{ "cells": [ { "cell_type": "code", "execution_count": 1, "id": "ab7baffe-bae1-4eba-aecf-a4eba1754d00", "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": "bffcaca9-b28c-4de7-bbea-f8039ca936fb", "metadata": {}, "source": [ "# Das Positionsmaß" ] }, { "cell_type": "code", "execution_count": 2, "id": "09dcd210-a6b5-499f-81ac-0f187ffea863", "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import pandas as pd\n", "import scipy.stats as stats" ] }, { "cell_type": "markdown", "id": "bce57223-61ad-4a66-98a6-92ff12f60571", "metadata": {}, "source": [ "Ein Positionsmaß bestimmt die Position eines einzelnen Wertes im Verhältnis zu anderen Werten in einer Stichprobe oder einem Populationsdatensatz. Anders als der Mittelwert und die Standardabweichung sind auf **Quantilen** basierende deskriptive Maße nicht empfindlich gegenüber dem Einfluss einiger weniger extremer Beobachtungen. Aus diesem Grund werden deskriptive Maße, die auf Quantilen basieren, häufig denjenigen vorgezogen, die auf dem Mittelwert und der Standardabweichung basieren ({cite:t}`fahrmeirstatistik` s.60).\n", "\n", "Quantile sind Punkte, die den Bereich der Daten in zusammenhängende Intervalle mit gleichen Wahrscheinlichkeiten unterteilen. Bestimmte Quantile sind besonders wichtig: Der **Median** eines Datensatzes unterteilt die Daten in zwei gleiche Teile: die unteren $50 \\%$ und die oberen $50 \\%$. **Quartile** unterteilen die Daten in vier gleiche Teile und **Perzentile** unterteilen sie in Hundertstel oder $100$ gleiche Teile. Beachten Sie, dass der Median auch das $50$-te Perzentil ist. **Dezile** unterteilen einen Datensatz in Zehntel ($10$ gleiche Teile), und die **Quintile** unterteilen einen Datensatz in Fünftel ($5$ gleiche Teile). Es gibt immer ein Quantil weniger als die Anzahl der gebildeten Gruppen (z. B. gibt es **3** Quartile, die die Daten in **4** gleiche Teile unterteilen!)." ] }, { "cell_type": "markdown", "id": "2a9bf3f1-5926-4995-bcd8-84a9991f08b5", "metadata": { "tags": [] }, "source": [ "## Quartile und Interquartilsbereich" ] }, { "cell_type": "markdown", "id": "6cc61d18-b090-4226-b135-93f4228b7595", "metadata": {}, "source": [ "**Quartile** unterteilen einen geordneten Datensatz in **vier gleiche Teile**. Diese drei Maße werden als **erstes Quartil** $(Q1)$, **zweites Quartil** $(Q2)$ und **drittes Quartil** $(Q3)$ bezeichnet. Das zweite Quartil ist dasselbe wie der Median eines Datensatzes. Das erste Quartil ist der Wert des mittleren Terms unter den Beobachtungen, die kleiner als der Median sind, und das dritte Quartil ist der Wert des mittleren Terms unter den Beobachtungen, die größer als der Median sind ({cite:t}`fahrmeirstatistik` s.59)." ] }, { "cell_type": "markdown", "id": "7bac4dcf-549f-41f9-971a-d96579ea46e1", "metadata": {}, "source": [ "![Alt-Text](_img/median.png)" ] }, { "cell_type": "markdown", "id": "57ca73e5-3f1a-4fd0-a874-5553f837758f", "metadata": {}, "source": [ "Ungefähr $25 \\%$ der Werte in einem geordneten Datensatz sind kleiner als $Q1$ und etwa $75 \\%$ sind größer als $Q1$. Das zweite Quartil, $Q2$, unterteilt einen geordneten Datensatz in zwei gleiche Teile; daher sind das zweite Quartil und der Median identisch. Etwa $75 \\%$ der Datenwerte sind kleiner als $Q3$ und etwa $25 \\%$ sind größer als $Q3$. Die Differenz zwischen dem dritten Quartil und dem ersten Quartil eines Datensatzes wird als **Interquartilsbereich** ($IQR$) bezeichnet ({cite:t}`fahrmeirstatistik` s.61)." ] }, { "cell_type": "markdown", "id": "2e56e957-0aa9-4283-b4d3-43f32e496b47", "metadata": {}, "source": [ "$$ IQR=Q3−Q1 $$" ] }, { "cell_type": "markdown", "id": "e1a22dae-d1e1-442d-ac5e-2daa76277345", "metadata": {}, "source": [ "Wechseln wir zu Python und testen wir seine Funktionalität zur Berechnung von Quantilen/Quartilen. Wir werden die `nc_score`-Variable des `students` Datensatzes verwenden, um Quartile und den $IQR$ zu berechnen. Die `nc_score`-Variable entspricht der Numerus-Clausus-Punktzahl jedes Studenten." ] }, { "cell_type": "markdown", "id": "de028378-a0de-47c8-af33-7152ead9eabe", "metadata": {}, "source": [ "Zunächst werden die Daten unterteilt und ein Histogramm erstellt, um die Verteilung der Variablen genauer zu untersuchen." ] }, { "cell_type": "code", "execution_count": 3, "id": "8cab92df-a8f1-4426-b633-7680e0e355f8", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Lese Daten ein\n", "df = pd.read_csv(\"../../data/students.csv\")\n", "\n", "# Histogramm\n", "df[\"nc_score\"].hist(bins=15)\n", "plt.xlabel(\"Numerus Clausus\")\n", "plt.ylabel(\"Häufigkeit\")\n", "plt.title(\"Histogramm von 'nc_score'\")\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "a8e11aa7-63a7-4610-970a-997717c6f3d0", "metadata": {}, "source": [ "Um die Quartile für die Variable nc_score zu berechnen, wenden wir die Funktion `np.quantile` an. Um die Quartile für die Variable `nc_score` zu berechnen, schreiben wir also einfach:" ] }, { "cell_type": "code", "execution_count": 4, "id": "2b4a7431-643d-4ab7-a6d0-63188a3addda", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1. Quantil des nc_score: 1.46\n", "2. Quantil des nc_score: 2.04\n", "3. Quantil des nc_score: 2.78\n", "4. Quantil des nc_score: 4.0\n" ] } ], "source": [ "for e, q in enumerate([0.25, 0.5, 0.75, 1]):\n", " print(f\"{e+1}. Quantil des nc_score: {np.quantile(df['nc_score'], q)}\")" ] }, { "cell_type": "markdown", "id": "26e101e6-04d0-4a87-ac05-165169f67963", "metadata": {}, "source": [ "**Hinweis:** Nicht alle Statistiker definieren Quartile auf genau dieselbe Weise. Eine ausführliche Diskussion der verschiedenen Methoden zur Berechnung von Quantilen finden Sie in dem Online-Artikel \"Quartiles in Elementary Statistics\" von E. Langford (2006)." ] }, { "cell_type": "markdown", "id": "a74919c9-ad25-4b97-9cfa-57f4dd746db7", "metadata": {}, "source": [ "Um den $IQR$ für die Variable `nc_score` zu berechnen, schreiben wir entweder..." ] }, { "cell_type": "code", "execution_count": 5, "id": "fb1db9b0-d0f8-4cf0-945a-639109f69bb7", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.3199999999999998" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Berechne Interquartil Abstand mit Funktion np.percentile()\n", "q1, q3 = np.percentile(df[\"nc_score\"], [25, 75])\n", "iqr = q3 - q1\n", "iqr" ] }, { "cell_type": "markdown", "id": "ebc2f8b4-4bc0-4249-b612-3afac9be6266", "metadata": {}, "source": [ "...oder wir wenden die eingebaute Funktion `iqr` aus dem Modul `scipy.stats` an:" ] }, { "cell_type": "code", "execution_count": 6, "id": "85243a86-924b-4a1c-aad4-0a5d4cb631af", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.3199999999999998" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stats.iqr(df[\"nc_score\"], rng=(25, 75))" ] }, { "cell_type": "markdown", "id": "f6e0ba95-83ba-4d7a-93e4-9820db3fe211", "metadata": { "tags": [] }, "source": [ "Wir können die Aufteilung der Variablen `nc_score` in Quartile visualisieren, indem wir ein Histogramm erstellen und ein paar zusätzliche Codezeilen hinzufügen." ] }, { "cell_type": "code", "execution_count": 7, "id": "40b59d1d-89a2-4f07-9dc7-8aa33364a78d", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Plotte die Liste als Histogramm mit Quartilen\n", "df[\"nc_score\"].hist(bins=15)\n", "plt.xlabel(\"nc_score\")\n", "plt.ylabel(\"Häufigkeit\")\n", "plt.title(\"Histogramm der Variable Numerus Clausus\")\n", "\n", "# Zeiche vertikale Linien bei Q1, Q2, Q3, Q4\n", "for e, q in enumerate([0.25, 0.5, 0.75, 1]):\n", " plt.axvline(x=np.quantile(df[\"nc_score\"], q), color=f\"C{e+1}\", label=f\"Q{e+1}\")\n", "plt.legend()" ] }, { "cell_type": "markdown", "id": "c18e90d1-55b1-4da2-8f2f-b5d8c4aa53fd", "metadata": { "tags": [] }, "source": [ "## Die 5-Punkte-Zusammenfassung" ] }, { "cell_type": "markdown", "id": "b8fb72e9-4b82-4ee8-8f70-6e92cdca3f7c", "metadata": {}, "source": [ "Aus den drei Quartilen $(Q1, Q2, Q3)$können wir ein Maß für die Lage der Mitte (den Median, $Q2$) und ein Maß für die Variation der beiden mittleren Quartale der Daten, $Q2-Q1$ für die zweite Quartile und $Q3-Q2$ für die dritte Quartile ableiten. Die drei Quartilen sagen jedoch nichts über die Variation der ersten und vierten Quartile aus." ] }, { "cell_type": "markdown", "id": "f142cc4c-f663-46f0-94a9-c1598cb8d1fb", "metadata": {}, "source": [ "Um diese Informationen zu erhalten, beziehen wir auch die Beobachtungen des Minimums und des Maximums mit ein. Die Variation der ersten Quartile kann als Differenz zwischen dem Minimum und der ersten Quartile, $Q1-Min$, gemessen werden, und die Variation der vierten Quartile kann als Differenz zwischen der dritten Quartile und dem Maximum, $Max-Q3$, gemessen werden. Somit liefern das Minimum, das Maximum und die Quartile zusammen unter anderem Informationen über Zentrum und Variation ({cite:t}`fahrmeirstatistik` s.62)." ] }, { "cell_type": "markdown", "id": "4dcdf2fd-50c6-410e-ac0e-a27a8fac4f60", "metadata": {}, "source": [ "Die so genannte **Tukey-Fünf-Punkte-Zusammenfassung** (nach dem Mathematiker John Wilder Tukey) eines Datensatzes besteht aus den Werten $Min, Q1, Q2, Q3$ und $Max$ des Datensatzes." ] }, { "cell_type": "markdown", "id": "870edf0a-6df7-4898-b62e-2bfb2520cd4c", "metadata": {}, "source": [ "Die Fünf-Punkte-Zusammenfassung lässt sich in Python durch `np.percentile` und die `min()`, `max()` Funktionen berechnen. Zu Demonstrationszwecken berechnen wir die Fünf-Punkte-Zusammenfassung für die Variable `nc_score`" ] }, { "cell_type": "code", "execution_count": 8, "id": "fda94f80-df22-4713-b7f3-f6c068eaad27", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Min: 1.0\n", "Q1: 1.46\n", "Median: 2.04\n", "Q3: 2.78\n", "Max: 4.0\n" ] } ], "source": [ "# Lese Datei students.csv als Dataframe ein; Indexspalte wird übersprungen\n", "df = pd.read_csv(\"../../data/students.csv\", index_col=0)\n", "\n", "# Berechne Fünf-Zahlen-Zusammenfassung\n", "scores = df[\"nc_score\"]\n", "\n", "# Berechne die Quartilen\n", "q1, median, q3 = np.percentile(scores, [25, 50, 75])\n", "\n", "# Berechne minimal/maximal Datenpunkte\n", "data_min, data_max = min(scores), max(scores)\n", "\n", "# Ausgabe der Daten\n", "print(f\"Min: {data_min}\")\n", "print(f\"Q1: {q1}\")\n", "print(f\"Median: {median}\")\n", "print(f\"Q3: {q3}\")\n", "print(f\"Max: {data_max}\")" ] }, { "cell_type": "markdown", "id": "d42b9b54-5ad6-4f0d-8914-0aafb06a89d9", "metadata": {}, "source": [ "Diese Funktion liefert Minimum, untere Quartile, Median, obere Quartile und Maximum für die Eingabedaten." ] }, { "cell_type": "markdown", "id": "c713d147-bd21-4259-863e-7301632cb0f5", "metadata": {}, "source": [ "In Python gibt es eine ähnliche Methode namens `describe()`, die ähnliche Statistiken liefert." ] }, { "cell_type": "code", "execution_count": 9, "id": "f11e6b39-8639-4cf8-a0f5-621b319b33c7", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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count8239.0000008239.0000008239.0000008239.0000004892.0000004892.0000008239.0000008239.0000001753.000000
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75%23.000000180.00000078.5000002.78000078.00000080.0000001.0000000.00000049372.540000
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" ], "text/plain": [ " age height weight nc_score score1 \\\n", "count 8239.000000 8239.000000 8239.000000 8239.000000 4892.000000 \n", "mean 22.541571 171.380750 72.998131 2.166481 68.164963 \n", "std 6.065111 11.077529 8.635162 0.811548 14.051762 \n", "min 18.000000 135.000000 51.400000 1.000000 30.000000 \n", "25% 20.000000 163.000000 66.500000 1.460000 58.000000 \n", "50% 21.000000 171.000000 71.800000 2.040000 70.000000 \n", "75% 23.000000 180.000000 78.500000 2.780000 78.000000 \n", "max 64.000000 206.000000 116.000000 4.000000 97.000000 \n", "\n", " score2 online_tutorial graduated salary \n", "count 4892.000000 8239.000000 8239.000000 1753.000000 \n", "mean 69.494685 0.386212 0.212769 42522.112253 \n", "std 14.395251 0.486910 0.409290 10333.139992 \n", "min 31.000000 0.000000 0.000000 11444.140000 \n", "25% 59.000000 0.000000 0.000000 35206.540000 \n", "50% 71.000000 0.000000 0.000000 41672.010000 \n", "75% 80.000000 1.000000 0.000000 49372.540000 \n", "max 98.000000 1.000000 1.000000 75596.790000 " ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df.describe()" ] }, { "cell_type": "markdown", "id": "27ffba86-812f-4d57-a445-7d461531ae2c", "metadata": { "tags": [] }, "source": [ "## Perzentile und Perzentilrang" ] }, { "cell_type": "markdown", "id": "07961b4f-1042-42fa-8d81-f97344e6e010", "metadata": { "jp-MarkdownHeadingCollapsed": true, "tags": [] }, "source": [ "**Perzentile** unterteilen einen geordneten Datensatz in $100$ gleiche Teile. Jeder (geordnete) Datensatz hat $99$ Perzentile, die ihn in $100$ gleiche Teile unterteilen. Das **k-te** Perzentil wird mit $P_k$ bezeichnet, wobei $k$ eine ganze Zahl im Bereich von $1$ bis $99$ ist. Das $25$-te Perzentil wird zum Beispiel mit $P_{25}$ bezeichnet." ] }, { "cell_type": "markdown", "id": "3303aaee-c62d-4449-ab3e-e65c0c8afc76", "metadata": {}, "source": [ "So kann das **k-te** Perzentil, $P_k$, als ein Wert in einem Datensatz definiert werden, bei dem etwa $k\\%$ der Messungen kleiner als der Wert von $P_k$ und etwa $(100-k)$ der Messungen größer als der Wert von $P_k$ sind\n", "\n", ".\n", "\n", "Der ungefähre Wert des **k-ten**.\n", "Perzentils, bezeichnet mit $P_k$, ist " ] }, { "cell_type": "markdown", "id": "68552dec-e707-4d6f-be89-1af1b4bae631", "metadata": { "tags": [] }, "source": [ "$$ P_k = \\frac{kn}{100} $$" ] }, { "cell_type": "markdown", "id": "dcf4b9c2-95a5-4d3f-aeb0-7de1b122e350", "metadata": { "tags": [] }, "source": [ "wobei **k** die Nummer des Perzentils bezeichnet und **n** den Stichprobenumfang darstellt.\n", "\n", "Als Übung berechnen wir das $38$-te, das $50$-te und das $73$-te Perzentil der Variablen `nc_score` in Python. Zunächst berechnen wir das 38. Perzentil gemäß der oben angegebenen Gleichung. Dann wenden wir die `np.percentile()`-Funktion von Python an, um das $38$-te, $50$-te und $73$-te Perzentil der Variablen `nc_score` zu ermitteln." ] }, { "cell_type": "code", "execution_count": 10, "id": "78263a25-c11e-427e-a028-f7658b7406e8", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Die 38-te Perzentile ist 3131.\n" ] } ], "source": [ "# Lese Datei students.csv als Dataframe ein; Indexspalte wird übersprungen\n", "df = pd.read_csv(\"../../data/students.csv\", index_col=0)\n", "\n", "scores = df[\"nc_score\"].sort_values()\n", "\n", "# Berechne 38-te Perzentile\n", "k = 38\n", "n = len(scores)\n", "print(f\"Die {k}-te Perzentile ist {round((k*n)/100)}.\")" ] }, { "cell_type": "code", "execution_count": 11, "id": "cc332043-7e7c-4fb3-a60a-f2cff96e2ef5", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "stud_id\n", "403145 1.0\n", "884117 1.0\n", "832302 1.0\n", "499028 1.0\n", "924359 1.0\n", " ... \n", "676841 4.0\n", "679521 4.0\n", "706167 4.0\n", "941727 4.0\n", "806767 4.0\n", "Name: nc_score, Length: 8239, dtype: float64" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "scores" ] }, { "cell_type": "markdown", "id": "2c6c3cad-b3d7-48aa-a5e9-5ee7a63823f1", "metadata": {}, "source": [ "Wir wählen den Wert anhand dieser Zahl in der geordneten Liste `nc_score` aus und vergleichen ihn mit den Perzentilwerten." ] }, { "cell_type": "code", "execution_count": 12, "id": "e5aad000-aa33-40f4-8660-d30bcc208e93", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.74" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "scores.iloc[3131]" ] }, { "cell_type": "code", "execution_count": 13, "id": "d75a9a1e-ff2f-4629-9d8e-57c2d8c87247", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1.74 2.04 2.71]\n" ] } ], "source": [ "quartiles = np.percentile(scores, [38, 50, 73])\n", "print(quartiles)" ] }, { "cell_type": "markdown", "id": "8c546576-912a-443e-b26f-56bd059883d8", "metadata": {}, "source": [ "Das hat gut funktioniert! Sie können prüfen, ob der Median der Variablen `nc_score` dem $50$-te Perzentil $(2,04)$ entspricht, wie oben berechnet.\n", "\n", "Wir können auch den **Perzentilrang** für einen bestimmten Wert $x_i$\n", "eines Datensatzes mit der folgenden Gleichung berechnen: " ] }, { "cell_type": "markdown", "id": "d8eb04f7-91df-46dd-b128-2308de09bd85", "metadata": {}, "source": [ "$$ \\text{Perzentil Rang für} \\ x_i = \\frac{ \\text{Werte kleiner als} \\ x_i}{ \\text{Gesamtanzahl der Werte im Datensatz}} $$" ] }, { "cell_type": "markdown", "id": "bd104765-7d5c-4a5a-80ae-63fb0e5fcddd", "metadata": {}, "source": [ "Der Perzentilrang von $x_i$ gibt den Prozentsatz der Werte im Datensatz an, die kleiner als $x_i$ sind.\n", "\n", "In Python gibt es keine eingebaute Funktion zur Berechnung des Perzentilrangs. Es ist jedoch relativ einfach, eine solche Funktion selbst zu schreiben." ] }, { "cell_type": "code", "execution_count": 14, "id": "ed9cd2d5-fcfa-4610-811b-44457d2dbe43", "metadata": {}, "outputs": [], "source": [ "# Definiere Funktion my_percentile_rank\n", "def my_percentile_rank(x, data: pd.Series):\n", " \"\"\"Computes the percentile rank\n", " Args:\n", " x: int or float number\n", " data: Pandas Series\n", " \"\"\"\n", " return sum(data < x) / len(data)" ] }, { "cell_type": "markdown", "id": "45ef2c9f-7960-488a-adb6-91a19d8d35f6", "metadata": {}, "source": [ "Jetzt berechnen wir zum Beispiel den Perzentilrang für einen Numerus clausus von $2,5$." ] }, { "cell_type": "code", "execution_count": 15, "id": "1f105ebb-fdd1-4b5d-ac26-51ed046485f3", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.6627017841971113" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "my_percentile_rank(2.5, scores)" ] }, { "cell_type": "markdown", "id": "f2cb164b-8754-4ee9-b36c-6a277be8ccc3", "metadata": {}, "source": [ "Wenn wir das Ergebnis auf den nächsten ganzzahligen Wert runden, können wir feststellen, dass etwa $66 \\%$ der Studenten in unserem Datensatz einen Numerus clausus von mehr als $2,5$ hatten." ] }, { "cell_type": "markdown", "id": "1bd8ad82-0afe-4533-8409-b0cfb015219b", "metadata": {}, "source": [ "## Ausreißer und Boxplots" ] }, { "cell_type": "markdown", "id": "6ccafe9a-b65f-4e48-9b38-e3ac24331c3b", "metadata": {}, "source": [ "### Ausreißer\n", "Bei der Datenanalyse ist die Identifizierung von Ausreißern und damit von Beobachtungen, die deutlich aus dem Gesamtmuster der Daten herausfallen, sehr wichtig. Ein Ausreißer erfordert besondere Aufmerksamkeit. Er kann das Ergebnis eines Mess- oder Aufzeichnungsfehlers, einer Beobachtung aus einer anderen Population oder einer ungewöhnlich extremen Beobachtung sein. Beachten Sie, dass eine extreme Beobachtung nicht zwangsläufig ein Ausreißer sein muss, sondern auch ein Hinweis auf eine Schieflage sein kann ({cite:t}`fahrmeirstatistik` s.62)." ] }, { "cell_type": "markdown", "id": "6e3e42f7-db5c-4e48-9666-85c2c5cb95f1", "metadata": {}, "source": [ "Wenn wir einen Ausreißer beobachten, sollten wir versuchen, seine Ursache zu ermitteln. Ist ein Ausreißer auf einen Mess- oder Aufzeichnungsfehler zurückzuführen oder gehört er aus einem anderen Grund eindeutig nicht zum Datensatz, kann er einfach entfernt werden. Wenn jedoch keine Erklärung für einen Ausreißer ersichtlich ist, ist die Entscheidung, ob er im Datensatz verbleiben soll, eine schwierige Ermessensentscheidung." ] }, { "cell_type": "markdown", "id": "c477b418-9216-4c26-b55b-59b5777d01f2", "metadata": {}, "source": [ "Als Diagnoseinstrument zum Aufspüren von Beobachtungen, die Ausreißer sein könnten, können wir Quartile und den **IQR** verwenden. Daher definieren wir die **Untergrenze** und die **Obergrenze** eines Datensatzes. Die untere Grenze ist die Zahl, die $1,5×IQRs$ unter dem ersten Quartil liegt; die obere Grenze ist die Zahl, die $1,5×IQRs$\n", "\n", "über dem dritten Quartil liegt. Beobachtungen, die unterhalb der Untergrenze oder oberhalb der Obergrenze liegen, sind potenzielle Ausreißer ({cite:t}`fahrmeirstatistik` s.61).\n", "\n" ] }, { "cell_type": "markdown", "id": "f056d830-effd-4897-97db-83cf5996fbd6", "metadata": {}, "source": [ "$$\\text{Untere Grenze}=Q1-1,5×IQR$$" ] }, { "cell_type": "markdown", "id": "d216bd92-1f12-4f4a-8be0-94d1b793cd44", "metadata": {}, "source": [ "$$\\text{Obere Grenze}=Q3+1,5×IQR$$" ] }, { "cell_type": "markdown", "id": "45c6aed6-d1cd-49c9-8f48-38c454651ce3", "metadata": {}, "source": [ "### Boxplots" ] }, { "cell_type": "markdown", "id": "56ae26ab-8876-4615-9983-f6f0363e44cb", "metadata": {}, "source": [ " Das Boxplot-Diagramm, auch **Box-and-Whisker-Diagramm** genannt, basiert auf der Fünf-Punkte-Zusammenfassung ({cite:t}`fahrmeirstatistik` s.62) und kann zur grafischen Darstellung von Zentrum und Variation eines Datensatzes verwendet werden. Diese Diagramme wurden von dem Mathematiker John Wilder Tukey erfunden. Es sind mehrere Arten von Boxplots gebräuchlich.\n", "\n", "Box-and-Whisker-Diagramm bieten eine grafische Darstellung der Daten anhand von fünf Maßzahlen: dem Median, dem ersten Quartil, dem dritten Quartil sowie dem kleinsten und dem größten Wert des Datensatzes zwischen der unteren und der oberen Grenze. Der Abstand zwischen den verschiedenen Teilen des Kastens zeigt den Grad der Streuung und Schiefe der Daten an. Durch die Erstellung von Box-and-Whisker-Diagrammen können verschiedene Verteilungen miteinander verglichen werden. Es hilft auch, Ausreißer zu erkennen ({cite:t}`fahrmeirstatistik` s.62). Box-Plots können entweder horizontal oder vertikal gezeichnet werden." ] }, { "cell_type": "markdown", "id": "90e91afd-d096-44b8-9b13-1dce81d75024", "metadata": {}, "source": [ "\n", "![Alt-Text](_img/boxplot.png)\n", "Die Ränder der Box sind immer das erste und dritte Quartil, und der Bereich innerhalb der Box ist immer das zweite Quartil (der Median). Die von den Boxen ausgehenden Linien (Whisker) zeigen die Variabilität außerhalb des oberen und unteren Quartils an. Um einen Boxplot zu erstellen, benötigen wir auch das Konzept der benachbarten Werte. Die **angrenzenden Werte** eines Datensatzes sind die extremsten Beobachtungen, die noch innerhalb der unteren und oberen Grenzen liegen; sie sind die extremsten Beobachtungen, die keine potenziellen Ausreißer sind. Ausreißer können als einzelne Punkte aufgetragen werden. Wenn es in einem Datensatz keine potenziellen Ausreißer gibt, sind die angrenzenden Werte lediglich das Minimum und das Maximum der Beobachtungen ({cite:t}`fahrmeirstatistik`).\n", "\n", "Lassen Sie uns nun eine Reihe von Boxplots erstellen, um den Datensatz `students` eingehender zu analysieren. Wir beginnen mit der Erstellung eines Boxplots für die Variable `nc_score`." ] }, { "cell_type": "code", "execution_count": 16, "id": "604fbf77-2a43-49d6-bd96-24f7697f159a", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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8239 rows × 4 columns

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" ], "text/plain": [ " gender height nc_score semester\n", "0 Female 160 1.91 1st\n", "1 Female 172 1.56 2nd\n", "2 Female 168 1.24 3rd\n", "3 Male 183 1.37 2nd\n", "4 Female 175 1.46 1st\n", "... ... ... ... ...\n", "8234 Male 181 2.91 6th\n", "8235 Male 178 2.03 2nd\n", "8236 Female 169 3.72 3rd\n", "8237 Male 195 2.74 4th\n", "8238 Female 170 3.29 >6th\n", "\n", "[8239 rows x 4 columns]" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Lese der Datei students.csv; nur Spalten 'nc_score','semester','gender','height' werden verwendet\n", "students = pd.read_csv(\n", " \"../../data/students.csv\", usecols=[\"nc_score\", \"semester\", \"gender\", \"height\"]\n", ")\n", "students" ] }, { "cell_type": "code", "execution_count": 17, "id": "65c48482-c860-415a-8e00-10562ccd9f9d", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "_ = plt.boxplot(students[\"nc_score\"])" ] }, { "cell_type": "markdown", "id": "aad5b7f7-393d-4023-9a21-561796221f32", "metadata": {}, "source": [ "Wir erhalten sofort einen Eindruck von der Streuung und Schiefe der Daten. Durch Hinzufügen des Arguments `vert = False` zum Boxplot drehen wir den Boxplot um $90^∘$.\n" ] }, { "cell_type": "code", "execution_count": 18, "id": "6abdda90-1b42-473a-8346-3ead9a9df536", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 1.0, 'Numerus Clausus')" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "ax.boxplot(students[\"nc_score\"], vert=False)\n", "ax.set_xlabel(\"Scores\")\n", "ax.set_title(\"Numerus Clausus\")" ] }, { "cell_type": "markdown", "id": "25e0720e-a37b-48cf-b6a0-eec814c182b9", "metadata": {}, "source": [ "Boxplots sind eine sehr leistungsfähige Technik für die explorative Datenanalyse, da es sehr einfach ist, die Variable von Interesse, in unserem Fall die `nc_score`-Variable, auf andere Variablen zu beziehen und in ihrer Relation darstellen. In Python können wir das erreichen indem wir das Argument `by` in der `boxplot` Methode anwenden. \n", "\n", "Zeichnen wir einen Boxplot der Variable `nc_score` in Abhängigkeit von der Variable `semester`. Die `semester`-Variable entspricht dem Semester, in dem der jeweilige Student studiert. Zu Ihrer Information: Die Mindeststudienzeit für die untersuchten Studiengänge ist auf $4$ Semester festgelegt." ] }, { "cell_type": "code", "execution_count": 19, "id": "e3b125ca-cae0-4a83-af12-39b00cdb1dd0", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "_ = students.boxplot(column=\"nc_score\", by=\"semester\", vert=False, notch=True)" ] }, { "cell_type": "markdown", "id": "add94d51-01af-4b09-942a-d74485a54419", "metadata": {}, "source": [ "Interessant, nicht wahr? Die Grafik zeigt, dass Studierende höherer Semester ($>5$-tes Semester) beim *Numerus clausus* tendenziell schlechter abschneiden. Mit anderen Worten: Studierende, die ihr Studium innerhalb der Mindeststudienzeit abschließen, haben tendenziell eine höhere *Numerus-clausus*-Punktzahl.\n", "\n", "Doch damit sind wir noch nicht fertig. Wir wollen wissen, ob das Geschlecht einen Einfluss auf diese Beobachtung hat. Wir können ganz einfach eine Interaktionsvariable einfügen, indem wir die Variable nach den gruppiert werden soll in eckige Klammern setzen : `[var1, var2]`. Außerdem verwenden wir das Argument `notch` in der `boxplot` Methode. Wenn sich die notches zweier Diagramme nicht überschneiden, ist dies ein \"starker Beweis\" dafür, dass sich die beiden Mediane unterscheiden [Chambers, et al. (1983): Graphical Methods for Data Analysis. Wadsworth & Brooks/Cole, S. 62)](https://www.worldcat.org/title/graphical-methods-for-data-analysis/oclc/1035370684). \n", "\n", "Bitte beachten Sie, dass wir eine zusätzliche Zeile Code schreiben müssen, um ein schöneres $y$-Label zu erhalten." ] }, { "cell_type": "code", "execution_count": 20, "id": "991be515-0dc6-47fe-b20f-500649f9632b", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "_ = students.boxplot(\n", " column=\"nc_score\", by=[\"semester\", \"gender\"], vert=False, notch=True\n", ")" ] }, { "cell_type": "markdown", "id": "69d0c1c4-3679-4585-97c2-9b517efd5596", "metadata": {}, "source": [ "Dieses Diagramm ist nicht so einfach zu interpretieren. Es scheint jedoch, dass die oben gemachte Beobachtung bestätigt wird: Studierende aus höheren Semestern ($>5$-tes) schneiden beim *Numerus clausus* tendenziell schlechter ab. Der Einfluss des Geschlechts auf die *Numerus-Clausus*-Werte ist jedoch nicht so eindeutig. Wir werden Methoden der **Inferenzstatistik** anwenden müssen, um zu beurteilen, ob diese Unterschiede *statistisch signifikant* sind oder ob diese Schwankungen um den Median auch rein zufällig sein könnten.\n", "\n", "Zum Abschluss dieses Abschnitts und um auch einen Boxplot mit Ausreißern zu sehen, stellen wir die Variable `height` gegen die Variable `gender` dar." ] }, { "cell_type": "code", "execution_count": 21, "id": "173b785a-b684-4922-b9bf-feeb54f58d9b", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "_ = students.boxplot(column=\"height\", by=\"gender\")" ] }, { "cell_type": "markdown", "id": "1081aba8-135e-4616-aad3-00d248196e1c", "metadata": {}, "source": [ "Offensichtlich, und sicherlich nicht unerwartet, gibt es einen Unterschied in der Größe der Studenten zwischen den verschiedenen Gruppen (männlich oder weiblich). Weibliche Studenten sind tendenziell kleiner als männliche, aber wenn wir uns die Extreme ansehen, gibt es in beiden Gruppen große und kleine Personen. Wie bereits erwähnt, müssen wir jedoch zunächst die Daten auf *statistische Signifikanz* prüfen, um sicher zu sein, dass der beobachtete Größenunterschied nicht nur zufällig ist." ] } ], "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 }