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{
"cells": [
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{
"cell_type": "markdown",
"id": "c88902ee",
"metadata": {},
"source": [
"# Úkol: BI-PST\n"
]
},
{
"cell_type": "markdown",
"id": "91241ee8",
"metadata": {},
"source": [
"Spolupracovali:\n",
" * Ondřej Hladůvka (reprezentant)\n",
" * Tomáš Kaňka"
]
},
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{
"cell_type": "code",
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"execution_count": 31,
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"id": "334be38a",
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"metadata": {},
"outputs": [],
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"source": [
"#import csv\n",
"#import math\n",
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"import numpy as np\n",
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"import matplotlib.pyplot as plt\n",
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"import pandas as pd\n",
"#np.set_printoptions(precision=3)\n",
"#from sympy import *\n",
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"from scipy import stats \n",
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"from scipy.stats import norm, uniform, expon\n",
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"#from scipy.optimize import minimize"
]
},
{
"cell_type": "code",
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"execution_count": 2,
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"id": "7c90184c-5f76-4277-b0ad-aeec2ac37d30",
"metadata": {},
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"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"M = 10\n",
"dataset ex0221\n"
]
}
],
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"source": [
"K = 28\n",
"L = 8\n",
"M = (((K + L) * 47) % 11) + 1\n",
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"print(\"M =\",M)\n",
"print(\"dataset ex0221\")"
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]
},
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{
"cell_type": "markdown",
"id": "129f8693",
"metadata": {},
"source": [
"## Úloha č. 1"
]
},
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{
"cell_type": "markdown",
"id": "503f77b6-1c9d-4406-8b30-ec3b792267e7",
"metadata": {},
"source": [
"(1b) Načtěte datový soubor a rozdělte sledovanou proměnnou na příslušné dvě pozorované skupiny.\n",
"Stručně popište data a zkoumaný problém. Pro každou skupinu zvlášť odhadněte střední hodnotu, rozptyl a medián příslušného rozdělení."
]
},
{
"cell_type": "code",
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"execution_count": 4,
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"id": "b80d5cec-db0c-42e7-a3b9-296803242269",
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"metadata": {
"scrolled": true
},
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"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Prvních 5 řádků:\n",
" Weight Status\n",
"0 24.500000 survived\n",
"1 26.900000 survived\n",
"2 26.900000 survived\n",
"3 24.299999 survived\n",
"4 24.100000 survived\n",
"Info\n",
"Počet řádků: 59\n",
"Datové typy:\n",
"<class 'pandas.core.frame.DataFrame'>\n",
"RangeIndex: 59 entries, 0 to 58\n",
"Data columns (total 2 columns):\n",
" # Column Non-Null Count Dtype \n",
"--- ------ -------------- ----- \n",
" 0 Weight 59 non-null float64\n",
" 1 Status 59 non-null object \n",
"dtypes: float64(1), object(1)\n",
"memory usage: 1.0+ KB\n"
]
},
{
"data": {
"text/plain": [
"None"
]
},
"metadata": {},
"output_type": "display_data"
}
],
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"source": [
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"# načtení dat\n",
"df = pd.read_csv(\"/data.csv\")\n",
"df = df.drop(df.columns[0], axis=1)\n",
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"survived = df[df['Status'] == 'survived']['Weight'].values\n",
"perished = df[df['Status'] == 'perished']['Weight'].values\n",
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"# informace\n",
"print(\"Prvních 5 řádků:\")\n",
"print(df.head())\n",
"print(\"Info\")\n",
"print(\"Počet řádků:\", df.shape[0])\n",
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"print(\"Datové typy:\")\n",
"display(df.info())\n"
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]
},
{
"cell_type": "markdown",
"id": "41e43831",
"metadata": {},
"source": [
"Tento datový soubor zkoumá, zda hmotnost dospělých samců vrabců hraje roli v jejich přežití během extrémních klimatických podmínek. Cílem je zjistit, zda vrabci, kteří přežili, měli významně jinou průměrnou hmotnost ve srovnání se vrabci, kteří zahynuli. \n",
"\n",
"Tabulak má dva sloupce weight a status, kde\n",
"**weight** udává hmotnost dospělých samců vrabců v gramech a\n",
"**status** udává, zda vrabec přežil nebo zahynul během zimní bouře. Může mít hodnoty \"survived\" (přežil) nebo \"perished\" (zahynul).\n"
]
},
{
"cell_type": "code",
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"execution_count": 5,
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"id": "717d3775",
"metadata": {},
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"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Index(['Weight', 'Status'], dtype='object')\n",
" Status mean var median\n",
"0 perished 26.275000 2.168043 26.000000\n",
"1 survived 25.462857 1.584756 25.700001\n"
]
}
],
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"source": [
"# Zobrazení názvů sloupců\n",
"print(df.columns)\n",
"\n",
"groups = df.groupby('Status')\n",
"summary_stats = groups['Weight'].agg(['mean', 'var', 'median']).reset_index()\n",
"\n",
"# Zobrazení výsledků\n",
"print(summary_stats)"
]
},
{
"cell_type": "markdown",
"id": "b370bf22",
"metadata": {},
"source": [
"## Úloha č. 2"
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]
},
{
"cell_type": "markdown",
"id": "29eef015-c103-4e7f-89e8-2b59526f4b1e",
"metadata": {},
"source": [
"(1b) Pro každou skupinu zvlášť odhadněte hustotu a distribuční funkci pomocí histogramu a empirické distribuční funkce."
]
},
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{
"cell_type": "code",
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"execution_count": 6,
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"id": "9c8f12d3",
"metadata": {},
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"outputs": [
{
"data": {
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"text/plain": [
"<Figure size 1000x600 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"--- Výsledky pro skupinu: perished ---\n",
" Weight CDF\n",
"0 24.600000 0.041667\n",
"1 24.600000 0.083333\n",
"2 24.900000 0.125000\n",
"3 25.000000 0.166667\n",
"4 25.000000 0.208333\n",
"5 25.100000 0.250000\n",
"6 25.500000 0.291667\n",
"7 25.600000 0.333333\n",
"8 25.600000 0.375000\n",
"9 25.799999 0.416667\n",
"10 25.900000 0.458333\n",
"11 26.000000 0.500000\n",
"12 26.000000 0.541667\n",
"13 26.000000 0.583333\n",
"14 26.000000 0.625000\n",
"15 26.100000 0.666667\n",
"16 26.500000 0.708333\n",
"17 26.500000 0.750000\n",
"18 27.100000 0.791667\n",
"19 27.500000 0.833333\n",
"20 27.600000 0.875000\n",
"21 28.299999 0.916667\n",
"22 28.299999 0.958333\n",
"23 31.100000 1.000000\n"
]
},
{
"data": {
"image/png": "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
"text/plain": [
"<Figure size 1000x600 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"--- Výsledky pro skupinu: survived ---\n",
" Weight CDF\n",
"0 23.200001 0.028571\n",
"1 23.600000 0.057143\n",
"2 23.700001 0.085714\n",
"3 23.799999 0.114286\n",
"4 23.900000 0.142857\n",
"5 24.100000 0.171429\n",
"6 24.200001 0.200000\n",
"7 24.299999 0.228571\n",
"8 24.299999 0.257143\n",
"9 24.500000 0.285714\n",
"10 24.600000 0.314286\n",
"11 24.700001 0.342857\n",
"12 24.700001 0.371429\n",
"13 24.799999 0.400000\n",
"14 24.900000 0.428571\n",
"15 25.400000 0.457143\n",
"16 25.600000 0.485714\n",
"17 25.700001 0.514286\n",
"18 25.700001 0.542857\n",
"19 25.700001 0.571429\n",
"20 25.700001 0.600000\n",
"21 25.900000 0.628571\n",
"22 26.200001 0.657143\n",
"23 26.200001 0.685714\n",
"24 26.299999 0.714286\n",
"25 26.299999 0.742857\n",
"26 26.500000 0.771429\n",
"27 26.600000 0.800000\n",
"28 26.700001 0.828571\n",
"29 26.700001 0.857143\n",
"30 26.900000 0.885714\n",
"31 26.900000 0.914286\n",
"32 27.000000 0.942857\n",
"33 27.900000 0.971429\n",
"34 28.000000 1.000000\n"
]
}
],
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"source": [
"def calculate_density_cdf(group):\n",
" sorted_weights = group.sort_values('Weight')\n",
" cdf = pd.Series(range(1, len(sorted_weights) + 1)) / len(sorted_weights)\n",
" results = pd.DataFrame({'Weight': sorted_weights['Weight'].values, 'CDF': cdf.values})\n",
" \n",
" return results\n",
"\n",
"groups = df.groupby('Status')\n",
"density_cdf_results = {}\n",
"\n",
"for name, group in groups:\n",
" density_cdf_results[name] = calculate_density_cdf(group)\n",
"\n",
"for name, results in density_cdf_results.items():\n",
" plt.figure(figsize=(10, 6))\n",
" plt.hist(df[df['Status'] == name]['Weight'], bins=20, density=True, alpha=0.5, label=f'Hustota {name}')\n",
" \n",
" # CDF\n",
" plt.plot(results['Weight'], results['CDF'], label=f'CDF {name}', color='red')\n",
" \n",
" # Nastavení g\n",
" plt.title(f'Hustota a CDF pro skupinu: {name}')\n",
" plt.xlabel('Hmotnost')\n",
" plt.ylabel('Hustota / Kumulativní pravděpodobnost (CDF)')\n",
" plt.legend()\n",
" plt.grid()\n",
" plt.show()\n",
" print(f\"\\n--- Výsledky pro skupinu: {name} ---\")\n",
" print(results)\n",
"\n",
"\n"
]
},
{
"cell_type": "markdown",
"id": "f98f6ad6",
"metadata": {},
"source": [
"Vytvořili jsme funkci calculate_density_cdf, která seřadila data podle hmotnosti a spočítala kumulativní distribuční funkci. Tato funkce vrátila DataFrame se seřazenými hmotnostmi a odpovídajícími hodnotami CDF."
]
},
{
"cell_type": "markdown",
"id": "9f9b7946",
"metadata": {},
"source": [
"## Úloha č. 3"
]
},
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{
"cell_type": "markdown",
"id": "626d8bce-65af-4659-96e9-c1fbe4ccb3cc",
"metadata": {},
"source": [
"(3b) Pro každou skupinu zvlášť najděte nejbližší rozdělení: \n",
"Odhadněte parametry normálního, exponenciálního a rovnoměrného rozdělení.\n",
"Zaneste příslušné hustoty s odhadnutými parametry do grafů histogramu. Diskutujte, které z rozdělení odpovídá pozorovaným datům nejlépe."
]
},
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{
"cell_type": "markdown",
"id": "542a742d-2c96-4d06-bf05-49823752ed6d",
"metadata": {},
"source": [
"Odhady získáme pomocí momentové metody"
]
},
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{
"cell_type": "code",
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"execution_count": 7,
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"id": "b1995dc6-a79c-4859-a720-5dca78d63e44",
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"metadata": {},
"outputs": [],
"source": [
"def show_distribution(data):\n",
" fig = plt.figure(figsize = (10, 14))\n",
" gs = fig.add_gridspec(4,2, figure = fig)\n",
" sp1 = fig.add_subplot(gs[0, 0])\n",
" sp2 = fig.add_subplot(gs[0, 1])\n",
" sp3 = fig.add_subplot(gs[1, 0])\n",
" sp4 = fig.add_subplot(gs[1, 1])\n",
" sp5 = fig.add_subplot(gs[ 2:, 0:])\n",
" \n",
" sp1.set_title('Data Histogram')\n",
" sp1.hist(data, bins=10, density=True, alpha=0.5)\n",
" sp2.hist(data, bins=10, density=True, alpha=0.5)\n",
" sp3.hist(data, bins=10, density=True, alpha=0.5)\n",
" sp4.hist(data, bins=10, density=True, alpha=0.5)\n",
" sp5.hist(data, bins=10, density=True, alpha=0.5)\n",
" \n",
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" mu, std = norm.fit(data)\n",
" xmin, xmax = sp1.get_xlim()\n",
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" x = np.linspace(xmin, xmax, 100)\n",
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" p_norm = norm.pdf(x, mu, std)\n",
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" sp2.plot(x, p_norm, 'red')\n",
" sp2.fill_between(x, p_norm, alpha=0.2, color='red')\n",
" sp2.set_title(f'Normal fit ($\\mu={mu:.2f}, \\sigma={std:.2f}$)')\n",
"\n",
" loc, scale = expon.fit(data)\n",
" p_exp = expon.pdf(x, loc, scale)\n",
" split0 = next((i for i, x in enumerate(p_exp) if x != 0), len(p_exp))\n",
" sp3.plot(x[split0:], p_exp[split0:], 'green')\n",
" sp3.fill_between(x[split0:], p_exp[split0:], alpha=0.2, color='green')\n",
" sp3.set_title(f'Exponential Distribution Fit (scale={scale:.2f})')\n",
"\n",
" loc_uni, scale_uni = uniform.fit(data)\n",
" p_uni = uniform.pdf(x, loc_uni, scale_uni)\n",
" split1 = next((i for i, x in enumerate(p_uni) if x != 0), len(p_uni))\n",
" split2 = -next((i for i, x in enumerate(reversed(p_uni)) if x != 0), len(p_uni))\n",
" sp4.plot(x[split1:split2], p_uni[split1:split2], 'purple')\n",
" sp4.plot(x[:split1], p_uni[:split1], 'purple')\n",
" sp4.plot(x[split2:], p_uni[split2:], 'purple')\n",
" sp4.fill_between(x[split1:split2], p_uni[split1:split2], alpha=0.1, color='purple')\n",
" sp4.set_title(f'Uniform Distribution Fit (range=({loc_uni:.2f}, {loc_uni+scale_uni:.2f}))')\n",
" \n",
" sp5.plot(x, p_norm, 'red', label=f'Normal fit: $\\mu={mu:.2f}, \\sigma={std:.2f}$')\n",
" sp5.plot(x[split0:], p_exp[split0:], 'green', label=f'Exponential fit: scale={scale:.2f}')\n",
" sp5.plot(x[split1:split2], p_uni[split1:split2], 'purple')\n",
" sp5.plot(x[:split1], p_uni[:split1], 'purple')\n",
" sp5.plot(x[split2:], p_uni[split2:], 'purple', label=f'Uniform fit: range=({loc_uni:.2f}, {loc_uni+scale_uni:.2f})')\n",
" #sp5.plot(x, p_uni, 'blue', label=f'Uniform fit: range=({loc_uni:.2f}, {loc_uni+scale_uni:.2f})')\n",
" sp5.set_title('Combined Distributions')\n",
" sp5.legend()"
]
},
{
"cell_type": "code",
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"execution_count": 8,
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"id": "2121c37e-edac-446d-8ed5-1f1fab942637",
"metadata": {},
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"outputs": [
{
"data": {
"image/png": "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
"text/plain": [
"<Figure size 1000x1400 with 5 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": "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
"text/plain": [
"<Figure size 1000x1400 with 5 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
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"source": [
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"show_distribution(survived)\n",
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"show_distribution(perished)"
]
},
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{
"cell_type": "markdown",
"id": "424b6dc3",
"metadata": {},
"source": [
"## Úloha č. 4"
]
},
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{
"cell_type": "markdown",
"id": "6226456c-fdf3-4537-830c-05f8ee7022c5",
"metadata": {},
"source": [
"(1b) Pro každou skupinu zvlášť vygenerujte náhodný výběr o 100 hodnotách z rozdělení, \n",
"které jste zvolili jako nejbližší, s parametry odhadnutými v předchozím bodě.\n",
"Porovnejte histogram simulovaných hodnot s pozorovanými daty."
]
},
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{
"cell_type": "code",
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"execution_count": 9,
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"id": "85df4788-b10c-48cd-aa08-10398d9c124a",
"metadata": {},
"outputs": [],
"source": [
"def showRandomData(mean, std, dataset, title):\n",
" data = np.random.normal(mean, std, 100)\n",
" plt.figure(figsize=(10, 6))\n",
" x = np.linspace(data.min() - 5, data.max() + 5, 100)\n",
" p_norm = norm.pdf(x, mean, std)\n",
" plt.plot(x, p_norm, 'black', linewidth = 2)\n",
" plt.hist(data, bins = 10, color = \"blue\", alpha=0.5 , density = True)\n",
" #plt.set_title(\"Náhodné hodnoty z normálního rozdělení\")\n",
" plt.hist(dataset, bins = 10, color = \"green\", alpha=0.5, density = True)\n",
" plt.show()"
]
},
{
"cell_type": "code",
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"execution_count": 10,
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"id": "c4466cb2-863a-4c61-8338-0f6a25014c6c",
"metadata": {},
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"outputs": [
{
"data": {
"image/png": "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
"text/plain": [
"<Figure size 1000x600 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": "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
"text/plain": [
"<Figure size 1000x600 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
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"source": [
"mean_survived, std_survived = norm.fit(survived)\n",
"showRandomData(mean_survived, std_survived, survived, \"survived\")\n",
"mean_perished, std_perished = norm.fit(perished)\n",
"showRandomData(mean_perished, std_perished, survived, \"perished\")"
]
},
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{
"cell_type": "markdown",
"id": "1e1d73c6",
"metadata": {},
"source": []
},
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{
"cell_type": "markdown",
"id": "d43bff73",
"metadata": {},
"source": [
"## Úloha č. 5"
]
},
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{
"cell_type": "markdown",
"id": "1c5f7d31-ca21-42b4-9a23-1111bbf599b9",
"metadata": {},
"source": [
"(1b) Pro každou skupinu zvlášť spočítejte oboustranný 95% konfidenční interval pro střední hodnotu."
]
},
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{
"cell_type": "markdown",
"id": "dec7a5cc-4c6b-4213-b3b8-8b58813f73cb",
"metadata": {},
"source": [
"Dle Studentova rozdělení:\n",
"$$\n",
"\\begin{align}\n",
"\\left( \\overset{\\_}{X_{n}} - t_{\\frac{\\alpha}{2},n-1}\\frac{s}{\\sqrt{n}}, \\overset{\\_}{X_{n}} + t_{\\frac{\\alpha}{2},n-1}\\frac{s}{\\sqrt{n}} \\right)\n",
"\\end{align}\n",
"$$"
]
},
{
"cell_type": "code",
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"execution_count": 11,
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"id": "69ad2d59-bdc0-4cc7-b51c-7453f2126157",
"metadata": {},
"outputs": [],
"source": [
"def conf_interval(data, name):\n",
" conf = stats.t.interval(confidence = 0.95, df = len(data) - 1, loc = np.mean(data), scale = stats.sem(data))\n",
" print(f\"Oboustranný konfidenční interval 95% střední hodnoty skupiny \\\"{name}\\\":\", conf)\n",
" return conf"
]
},
{
"cell_type": "code",
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"execution_count": 12,
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"id": "16ee6a87-8b6a-472c-9689-9d3877d31084",
"metadata": {},
"outputs": [],
"source": [
"def plot_conf_interval(title, list, interval):\n",
" fig, ax = plt.subplots(figsize = (6, 4))\n",
" ax.hist(list, bins = 10, color = \"blue\", alpha=0.5)\n",
" ax.set_title(f\"Oboustranný 95% interval skupiny \\\"{title}\\\"\")\n",
" ax.axvline(x = interval[0], color = \"red\")\n",
" ax.axvline(x = interval[1], color = \"red\")\n",
" plt.show()"
]
},
{
"cell_type": "code",
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"execution_count": 13,
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"id": "b5fd12a4-8517-4c5e-9f18-eaf627c56afa",
"metadata": {},
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"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Oboustranný konfidenční interval 95% střední hodnoty skupiny \"survived\": (np.float64(25.030419953409798), np.float64(25.895294593883747))\n",
"Oboustranný konfidenční interval 95% střední hodnoty skupiny \"perished\": (np.float64(25.653248327602988), np.float64(26.89675170418613))\n"
]
}
],
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"source": [
"conf_survived = conf_interval(survived, \"survived\")\n",
"conf_perished = conf_interval(perished, \"perished\")"
]
},
{
"cell_type": "code",
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"execution_count": 14,
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"id": "f17915e9-aef8-430d-8096-c13f078e25eb",
"metadata": {},
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"outputs": [
{
"data": {
"image/png": "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
"text/plain": [
"<Figure size 600x400 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": "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
"text/plain": [
"<Figure size 600x400 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
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"source": [
"plot_conf_interval(\"survived\", survived, conf_survived)\n",
"plot_conf_interval(\"perished\", perished, conf_perished)"
]
},
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{
"cell_type": "markdown",
"id": "743db93d",
"metadata": {},
"source": []
},
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{
"cell_type": "markdown",
"id": "1c7cf77b",
"metadata": {},
"source": [
"## Úloha č. 6"
]
},
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{
"cell_type": "markdown",
"id": "53a61e4f-fc67-4237-ab38-f5f9fb7767c5",
"metadata": {},
"source": [
"(1b) Pro každou skupinu zvlášť otestujte na hladině významnosti 5 % hypotézu,\n",
"zda je střední hodnota rovná hodnotě K (parametr úlohy), proti oboustranné alternativě.\n",
"Můžete použít buď výsledek z předešlého bodu, nebo výstup z příslušné vestavěné funkce vašeho softwaru."
]
},
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{
"cell_type": "code",
"execution_count": 33,
"id": "379f961c",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"--- Výsledky t-testu pro skupinu: perished ---\n",
"T-statistika: 4.2421\n",
"P-hodnota: 0.0003\n",
"Zamítáme nulovou hypotézu (střední hodnota se statisticky významně liší od K).\n",
"\n",
"--- Výsledky t-testu pro skupinu: survived ---\n",
"T-statistika: 2.1752\n",
"P-hodnota: 0.0367\n",
"Zamítáme nulovou hypotézu (střední hodnota se statisticky významně liší od K).\n"
]
}
],
"source": [
"for name, group in groups:\n",
" t_stat, p_value = stats.ttest_1samp(group['Weight'], 25)\n",
" print(f\"\\n--- Výsledky t-testu pro skupinu: {name} ---\")\n",
" print(f\"T-statistika: {t_stat:.4f}\")\n",
" print(f\"P-hodnota: {p_value:.4f}\")\n",
" \n",
" # Vyhodnocení na hladině významnosti 5 %\n",
" if p_value < 0.05:\n",
" print(\"Zamítáme nulovou hypotézu (střední hodnota se statisticky významně liší od K).\")\n",
" else:\n",
" print(\"Nezamítáme nulovou hypotézu (střední hodnota se statisticky významně neliší od K).\")\n"
]
},
{
"cell_type": "markdown",
"id": "ccd22286",
"metadata": {},
"source": [
"Postupovalo se tak, že se pro každou skupinu provedl t-test k ověření, zda se střední hmotnost vrabců významně liší od hodnoty 25, přičemž se hodnotily p-hodnoty a rozhodovalo se o zamítnutí nulové hypotézy na základě hladiny významnosti 0,05."
]
},
{
"cell_type": "markdown",
"id": "7f993c66",
"metadata": {},
"source": [
"Můžeme tedy říci, zda střední váha vrabců v každé skupině odpovídá hodnotě KK, nebo zda se významně liší."
]
},
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{
"cell_type": "markdown",
"id": "617cf82f",
"metadata": {},
"source": [
"## Úloha č. 7"
]
},
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{
"cell_type": "markdown",
"id": "7007c195-97a3-4cd4-8427-dcc8417eedf8",
"metadata": {},
"source": [
"(2b) Na hladině významnosti 5 % otestujte, jestli mají pozorované skupiny stejnou střední hodnotu.\n",
"Typ testu a alternativy stanovte tak, aby vaše volba nejlépe korespondovala s povahou zkoumaného problému."
]
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},
{
"cell_type": "markdown",
"id": "0736883a",
"metadata": {},
"source": [
"Byl proveden t-test pro nezávislé vzorky, aby se zjistilo, zda existuje rozdíl ve středních hodnotách mezi skupinami přežití a úmrtí, přičemž byla vyhodnocena p-hodnota a porovnána s hladinou významnosti 0.05."
]
},
{
"cell_type": "code",
"execution_count": 34,
"id": "557d6c95",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"T-test: T-statistika = -2.27141, p-hodnota = 0.02692\n",
"Zamítáme nulovou hypotézu. Skupiny mají různé střední hodnoty.\n"
]
}
],
"source": [
"t_test = stats.ttest_ind(survived, perished, equal_var=True) \n",
"print(f\"T-test: T-statistika = {t_test.statistic:.5f}, p-hodnota = {t_test.pvalue:.5f}\")\n",
"\n",
"alpha = 0.05\n",
"if t_test.pvalue < alpha:\n",
" print(\"Zamítáme nulovou hypotézu. Skupiny mají různé střední hodnoty.\")\n",
"else:\n",
" print(\"Nepodařilo se zamítnout nulovou hypotézu. Skupiny mají stejné střední hodnoty.\")\n",
"\n"
]
},
{
"cell_type": "markdown",
"id": "984140bc",
"metadata": {},
"source": [
"Pokud byla p-hodnota t-testu menší než 0.05, zamítli jsme nulovou hypotézu, což znamená, že střední váha vrabců se mezi skupinami liší. To naznačuje, že faktory ovlivňující přežití mohou souviset s hmotností vrabců, což by mohlo mít vliv na jejich schopnost se přizpůsobit obtížným podmínkám.\n",
"\n",
"Z analýzy tedy vyplývá, že mezi skupinami existuje významný rozdíl ve středních hodnotách."
]
2024-10-18 18:42:33 +02:00
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