{ "cells": [ { "cell_type": "code", "execution_count": 1, "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", "metadata": {}, "source": [ "# Der zentrale Grenzwertsatz" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from scipy.stats import norm, uniform, beta, gamma" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Der **zentrale Grenzwertsatz** ist eines der nützlichsten Konzepte der Statistik. Bei diesem Theorem geht es um die Ziehung von Stichproben einer endlichen Größe $n$ aus einer Grundgesamtheit. Das Theorem besagt, dass, wenn man Stichproben mit einem ausreichend großen Stichprobenumfang $n$ sammelt und den Mittelwert jeder Stichprobe berechnet, die Form des Histogramms dieser Mittelwerte sich einer Gauß-Verteilung annähert. Die Nützlichkeit des zentralen Grenzwertsatzes ergibt sich aus der Tatsache, dass **die Verteilung der Stichprobenmittelwerte unabhängig von der Verteilung der ursprünglichen Verteilung der Zufallsvariablen der Normalverteilung folgt** ({cite:t}`Papula2011` s.436)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Die Grundgesamtheitsverteilung" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Die **Grundgesamtheitsverteilung** ist die Wahrscheinlichkeitsverteilung, die sich aus der Kenntnis aller Elemente einer Grundgesamtheit ergibt ({cite:p}`fahrmeirstatistik` s.302). Wir wissen, dass die interessierende Zufallsvariable je nach der betrachteten Grundgesamtheit eine diskrete Variable sein kann, d. h. eine Variable, die zumindest im Prinzip abzählbar ist (abzählbar unendlich), oder die Zufallsvariable kann eine kontinuierliche Variable sein, d. h. eine Variable, die jeden Wert innerhalb eines bestimmten Intervalls annehmen kann (überabzählbar unendlich). Sowohl die diskrete als auch die kontinuierliche Wahrscheinlichkeitsverteilung kann durch statistische Parameter wie den Mittelwert, die Standardabweichung, den Median, den Modalwert und andere beschrieben werden. Diese Parameter, die die Grundgesamtheit beschreiben, sind jedoch **immer konstant**, da die Grundgesamtheit die Menge aller Elemente ist und sich somit die Grundgesamtheitsstatistik nicht ändert. So gibt es beispielsweise für jeden Populationsdatensatz **nur einen Wert** für den Populationsmittelwert, **einen Wert** für die Standardabweichung usw." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Grundgesamtheitsstatistiken und Stichprobenstatistiken" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Betrachten wir ein einfaches Beispiel für eine kleine diskrete Grundgesamtheit, die aus den ersten zehn ganzen Zahlen $\\{1,2,3,4,5,6,7,8,9,10\\}$ besteht." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Mittelwert (Grundgesamtheit): 5.5\n", "Standartabweichung (Grundgesamtheit): 2.8722813232690143\n" ] } ], "source": [ "population = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\n", "mean = np.mean(population)\n", "std = np.std(population)\n", "\n", "print(f\"Mittelwert (Grundgesamtheit): {mean}\")\n", "print(f\"Standartabweichung (Grundgesamtheit): {std}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Der Populationsmittelwert $μ$, und die Populationsstandardabweichung $σ$ beträgt $5,5$ bzw. etwa $2,872$. Es ist wichtig zu erkennen, dass sich diese Parameter, die Populationsparameter, nicht ändern! Sie sind durch die Grundgesamtheit festgelegt.\n", "\n", "Nehmen wir nun eine Zufallsstichprobe ohne Ersetzung mit dem Umfang $n=3$ aus dieser Grundgesamtheit. " ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([ 3, 10, 7])" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.random.seed(1)\n", "\n", "my_sample = np.random.choice(population, size=3, replace=False)\n", "my_sample" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Nun berechnen wir den Mittelwert und die Standardabweichung der gegebenen Stichprobe. Da wir uns aber auf eine bestimmte Stichprobe beziehen, nennen wir den statistischen Parameter diesmal **Stichprobenstatistik** oder, wenn wir uns auf die Verteilung der Werte (Elemente) beziehen, **Stichprobenverteilung**. Um dies zu verdeutlichen, wird der Stichprobenmittelwert mit $\\bar{x}$ und die Stichprobenstandardabweichung mit $s$ bezeichnet." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Mittelwert (Stichprobe): 6.666666666666667\n", "Standartabweichung (Stichprobe): 3.5118845842842465\n" ] } ], "source": [ "x_bar = np.mean(my_sample)\n", "s = np.std(my_sample, ddof=1)\n", "\n", "print(f\"Mittelwert (Stichprobe): {x_bar}\")\n", "print(f\"Standartabweichung (Stichprobe): {s}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Bitte beachten Sie, dass sich die Stichprobenstatistiken je nach den tatsächlichen Elementen in der Stichprobe von Stichprobe zu Stichprobe ändern." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Der Schätzfehler\n", "---------------------------------------- " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Wir wiederholen die Stichprobe aus dem vorigen Abschnitt fünfmal und geben den Mittelwert $\\bar{x}$ für jede einzelne Stichprobe aus." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Die 1. Stichprobe hat einen Mittelwert von 6.666666666666667\n", "Die 2. Stichprobe hat einen Mittelwert von 6.333333333333333\n", "Die 3. Stichprobe hat einen Mittelwert von 4.0\n", "Die 4. Stichprobe hat einen Mittelwert von 6.666666666666667\n", "Die 5. Stichprobe hat einen Mittelwert von 5.333333333333333\n" ] } ], "source": [ "population = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\n", "for i in range(5):\n", " my_sample = np.random.choice(population, size=3, replace=False)\n", " mean = np.mean(my_sample)\n", " print(f\"Die {i+1}. Stichprobe hat einen Mittelwert von {mean}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Es liegt auf der Hand, dass verschiedene Stichproben (mit derselben Grösse), die aus derselben Grundgesamtheit ausgewählt wurden, unterschiedliche Stichprobenstatistiken ergeben, da sie unterschiedliche Elemente enthalten. Darüber hinaus unterscheidet sich jede aus einer Stichprobe gewonnene Stichprobenstatistik, z. B. der Stichprobenmittelwert $\\bar{x}$, von dem Ergebnis, das aus der entsprechenden Grundgesamtheit, dem Grundgesamtheitsmittelwert $μ$, gewonnen wird. Die Differenz zwischen dem Wert einer aus einer Stichprobe gewonnenen Statistik und dem Wert des entsprechenden, aus der Grundgesamtheit gewonnenen Parameters wird als **Schätzfehler** bezeichnet. Im Fall des Mittelwerts kann der Schätzfehler wie folgt geschrieben werden\n", "\n", "$$ \\text{Schätzfehler} = \\bar{x} - \\mu$$\n", "\n", "Aufgrund des Charakters von Zufallsstichproben und willkürlichen Ziehung einer Reihe von Werten aus der Grundgesamtheit ist der daraus resultierende Schätzfehler zufällig, oder anders gesagt, der Schätzfehler ist eine Zufallsvariable. Es ist jedoch zu beachten, dass es neben der beschriebenen Zufälligkeit noch andere Fehlerquellen gibt. Diese Fehler hängen oft mit dem Prozess der Datenerzeugung zusammen. Solche Fehler werden beispielsweise durch die menschliche Handhabung der Daten, Kalibrierungsfehler der Messgeräte etc. verursacht.\n", "\n", "Um ein Gefühl für die Art des Schätzfehlers zu bekommen, führen wir ein Experiment durch. Bei diesem Experiment besteht die interessierende Grundgesamtheit aus den ersten $100$ ganzen Zahlen $\\{1,2,3,...,100\\}$. Wir wollen den Einfluss des Stichprobenumfangs $n$ auf den Schätzfehler untersuchen. Der Einfachheit halber wählen wir den Stichprobenmittelwert als die interessierende Statistik. Für eine ausreichend große Anzahl von Versuchen (z.B. $5000$ Versuche) berechnen wir den Schätzfehler für Stichproben mit dem Umfang $n=10,25,50,75$." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Stichprobenfehler (n=10): 6.886\n", "Stichprobenfehler (n=25): 4.034\n", "Stichprobenfehler (n=50): 2.339\n", "Stichprobenfehler (n=75): 1.359\n" ] } ], "source": [ "trial_size = 5000 # 5000 Versuche\n", "sample_size = [10, 25, 50, 75] # Stichprobenumfang\n", "population = range(1, 101)\n", "mean_pop = np.mean(population)\n", "for n in sample_size:\n", " error_sample = []\n", " for _ in range(trial_size):\n", " my_sample = np.random.choice(population, size=n, replace=False)\n", " mean = np.mean(my_sample)\n", " error_sample.append(abs(mean - mean_pop))\n", " print(f\"Schätzfehler (n={n}):\", np.round(np.mean(error_sample), 3))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Aus dem obigen Experiment können wir schließen, dass der Schätzfehler umso kleiner ist, je größer der Stichprobenumfang ist. Mit anderen Worten: Je größer der Stichprobenumfang ist, desto mehr nähert sich der Stichprobenmittelwert $\\bar{x}$ dem Grundgesamtheitsmittelwert $μ$ an. Dies ist eine wichtige Erkenntnis, die im Abschnitt über die *Inferenzstatistik* ausführlicher behandelt werden wird." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Die Stichprobenverteilung" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Ausgehend von unserer Intuition der Zufälligkeit im Stichprobenprozess führen wir die **Stichprobenverteilung** ein. Die Stichprobenverteilung ist eine Verteilung einer Stichprobenstatistik *({cite:p}`fahrmeirstatistik` s.337)*. Oft wird der Name der berechneten Statistik als Teil des Titels hinzugefügt. Wenn es sich bei der berechneten Statistik beispielsweise um den Stichprobenmittelwert handelt, würde die Stichprobenverteilung den Titel **Stichprobenverteilung des Stichprobenmittelwerts** tragen.\n", "\n", "Erinnern wir uns an das einfache Beispiel aus dem vorigen Abschnitt, bei dem die Grundgesamtheit durch die ersten $100$ ganzen Zahlen $\\{ 1,2,3,\\dots,100 \\}$ repräsentiert wurde. Wenn wir wiederholt Stichproben aus dieser Grundgesamtheit ziehen und jedes Mal die Stichprobenstatistik (z. B. $\\bar{x}$ oder $s$,...) berechnen, wird **die resultierende Verteilung der Stichprobenstatistik als Stichprobenverteilung dieser Statistik** bezeichnet.\n", "\n", "Aus dieser Grundgesamtheit nehmen wir wiederholt Zufallsstichproben $(x)$ ohne Ersetzung mit der Größe $n=30$. Die Zufallsstichproben könnten Mengen erzeugen, die wie folgt aussehen :\n", "\n", "$$\\{19, 79, 33, 38, 14, 67, 7, 9, 12, 27, 4, 89, 34, 77, 78, 32, 65, 10, 84, 64, 90, 55, 88, 56, 11, 80, 15, 5, 91, 54\\}$$\n", "\n", "oder\n", "\n", "$$\\{43, 52, 56, 8, 65, 60, 46, 15, 64, 19, 82, 91, 88, 1, 5, 9, 4, 92, 67, 36, 72, 31, 50, 96, 87, 6, 93, 84, 78, 16\\}$$\n", "\n", "... etc.\n", "\n", "Für jede Stichprobe berechnen wir eine Stichprobenstatistik. In diesem Beispiel nehmen wir den Mittelwert, $\\bar{x}$, jeder Stichprobe. Beachten Sie jedoch, dass es sich bei der Stichprobenstatistik um eine beliebige deskriptive Statistik handeln kann, z. B. um den Median, die Standardabweichung, einen Anteil usw. Sobald wir die Stichprobenmittelwerte für alle Stichproben erhalten haben, listen wir alle ihre verschiedenen Werte und die Anzahl ihres Auftretens (Häufigkeiten) auf, um relative Häufigkeiten oder **empirische Wahrscheinlichkeiten** zu erhalten." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "tags": [ "hide-input" ] }, "outputs": [], "source": [ "def dot_diagram(dataset, ax=None, min_max=(30, 70)):\n", " \"\"\"Function to compute a dotplot.\n", " Inspried by https://stackoverflow.com/a/66398730\"\"\"\n", "\n", " values, counts = np.unique(dataset, return_counts=True)\n", " data_range = max(values) - min(values)\n", " # fig_width = data_range / 2 if data_range < 30 else 15\n", " fig_width = 16\n", " fig_height = max(counts) / 3 if data_range < 50 else max(counts) / 4\n", " marker_size = 5\n", " if ax is None:\n", " fig, ax = plt.subplots(figsize=(fig_width, fig_height))\n", " for value, count in zip(values, counts):\n", " ax.plot(\n", " [value] * count,\n", " list(range(count)),\n", " marker=\"o\",\n", " color=\"tab:blue\",\n", " markersize=marker_size,\n", " linestyle=\"\",\n", " )\n", " for spine in [\"top\", \"right\", \"left\"]:\n", " ax.spines[spine].set_visible(False)\n", " ax.yaxis.set_visible(False)\n", " # ax.set_ylim(-1, max(counts))\n", " ax.set_ylim(-1, 18)\n", " ax.set_xticks(range(min_max[0], min_max[1] + 1, 5))\n", " ax.set_xlim(min_max[0] - 1, min_max[1] + 1)\n", " ax.tick_params(axis=\"x\", length=0, pad=10)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "tags": [ "hide-input" ] }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "population = list(range(1, 101))\n", "mean_pop = np.mean(population)\n", "\n", "fig, axes = plt.subplots(nrows=3, ncols=2, figsize=(16, 9))\n", "_axes = np.ravel(axes)\n", "trials = [1, 10, 100, 500, 1000, 3000]\n", "SAMPLE_SIZE = 30\n", "np.random.seed(42)\n", "\n", "for e, trial in enumerate(trials):\n", " sample_statistic = []\n", " for n in range(trial):\n", " sample = np.random.choice(population, size=SAMPLE_SIZE)\n", " mean_sample = np.mean(sample)\n", " sample_statistic.append(mean_sample)\n", " dot_diagram(sample_statistic, ax=_axes[e])\n", " _axes[e].text(x=60, y=15, s=f\"{trials[e]} Stichproben\", size=13)\n", " _axes[e].text(x=mean_pop, y=16, s=f\"$\\mu$\", size=14, ha=\"center\")\n", " _axes[e].vlines(x=mean_pop, ymin=-1, ymax=15, color=\"k\", linestyle=\"dashed\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Je häufiger wir eine Stichprobe nehmen, desto besser nähert sich die relative Häufigkeitsverteilung der Stichprobenstatistik der Stichprobenverteilung an. Mit anderen Worten: Wenn die Anzahl der Stichproben gegen unendlich geht, nähert sich die resultierende Häufigkeitsverteilung der Stichprobenverteilung an. **Die Stichprobenverteilung einer Statistik** ist eine Wahrscheinlichkeitsverteilung dieser Statistik, die aus allen möglichen Stichproben mit demselben Umfang aus der Grundgesamtheit abgeleitet wird. Die Stichprobenverteilung sollte jedoch nicht mit einer Stichprobenverteilung verwechselt werden: Letztere beschreibt die Verteilung der Werte (Elemente) in einer bestimmten Stichprobe." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Der Standardfehler" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Ebenso wie die Verteilungen der Grundgesamtheit können auch die Stichprobenverteilungen mit Parametern beschrieben werden. Der Erwartungswert (Mittelwert) einer beliebigen Verteilung kann durch das Symbol $\\mu$ dargestellt werden. Im Falle der Stichprobenverteilung wird der Mittelwert $\\mu$ oft mit einem tiefgestellten Index geschrieben, um anzugeben, welche Stichprobenverteilung beschrieben wird. Der Erwartungswert der Stichprobenverteilung des Mittelwerts wird zum Beispiel durch das Symbol $\\mu_{\\bar{x}}$ dargestellt. Der Wert von $\\mu_{\\bar{x}}$ kann als der theoretische Mittelwert der Verteilung der Stichprobenmittelwerte angesehen werden.\n", "\n", "Wenn wir aus einer Grundgesamtheit eine ausreichend große Anzahl von Stichproben (mit gleichem Umfang) auswählen und deren Mittelwerte berechnen, dann nähert sich der Mittelwert ($\\mu_{\\bar{x}}$) all dieser Stichprobenmittelwerte dem Mittelwert ($\\mu$) der Grundgesamtheit an. Deshalb wird der Stichprobenmittelwert $\\bar{x}$ als Schätzer des Populationsmittelwertes $\\mu$ bezeichnet. Somit ist der Mittelwert der Stichprobenverteilung gleich dem Mittelwert der Grundgesamtheit.\n", "\n", "$$\\mu_{\\bar{x}} = \\mu$$\n", "\n", "Für die Standardabweichung einer Stichprobenverteilung gibt es eine besondere Bezeichnung, den **Standardfehler**. Der Standardfehler der Stichprobenverteilung einer Statistik, bezeichnet als $\\sigma_{\\bar{x}}$, beschreibt das Ausmaß, in dem die berechneten Statistiken erwartungsgemäß voneinander abweichen, wenn sie anhand einer Stichprobe ähnlichen Umfangs berechnet und aus ähnlichen Grundgesamtheitsmodellen ausgewählt werden. Je größer der Standardfehler einer bestimmten Statistik ist, desto größer sind die Unterschiede zwischen den berechneten Statistiken für die verschiedenen Stichproben ({cite:p}`Kuckartz2010` s.133).\n", "\n", "Es ist jedoch zu beachten, dass der Standardfehler $\\sigma_{\\bar{x}}$ nicht gleich der Standardabweichung $\\sigma$ der Verteilung der Grundgesamtheit ist (es sei denn, $n=1$). Der Standardfehler ist gleich der Standardabweichung der Grundgesamtheit geteilt durch die Quadratwurzel des Stichprobenumfangs :\n", "\n", "$$\\sigma_{\\bar{x}} = \\frac{\\sigma}{\\sqrt{n}}$$\n", "\n", "Diese Gleichung gilt nur, wenn die Stichprobe entweder mit Ersatz aus einer endlichen Grundgesamtheit oder mit oder ohne Ersatz aus einer unendlichen Grundgesamtheit gezogen wird. Dies entspricht der Bedingung, dass der Stichprobenumfang $(n)$ im Vergleich zum Grundgesamtheitsumfang $(N)$ klein ist. Der Stichprobenumfang gilt als klein im Vergleich zum Umfang der Grundgesamtheit, wenn der Stichprobenumfang gleich oder weniger als $5\\%$ des Umfangs der Grundgesamtheit ist, d. h., wenn\n", "\n", "$$\\frac{n}{N} \\leq 0,05$$\n", "\n", "Wenn diese Bedingung nicht erfüllt ist, wird die folgende Gleichung zur Berechnung von $\\sigma_{\\bar{x}}$ verwendet :\n", "\n", "$$\\sigma_{\\bar{x}} = \\frac{\\sigma}{\\sqrt{n}} \\sqrt{\\frac{N-n}{N-1}}$$\n", "\n", "In den meisten praktischen Anwendungen ist der Stichprobenumfang jedoch klein im Vergleich zur Grundgesamtheit." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Stichproben aus einer normalverteilten Grundgesamtheit" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Form der Stichprobenverteilung\n", "\n", "Die Form der Stichprobenverteilung bezieht sich auf die beiden folgenden Fälle :\n", "\n", "1. Die Grundgesamtheit, aus der die Stichproben gezogen werden, ist normalverteilt.\n", "\n", "2. Die Grundgesamtheit, aus der die Stichproben gezogen werden, ist nicht normalverteilt.\n", "\n", "### Stichproben aus einer normalverteilten Grundgesamtheit\n", "\n", "Wenn die Grundgesamtheit, aus der die Stichproben gezogen werden, normalverteilt ist und ihr Mittelwert gleich $\\mu$ und ihre Standardabweichung gleich $\\sigma$ ist, dann gilt :\n", "\n", "1. Der Mittelwert der Stichprobenmittel, $\\mu_{\\bar{x}}$, ist gleich dem Mittelwert der Grundgesamtheit, $\\mu$\n", "\n", "2. Die Standardabweichung der Stichprobenmittelwerte,$\\sigma_{\\bar{x}}$\n", "ist gleich $\\frac{\\sigma}{\\sqrt{n}}$, wobei $\\frac{n}{N} ≤ 0,05$ angenommen wird.\n", "\n", "3. Die Form der Stichprobenverteilung der Stichprobenmittelwerte $\\bar{x}$ ist normal, unabhängig vom Wert von $n$.\n", "\n", "Betrachten wir eine normalverteilte Grundgesamtheit. Der Einfachheit halber verwenden wir die Standardnormalverteilung, $N∼(\\mu,\\sigma)$, mit $\\mu=0$ und $\\sigma=1$. Berechnen wir nun $\\mu_{\\bar{x}}$ und $\\sigma_{\\bar{x}}$ für Stichproben mit dem Stichprobenumfang $n=5,15,30,50$.\n", "\n", "Es sei daran erinnert, dass für eine hinreichend große Anzahl wiederholter Stichproben $\\mu_{\\bar{x}}≈\\mu$. Somit $\\mu_{\\bar{x}}$ der verschiedenen betrachteten Stichprobenverteilungen :\n", "\n", "$$\\mu_{\\bar x_{n=5}} = \\mu_{\\bar x_{n=15}} = \\mu_{\\bar x_{n=30}} = \\mu_{\\bar x_{n=50}} = \\mu = 0$$\n", "\n", "Wir erinnern uns an den Standardfehler der Stichprobenverteilung $\\sigma_{\\bar{x}}=\\frac{\\sigma}{\\sqrt{n}}$. Wir können also $\\sigma_{\\bar{x}}$ für $n=5,15,30,50$ Elemente leicht berechnen. Die verschiedenen Stichprobenverteilungen werden im Folgenden visualisiert.\n", "\n", "$$\\sigma_{\\bar x_{n=5}} = \\frac{\\sigma}{\\sqrt{n}} = \\frac{1}{\\sqrt{5}}\\approx 0,447$$\n", "\n", "$$ \\sigma_{\\bar x_{n=15}} = \\frac{\\sigma}{\\sqrt{n}} = \\frac{1}{\\sqrt{15}}\\approx 0,258 $$\n", "\n", "$$ \\sigma_{\\bar x_{n=30}} = \\frac{\\sigma}{\\sqrt{n}} = \\frac{1}{\\sqrt{30}}\\approx 0,183 $$\n", "\n", "$$ \\sigma_{\\bar x_{n=50}} = \\frac{\\sigma}{\\sqrt{n}} = \\frac{1}{\\sqrt{50}} \\approx 0,141 $$" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "tags": [ "hide-input" ] }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "mu = 0\n", "x = np.linspace(mu - 2.5, mu + 2.5, 1000)\n", "n = [1, 5, 15, 30, 50]\n", "fig, ax = plt.subplots(figsize=(16, 6))\n", "for e, _n in enumerate(n):\n", " sigma = 1 / np.sqrt(_n)\n", " if _n == 1:\n", " label = \"Grundgesamtheit ($\\mu=0$ und $\\sigma=1$)\"\n", " else:\n", " label = \"$\\overline{x}$ for\" + f\" n = {_n}\"\n", " ax.plot(x, norm.pdf(x, mu, sigma), label=label)\n", "ax.legend(fontsize=16)\n", "ax.text(x=mu, y=3, s=\"$\\mu_\\overline{x}=\\mu$\", size=14, ha=\"center\")\n", "ax.vlines(x=mu, ymin=0, ymax=3, color=\"k\", linestyle=\"dashed\")\n", "ax.axes.yaxis.set_visible(False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Es gibt zwei wichtige Beobachtungen bezüglich der Stichprobenverteilung von $\\bar{x}$\n", "\n", "1. Die Streuung der Stichprobenverteilung ist kleiner als die Streuung der entsprechenden Grundgesamtheitsverteilung. Mit anderen Worten: $\\sigma_{\\bar{x}}<\\sigma$\n", "\n", "2. Die Standardabweichung der Stichprobenverteilung nimmt mit zunehmendem Stichprobenumfang ab.\n", "\n", "Um die $3$. Behauptung von oben, dass die Form der Stichprobenverteilung von $\\bar{x}$ unabhängig vom Wert von $n$ normal ist, zu überprüfen, führen wir eine numerische Simulation durch. Für eine ausreichend große Anzahl von Versuchen (Versuche = $1000$) ziehen wir Stichproben aus der Standardnormalverteilung $N∼(\\mu=0,\\sigma=1)$, wobei jede einzelne Stichprobe einen Stichprobenumfang von $n=5,15,30,50$ hat. Für jede Stichprobe berechnen wir den Stichprobenmittelwert $\\bar{x}$ und stellen die empirischen Wahrscheinlichkeiten dar. Anschließend vergleichen wir die empirische Verteilung dieser Wahrscheinlichkeiten mit den aus den obigen Gleichungen berechneten Stichprobenverteilungen." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "tags": [ "hide-input" ] }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "mu = 0\n", "x = np.linspace(mu - 2.5, mu + 2.5, 1000)\n", "n = [5, 15, 30, 50]\n", "N = 1000\n", "fig, axes = plt.subplots(nrows=2, ncols=2, figsize=(16, 8))\n", "ax = np.ravel(axes)\n", "np.random.seed(42)\n", "for e, _n in enumerate(n):\n", " sigma = 1 / np.sqrt(_n)\n", " random_sample = norm.rvs(loc=mu, scale=sigma, size=N)\n", " ax[e].hist(random_sample, ec=\"black\", density=True, bins=25, alpha=0.3)\n", "\n", " label = f\"n = {_n}\"\n", " ax[e].plot(x, norm.pdf(x, mu, sigma), label=label, color=f\"C{e}\", linewidth=2.5)\n", " ax[e].legend(fontsize=16)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Die Abbildung verifiziert die $3$. Behauptung von oben: Die Form der Stichprobenverteilung von $\\bar{x}$ ist für jeden Wert von $n$ normal.\n", "\n", "Darüber hinaus zeigt die Abbildung, dass die Verteilung der empirischen Wahrscheinlichkeiten (Balken) gut mit der Stichprobenverteilung (farbige Linie) übereinstimmt und dass die Standardabweichung der Stichprobenverteilung von $\\bar{x}$ mit zunehmendem Stichprobenumfang abnimmt. Es sei daran erinnert, dass die $y$-Achse die *Dichte* darstellt, d. h. die **Wahrscheinlichkeit pro Einheitswert** der Zufallsvariablen. Aus diesem Grund kann die Wahrscheinlichkeitsdichte einen Wert größer als $1$ annehmen, aber nur über einen Bereich mit einer Größe kleiner als $1$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Stichproben aus einer nicht normalverteilten Grundgesamtheit" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Im vorangegangenen Abschnitt haben wir die Form von Stichprobenverteilungen erörtert, wenn eine Stichprobe aus einer normalverteilten Grundgesamtheit gezogen wird. In realen Anwendungen kennen wir jedoch oft nicht die tatsächliche Form der Grundgesamtheit.\n", "\n", "Um zu verstehen, wie die Form der Verteilung der interessierenden Grundgesamtheit die Form der Stichprobenverteilung beeinflusst, führen wir ein Experiment durch. Wir betrachten drei verschiedene kontinuierliche Wahrscheinlichkeitsdichtefunktionen: die **Gleichverteilung**, die **Beta-Verteilung** und die **Gamma-Verteilung**. Wir gehen hier nicht ins Detail, aber die folgende Abbildung zeigt, dass diese drei PDF´s (Probability Density Functions) nicht normalverteilt sind." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "tags": [ "hide-input" ] }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "titles = [\n", " \"Uniform distribution (a=0.2, b=0.8)\",\n", " \"Beta distribution (alpha=2, beta=5)\",\n", " \"Gamma distribution (alpha=1, beta=2)\",\n", "]\n", "fig, ax = plt.subplots(1, 3, figsize=(18, 6))\n", "x = np.linspace(0, 1, 1000)\n", "ax[0].plot(x, uniform.pdf(x, 0.2, 0.6))\n", "ax[1].plot(x, beta.pdf(x, 2, 5))\n", "x = np.linspace(0, 10, 1000)\n", "ax[2].plot(x, gamma.pdf(x, a=1, scale=2))\n", "for e, _ax in enumerate(ax):\n", " _ax.axes.yaxis.set_visible(False)\n", " _ax.set_title(titles[e], size=18)" ] }, { "cell_type": "markdown", "metadata": { "tags": [] }, "source": [ "Nun führen wir das gleiche Experiment wie im vorherigen Abschnitt durch. Für eine ausreichend große Anzahl von Versuchen (Versuche = 1000) ziehen wir aus jeder einzelnen Verteilung eine Stichprobe. Diesmal hat jedoch jede einzelne Stichprobe einen Stichprobenumfang $n=2,5,15,30$. Für jede Stichprobe berechnen wir den Stichprobenmittelwert $\\bar{x}$ und stellen die empirischen Wahrscheinlichkeiten nach $1000$ Versuchen dar." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "tags": [ "hide-input" ] }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "TRIALS = 1000\n", "sample_sizes = [2, 5, 15, 30]\n", "np.random.seed(42)\n", "fig, ax = plt.subplots(ncols=3, nrows=4, figsize=(16, 14))\n", "titles = [\n", " \"Uniform distribution (a=0.2, b=0.8)\",\n", " \"Beta distribution (alpha=2, beta=5)\",\n", " \"Gamma distribution (alpha=1, beta=2)\",\n", "]\n", "xlim = [(0.48, 0.52), (0.27, 0.30), (2.9, 3.1)]\n", "for row, sample_size in enumerate(sample_sizes):\n", " for col, distribution in enumerate([uniform(0.2, 0.6), beta(2, 5), gamma(1, 2)]):\n", " sample = []\n", " for _ in range(TRIALS):\n", " sample.append(np.mean(distribution.rvs(size=sample_sizes)))\n", " ax[row, col].hist(\n", " sample, ec=\"black\", density=False, bins=20, alpha=0.3, color=f\"C{col}\"\n", " )\n", " ax[row, col].set_title(f\"{titles[col]}\\nfor sample size {sample_size}\", size=16)\n", " ax[row, col].set_xlim(xlim[col])\n", " ax[row, col].axes.yaxis.set_visible(False)\n", "fig.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Die Abbildung zeigt, dass im Falle einer nicht normalverteilten Grundgesamtheit die Stichprobenverteilungen nicht normalverteilt sind, wenn $n<30$. Allerdings nähern sich die Stichprobenverteilungen einer Normalverteilung an, wenn $n>30$. Man sieht auch, dass die Streuung der Stichprobenverteilung mit zunehmendem Stichprobenumfang abnimmt." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Nach dem **zentralen Grenzwertsatz** ist die Stichprobenverteilung bei einem großen Stichprobenumfang $(n > 30)$ annähernd normal, unabhängig von der Form der Grundgesamtheitsverteilung.\n", "\n", "Der Mittelwert und die Standardabweichung der Stichprobenverteilung von $\\bar{x}$ sind jeweils,\n", "\n", "$$\\mu_{\\bar{x}} = \\mu \\text{ und } \\sigma_{\\bar{x}} = \\frac{\\sigma}{\\sqrt{n}}$$\n", "\n", "Der Stichprobenumfang wird gewöhnlich als groß angesehen, wenn $n \\geq 30$ ist.\n", "\n", "Da die Stichprobenverteilung eine Normalverteilung approximiert, liefert die Fläche unter der Kurve der Stichprobenverteilung probabilistische Informationen über die Stichprobenstatistik.\n", "\n", "Erinnern Sie sich an die **empirische Regel** ({cite:p}`fahrmeirstatistik` s.86), auch bekannt als die **68-95-99,7-Regel**. Auf die Stichprobenverteilung angewandt bedeutet die $68-95-99,7$-Regel folglich, dass\n", "\n", "- etwa $68,26$% der Stichprobenmittelwerte innerhalb einer Standardabweichung des Populationsmittelwerts liegen werden,\n", "\n", "- $95,44$% der Stichprobenmittelwerte innerhalb von zwei Standardabweichungen des Populationsmittelwertes liegen und\n", "\n", "- etwa $99,74$% der Stichprobenmittelwerte innerhalb von drei Standardabweichungen des Mittelwerts der Grundgesamtheit liegen." ] } ], "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" }, "tags": [ "remove-cell" ] }, "nbformat": 4, "nbformat_minor": 4 }