{ "cells": [ { "cell_type": "markdown", "id": "1bd16b8f-9a3f-4173-8168-ba9e10ea99c7", "metadata": {}, "source": [ "## Inferenz für die Standardabweichung der Grundgesamtheit\n", "----------------------------------------" ] }, { "cell_type": "markdown", "id": "cf5934a4-1737-49e0-880c-14a2a5abde8c", "metadata": {}, "source": [ "Bisher haben wir Methoden der Inferenzstatistik erörtert, die sich auf Aussagen über einen oder mehrere Grundgesamtheitsmittelwerte konzentrieren. In den folgenden Abschnitten betrachten wir Methoden der Inferenzstatistik, die Aussagen über die Varianzen (oder Standardabweichungen) der Grundgesamtheit liefern. Wir erinnern daran, dass die Varianz ($\\sigma^2$) und die Standardabweichung ($\\sigma$) ein Maß für die Streuung und Variabilität einer Variablen sind." ] }, { "cell_type": "code", "execution_count": 1, "id": "335e80ef-5b5d-400a-83b1-add5312d602e", "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": "e7b4ba76-cc2c-4eb6-9d8b-1bae0e586637", "metadata": {}, "source": [ "## Inferenz für die Standardabweichung einer Grundgesamtheit\n", "----------------------------------------" ] }, { "cell_type": "code", "execution_count": 5, "id": "f0bd980e-6bb4-4c25-b605-fc8ef2c2845e", "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import pandas as pd\n", "from random import sample\n", "import statsmodels.api as smi" ] }, { "cell_type": "markdown", "id": "9777822d-a02d-4573-981a-80d85195e144", "metadata": {}, "source": [ "Inferenz für eine Grundgesamtheitsstandardabweichung basiert auf der Chi-Quadrat ($\\chi^2$)-Verteilung. Eine $\\chi^2$-Verteilung ist eine rechtsschiefe Wahrscheinlichkeitsdichtekurve. Die Form der $\\chi^2$-Kurve wird durch ihre Freiheitsgrade ($df$) bestimmt." ] }, { "cell_type": "code", "execution_count": 6, "id": "451b697e-df27-49dd-ac50-2be89f471aba", "metadata": { "tags": [ "hide-cell" ] }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from scipy.stats import chi2\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "df = [1, 2, 3, 5, 7, 10]\n", "\n", "x = np.linspace(0, 14, 1000)\n", "fig, ax = plt.subplots()\n", "for _df in df:\n", " ax.plot(x, chi2.pdf(x, df=_df), label=f\"df={_df}\")\n", "ax.set_title(\n", " \"$\\chi^2$-Warscheinlichkeitsdichtefunktion mit unterschiedlichen Freiheitsgraden (df)\"\n", ")\n", "ax.legend(fontsize=18)\n", "ax.set_ylim(-0.02, 0.5)\n", "ax.axvline(0, color=\"k\")" ] }, { "cell_type": "markdown", "id": "1fbfe085-2ecf-46b6-b9ea-007ac035146e", "metadata": {}, "source": [ "Um einen Hypothesentest für eine Populationsstandardabweichung durchzuführen, wird ein $\\chi^2$-Wert mit einer bestimmten Fläche unter einer $\\chi^2$-Kurve in Beziehung gesetzt. Entweder wir ziehen eine $\\chi^2$-Tabelle, um diesen Wert nachzuschlagen, oder wir machen von der Python-Maschinerie Gebrauch.\n", "\n", "Bei gegebenen $\\alpha$, wobei $\\alpha$ einer Wahrscheinlichkeit zwischen $0$ und $1$ entspricht, bezeichnet $\\chi^2_\\alpha$ den $\\chi^2$ -Wert, der die Fläche $\\alpha$ zu seiner Rechten unter einer $\\chi^2$ -Kurve hat." ] }, { "cell_type": "code", "execution_count": 7, "id": "aceda4e5-7223-4621-b0fa-de6d0ae8271f", "metadata": { "tags": [ "hide-cell" ] }, "outputs": [ { "data": { "text/plain": [ "Text(2.5, 0.07, 'Fläche = $1 - \\\\alpha$')" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from scipy.stats import chi2\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "df = 5\n", "alpha = 0.9\n", "x = np.linspace(0, 16, 1000)\n", "fig, ax = plt.subplots(figsize=(16, 7))\n", "ax.plot(x, chi2.pdf(x, df=df))\n", "ax.set_xlim(-0.02, 14)\n", "ax.axvline(0, color=\"k\")\n", "ax.axhline(0, color=\"k\")\n", "ax.vlines(\n", " chi2.ppf(alpha, df=df),\n", " ymin=0,\n", " ymax=chi2.pdf(chi2.ppf(alpha, df=df), df=df),\n", " color=\"k\",\n", " linestyle=\"dashed\",\n", ")\n", "\n", "ax.fill_between(\n", " x, chi2.pdf(x, df=df), where=x >= chi2.ppf(alpha, df=df), color=\"r\", alpha=0.5\n", ")\n", "\n", "ax.set_title(r\"$\\chi^2$-Dichtefunktion, $df=5$, $\\alpha=0.1$\")\n", "\n", "\n", "ax.annotate(\n", " r\"$\\chi^2$\",\n", " xy=(7, 0.075),\n", " xytext=(10, 0.13),\n", " # textcoords=\"data\",\n", " arrowprops=dict(headwidth=15, headlength=30, width=4, color=\"k\"),\n", " size=18,\n", ")\n", "\n", "ax.annotate(\n", " r\"Fläche = 0.1\",\n", " xy=(10, 0.018),\n", " xytext=(11, 0.07),\n", " # textcoords=\"data\",\n", " arrowprops=dict(headwidth=15, headlength=30, width=4, color=\"k\"),\n", " size=18,\n", ")\n", "\n", "ax.text(s=\"$\\chi^2_{0.1}$\", x=chi2.ppf(alpha, df=df), y=0.04, size=18)\n", "ax.text(s=r\"Fläche = $1 - \\alpha$\", x=2.5, y=0.07, size=18)" ] }, { "cell_type": "markdown", "id": "82cd3379-b4b3-4637-9fd2-a69de1edd1d9", "metadata": {}, "source": [ "### Intervall-Schätzung von $\\sigma$" ] }, { "cell_type": "markdown", "id": "916d39bb-cbc0-415b-83ef-9663ea80a42c", "metadata": {}, "source": [ "Das $100(1-\\alpha)\\%$-Konfidenzintervall für $\\sigma$ beträgt" ] }, { "cell_type": "markdown", "id": "7c5ff91a-66fb-4230-a986-7fb39d9ba80f", "metadata": {}, "source": [ "$$\\sqrt{\\frac{n-1}{\\chi^2_{\\alpha/2}}} \\le \\sigma \\le \\sqrt{\\frac{n-1}{\\chi^2_{1-\\alpha/2}} }$$" ] }, { "cell_type": "markdown", "id": "8a299ea2-1058-479f-8094-e5c8ffc778fc", "metadata": {}, "source": [ "### $\\chi^2$-Test auf Standardabweichung" ] }, { "cell_type": "markdown", "id": "0e04aa8d-81a8-44dd-872b-d187e2fc452b", "metadata": {}, "source": [ "Das Hypothesentestverfahren für eine Standardabweichung wird als **$\\chi^2$-Test auf Standardabweichung** bezeichnet. Hypothesentests für Varianzen folgen demselben schrittweisen Verfahren wie Hypothesentests für den Mittelwert. " ] }, { "cell_type": "markdown", "id": "de6a4d90-5893-48e4-82b5-4ca1a7ed8c4f", "metadata": {}, "source": [ "$$\n", "\\begin{array}{l}\n", "\\hline\n", "\\ \\text{Schritt 1} & \\text{Geben Sie die Nullhypothese } H_0 \\text{ und alternative Hypothese } H_A \\text{ an.}\\\\\n", "\\ \\text{Schritt 2} & \\text{Legen Sie das Signifikanzniveau, } \\alpha\\text{ fest.} \\\\\n", "\\ \\text{Schritt 3} & \\text{Berechnen Sie den Wert der Teststatistik.} \\\\\n", "\\ \\text{Schritt 4} &\\text{Bestimmen Sie den p-Wert.} \\\\\n", "\\ \\text{Schritt 5} & \\text{Wenn }p \\le \\alpha \\text{, } H_0 \\text{ ablehnen } \\text{; ansonsten } H_0 \\text{ nicht ablehnen} \\text{.} \\\\\n", "\\ \\text{Schritt 6} &\\text{Interpretieren Sie das Ergebnis des Hypothesentests.} \\\\\n", "\\hline \n", "\\end{array}\n", "$$" ] }, { "cell_type": "markdown", "id": "fed2dbca-9f64-4f76-9202-c8c49747867f", "metadata": {}, "source": [ "Die Teststatistik für einen Hypothesentest mit der Nullhypothese $H_0: \\,\\sigma = \\sigma_0$ für eine normalverteilte Variable ist gegeben durch" ] }, { "cell_type": "markdown", "id": "9eae70b3-5570-477e-9ef0-4ff44869b2be", "metadata": {}, "source": [ "$$\\chi^2 = \\frac{n-1}{\\sigma^2_0}s^2$$" ] }, { "cell_type": "markdown", "id": "b10138fe-feed-4772-8958-89db0b0974fb", "metadata": {}, "source": [ "wobei $n$ der Stichprobenumfang und $s$ die Standardabweichung der Stichprobendaten ist." ] }, { "cell_type": "markdown", "id": "e8dd3975-cc20-4e2c-9a60-927daab07029", "metadata": {}, "source": [ "Die Variable folgt einer $\\chi^2$-Verteilung mit $n-1$ Freiheitsgraden.\n", "\n", "Beachten Sie, dass der Test auf eine Standardabweichung $\\chi^2$-Test nicht robust gegenüber Abweichungen von der Normalverteilung ist (Weiss 2010)." ] }, { "cell_type": "markdown", "id": "3ac4c514-150a-4190-a71b-f24d8f8c18fd", "metadata": {}, "source": [ "### $\\chi^2$ -Test auf Standardabweichung : Ein Beispiel" ] }, { "cell_type": "markdown", "id": "159d2c2a-85f3-44ea-af3d-a873eea312fe", "metadata": {}, "source": [ "Um praktische Erfahrungen zu sammeln, wenden wir den $\\chi^2$-Test mit einer Standardabweichung in einer Übung an. Dazu laden wir den `students` Datensatz. Sie können die Datei `students.csv` hier herunterladen. Importieren Sie den Datensatz und geben Sie ihm einen passenden Namen." ] }, { "cell_type": "code", "execution_count": 8, "id": "61de612b-0984-448b-ab4b-ec2fef58d2b8", "metadata": {}, "outputs": [], "source": [ "# Lese Datei students.csv als Dataframe ein; Indexspalte wird übersprungen\n", "students = pd.read_csv(\"../../data/students.csv\", index_col=0)" ] }, { "cell_type": "markdown", "id": "5767b967-8614-4f68-8a17-e1eadec0adfd", "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": "e0e56741-c964-4f43-9936-34d4b5ef7453", "metadata": {}, "source": [ "Um den **$\\chi^2$-Test auf Standardabweichung** zu demonstrieren, untersuchen wir die Streuung der Körpergröße in cm der Studentinnen und vergleichen sie mit der Streuung der Körpergröße aller Studenten (unserer Grundgesamtheit). **Wir wollen testen, ob die Standardabweichung der Körpergröße der Studentinnen kleiner ist als die Standardabweichung der Körpergröße aller Studenten.**" ] }, { "cell_type": "markdown", "id": "047bc69e-1b30-4fb8-a75b-b1597366ccf7", "metadata": {}, "source": [ "### Vorbereitung der Daten" ] }, { "cell_type": "markdown", "id": "4ced0c9f-2db6-4977-acc5-c75de6a7f901", "metadata": {}, "source": [ "Wir beginnen mit der Datenaufbereitung.\n", "\n", "- Zunächst definieren wir die Standardabweichung der Grundgesamtheit. In unserem Beispiel entspricht die Grundgesamtheit der Körpergröße aller $8239$ Studenten im Datensatz. Wir berechnen die Standardabweichung für die Variable `height` und weisen ihr den Variablennamen `sigma0` zu.\n", "- Zweitens unterteilen wir den Datensatz anhand der Variable `gender`.\n", "- Drittens nehmen wir eine Stichprobe von $30$ Studentinnen und extrahieren die interessierende Statistik, die Standardabweichung der Größe der Studentinnen in unserer Stichprobe." ] }, { "cell_type": "code", "execution_count": 9, "id": "7e1dd217-d0a6-48e0-bc76-3b866646ecee", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "11.077529134763823" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sigma0 = students[\"height\"].std()\n", "sigma0" ] }, { "cell_type": "markdown", "id": "4f41971c-d4dc-40b4-b660-c3734161efd3", "metadata": {}, "source": [ "Die Standardabweichung der interessierenden Grundgesamtheit ($\\sigma_0$) beträgt $\\approx$ $11,08$ cm." ] }, { "cell_type": "code", "execution_count": 10, "id": "92d71995-7441-4745-816b-f397adf07a4d", "metadata": {}, "outputs": [], "source": [ "female = students.loc[students[\"gender\"] == \"Female\"]\n", "\n", "n = 30\n", "female_sample = female[\"height\"].sample(n=30, random_state=1)\n", "sample_std = female_sample.std()" ] }, { "cell_type": "markdown", "id": "fb75b866-2709-4738-abb5-e437d07d19b1", "metadata": {}, "source": [ "Außerdem überprüfen wir die Normalverteilungsannahme, indem wir ein Q-Q-Diagramm erstellen. In Python können wir die Funktion `qqplot()` verwenden, um Q-Q-Plots zu erstellen." ] }, { "cell_type": "code", "execution_count": 11, "id": "d0d721b4-d0af-4575-b877-fd32557eccbf", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Stichproben Quantillen')" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Erzeuge Q-Q Plot\n", "qqp = smi.qqplot(female_sample, line=\"r\")\n", "ax = qqp.gca()\n", "ax.set_title(\n", " \"Q-Q-Diagramm für die Körpergrösse der \\n in der Stichprobe befindlichen Studentinnen\"\n", ")\n", "ax.set_xlabel(\"Theoretische Quantillen\")\n", "ax.set_ylabel(\"Stichproben Quantillen\")" ] }, { "cell_type": "markdown", "id": "775fd3eb-329f-4a16-bada-8e5186c700fc", "metadata": {}, "source": [ "Wir sehen, dass die Daten ungefähr auf einer Geraden liegen. Auf der Grundlage des grafischen Auswertungsansatzes kommen wir zu dem Schluss, dass die interessierende Variable ungefähr normalverteilt ist." ] }, { "cell_type": "markdown", "id": "ea6d2ae1-97cd-423c-b6e8-f158a6775044", "metadata": {}, "source": [ "### Überprüfung der Hypothesen" ] }, { "cell_type": "markdown", "id": "decc4831-dca4-4616-abfd-f51d14f691b6", "metadata": {}, "source": [ "Zur Durchführung des **$\\chi^2$-Tests auf Standardabweichung** folgen wir dem Verfahren der schrittweisen Durchführung von Hypothesentests." ] }, { "cell_type": "markdown", "id": "b0db16fb-3712-4218-b1f1-13a421192817", "metadata": {}, "source": [ "**Schritt 1 : Geben Sie die Nullhypothese $H_0$ und alternative Hypothese $H_A$ an**" ] }, { "cell_type": "markdown", "id": "935e6e93-8d04-4b39-8a33-03d08432ff83", "metadata": {}, "source": [ "Die Nullhypothese besagt, dass die Standardabweichung der Körpergröße der Studentinnen ($\\sigma$) gleich der Standardabweichung der Grundgesamtheit ($\\sigma_0 \\approx 11,08$ cm) ist." ] }, { "cell_type": "markdown", "id": "3658df4d-4c7e-4afc-ada9-c6be97c11328", "metadata": {}, "source": [ "$$H_0: \\quad \\sigma = \\sigma_0$$" ] }, { "cell_type": "markdown", "id": "328cb671-b216-4aea-8873-9e8b4c501b96", "metadata": {}, "source": [ "**Alternative Hypothese**" ] }, { "cell_type": "markdown", "id": "41c9944d-079f-4e94-a13c-a698c3b6b03a", "metadata": {}, "source": [ "$$H_A: \\quad \\sigma < \\sigma_0$$" ] }, { "cell_type": "markdown", "id": "450f4e53-5c28-4226-ba81-95e245a69613", "metadata": {}, "source": [ "Diese Formulierung führt zu einem linksseitigen Hypothesentest." ] }, { "cell_type": "markdown", "id": "4c18e2ac-ece6-4f22-afa9-65fe23698a0f", "metadata": {}, "source": [ "**Schritt 2: Legen Sie das Signifikanzniveau,$\\alpha$ fest**" ] }, { "cell_type": "markdown", "id": "bc4c1def-ede9-40ec-8698-39b3e5aca3df", "metadata": {}, "source": [ "$$\\alpha = 0,05$$" ] }, { "cell_type": "code", "execution_count": 12, "id": "13d454c2-a0e0-40b4-ae93-40a4153ccdaf", "metadata": {}, "outputs": [], "source": [ "alpha = 0.05" ] }, { "cell_type": "markdown", "id": "1fbf8e56-b281-4166-949c-d5678cbd52e4", "metadata": {}, "source": [ "**Schritt 3 und 4: Berechnen Sie den Wert der Teststatistik und den $p$-Wert**" ] }, { "cell_type": "markdown", "id": "4056dbf4-e25e-44cf-98f5-18a68e5403b3", "metadata": {}, "source": [ "Zur Veranschaulichung berechnen wir die Teststatistik manuell in Python. Erinnern Sie sich an die Gleichung für die Teststatistik von oben:" ] }, { "cell_type": "markdown", "id": "ee0fade8-03a5-4901-8243-d3923acd18a0", "metadata": {}, "source": [ "$$\\chi^2 = \\frac{n-1}{\\sigma^2_0}s^2$$" ] }, { "cell_type": "code", "execution_count": 22, "id": "421fa43e-60c1-4862-bfbe-69cab86be5b2", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "14.272211660048107" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Berechne Teststatistik\n", "n = len(female_sample)\n", "s_2 = np.var(female_sample,ddof=1)\n", "sigma0_2 = np.var(students[\"height\"],ddof=1)\n", "x2 = ((n - 1) / sigma0_2) * s_2\n", "x2" ] }, { "cell_type": "markdown", "id": "b6fcce28-b4d7-4131-9735-566013b42b0b", "metadata": {}, "source": [ "Der numerische Wert der Teststatistik ist $14,27221166$.\n", "\n", "Um den $p$-Wert zu berechnen, wenden wir die Funktion `chi2.ppf()` an. Erinnern Sie sich daran, wie man die Freiheitsgrade berechnet:" ] }, { "cell_type": "markdown", "id": "3c5bccc2-08d8-478d-9c91-3e1e6ead20e2", "metadata": {}, "source": [ "$$df=n-1$$" ] }, { "cell_type": "code", "execution_count": 23, "id": "b8b066a9-aebf-4c5a-a228-7584d7b20046", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.010089951471801363" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Berechne df\n", "df = n - 1\n", "\n", "# Berechne p-Wert\n", "p = chi2.cdf(x2, df=df)\n", "p" ] }, { "cell_type": "markdown", "id": "c1ae44a4-c4a8-465e-bb2c-2ef8afc73010", "metadata": {}, "source": [ "**Schritt 5: Wenn $p \\le \\alpha , H_0$ ablehnen; ansonsten $H_0$ nicht ablehnen**" ] }, { "cell_type": "code", "execution_count": 24, "id": "37d4fe3f-ea6e-41f3-8115-0ded6ff9e743", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "p <= alpha" ] }, { "cell_type": "markdown", "id": "b318f422-5b3c-4297-ba43-4bbdf40ff86c", "metadata": {}, "source": [ "Der $p$-Wert ist kleiner als das angegebene Signifikanzniveau von $0,05$; wir verwerfen $H_0$. Die Testergebnisse sind statistisch signifikant auf dem $5 \\%$-Niveau und liefern starke Beweise gegen die Nullhypothese." ] }, { "cell_type": "markdown", "id": "5bba3ef9-e297-42f0-aefc-69b3e0bc2b14", "metadata": {}, "source": [ "**Schritt 6: Interpretieren Sie das Ergebnis des Hypothesentests**" ] }, { "cell_type": "markdown", "id": "a8cf0dc0-30a2-4ac7-b293-3aec4c3547f3", "metadata": {}, "source": [ "$p=0,01008995$. Bei einem Signifikanzniveau von $5 \\%$ lassen die Daten den Schluss zu, dass die Standardabweichung der Körpergröße von Studentinnen weniger als $11$ cm beträgt." ] }, { "cell_type": "markdown", "id": "4962de4c-0246-4265-930f-e042848d0279", "metadata": {}, "source": [ "### Hypothesentests in Python" ] }, { "cell_type": "markdown", "id": "e7183808-23d8-4020-993c-7651eb2648a4", "metadata": {}, "source": [ "Wir haben gerade einen $\\chi^2$-Test mit einer Standardabweichung in Python manuell durchgeführt. Meines Wissens bietet Python keine eingebaute Funktion zur Berechnung eines Standardabweichung $\\chi^2$-Test. Wir können jedoch eine solche Funktion selbst implementieren. Unsere Funktion `simple_chi2_test()` nimmt als Eingabe einen Stichprobenvektor `x`, die Standardabweichung der Grundgesamtheit `sigma0`, das Signifikanzniveau `alpha` und die angegebene Methode, `right`, `left` und `two-sided`." ] }, { "cell_type": "code", "execution_count": 25, "id": "adbc86eb-a4f2-4d49-a207-ac4cf6588899", "metadata": {}, "outputs": [], "source": [ "def simple_chi2_test(x, sigma0, alpha, method=\"two-sided\"):\n", " df = len(x) - 1\n", " v = np.var(x,ddof=1)\n", " # Berechne Teststatistik\n", " testchi = df / (sigma0**2) * v\n", "\n", " # linksseitiger Test\n", " if method == \"left\":\n", " p = chi2.cdf(x=testchi, df=df)\n", " # rechtsseitiger Test\n", " elif method == \"right\":\n", " p = 1 - chi2.cdf(x=testchi, df=df)\n", "\n", " # beidseitiger Test (default)\n", " else:\n", " p_upper = 1 - chi2.cdf(x=testchi, df=df)\n", " p_lower = chi2.cdf(x=testchi, df=df)\n", " if p_upper * 2 > 1:\n", " p = p_lower * 2\n", " else:\n", " p = p_upper * 2\n", " # evaluiere p < alpha\n", " if p < alpha:\n", " reject = True\n", " else:\n", " reject = False\n", "\n", " # Ausgabe\n", " print(\"Significance level:\", alpha)\n", " print(\"Degrees of freedom:\", df)\n", " print(\"Test statistic:\", round(testchi, 4))\n", " print(\"p-value:\", p)\n", " print(\"Reject H0:\", reject)" ] }, { "cell_type": "markdown", "id": "d3d28277-c5c6-42dc-92f8-8c18c3ce31c5", "metadata": {}, "source": [ "Wenden wir nun unsere selbst erstellte Funktion `simple_x2_test()` auf die obigen Beispieldaten an." ] }, { "cell_type": "code", "execution_count": 26, "id": "fb1125df-ab6d-4183-be81-d390a5bee7df", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Significance level: 0.05\n", "Degrees of freedom: 29\n", "Test statistic: 14.2722\n", "p-value: 0.010089951471801363\n", "Reject H0: True\n" ] } ], "source": [ "simple_chi2_test(x=female_sample, sigma0=sigma0, alpha=0.05, method=\"left\")" ] }, { "cell_type": "markdown", "id": "ca681053-bfc8-47e3-a76b-b6dd22400af9", "metadata": {}, "source": [ "Perfekt! Vergleichen Sie die Ausgabe der Funktion `simple_chi2_test()` mit unserem Ergebnis von oben. Auch hier können wir zu dem Schluss kommen, dass die Daten bei einem Signifikanzniveau von $5 \\%$ starke Anhaltspunkte dafür liefern, dass die Standardabweichung der Körpergröße von Studentinnen weniger als $11$ cm beträgt." ] }, { "cell_type": "code", "execution_count": 1, "id": "9b6039be-79c1-4768-a8ef-3cf2318f23de", "metadata": {}, "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": "2d9d0bbf-d1c6-458d-b642-1becd42e6031", "metadata": { "tags": [] }, "source": [ "## Inferenz für Standardabweichungen zweier Grundgesamtheiten\n", "----------------------------------------" ] }, { "cell_type": "code", "execution_count": 27, "id": "0dee29d0-aea6-47ef-bff2-f435d84f1665", "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import pandas as pd\n", "from random import sample\n", "from scipy.stats import f\n", "import statsmodels.api as smi" ] }, { "cell_type": "markdown", "id": "25d7551f-9717-427e-af1a-dfd1a07864aa", "metadata": {}, "source": [ "In diesem Abschnitt werden Hypothesentests für die Standardabweichungen zweier Grundgesamtheiten behandelt. Oder anders ausgedrückt, wir erörtern Methoden der Inferenz für die Standardabweichungen einer Variablen aus zwei verschiedenen Grundgesamtheiten. Diese Methoden beruhen auf der $F$-Verteilung, benannt zu Ehren von Sir Ronald Aylmer Fisher.\n", "\n", "Die $F$-Verteilung ist eine rechtsschiefe Wahrscheinlichkeitsdichteverteilung mit zwei Formparametern, $v_1$ und $v_2$, den Freiheitsgraden für den Zähler ($v_1$) und den Freiheitsgraden für den Nenner ($v_2$)." ] }, { "cell_type": "markdown", "id": "a8156479-a44d-41b4-bdcd-ff79eddaec2c", "metadata": {}, "source": [ "$$df = (v_1,v_2)$$" ] }, { "cell_type": "markdown", "id": "b56a0197-7315-4ffe-ad61-6be54f9d98b1", "metadata": {}, "source": [ "Wie bei jeder anderen Dichtekurve entspricht die Fläche unter der Kurve der $F$-Verteilung den Wahrscheinlichkeiten. Die Fläche unter der Kurve und damit die Wahrscheinlichkeit für ein gegebenes Intervall und einen gegebenen $df$-Wert wird mittels Software berechnet. Alternativ kann man sie auch in einer Tabelle nachschlagen. In diesen Tabellen werden im Allgemeinen die Freiheitsgrade für den Zähler ($v_1$) am oberen Rand angezeigt, während die Freiheitsgrade für den Nenner ($v_2$) in den äußeren Spalten auf der linken Seite angezeigt werden.\n", "\n", "Um einen Hypothesentest für zwei Grundgesamtheitsstandardabweichungen durchzuführen, wird der Wert berechnet, der einer bestimmten Fläche unter einer $F$-Kurve entspricht, berechnet.\n", "\n", "Für gegebenes $\\alpha$,wobei $\\alpha$ einer Wahrscheinlichkeit zwischen $0$ und $1$ entspricht, bezeichnet $F_\\alpha$ den Wert, der eine Fläche $\\alpha$ zu seiner Rechten unter einer $F$-Kurve hat." ] }, { "cell_type": "code", "execution_count": 28, "id": "2df9f1c3-869f-4469-aaf3-da6d9dd9cc9c", "metadata": { "tags": [ "hide-cell" ] }, "outputs": [ { "data": { "text/plain": [ "[,\n", " ,\n", " ,\n", " ,\n", " ,\n", " ]" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from scipy.stats import chi2\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "v1 = 9\n", "v2 = 14\n", "alpha = 0.95\n", "x = np.linspace(0, 5, 1000)\n", "fig, ax = plt.subplots(figsize=(16, 7))\n", "ax.plot(x, f.pdf(x, v1, v2))\n", "ax.set_xlim(-0.05, 4)\n", "ax.axvline(0, color=\"k\")\n", "ax.axhline(0, color=\"k\")\n", "ax.vlines(\n", " f.ppf(alpha, v1, v2),\n", " ymin=0,\n", " ymax=f.pdf(f.ppf(alpha, v1, v2), v1, v2),\n", " color=\"k\",\n", " linestyle=\"dashed\",\n", ")\n", "\n", "ax.fill_between(\n", " x, f.pdf(x, v1, v2), where=x >= f.ppf(alpha, v1, v2), color=\"r\", alpha=0.5\n", ")\n", "\n", "ax.set_title(r\"$F$-Dichtefunktion, $df(v1=9, v2=14)$, $\\alpha=0.05$\")\n", "\n", "\n", "ax.annotate(\n", " r\"F-Kurve\",\n", " xy=(1.5, 0.35),\n", " xytext=(2, 0.5),\n", " # textcoords=\"data\",\n", " arrowprops=dict(headwidth=15, headlength=30, width=4, color=\"k\"),\n", " size=18,\n", ")\n", "\n", "ax.annotate(\n", " r\"Fläche = 0.05\",\n", " xy=(2.9, 0.015),\n", " xytext=(3, 0.3),\n", " # textcoords=\"data\",\n", " arrowprops=dict(headwidth=15, headlength=30, width=4, color=\"k\"),\n", " size=18,\n", ")\n", "\n", "ax.text(s=\"$F_{0.05}$\", x=f.ppf(alpha, v1, v2), y=0.08, size=18)\n", "ax.text(s=r\"Fläche = $1 - \\alpha$\", x=0.5, y=0.4, size=18)\n", "\n", "ticks = [0, 1, 2, f.ppf(alpha, v1, v2), 3, 4]\n", "ax.set_xticks(ticks)" ] }, { "cell_type": "markdown", "id": "3eb1fa64-7c30-40db-ba11-04b43bf2fe84", "metadata": {}, "source": [ "In der obigen Abbildung ergibt $F_{0,05}$ für $df=(9,14)$ den Wert $\\approx 2,6458$.\n", "\n", "Eine interessante Eigenschaft von $F$-Kurven ist die **reziproke Charakteristik**. Sie besagt, dass für eine $F$-Kurve mit $df=(v_1,v_2)$ der $F$-Wert mit der Fläche $\\alpha$ auf der linken Seite gleich dem Kehrwert des $F$-Wertes mit der Fläche $\\alpha$ auf der rechten Seite für eine $F$-Kurve mit $df=(v_2,v_1)$ ist ({cite:t}`fahrmeirstatistik` s.282). Übertragen auf das obige Beispiel, bei dem $F_{0,05}$ für $df=(9,14) \\approx 2,6458$ beträgt, bedeutet dies, dass $F_{0,95}$ für $df=(14,9) \\ ; \\ \\frac{1}{2,6458}=0,378$ beträgt." ] }, { "cell_type": "code", "execution_count": 29, "id": "1d978b65-823d-403a-9671-dc0430e0c6d7", "metadata": { "tags": [ "hide-cell" ] }, "outputs": [ { "data": { "text/plain": [ "[,\n", " ,\n", " ,\n", " ,\n", " ,\n", " ]" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from scipy.stats import chi2\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "v1 = 14\n", "v2 = 9\n", "alpha = 0.05\n", "x = np.linspace(0, 5, 1000)\n", "fig, ax = plt.subplots(figsize=(16, 7))\n", "ax.plot(x, f.pdf(x, v1, v2))\n", "ax.set_xlim(-0.05, 4)\n", "ax.axvline(0, color=\"k\")\n", "ax.axhline(0, color=\"k\")\n", "ax.vlines(\n", " f.ppf(alpha, v1, v2),\n", " ymin=0,\n", " ymax=f.pdf(f.ppf(alpha, v1, v2), v1, v2),\n", " color=\"k\",\n", " linestyle=\"dashed\",\n", ")\n", "\n", "ax.fill_between(\n", " x, f.pdf(x, v1, v2), where=x <= f.ppf(alpha, v1, v2), color=\"r\", alpha=0.5\n", ")\n", "\n", "ax.set_title(r\"$F$-Dichtefunktion, $df(v1=14, v2=9)$, $\\alpha=0.95$\")\n", "\n", "\n", "ax.annotate(\n", " r\"F-Kurve\",\n", " xy=(1.5, 0.35),\n", " xytext=(2, 0.5),\n", " # textcoords=\"data\",\n", " arrowprops=dict(headwidth=15, headlength=30, width=4, color=\"k\"),\n", " size=18,\n", ")\n", "\n", "ax.annotate(\n", " r\"Fläche = 0.05\",\n", " xy=(0.27, 0.15),\n", " xytext=(0.28, 0.7),\n", " # textcoords=\"data\",\n", " arrowprops=dict(headwidth=15, headlength=30, width=4, color=\"k\"),\n", " size=18,\n", " horizontalalignment=\"center\",\n", ")\n", "\n", "ax.text(s=\"$F_{0.05}$\", x=f.ppf(alpha, v1, v2), y=0.08, size=18)\n", "ax.text(s=r\"Fläche = $1 - \\alpha$\", x=0.5, y=0.4, size=18)\n", "\n", "ticks = [0, 1, 2, f.ppf(alpha, v1, v2), 3, 4]\n", "ax.set_xticks(ticks)" ] }, { "cell_type": "markdown", "id": "12457b42-e401-4cc2-be2b-81a69b4bfc16", "metadata": {}, "source": [ "### Intervall-Schätzung von $\\sigma_1-\\sigma_2$" ] }, { "cell_type": "markdown", "id": "b19eb24e-7a9c-4e1c-9788-107445f9acfb", "metadata": {}, "source": [ "Das $100(1-\\alpha)\\%$-Konfidenzintervall für $\\sigma$ beträgt" ] }, { "cell_type": "markdown", "id": "8906daaa-678a-415f-9525-28afdca16014", "metadata": {}, "source": [ "$$\\frac{1}{\\sqrt{F_{\\alpha /2}}} \\times \\frac{s_1}{s_2} \\le \\sigma \\le \\frac{1}{\\sqrt{F_{1-\\alpha /2}}} \\times \\frac{s_1}{s_2}\\text{,}$$" ] }, { "cell_type": "markdown", "id": "4a6f50a3-ceb1-4a97-aa23-d7a87b2942a0", "metadata": {}, "source": [ "wobei $s_1$ und $s_2$ die Standardabweichungen der Stichprobe sind." ] }, { "cell_type": "markdown", "id": "c30c39ae-ae99-4f01-8481-2236b8e23058", "metadata": { "tags": [] }, "source": [ "### $F$-Test für zwei Standardabweichungen" ] }, { "cell_type": "markdown", "id": "84d9f024-89e7-443e-8979-a1db268e215d", "metadata": {}, "source": [ "Das Hypothesentestverfahren für die Standardabweichung wird als F-Test für zwei Standardabweichungen bezeichnet. Der Hypothesentest für zwei Standardabweichungen der Grundgesamtheit folgt demselben schrittweisen Verfahren wie andere Hypothesentests." ] }, { "cell_type": "markdown", "id": "48346e81-8632-479a-9e0d-df030e55c67d", "metadata": {}, "source": [ "$$\n", "\\begin{array}{l}\n", "\\hline\n", "\\ \\text{Schritt 1} & \\text{Geben Sie die Nullhypothese } H_0 \\text{ und alternative Hypothese } H_A \\text{ an.}\\\\\n", "\\ \\text{Schritt 2} & \\text{Legen Sie das Signifikanzniveau, } \\alpha\\text{ fest.} \\\\\n", "\\ \\text{Schritt 3} & \\text{Berechnen Sie den Wert der Teststatistik.} \\\\\n", "\\ \\text{Schritt 4} &\\text{Bestimmen Sie den p-Wert.} \\\\\n", "\\ \\text{Schritt 5} & \\text{Wenn }p \\le \\alpha \\text{, } H_0 \\text{ ablehnen } \\text{; ansonsten } H_0 \\text{ nicht ablehnen} \\text{.} \\\\\n", "\\ \\text{Schritt 6} &\\text{Interpretieren Sie das Ergebnis des Hypothesentests.} \\\\\n", "\\hline \n", "\\end{array}\n", "$$" ] }, { "cell_type": "markdown", "id": "a4350189-69c9-4ff8-a2b2-12996a5cf537", "metadata": {}, "source": [ "Die Teststatistik für einen Hypothesentest für eine normalverteilte Variable und für unabhängige Stichproben der Größen $n_1$ und $n_2$ ist gegeben durch" ] }, { "cell_type": "markdown", "id": "1002d2b3-0d2e-45e3-b4cb-1d33ece88865", "metadata": {}, "source": [ "$$F = \\frac{s_1^2/\\sigma_1^2}{s_2^2/\\sigma_2^2}\\text{,}$$" ] }, { "cell_type": "markdown", "id": "e26ae144-0f4b-47f8-b114-0ec1f12ef164", "metadata": {}, "source": [ "mit $df=(n_1-1,n_2-1)$.\n", "\n", "Wenn $H_0: \\sigma_1 = \\sigma_2$ wahr ist, dann vereinfacht sich die Gleichung zu" ] }, { "cell_type": "markdown", "id": "912318f6-534e-49b7-9a45-fe94960f28e3", "metadata": {}, "source": [ "$$F = \\frac{s_1^2}{s_2^2}$$" ] }, { "cell_type": "markdown", "id": "44488088-59ac-4dfd-beb1-2fcdc766e475", "metadata": {}, "source": [ "### $F$-Test für zwei Standardabweichungen : Ein Beispiel" ] }, { "cell_type": "markdown", "id": "288ef57c-8517-4c33-bf13-20e0361afeee", "metadata": {}, "source": [ "Um einige praktische Erfahrungen zu sammeln, wenden wir den **$F$-Test für zwei Standardabweichungen** in einer Übung an. Dazu laden wir den `students` Datensatz. Sie können die Datei `students.csv` hier herunterladen. Importieren Sie den Datensatz und geben Sie ihm einen passenden Namen." ] }, { "cell_type": "code", "execution_count": 30, "id": "036bed03-c382-4f19-b3c1-6710e2997a1f", "metadata": {}, "outputs": [], "source": [ "# Lese Datei students.csv als Dataframe ein; Indexspalte wird übersprungen\n", "students = pd.read_csv(\"../../data/students.csv\", index_col=0)" ] }, { "cell_type": "markdown", "id": "d5c2a98e-3292-4007-8e69-a1df1253163c", "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": "8832e32a-78d2-4e2a-8724-5a6fa2e34187", "metadata": {}, "source": [ "Um den **$F$-Test für zwei Standardabweichungen** zu zeigen, untersuchen wir die Streuung der Körpergröße in cm der Studentinnen und vergleichen sie mit der Streuung der Körpergröße aller Studenten (unserer Grundgesamtheit). **Wir wollen testen, ob sich die Standardabweichung der Körpergröße der weiblichen Studenten ($\\sigma_1$) von der Standardabweichung der Körpergröße der männlichen Studenten ($\\sigma_2$) unterscheidet**." ] }, { "cell_type": "markdown", "id": "70a678f1-ee18-4eee-b23c-877d070ecedc", "metadata": {}, "source": [ "### Vorbereitung der Daten" ] }, { "cell_type": "markdown", "id": "6cba4b2c-d439-40c0-a0c1-5be3d78f6cb1", "metadata": {}, "source": [ "\n", "- Wir unterteilen den Datensatz anhand der Variable `gender`.\n", "- Dann nehmen wir $25$ weibliche und $25$ männliche Studenten in die Stichprobe auf.\n", "- Dann berechnen wir die Standardabweichungen der interessierenden Variable (Körpergröße in cm) für beide Stichproben und weisen ihnen die Variablen `std_female` und `std_male` zu." ] }, { "cell_type": "code", "execution_count": 31, "id": "a14938df-ba44-4d57-a958-59f3d794119f", "metadata": {}, "outputs": [], "source": [ "# Unterteile Datensatz nach Variable `gender`\n", "male = students.loc[students[\"gender\"] == \"Male\"]\n", "female = students.loc[students[\"gender\"] == \"Female\"]\n", "\n", "# Entnehme Probe von jeweils 25 Studenten\n", "n = 25\n", "male_sample = male[\"height\"].sample(n=25, random_state=1)\n", "female_sample = female[\"height\"].sample(n=25, random_state=1)" ] }, { "cell_type": "code", "execution_count": 32, "id": "f54b81f8-499e-4e99-8984-a4b94cc1e5b3", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "7.009041779492163" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "std_female = np.std(female_sample, ddof=1)\n", "std_female" ] }, { "cell_type": "code", "execution_count": 33, "id": "83a0dd60-8555-4a2f-b965-53fc0a108c97", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "8.203251387915241" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "std_male = np.std(male_sample, ddof=1)\n", "std_male" ] }, { "cell_type": "markdown", "id": "a27679fd-5a8e-4e64-bdc3-1fc7f55ff556", "metadata": {}, "source": [ "Außerdem überprüfen wir die Normalverteilungsannahme, indem wir ein Q-Q-Diagramm erstellen. In Python können wir die Funktion `qqplot()` verwenden, um Q-Q-Plots zu erstellen." ] }, { "cell_type": "code", "execution_count": 34, "id": "47ef6bcd-8392-4fdb-aed9-719b4e9b2015", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Stichproben Quantillen')" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Erzeuge Q-Q Plot\n", "qqp = smi.qqplot(female_sample, line=\"r\")\n", "ax = qqp.gca()\n", "ax.set_title(\n", " \"Q-Q-Diagramm für die Körpergrösse der \\n in der weiblichen Studentinnen (Stichprobe)\"\n", ")\n", "ax.set_xlabel(\"Theoretische Quantillen\")\n", "ax.set_ylabel(\"Stichproben Quantillen\")" ] }, { "cell_type": "code", "execution_count": 35, "id": "9b8f2769-0989-4db4-9103-71a1c810dd85", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Stichproben Quantillen')" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Erzeuge Q-Q Plot\n", "qqp = smi.qqplot(male_sample, line=\"r\")\n", "ax = qqp.gca()\n", "ax.set_title(\n", " \"Q-Q-Diagramm für die Körpergrösse der \\n in der männlichen Studenten (Stichprobe)\"\n", ")\n", "ax.set_xlabel(\"Theoretische Quantillen\")\n", "ax.set_ylabel(\"Stichproben Quantillen\")" ] }, { "cell_type": "markdown", "id": "ba6d5c46-07ca-4a9d-9e96-b33dd8233ff5", "metadata": {}, "source": [ "Wir sehen, dass die Daten ungefähr auf einer Geraden liegen. Auf der Grundlage des grafischen Auswertungsansatzes kommen wir zu dem Schluss, dass die interessierende Variable ungefähr normalverteilt ist." ] }, { "cell_type": "markdown", "id": "104666fc-9eff-472c-9d66-150c60e1e853", "metadata": {}, "source": [ "### Überprüfung der Hypothesen" ] }, { "cell_type": "markdown", "id": "307af3d3-10eb-4953-a89d-679e01efa9ed", "metadata": {}, "source": [ "Zur Durchführung des **$F$-Tests für zwei Standardabweichungen** folgen wir dem Verfahren der schrittweisen Durchführung von Hypothesentests." ] }, { "cell_type": "markdown", "id": "2a423dc7-fab0-49b0-b85f-e568c40e8298", "metadata": {}, "source": [ "**Schritt 1 : Geben Sie die Nullhypothese $H_0$ und alternative Hypothese $H_A$ an**" ] }, { "cell_type": "markdown", "id": "c94810ca-86d9-4e56-b90c-e332f846d159", "metadata": {}, "source": [ "Die Nullhypothese besagt, dass die Standardabweichung der Körpergröße der weiblichen Studenten ($\\sigma_1$) gleich der Standardabweichung der Körpergröße der männlichen Studenten ($\\sigma_2$) ist." ] }, { "cell_type": "markdown", "id": "4edfff4a-21f9-4fe4-aef6-a1f88ad54284", "metadata": {}, "source": [ "$$H_0: \\quad \\sigma_1 = \\sigma_2$$" ] }, { "cell_type": "markdown", "id": "e3fac2df-b9f4-48d9-899f-99bb5d6c96e0", "metadata": {}, "source": [ "**Alternative Hypothese**" ] }, { "cell_type": "markdown", "id": "6928bdd2-304d-401e-9737-1ee0ab5adb8a", "metadata": {}, "source": [ "$$H_A: \\quad \\sigma_1 \\ne \\sigma_2$$" ] }, { "cell_type": "markdown", "id": "c258df2a-c3d5-48ed-a20e-77ff462c68bf", "metadata": {}, "source": [ "Diese Formulierung führt zu einem zweiseitigen Hypothesentest." ] }, { "cell_type": "markdown", "id": "896119f6-1624-4484-9308-4bc0b8a3cc0a", "metadata": {}, "source": [ "**Schritt 2: Legen Sie das Signifikanzniveau,$\\alpha$ fest**" ] }, { "cell_type": "markdown", "id": "78946df7-f7d5-441d-b80f-9961dd8ab746", "metadata": {}, "source": [ "$$\\alpha = 0,05$$" ] }, { "cell_type": "code", "execution_count": 36, "id": "21f4b2fb-35c1-49f0-88fb-6339a5215104", "metadata": {}, "outputs": [], "source": [ "alpha = 0.05" ] }, { "cell_type": "markdown", "id": "20191cd5-abfd-4474-bfbe-e7887aea61f6", "metadata": {}, "source": [ "**Schritt 3 und 4: Berechnen Sie den Wert der Teststatistik und den $p$-Wert**" ] }, { "cell_type": "markdown", "id": "09896237-db5b-4bf5-8bcb-394c812238a5", "metadata": {}, "source": [ "Zur Veranschaulichung berechnen wir die Teststatistik manuell in Python. Erinnern Sie sich an die Gleichung für die Teststatistik von oben:" ] }, { "cell_type": "markdown", "id": "878f2436-0f14-486a-9545-6ca5feb0474f", "metadata": {}, "source": [ "$$F = \\frac{s_1^2}{s_2^2}$$" ] }, { "cell_type": "code", "execution_count": 37, "id": "ce0c013f-57e6-451d-9a36-8cf7ba820256", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.7300376461264116" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Berechne die Teststatistik\n", "Ftest = std_female**2 / std_male**2\n", "Ftest" ] }, { "cell_type": "markdown", "id": "ac667f43-3c65-48ec-b5cc-0d9adabf7058", "metadata": {}, "source": [ "Der numerische Wert der Teststatistik beträgt $\\approx 0,73$.\n", "\n", "Um den $p$-Wert zu berechnen, wenden wir die Funktion `f.cdf()` an. Erinnern Sie sich daran, wie man die Freiheitsgrade berechnet." ] }, { "cell_type": "markdown", "id": "59add00f-75c6-4e96-9cd9-f9ad0750e075", "metadata": {}, "source": [ "$$df = (n_1 - 1, n_2 - 1)$$" ] }, { "cell_type": "code", "execution_count": 38, "id": "1f6026e6-13b7-424f-8a40-a7a2762a1f8e", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.4465246946119613" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Berechne df\n", "df1 = len(female_sample) - 1\n", "df2 = len(male_sample) - 1\n", "\n", "# Berechne p-Wert\n", "p_upper = 1 - f.cdf(Ftest, dfn=df1, dfd=df2)\n", "p_lower = f.cdf(Ftest, dfn=df1, dfd=df2)\n", "\n", "if p_upper * 2 > 1:\n", " p = p_lower * 2\n", "else:\n", " p = p_upper * 2\n", "p" ] }, { "cell_type": "markdown", "id": "e925335a-33f3-4b89-9f02-d1685495706d", "metadata": {}, "source": [ "**Schritt 5: Wenn $p \\le \\alpha , H_0$ ablehnen; ansonsten $H_0$ nicht ablehnen**" ] }, { "cell_type": "code", "execution_count": 39, "id": "6de50b47-1cc6-420d-afdd-fb4be50e1bb2", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "False" ] }, "execution_count": 39, "metadata": {}, "output_type": "execute_result" } ], "source": [ "p <= alpha" ] }, { "cell_type": "markdown", "id": "30d2942a-893f-4f33-adf1-e8d7563c4093", "metadata": {}, "source": [ "Der $p$-Wert ist größer als das angegebene Signifikanzniveau von $0,05$; wir verwerfen $H_0$ nicht. Die Testergebnisse sind auf dem $5 \\%$-Niveau statistisch signifikant und liefern keinen ausreichenden Beweis gegen die Nullhypothese." ] }, { "cell_type": "markdown", "id": "abe8fd70-960a-4c80-a8c0-8f41a308aab5", "metadata": {}, "source": [ "**Schritt 6: Interpretieren Sie das Ergebnis des Hypothesentests**" ] }, { "cell_type": "markdown", "id": "cb145141-8c18-4a98-9067-e7f756c0b8fd", "metadata": {}, "source": [ "$p=0,44652469$. Bei einem Signifikanzniveau von $5 \\%$ liefern die Daten keine ausreichenden Beweise für die Schlussfolgerung, dass die Standardabweichungen der Körpergröße von weiblichen und männlichen Studenten unterschiedlich sind." ] }, { "cell_type": "markdown", "id": "57592b0f-866c-4462-8b05-c097e4c9b4a3", "metadata": {}, "source": [ "### Hypothesentests in Python" ] }, { "cell_type": "markdown", "id": "ee2ab916-89fd-4866-aa21-df1edd5c3506", "metadata": {}, "source": [ "Wir haben gerade einen $F$-Test für zwei Standardabweichungen in Python manuell durchgeführt. OK, wir haben eine Menge gelernt, aber jetzt nutzen wir die Mittel von Python, um das gleiche Ergebnis wie oben mit nur einer Zeile Code zu erhalten!\n", "\n", "Um einen $F$-Test für zwei Standardabweichungen in Python durchzuführen, verwenden wir unsere Funktion `simple_x2_test()` und verändern sie geringfügig. Wir geben zwei Vektoren als Dateneingabe an: `female_sample` und `male_sample`. Das Argument `alternative` muss nicht angegeben werden, da `alternative = 'two-sided'` die Vorgabe ist." ] }, { "cell_type": "code", "execution_count": 40, "id": "6b8426cc-3578-4312-8575-835f10f6b9df", "metadata": {}, "outputs": [], "source": [ "def simple_f_test(x, y, dfn, dfd, alpha, method=\"two-sided\"):\n", " df1 = len(female_sample) - 1\n", " df2 = len(male_sample) - 1\n", " std_male = np.std(male_sample, ddof=1)\n", " std_female = np.std(female_sample, ddof=1)\n", " # Berechne Teststatistik\n", " Ftest = std_female**2 / std_male**2\n", "\n", " # linksseitiger Test\n", " if method == \"left\":\n", " p = scipy.stats.f.cdf(x=Ftest, dfn=df1, dfd=df2)\n", " # rechtsseitiger Test\n", " elif method == \"right\":\n", " p = 1 - scipy.stats.f.cdf(x=Ftest, dfn=df1, dfd=df2)\n", "\n", " # beidseitiger Test (default)\n", " else:\n", " p_upper = 1 - f.cdf(Ftest, dfn=df1, dfd=df2)\n", " p_lower = f.cdf(Ftest, dfn=df1, dfd=df2)\n", "\n", " if p_upper * 2 > 1:\n", " p = p_lower * 2\n", " else:\n", " p = p_upper * 2\n", " # evaluiere p < alpha\n", " if p < alpha:\n", " reject = True\n", " else:\n", " reject = False\n", "\n", " # Ausgabe\n", " print(\"Significance level:\", alpha)\n", " print(\"Degrees of freedom:\", df1, df2)\n", " print(\"Test statistic:\", round(Ftest, 4))\n", " print(\"p-value:\", p)\n", " print(\"Reject H0:\", reject)" ] }, { "cell_type": "code", "execution_count": 41, "id": "f1fbdcf8-f1eb-42e8-b818-be3f59b39aef", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Significance level: 0.05\n", "Degrees of freedom: 24 24\n", "Test statistic: 0.73\n", "p-value: 0.4465246946119613\n", "Reject H0: False\n" ] } ], "source": [ "simple_f_test(female_sample, male_sample, df1, df2, alpha=alpha)" ] }, { "cell_type": "markdown", "id": "071c0cf0-582c-4323-b25a-dc6895cf7e45", "metadata": {}, "source": [ "Es hat gut funktioniert! Vergleichen Sie die Ausgabe der Funktion `simple_f_test()` mit unserem Ergebnis von oben. Auch hier können wir zu dem Schluss kommen, dass die Daten bei einem Signifikanzniveau von $5 \\%$ keine ausreichenden Beweise dafür liefern, dass die Standardabweichungen der Körpergröße von weiblichen und männlichen Studenten unterschiedlich sind." ] } ], "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 }