.05)\n",
    "tukey.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bbf0cd38-481e-443b-bbb9-cb34cf5beedb",
   "metadata": {},
   "source": [
    "Bitte beachten Sie, dass wir im Fall ohne $p$-Wert-Anpassung die Nullhypothese für $10$ Kombinationen abgelehnt haben. Beim paarweisen $t$-Test mit der Tukey-Anpassung wurde die Nullhypothese für $9$ Kombinationen verworfen."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "008436ff-eaff-4955-8006-d960ec8efb65",
   "metadata": {},
   "source": [
    "Die Tabelle zeigt die Differenz zwischen den einzelnen Paaren, die $95 \\%$-Konfidenzintervalle und den $p$-Wert der paarweisen Vergleiche. Schauen Sie sich die Tabelle genau an, und Sie werden sehen, dass für alle $6$ Vergleiche, bei denen das Konfidenzintervall $0$ einschließt, der $p$-Wert höher ist als das Signifikanzniveau $\\alpha$. Wenn $p \\gt \\alpha$ ist, verwerfen wir $H_0$ nicht, d. h. es gibt keinen statistisch signifikanten Unterschied zwischen den Mittelwerten dieser beiden Gruppen. Für alle Paare, bei denen $p \\le \\alpha$ ist, verwerfen wir dagegen $H_0$ und stellen fest, dass ein statistisch signifikanter Unterschied zwischen den Mittelwerten dieser Paare besteht. Die `tukey.plot_simultaneous()`-Funktion bietet eine nette Plot-Funktion, die die Konfidenzintervalle für jedes Paar visualisiert."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "531880e9-25b2-42a5-9d11-949ccdd06b1e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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LlCHA51A+3I/LzD8ARMSVwFua2xsoB20fRukFGOt4pRVk5v0RcT7w9oi4gRJAH0vZjhdk5tXN+r4MvKc5XuosSvj4EOXYoclcjf/HlG37nWY73U4Jn4+gHDc1lvUiYn7L/XUoZ+F+iHJG7fBlCz5IOfPtjIj4LCX8vZrSu/ifTSiHsj89OyJ2An6RmbdQLl76Zcq+86Wm3q958DV+7/DKM/N3EfFV4HNRzi6+kPJl+iHKcVfDPXsTbc+kRDnb+lmUHt6VNO37OfC6iHjPSHWm2SLK8asXUY4Dezblx9Gk9snGucBRzT7yQ8oPhQ82y/35SA/IzGURcR5lO43WWzmWSX+eZebJUS6X8eGI+G5mXhERh1N61e6hjD6s3yzn+ZShz1bHUc76vY9yeZSRvIDyGqhmq+NMBKe1b2Lks5d+TxnaWr+lrP0sznUol8v4K6VX6TzKF8ZdjHIWZ1N2NOWL+RbKh9cJrHwW5yLKF8/1lGNaTgZ6WuqMtNweyjDLjZSA9ftmGetM4DVYh/KFeX6zzmWUX8OfAB49Qv03UcLJckowOwHYomX+frSdIccoZ5BRju06oeU5JOXsveGguITyRbdOy2OeRunZ+XuznS6i9Mh8n9Kj0rqst7Stb4W2NdvgI8Afm213HeWLY5O21+cwSi/V3ZRLmBwNPKKlzgeb5T6kbX1LgK+33N+e0hN4U/P8FgP7jLN9TmDlszfvpnxhf4FyTFRr/WdQvnCXNtvyV8ABbXVeRBlWXQ68tqX8QkqP6yNbyr7RrHPbEfabwylD6HdThhkHgcevQnseOLtxrP2oZd4XmnZuOcbr9tbm8X1M4SzOCX6ObAl8h/K+/jvl8IEDKWc73kTzWdL6PBllH23mHUwZPl9G2cdPouUzYJQ29FE+WzYYZf5YZ3Gu6ufZ4ygnkpwHRFP2Cspn2J3N63EOsOMobboc+N4o8x5HCW97jvW8nTo/DW94aY0WEQspX/Lzx6u7pomIHkroeGtmHtPh5kizSnMixxWUAFj9f5aIiCdRfkjukZk/GGH+RyjH9D0rDQBV8xg0SZJGkeWyLu8BDmnCWpUi4gXN4RunUobQVxrCbC6rcQDwLsNZ/QxokiSNITMHKcepHdzptoxhY8qFfe8C9h0lgH2IcuHfM0eYp8o4xClJklQZe9AkSZIqY0CTJEmqzBpxHbSI6KOcCs3DHvaw52yzzTbjPEKSJKnzLr744hszc6X/dLPGHYM2b968XLx4Iv9BRJIkqbMi4uLMnNde7hCnJElSZQxokiRJlTGgSZIkVcaAJkmSVBkDmiRJUmUMaJIkSZUxoEmSJFXGgCZJklQZA5okSVJlDGiSJEmVMaBJkiRVxoAmSZJUGQOaJElSZQxokiRJlTGgSZIkVcaAJkmSVBkDmiRJUmUMaJIkSZUxoEmSJFXGgCZJklQZA5okSVJlDGiSJEmVMaBJkiRVxoAmSZJUGQOaJElSZQxokiRJlTGgSZIkVcaAJkmSVBkDmiRJUmUMaJIkSZUxoEmSJFXGgCZJklQZA5okSVJlDGiSJEmVMaBJkiRVxoAmSZJUGQOaJElSZQxokiRJlTGgSZIkVWZaAlpE7BwRP4qIWyLiroj4fUT0R8QGk1zOhhFxZERcERHLI+KmiPhBROw4He2UJEmaDaYc0CJid+AM4C/AvwG7A8cCBwA/ioh1JricAE4HXgN8Angx8CbgXuCsiNhjqm2VJEmaDaajB+1dwBmZ+abMPC0zz8nMo4DXA9tTgtZE7NDUf01mDmTmwsw8BXg5sBh4/zS0VZUaHBykp6eHOXPm0NPTw+DgYKebJElSx0xHQHv0KMs5A3gfcDVARPRExEkRcV1E3BYR342IrduWs1KbMvP+ZjnHT0NbVaHBwUH6+voYGhoiMxkaGqKvr8+QJklaa0VmTm0BEZ8EDgFOAwaBhZl5bVudxwKXANcAHwGC0iO2GfCszPxrRGwG/Am4HTgG+CFwcWbeO5n2zJs3LxcvXjyl59QJCxYs6HQTOmbRokUsX758pfK5c+cyf/78DrSoDgsXLux0EyRJMywiLs7Mee3l09GDNty7tTvwNeBvEXFZRBwRERs3dQ4CHgrskpnfysyTgZ2askMAMvM6YE9gOfABYBGwtOlp23WcJ9cXEYsjYvENN9wwDU9Jq9NI4WysckmS1nRT7kF7YEGll2xPYBdgAbAx8Ffgn4GTgL9l5kvbHnMK8LjW5NicVLAj8BJKiHsmpcftyMx873jtmK09aGuznp4ehoaGVirv7u5myZIlq79BkiStJjPZgwZAZl6dmV/MzL0ox5O9EdgU+CAlrF03wsOuAzZsW859mXlWZh6Smc8CHg+cCxweEU+YrvaqHv39/XR1da1Q1tXVRX9/f4daJElSZ00poEXE/Oag/+1ayzPz3sw8Hvg+8BTgZsrxZu02B25qlnVS06O2gsxcQhkiDeDJU2mv6tTb28vAwADd3d1EBN3d3QwMDNDb29vppkmS1BFT7UH7A7AB8I72Gc1Q5eOB3wLnAztGxCYt8zcBdgYuaIquBP4lIrYdYT1bA/cDl02xvapUb28vS5Ys4f7772fJkiWGM0nSWm3dqTw4M2+OiPcB/90ErhMol9XYgnKh2scCewF3A/sBZ0bEEZTesP9oyj/dLO4TwN7ATyLi08CFlFD2z8ChwGcz88qptFeSJGk2mFJAA8jMT0XEFcCBwGeAjYAbKddB2384VEXEC4CPAydS/jvAQuDVmXl1s5wbm6HS9wD7Aoc1q7iUcqbncVNtqyRJ0mwwbWdx1sKzOCVJ0mwx42dxSpIkaXoY0CRJkipjQJMkSaqMAU2SJKkyBjRJkqTKGNAkSZIqY0CTJEmqjAFNkiSpMgY0SZKkyhjQJEmSKmNAkyRJqowBTZIkqTIGNEmSpMoY0CRJkipjQJMkSaqMAU2SJKkyBjRJkqTKGNAkSZIqY0CTJEmqjAFNkiSpMgY0SZKkyhjQJEmSKmNAkyRJqowBTZIkqTIGNEmSpMoY0CRJkipjQJMkSaqMAU2SJKkyBjRJkqTKGNAkSZIqY0CTJEmqjAFNkiSpMgY0SZKkykw5oEXEwojItmlZRPwqIg6c5LLmRsThEfHbiLgzIpY2y997qu2UJEmaLdadpuVcABzacv/hwH7AZyOCzPzcBJfzVWBn4KPAr4CHAa8ATo6It2XmF6epvZIkSdWaroC2NDMXtRZExDnAPOBAYNyAFhE9wKuB12TmN1pmnRoRGwAfAgxokiRpjTdjx6Bl5v2UXrBugIjYJCKOjYirmyHQcyJiXstDNh2jTR8HPh4R681Ue6WpGBwcpKenhzlz5tDT08Pg4GCnmyRJmsWmqwdtNFsDV0bEw4ELgfWAw4FbgYOB8yJiu8z8DfBr4BrgmIh4NnAacFFm3pWZPwd+PsNtlVbJ4OAgfX19LFu2DIChoSH6+voA6O3t7WTTJEmzVGTm1BYQsRC4A3jZcBHwD8BbKWHsIOA+4NPA0zPz0uZx6wN/AC7OzL2bsmcCg8C2zbKWAz8Bjmsb9hzVvHnzcvHixVN6TuqcBQsWdLoJk7Zo0SKWL1++UvncuXOZP39+B1o0NQsXLux0EyRprRERF2fmvPby6epB2x24p63sTuBTlOPPvgb8bjicAWTm3RFxCvBvLWW/ioinA9s3y9wZ2BF4UUS8LDNfO9LKI6IP6APYcsstp+kpSRMzUjgbq1ySpPFMVw/aOpSeMoAEbgf+nJn3NHXOAjIzd2l77OHAhzNz/TGW/2jgs8CrgJ0y89yx2mMPmla3np4ehoaGVirv7u5myZIlq79BkqRZY7QetOk6SeDWzFzcTBdn5uXD4axxM7DZCI/bHLipaeBREbFSssrM62l6x4CnTFN7pWnT399PV1fXCmVdXV309/d3qEWSpNludf0ngfOBbSPigYDVHIP2Cso11AD+CDwnInYd4fFbN7e/ndFWSqugt7eXgYEBuru7iQi6u7sZGBjwBAFJ0iqbriHO2zNzjzHqbEC55EYA/0E5i/Mg4J+A7TPzFxHxEGAh8Azg88DZlOPYngO8G1iUmS8frz0OcUqSpNlipk8SGFNm3hYROwCfpISvdYGfAjtk5i+aOndFxE6U/0iwF/CWpt4fgf+mnHAgSZK0xptyD1pt7EGTJEmzxUyfJCBJkqRpYkCTJEmqjAFNkiSpMgY0SZKkyhjQJEmSKmNAkyRJqowBTZIkqTIGNEmSpMoY0CRJkipjQJMkSaqMAU2SJKkyBjRJkqTKGNAkSZIqY0CTJEmqjAFNkiSpMgY0SZKkyhjQJEmSKmNAkyRJqowBTZIkqTIGNEmSpMoY0CRJkipjQJMkSaqMAU2SJKkyBjRJkqTKGNAkSZIqY0CTJEmqjAFNkiSpMgY0SZKkyhjQJEmSKmNAkyRJqowBTZIkqTIGNEmSpMoY0CRJkiozKwJaRESn2yBJkrS6jBvQImJJRGREfHKU+d3N/IyITSa64oh4YkScGBF/i4i7I+LqiDghIh7fVu/NwBETXa4kSdJsN9EetAT2GmXePpNdaUQ8Fvgp0A38P2AX4L3Ac4CLImLLlurvAzaa7DokSZJmq4kGtAuBrSLiWSPMeyXw60mud39gHeDFmXlSZv44M08EdgYeChw4yeVJklS9wcFBenp6mDNnDj09PQwODna6SarURAPaL4E/AXu3FjY9Xc8FTm4pi4j4fxHxm4i4KyJui4gzI+LpLQ999Ejrz8zrgXcAP26WtYTSy/bvEZETflaSJFVmcHCQvr4+hoaGyEyGhobo6+szpGlEkTl27mlC0mnAMmCPzHxqy7yDKUOcA8DxwKbAfsBHgMMowW4roB+4NjOf0zxuD+BUSs/bAHBWZl4+wrqfBfwAOB84KjMXjfeE5s2bl4sXLx6vmiRpllqwYEGnm7BKFi1axPLly1cqnzt3LvPnz+9Ai1bdwoULO92ENUZEXJyZ89rLJ3MW58nAUyJim5ayVwLfbKv3OOCIzDy6Gbo8Afgk8OyIeDhAZp4GvBN4AvA54PfNyQLHtS4/M38BLAeuGyucRURfRCyOiMU33HDDJJ6SJEmrx0jhbKxyrd0m3IOWmQdGxBAwkJn9zYH+Q0AP5dix44FNM/PG5nGbAts0077AjsAmmXlTy7I3AHYHXgzsRBnOvBvYuwlxK6x/Ik/IHjRJUo16enoYGhpaqby7u5slS5as/gapCtPRgwbwbR48m3Mf4GeZ+Ze2FW0TET8BrgdOB95ACV0AK1zPLDNvy8xvZOYbM7MHeEHzuM9Psl2SJFWtv7+frq6uFcq6urro7+/vUItUs8kGtG9Rhip7KAHtpBGWdyqwHvB0YIPMfD7wveEKEbFORAxFxKHtC8/M8ynDoVtGRFf7fEmSZqve3l4GBgbo7u4mIuju7mZgYIDe3t5ON00VWneS9S8E/gYcAMynDF22CuCJwJGZ+duW8t2G52fmfRFxLfDmiDgmM29vW8bWwJWZuay5f98k2yhJUpV6e3sNZJqQSQW0zLw/Ik4BDgF+3j68SQlTVwHvjIjrmvuvB/Zo5g/3ih0EnAX8PCI+A1wKPBx4OfBGyskHw5YCz4mIHYCf5HgHzUmSJM1yq/K/OL9FGcJsP3tz2F7A7ZThz+MpoexFzbztATLzQsr10y6m/AeBM4D/pZwBunNmfrtleR+l9MqdDjxmFdorSZI0q4x7Fuds41mckiRptpiuszglSZI0wwxokiRJlTGgSZIkVcaAJkmSVBkDmiRJUmUMaJIkSZUxoEmSJFXGgCZJklQZA5okSVJlDGiSJEmVMaBJkiRVxoAmSZJUGQOaJElSZQxokiRJlTGgSZIkVcaAJkmSVBkDmiRJUmUMaJIkSZUxoEmSJFXGgCZJklQZA5okSVJlDGiSJEmVMaBJkiRVxoAmSZJUGQOaJElSZQxokiRJlTGgSZIkVcaAJkmSVBkDmiRJUmUMaJIkSZUxoEmSJFXGgCZJklQZA5okSVJlDGiSJEmVmXJAi4iFEZFjTIdPYlkbRsSREXFFRCyPiJsi4gcRseNU2ylJkjRbrDtNy7kAOHSUeVdNZAEREcDpwD8ARwJ/ADYG3gCcFREvy8zTpqGtkiRJVZuuIc6lmblolOmvE1zGDsD2wGsycyAzF2bmKcDLgcXA+6eprZLaDA4O0tPTw5w5c+jp6WFwcLDTTZKktdpqOQYtIvaLiBsjYueI+GUzfHlpRLy0pdqjR2pTZt4PvA84fnW0VVrbDA4O0tfXx9DQEJnJ0NAQfX19hjRJ6qDIzKktIGIhcAfwspHmZ+a9EbEf8CXgWuAjwBLgP4HnAo/JzJsjYjPgT8DtwDHAD4GLM/PeybRn3rx5uXjx4lV6LtJ0WbBgQaebMGGLFi1i+fLlK5XPnTuX+fPnd6BFk7Nw4cJON0GSVllEXJyZ89rLp6sHbXfgnpGmiHhIU2d94F2ZeWxmngkcCDwE2BEgM68D9gSWAx8AFgFLI+K7EbHrWCuPiL6IWBwRi2+44YZpekrS2mGkcDZWuSRp5k3XSQLnAweNMq/1U35Ry99XN7cPGy7IzHMj4vGU0PYSYCdKaHtpRByZme8daQWZOQAMQOlBW6VnIE2j2dSr09PTw9DQ0Erl3d3ds+p5SNKaZLp60G7NzMWjTK2BaVnL3/eP1IbMvC8zz8rMQzLzWcDjgXOBwyPiCdPUXkmN/v5+urq6Vijr6uqiv7+/Qy2SJFVzodqIOCkiTmkvz8wllN65AJ68utslrel6e3sZGBigu7ubiKC7u5uBgQF6e3s73TRJWmtN1xDndLgSOCgits3M37XN25rS43bZ6m+WtObr7e01kElSRaYroG0UEaOd7nXrBJfxCWBv4CcR8WngQkoo+2fKRXA/m5lXTrWhkiRJtZuugPZPwE9HmXc28L/jLSAzb4yI7YD3APsChzWzLgUOAY6bhnZKkiRVb8rXQauN10GTJEmzxUxfB02SJEnTxIAmSZJUGQOaJElSZQxokiRJlTGgSZIkVcaAJkmSVBkDmiRJUmUMaJIkSZUxoEmSJFXGgCZJklQZA5okSVJlDGiSJEmVMaBJkiRVxoAmSZJUGQOaJElSZQxokiRJlTGgSZIkVcaAJkmSVBkDmiRJUmUMaJIkSZUxoEmSJFXGgCZJklQZA5okSVJlDGiSJEmVMaBJkiRVxoAmSZJUGQOaJElSZQxokiRJlTGgSZIkVcaAJkmSVBkDmiRJUmUMaJIkSZUxoEmSJFVmlQNaRCyMiBxjOnwCy+gZZxkfa1nXaavaVkmSpNlk3Sk+/gLg0FHmXTWJ5bwXOHeE8mua27cB901ieZIkSbPWVAPa0sxcNA3tuGKs5WTmpdOwDkmSpFlhxo9Bi4juiDgpIm6OiJsi4lsRseUkl+EQpyRJjcHBQXp6epgzZw49PT0MDg52ukmaZlPtQYuIGHEZmXlvRGwInA/cQRmmvAP4GPDDiHhGS/U5Iyzn/sy8f4rtkyRpjTI4OEhfXx/Lli0DYGhoiL6+PgB6e3s72TRNo6kGtN2Be0aaEREPBd4AbA48KTOvbMr/ApwCbEMJbADfGGER3wf2mGL7JEka0YIFCzrdhFWyaNEili9fvkLZsmXL2H///Tn22GM71KpVt3Dhwk43oUpTDWjnAweNMm858Hzgd8PhDCAzfwlsBeUszqb4MOCctscvnWgjIqIP6APYcstJjZ5KkjSrtIez8co1O001oN2amYtHmxkRjwSun8By/jzWcsaTmQPAAMC8efNyVZcjSVp7zNaem56eHoaGhlYq7+7unrXPSSub6ZMEbgU2bS+MiJdExGYzvG5JktY4/f39dHV1rVDW1dVFf39/h1qkmTDTAe1C4GkR0T1cEBFPAX4APHOG1y1J0hqnt7eXgYEBuru7iQi6u7sZGBjwBIE1zFSHODeKiPmjzLsV+ArlGLXTIuKDlIvNHgH8jHLM2WOnuH5JktY6vb29BrI13FQD2j8BPx1l3tmZ+aKI2AH4b+AEyokDPwQOaS7DMcXVS5IkrXlWOaBl5oIJ1rsSeMUo85YA46a0ia5LkiRpTTDj/0lAkiRJk2NAkyRJqowBTZIkqTIGNEmSpMoY0CRJkipjQJMkSaqMAU2SJKkyBjRJkqTKGNAkSZIqY0CTJEmqjAFNkiSpMgY0SZKkyhjQJEmSKmNAkyRJqowBTZIkqTIGNEmSpMoY0CRJkipjQJMkSaqMAU2SJKkyBjRJkqTKGNAkSZIqY0CTJEmqjAFNkiSpMgY0SZKkyhjQJEmSKmNAkyRJqowBTZIkqTIGNEmSpMoY0CRJkipjQJMkSaqMAU2SJKkyBjRJkqTKGNAkSZIqY0CTJEmqzIwGtIhYEhHZMt0bEddExDERsVFTZ79m3iYz2RZJkqTZYt3VsI6TgaOav+cCWwMfBnqA3YDvA9sDS1dDWyRJkqq3OoY4r8vMRc3048w8DngP8OKI6M7MG5p5966GtkiSpFEMDg7S09PDnDlz6OnpYXBwsNNNWmt16hi0pcN/tA9xRvHmiPhNRNwZEVdExDs71E5JktYKg4OD9PX1MTQ0RGYyNDREX1+fIa1DVscQZ0TE8HrWBZ4IvA/4YWYORUR7/Y8C7wI+BpwHLAA+GRGbZOZ/rIb2SpI07RYsWNDpJoxp0aJFLF++fIWyZcuWsf/++3Psscd2qFUTs3Dhwk43YdqtjoD2tmZqdRPwb+0VI+JRwMHAJ1rC2BlRUty7IuLTmXnjCI/rA/oAttxyy+lsuyRJa4X2cDZeuWZWZObMLTxiCXAR8ImmaD2gm3IM2hbAfOAFwPHApsB2wGnAczLzkpblPBP4JbBnZp421jrnzZuXixcvntbnIUnSmq6np4ehoaGVyru7u1myZMnqb9BaIiIuzsx57eWr4xi0GzJzcTP9NDO/DuwObAwc1FZ34+b2urby4fsbzmA7JUlaa/X399PV1bVCWVdXF/39/R1q0dqtIycJZOY1wM2U49Fa3dzcbtZWvnlze9NMtkuSpLVVb28vAwMDdHd3ExF0d3czMDBAb29vp5u2Vlodx6CtJCJ6KEOaf2yb9TPgHuCVwCUt5a8G7m3mS5KkGdDb22sgq8TqCGibRcT8lvtbAO8H7gK+ADxveEZm3hgRn6GcEHAv5SzOHShndR6VmbeshvZKkiR11OoIaPs0E0BSroF2PvCmzLw0Ip7XVv/dwA3AAc3fS4BDgaNXQ1slSZI6bkbP4uwEz+KUJEmzRSfP4pQkSdIkGNAkSZIqY0CTJEmqjAFNkiSpMgY0SZKkyhjQJEmSKmNAkyRJqowBTZIkqTIGNEmSpMoY0CRJkipjQJMkSaqMAU2SJKkyBjRJkqTKGNAkSZIqY0CTJEmqjAFNkiSpMgY0SZKkyhjQJEmSKmNAkyRJqowBTZIkqTIGNEmSpMoY0CRJkipjQJMkSaqMAU2SJKkyBjRJkqTKGNAkSZIqY0CTJEmqjAFNkiSpMgY0SZKkyhjQJEmSKmNAkyRJqowBTZIkqTIGNEmSpMoY0CRJkipjQJMkSaqMAU2SJKkyBjRJkqTKGNAkSZIqY0CTJEmqzLqdbsB0iIg+oK+5e3tEXN7J9jQ2AW7sdCM0aW632cttNzu53WYnt9v06R6pMDJzdTdkrRARizNzXqfboclxu81ebrvZye02O7ndZp5DnJIkSZUxoEmSJFXGgDZzBjrdAK0St9vs5babndxus5PbbYZ5DJokSVJl7EGTJEmqjAGtERHrR8RHImIoIu6IiHMi4tkt8yMi3hcRV0XEsog4MyK2aVvG3Ij4VERcGxG3RcTJEbFFW52NI+KEiLgpIm6JiOMiYsO2Oo+LiFMi4taIuC4iPh4R68/sKzA7TWC7zYuIHGH6ZEsdt1sHNa//ZRFxQkuZ77fKjbLdfL9VKiIeNcq2ObmZ73uuNpnpVIZ5Pw/8HXgrsCtwGnAr0N3M/wBwJ/AO4KXAz4BrgEe0LON44CZgP2Af4Argl8A6LXXOAZYArwReD1wPnNYyfy5wGXBJs54DgTuAz3X6NapxmsB2eyNwOzC/bdrS7VbHBHwUSOCEljLfb5VPo2w332+VTsBOzfbatW3bbN3M9z1X2dTxBtQwAY8A7gYObil7KLAM+A9gA+A24LCW+RtTgsHBzf0nAPcBr26pszVwP7BXc3/H5g2yXUudnZuyZzf33wDcAzy2pc7+TdlmnX6taprG227N/U8Di8ZYhtuts9vwWZQv9Btovuh9v9U/jbTdmnLfb5VOwDuBa0eZ53uuwskhzuIOYDvKr4Nh91B2qrmUXxkPB743PDMzbwF+DOzWFO3U3J7WUucK4HctdV4EXJ+ZF7Ws51zKm6C1ziWZeXVLne9Q/uvDzqv07NZc4203gGcAvx5jGW63DomIdYGvAJ+g/FIf5vutYmNsN/D9VrOxto3vuQoZ0IDMvDczf5GZt0TEnIjYivIBlMD/Ak9qqv6p7aF/bpn3JMqvkzvGqfPHtnXfT+kOHqvOTZQd/EnoARPYbgBPBx4XEb+MiLsj4o8R8fqWxbjdOucwYH3gyLZy3291G227ge+3mj0D6IqICyPiroi4OiLeHRGB77kqrRH/i3Oa/Sfwwebv92fm5RGxF7A8M+9uq3sbMHzw44bN/Xa3AY+bQJ2JLGfDEcpVjLTdtqD8v7itgfcAtwD7AidERGbmibjdOqI5+Ph9wM6ZeXf5jnjAhvh+q9JY2833W70iYg7wVMqow6HAVcDulJD9EMrIg++5yhjQVnYKsJAylv7+5sySOym9Mu2CMv4+/PdE6tw/gTrjLUcrG2m7HUnpVv91Zv6tqXdW80XyAeBE3G6rXfNl8WXgy5n505Gq4PutOhPYbkvx/VarAPYArsrM4d6rcyPi4ZQe0X58z1XHgNYmM4fH6H8cERsA76LswHMjYr3MvKel+sMpZwzS3G4wwiLb6/zDBOqMtxy1GWW7fTgzfzRC9dOB3ZoPJ7fb6vd2oBvYozmeaVg092/F91uNxtxumbkM8P1Wocy8j3J2ZbvTgbdQetZ8z1XGY9CAiNg8It7QfLG3+gXlYPNbKOl+q7b5jwcub/6+Atg8Ih46Tp3Ht617DtAzTp1HUbp+L0cPmMB22z4i3hIRc9vmP5TSK3oHbrdOeAXwGOBmytDKPcAzgde13Pf9Vp8xt1tEPMn3W50iYouI6IuITdtmDW8Hv+MqZEArNqIcXL5PW/mulGu4fAe4C3j58IyI2Bh4IXB2U3Q2sA6wZ0udrYFt2+r8Q0Q8r2UdO1J2zNY68yLisS11Xk75MDxv8k9tjbYRY2+39YAvUo61AMpPfWAv4CeZmbjdOuEA4Llt0x8oZ4c9F/g6vt9qNN522wrfb7WaC3wJ+Ne28r0p2/Db+J6rT6ev81HLBJxM+WV4ALAL5YMmgTc08z9OuebWoZSL610EXM2KF/E7idJF+2ZGuIgf5RfKouZx+1J+ebZfxK+LcsbLbym/WP8dL+K3StuN8mHyE+A6ygU0X8KDYXue262eqXm9T2i57/ttFkyt2833W90T8H+Ua9f9P8qP2GMpx3y9tJnve66yqeMNqGVqdpr/anac5ZRhsn1a5q8LfAy4ttnJzwC2aVvGw4ABSmBYSgkPW7TVeTTwDcoZKzdSDrrdsK3OEynHBiwD/ka53tB6nX6NapwmsN0eCRzTfGDcCVwAvMDtVtfEygHN99ssmEbYbr7fKp0ow5kfBa6khOZfAK9ome97rrIpmhdLkiRJlfAYNEmSpMoY0CRJkipjQJMkSaqMAU2SJKkyBjRJkqTKGNAkSZIqY0CTJEmqjAFNkiSpMgY0SZKkyvx/W5OLBFxbaskAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ = tukey.plot_simultaneous()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.10.2"
  },
  "vscode": {
   "interpreter": {
    "hash": "31f2aee4e71d21fbe5cf8b01ff0e069b9275f58929596ceb00d14d90e3e16cd6"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}