Intervaly_spolehlivosti.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Materiály vznikají průběžně a jsou bez záruky - prosím o report chyb :-)**\n",
    "\n",
    "**Update**\n",
    "\n",
    "- kritické hodnoty můžeme najít přímo metodou `isf(alpha, params)`, např. `t.isf(0.05, df=10)`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "np.set_printoptions(precision=3)\n",
    "from scipy.stats import norm, t, chi2\n",
    "import matplotlib.pylab as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# [Teorie odhadu](https://en.wikipedia.org/wiki/Estimation_theory) - [intervalové odhady](https://en.wikipedia.org/wiki/Confidence_interval)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Příklad\n",
    "\n",
    "Nástupní platy 16 brazilských IT odborníků v nestátní sféře měly v průměru $\\bar{X}_n = 10.3$ tisíce BRL (brazilský real). \n",
    "\n",
    "Předpokládejme, že platy jsou normálně rozdělené se směrodatnou odchylkou 1.2 tisíce, tj.\n",
    "\n",
    "$$\n",
    "X \\sim \\mathcal{N}(\\mu, 1.2^2).\n",
    "$$\n",
    "\n",
    "Střední hodnotu $\\mu$ neznáme a máme ji nějak odhadnout.\n",
    "\n",
    "Nápověda: Můžeme vyjít z podmínky, že bude existovat kvantil $q$ takový, že\n",
    "\n",
    "$$\n",
    "P(\\bar{X}_n > q) = \\alpha,\n",
    "$$\n",
    "\n",
    "kde $\\alpha = 0.1$.\n",
    "\n",
    "---\n",
    "\n",
    "**To už dávno umíme :-)**  - prostě uděláme standardizaci do $\\mathcal{N}(0,1)$ a najdeme odpovídající kvantil $1-\\alpha$. A protože **kvantil $u_{1-\\alpha}$ je totéž, co kritická hodnota $z_\\alpha$**, pro niž máme rovněž tabulky, tak budeme pracovat s ní.\n",
    "\n",
    "![img](img/krit_hod.jpg)\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "\\alpha = P(\\bar{X}_n > q) &=\n",
    "P\\left( \\frac{\\bar{X}_n - \\mu}{\\sigma/\\sqrt{n}} > z_\\alpha \\right) \\\\\n",
    "&= P\\left(\\bar{X}_n - \\mu > \\frac{z_\\alpha \\cdot \\sigma}{\\sqrt{n}} \\right) \\\\\n",
    "&= P \\left( \\bar{X}_n - \\frac{z_\\alpha \\cdot \\sigma}{\\sqrt{n}} > \\mu \\right) = \\alpha = 0.1\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "Z prvního a posledního řádku máme tedy tuto interpretaci:\n",
    "\n",
    "**Pravděpodobnost, že průměr $\\bar{X}_n$ překročí $\\alpha$-kritickou hodnotu - tj. $(1-\\alpha)$-kvantil $q$ je stejná, jako pravděpodobnost, že střední hodnota $\\mu$ bude menší než $\\bar{X}_n - \\frac{z_\\alpha \\cdot \\sigma}{\\sqrt{n}}$. A v obou případech bude $\\alpha$.**\n",
    "\n",
    "To znamená, že interval\n",
    "\n",
    "$$\n",
    "\\left(\\bar{X}_n - \\frac{z_\\alpha \\cdot \\sigma}{\\sqrt{n}}, \\infty\\right)\n",
    "$$\n",
    "\n",
    "pokrývá skutečnou (leč neznámou) hodnotu $\\mu$ s pravděpodobností $1-\\alpha$. Takový interval nazýváme **pravostranným $(1-\\alpha)$% intervalem spolehlivosti**.\n",
    "\n",
    "Zcela analogickým postupem bychom došli k **levostrannému intervalu spolehlivosti** ve tvaru\n",
    "\n",
    "$$\n",
    "\\left(-\\infty, \\bar{X}_n + \\frac{z_\\alpha \\cdot \\sigma}{\\sqrt{n}}\\right).\n",
    "$$\n",
    "\n",
    "**Oboustranný interval spolehlivosti** rozdělí hodnotu $\\alpha$ na levou a pravou stranu stejnoměrně. A protože standardní \"gaussovka\" se symetrická kolem nuly, jsou i obě kritické hodnoty rozdílné jen znaménkem, $\\pm z_{\\alpha/2}$.\n",
    "\n",
    "![img](img/z_alpha.jpg)\n",
    "\n",
    "Oboustranný interval spolehlivosti tedy bude (dokaže si to!)\n",
    "\n",
    "$$\n",
    "\\left(\\bar{X}_n - \\frac{z_{\\alpha/2} \\cdot \\sigma}{\\sqrt{n}}, \\bar{X}_n + \\frac{z_{\\alpha/2} \\cdot \\sigma}{\\sqrt{n}}\\right).\n",
    "$$\n",
    "\n",
    "Spočtěme si tedy 90% intervaly spolehlivosti pro střední hodnotu platu brazilských ajťáků :-)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10.0% kritická hodnota rozdělení N(0,1):\n",
      "z(0.1)=1.2816\n",
      "\n",
      "5.0% kritická hodnota rozdělení N(0,1):\n",
      "z(0.05)=1.6449\n",
      "\n",
      "Pravostranný IS:  [9.916   inf]\n",
      "Levostranný IS:  [  -inf 10.684]\n",
      "Oboustranný IS:  [ 9.807 10.793]\n"
     ]
    }
   ],
   "source": [
    "Xn = 10.3\n",
    "n = 16\n",
    "sigma = 1.2\n",
    "alpha = 0.1\n",
    "\n",
    "kriticka_hodnota_jedno = norm.isf(alpha)\n",
    "kriticka_hodnota_obou = norm.isf(alpha/2)\n",
    "print('{0}% kritická hodnota rozdělení N(0,1):\\nz({1})={2:.4f}'\n",
    "      .format(100*alpha, alpha, kriticka_hodnota_jedno))\n",
    "print('\\n{0}% kritická hodnota rozdělení N(0,1):\\nz({1})={2:.4f}'\n",
    "      .format(100*alpha/2, alpha/2, kriticka_hodnota_obou))\n",
    "delta = kriticka_hodnota_jedno * sigma / np.sqrt(n)\n",
    "delta_obou = kriticka_hodnota_obou * sigma / np.sqrt(n)\n",
    "ISpravy = np.array([Xn - delta, np.inf])\n",
    "ISlevy = np.array([-np.inf, Xn + delta])\n",
    "IS = np.array([Xn - delta_obou, Xn + delta_obou])\n",
    "print('\\nPravostranný IS: ', ISpravy)\n",
    "print('Levostranný IS: ', ISlevy)\n",
    "print('Oboustranný IS: ', IS)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Pojďme testovat hypotézu o střední hodnotě...\n",
    "\n",
    "**Máme na hladině 0.1 otestovat hypotézu, že střední hodnota $\\mu$ nástupního platu brazilských ajťáků je rovna 11 tisícům proti alternativě, že není.**\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "&H_0: \\mu = \\mu_0 = 11 \\\\\n",
    "&H_A: \\mu \\ne \\mu_0 = 11.\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "Naším cílem je, aby:\n",
    "$$\n",
    "\\begin{align}\n",
    "&P(\\text{Zamítnu}\\ H_0 | \\text{platí}\\ H_0) \\leq \\alpha,\n",
    "\\qquad\\qquad\\quad\\qquad\\text{(chyba 1. druhu)} \\\\\n",
    "&P(\\text{Nezamítnu}\\ H_0 | \\text{neplatí}\\ H_0)\\ \\text{byla minimální.}\\qquad\\text{(chyba 2. druhu)}\\\\\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "Zde $\\alpha$ nazveme **hladinou testu**, splývá nám zde s **hladinou významnosti**. Podle toho, zda $\\mu_0$ leží či neleží v příslušném intervalu spolehlivosti buď $H_0$ **nezamítneme** nebo **zamítneme**. Hypotézy se **nikdy nepřijímají**!\n",
    "\n",
    "**V příkladu $\\mu_0 \\notin [9.807, 10.793] \\Longrightarrow$ zamítáme $H_0$.** Brazilští ajťáci prostě nenastupují za platy, jež by měly střední hodnotu 11 tisíc realů."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Intervalový odhad potřebuje rozptyl. Co když jej nemáme?\n",
    "\n",
    "**Nahradíme-li rozptyl $\\sigma^2$ jeho bodovým odhadem - výběrovým rozptylem**\n",
    "\n",
    "$$\n",
    "s^2 = \\frac{1}{n-1} \\sum_{i=1}^n (X_i - \\bar{X}_n)^2,\n",
    "$$\n",
    "\n",
    "**dostaneme veličinu se [Studentovým $t$ rozdělením](https://en.wikipedia.org/wiki/Student%27s_t-distribution) s $n-1$ stupni volnosti**,\n",
    "\n",
    "$$\n",
    "\\frac{\\bar{X}_n - \\mu}{s/\\sqrt{n}} \\sim t_{n-1}.\n",
    "$$\n",
    "\n",
    "Toto rozdělení pochází do [W.S. Gosseta aka Studenta](https://en.wikipedia.org/wiki/William_Sealy_Gosset), v té době zaměstnance firmy Guiness. Používá se pro popis veličin s (přibližně) normálním rozdělením a to zejména v případech, kdy je k dispozici pouze malý rozsah výběru a tedy odhad rozptylu má \"větší nejistotu\". Proto má Studentovo rozdělení při malém počtu stupňů volnosti (\"málo datech\") plošší hustotu. V limitě potom přejde do normálního rozdělení. Proto v důsledku limitních vět lze použít i pro jiná rozdělení, zvl. pokud je rozumný rozsah výběru.\n",
    "\n",
    "Speciální případ [Studentova rozdělení](https://en.wikipedia.org/wiki/Student%27s_t-distribution) je $n=1$, tzv. [Cauchyho rozdělení](https://en.wikipedia.org/wiki/Cauchy_distribution). To je příkladem degenerovaného rozdělení, neboť jeho střední hodnota ani rozptyl pro příliš [těžké chvosty](https://en.wikipedia.org/wiki/Heavy-tailed_distribution) neexistují.\n",
    "\n",
    "Hustoty rozdělení pro pár stupňů volnosti a porovnání s hustotou $\\mathcal{N}(0,1)$ znázorňuje následující obrázek. Současně dává tušit, že intervaly spolehlivosti při stejné hladině budou širší, než při známém rozptylu. Proč? ;-)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(-4, 4, 1000)\n",
    "plt.figure(figsize=(10,5))\n",
    "plt.plot(x, norm.pdf(x), label='N(0,1)')\n",
    "for df in [1, 2, 5, 15]:\n",
    "    plt.plot(x, t.pdf(x, df=df), label=r'$t_{' + str(df) + '}$')\n",
    "plt.legend()\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('f(x)')\n",
    "plt.title('Hustoty rozdělení t a N(0,1)')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Zpátky k příkladu\n",
    "\n",
    "Předpokládejme nyní, že v příkladu výše neznáme rozptyl, ale výběrový rozptyl nám vyšel $1.2^2$ (tedy stejně jako rozptyl výše, pro porovnání). Budeme počítat intervaly spolehlivosti pomocí Studentova t rozdělení. Jaké jsou v porovnání s předchozími?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10.0% kritická hodnota rozdělení t:\n",
      "t(0.1)=1.3406\n",
      "\n",
      "5.0% kritická hodnota rozdělení t:\n",
      "t(0.05)=1.7531\n",
      "\n",
      "Levostranný IS:  [  -inf 10.702]\n",
      "Pravostranný IS:  [9.898   inf]\n",
      "Oboustranný IS:  [ 9.774 10.826]\n"
     ]
    }
   ],
   "source": [
    "Xn = 10.3\n",
    "n = 16\n",
    "s= 1.2\n",
    "alpha = 0.1\n",
    "\n",
    "kriticka_hodnota_jedno = t.isf(alpha, df=n-1)\n",
    "kriticka_hodnota_obou = t.isf(alpha/2, df=n-1)\n",
    "\n",
    "print('{0}% kritická hodnota rozdělení t:\\nt({1})={2:.4f}'\n",
    "      .format(100*alpha, alpha, kriticka_hodnota_jedno))\n",
    "print('\\n{0}% kritická hodnota rozdělení t:\\nt({1})={2:.4f}'\n",
    "      .format(100*alpha/2, alpha/2, kriticka_hodnota_obou))\n",
    "\n",
    "delta = kriticka_hodnota_jedno * s / np.sqrt(n)\n",
    "delta_obou = kriticka_hodnota_obou * s / np.sqrt(n)\n",
    "\n",
    "ISpravy = np.array([Xn - delta, np.inf])\n",
    "ISlevy = np.array([-np.inf, Xn + delta])\n",
    "IS = np.array([Xn - delta_obou, Xn + delta_obou])\n",
    "\n",
    "print('\\nLevostranný IS: ', ISlevy)\n",
    "print('Pravostranný IS: ', ISpravy)\n",
    "print('Oboustranný IS: ', IS)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### [Test hypotézy](https://en.wikipedia.org/wiki/Statistical_hypothesis_testing#Definition_of_terms)\n",
    "\n",
    "Máme navíc na stejné hladině $\\alpha$ otestovat\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "&H_0: \\mu = 10 \\\\\n",
    "&H_A: \\mu < 10.\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "Jelikož $10 \\in [-\\infty, 10.702]$, nulovou hypotézu nezamítáme.\n",
    "\n",
    "Teď už by mělo být zřejmé, že testy jsou rovněž jednostranné nebo oboustranné a používáme k nim související intervaly spolehlivosti :)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Intervaly spolehlivosti pro rozptyl normálního rozdělení\n",
    "\n",
    "Vyjdeme z toho, že pro výběr $X_1, \\ldots, X_n$, $n\\geq 2$ z normálního rozdělení $\\mathcal{N}(\\mu, \\sigma^2)$, kde $\\sigma^2>0$ a výběrový (nevychýlený) rozptyl $s^2$ má náhodná veličina\n",
    "\n",
    "$$\n",
    "\\frac{(n-1)s^2}{\\sigma^2} \\sim \\chi_{n-1}^2,\n",
    "$$\n",
    "\n",
    "tj. má [chí-kvadrát rozdělení](https://en.wikipedia.org/wiki/Chi-squared_distribution) s $n-1$ stupni volnosti. Graf hustoty pro různé stupně volnosti vypadá následovně:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(1e-10, 15, 1000)\n",
    "plt.figure(figsize=(10,5))\n",
    "for df in [2, 4, 5, 8]:\n",
    "    plt.plot(x, chi2.pdf(x, df=df), label=r'$\\chi_{' + str(df) + '}^2$')\n",
    "plt.legend()\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('f(x)')\n",
    "plt.title('Hustoty chí-kvadrát rozdělení')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Řekněme, že máme udělat takový interval pro $\\sigma^2$, aby pro zjištěný výběrový rozptyl $s^2$ a zadanou kritickou hodnotu $\\alpha$ platilo\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "\\alpha = P(s^2 > q) &= P\\left( \\frac{(n-1)s^2}{\\sigma^2} > \\chi_{n-1}^2(\\alpha) \\right) \\\\\n",
    "&= P\\left( \\frac{(n-1)s^2}{\\chi_{n-1}^2(\\alpha)} > \\sigma^2 \\right).\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "Stejně jako výše jsme tedy současně našli **$(1-\\alpha)$% pravostranný interval spolehlivosti pro rozptyl** ve tvaru\n",
    "\n",
    "$$\n",
    "\\left(\\frac{(n-1)s^2}{\\chi_{n-1}^2(\\alpha)}, \\infty\\right).\n",
    "$$\n",
    "\n",
    "Interval levostranný nelze hledat symetrií, neboť chí-kvadrát rozdělení není symetrické ani centrované v nule. Budeme tedy hledat pro kritickou hodnotu $1-\\alpha$ a získáme **$(1-\\alpha)$% levostranný interval spolehlivosti pro rozptyl**\n",
    "\n",
    "$$\n",
    "\\left( 0, \\frac{(n-1)s^2}{\\chi_{n-1}^2(1-\\alpha)} \\right).\n",
    "$$\n",
    "\n",
    "Oboustranný interval se hledá z \"úmluvy\", že se navzdory asymetrii $\\alpha$ rozdělí symetricky a budeme hledat s kritickými hodnotami $\\chi_{n-1}^2(1-\\alpha/2)$ a $\\chi_{n-1}^2(\\alpha/2)$. Výsledný **oboustranný interval spolehlivosti** pro rozptyl je\n",
    "\n",
    "$$\n",
    "\\left(\n",
    "\\frac{(n-1)s^2}{\\chi_{n-1}^2 \\left(\\frac{\\alpha}{2}\\right)},\n",
    "\\frac{(n-1)s^2}{\\chi_{n-1}^2 \\left(1-\\frac{\\alpha}{2} \\right)} \\right)\n",
    "$$\n",
    "\n",
    "Pozor na meze jednostranných IS (nuly). Tyto IS platí jen pro rozptyl normálního rozdělení!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### A naposled k příkladu výše\n",
    "\n",
    "Máme sestavit interval spolehlivosti pro rozptyl $\\sigma^2$, pokud výběrová směrodatná odchylka vyšla $s=1.2$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Výběrový rozptyl s2 =  1.44\n",
      "Pravostranný IS:  [0.968   inf]\n",
      "Levostranný IS:  [0.    2.527]\n",
      "Oboustranný IS:  [0.864 2.975]\n"
     ]
    }
   ],
   "source": [
    "s2 = 1.2**2\n",
    "alpha = 0.1\n",
    "print('Výběrový rozptyl s2 = ', s2)\n",
    "\n",
    "kriticka_hodnota_levy = chi2.isf(1-alpha, df=n-1)\n",
    "kriticka_hodnota_pravy = chi2.isf(alpha, df=n-1)\n",
    "kriticka_hodnota_oboustr = chi2.isf([alpha/2, 1-alpha/2], df=n-1)\n",
    "\n",
    "IS_pravy = np.array([(n-1) * s2 / kriticka_hodnota_pravy, np.inf])\n",
    "IS_levy = np.array([0, (n-1) * s2 / kriticka_hodnota_levy])\n",
    "IS = (n - 1) * s2 / kriticka_hodnota_oboustr\n",
    "\n",
    "print('Pravostranný IS: ', IS_pravy)\n",
    "print('Levostranný IS: ', IS_levy)\n",
    "print('Oboustranný IS: ', IS)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Shrnutí intervalů spolehlivosti a testů\n",
    "\n",
    "Následující tabulka shrnuje tři uvedené typy intervalů spolehlivosti. Na konci máme ještě podobu alternativní hypotézy. Pokud testujeme střední hodnotu, pak za $\\theta$ dosazujeme $\\mu$, a $\\theta_0$ je testovaná hodnota. Obecně ve statistice je $\\theta$ univerzální písmenko, kterým značíme parametry, většinou neznámé a odhadované.\n",
    "\n",
    "Pokud máme např. na hladině $\\alpha=0.01$ testovat, že střední hodnota je 10 proti alternativě, že je menší a rozptyl neznáme, tj.\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "&H_0: \\mu = 10 \\\\\n",
    "&H_A: \\mu < 10\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "použijeme příslušný 99% levostranný interval spolehlivosti a ověříme, zda do něj hodnota $\\mu_0 = 10$ patří či nikoliv. Podle toho $H_0$ nezamítneme či zamítneme. Pozor, pokud zamítneme, tak to děláme ve prospěch alternativní hypotézy. Pokud ovšem nezamítneme, nevíme nic :) **Hypotézy nikdy nepřijímáme!** Pokud test vychází tak, že zamítáme $H_0$, mluvíme o statisticky významném testu.\n",
    "\n",
    "| Parametr | Levostranný | Pravostranný | Oboustranný |\n",
    "|---|:---:|:---:|:---:|\n",
    "| $\\mu=?$, známé $\\sigma^2$| $\\left(-\\infty, \\bar{X}_n + \\frac{z_\\alpha \\cdot \\sigma}{\\sqrt{n}}\\right)$| $\\left(\\bar{X}_n - \\frac{z_\\alpha \\cdot \\sigma}{\\sqrt{n}}, \\infty\\right)$ | $\\left(\\bar{X}_n - \\frac{z_{\\alpha/2} \\cdot \\sigma}{\\sqrt{n}}, \\bar{X}_n + \\frac{z_{\\alpha/2} \\cdot \\sigma}{\\sqrt{n}}\\right)$ |\n",
    "| $\\mu=?$, neznámé $\\sigma^2$| $\\left(-\\infty, \\bar{X}_n + \\frac{t_{n-1}(\\alpha) \\cdot s}{\\sqrt{n}}\\right)$| $\\left(\\bar{X}_n - \\frac{t_{n-1}(\\alpha) \\cdot s}{\\sqrt{n}}, \\infty\\right)$ | $\\left(\\bar{X}_n - \\frac{t_{n-1}\\left(\\frac{\\alpha}{2}\\right) \\cdot s}{\\sqrt{n}}, \\bar{X}_n + \\frac{t_{n-1}\\left(\\frac{\\alpha}{2}\\right) \\cdot s}{\\sqrt{n}}\\right)$ |\n",
    "| $\\sigma^2=?$ | $\\left( 0, \\frac{(n-1)s^2}{\\chi_{n-1}^2(1-\\alpha)} \\right)$ | $\\left(\\frac{(n-1)s^2}{\\chi_{n-1}^2(\\alpha)}, \\infty\\right)$ | $\\left(\\frac{(n-1)s^2}{\\chi_{n-1}^2 \\left(\\frac{\\alpha}{2}\\right)},\\frac{(n-1)s^2}{\\chi_{n-1}^2 \\left(1-\\frac{\\alpha}{2} \\right)} \\right)$ |\n",
    "|$H_A$| $\\theta < \\theta_0$| $\\theta > \\theta_0$| $\\theta \\ne \\theta_0$ |\n",
    "\n",
    "Uvedené testy nazýváme celkem přímočaře [Z-test hypotézy o střední hodnotě](https://en.wikipedia.org/wiki/Z-test), [t-test hypotézy o střední hodnotě](https://en.wikipedia.org/wiki/Student%27s_t-test#One-sample_t-test) a [chí-kvadrát test hypotézy o rozptylu normální veličiny](https://en.wikipedia.org/wiki/Chi-squared_test#Chi-squared_test_for_variance_in_a_normal_population).\n",
    "\n",
    "Celá problematika intervalových odhadů a testování hypotéz je daleko bohatší, než lze v PST probrat. Ale stojí za to si o tom před zkouškou něco přečíst - viz odkazy v celém notebooku."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Co jsou a nejsou intervaly spolehlivosti\n",
    "\n",
    "[**Pozor, v tomto chybují i experti! Ale student PST nesmí!**](https://en.wikipedia.org/wiki/Confidence_interval#Meaning_and_interpretation)\n",
    "\n",
    "Víme, že průměr náhodných veličin je náhodná veličina. Proto i interval spolehlivosti zkonstruovaný z výběru bude v nějakém smyslu náhodný, pro různá pozorování bude různý.\n",
    "\n",
    "$(1-\\alpha)$% interval spolehlivosti je takový interval, který s pravděpodobností $1-\\alpha$ **pokryje** odhadovaný neznámý parametr. Jinými slovy, ze 100 zkonstruovaných intervalů jich v průměru $\\alpha$ parametr nepokryje - viz následující simulace.\n",
    "\n",
    "**Není pravdivé tvrzení**, že $(1-\\alpha)$% interval spolehlivosti obsahuje neznámý parametr s pravděpodobností $1-\\alpha$. To dělají bayesovské intervaly spolehlivosti!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1008x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "EX = 0\n",
    "sigma2 = 1\n",
    "n = 30\n",
    "alpha=0.05\n",
    "repeats = 100\n",
    "\n",
    "Xis = norm.rvs(loc=EX, scale=np.sqrt(sigma2), size=(repeats, n))\n",
    "Xbars = Xis.mean(axis=1)\n",
    "z_krit = norm.isf(alpha/2)\n",
    "deltas = z_krit * np.sqrt(sigma2) / np.sqrt(n)\n",
    "ISs = np.c_[Xbars - deltas, Xbars + deltas]\n",
    "ISs_out_ind = np.r_[np.argwhere(ISs[:,0]>EX).flatten(), \n",
    "                    np.argwhere(ISs[:,1]<EX).flatten()]\n",
    "\n",
    "plt.figure(figsize=(14,4))\n",
    "plt.vlines(range(repeats), ymin=ISs[:,0], ymax=ISs[:,1])\n",
    "plt.vlines(ISs_out_ind, ymin=ISs[ISs_out_ind,0], ymax=ISs[ISs_out_ind, 1], color='red')\n",
    "plt.axhline(EX, color='blue', label='EX')\n",
    "plt.legend()\n",
    "plt.title('{0}% intervaly spolehlivosti pro EX. Parametr nepokrylo: {1} ({2:.1f}%)'\n",
    "          .format((1-alpha)*100, ISs_out_ind.size, 100*ISs_out_ind.size/repeats))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Příklad 10.1\n",
    "\n",
    "**Uvažujme náhodný výběr $n = 16$ hodnot z normálního rozdělení. Výběrový průměr a směrodatnou odchylku jsme spočetli jako $\\bar X_n = 10.3$ a $s_n = 1.2$.**\n",
    "\n",
    "**a) Najděte oboustranný a levý (dolní) jednostranný 90% interval spolehlivosti pro střední hodnotu $\\mu$.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10.0% kritická hodnota rozdělení t:\n",
      "t(0.1)=1.3406\n",
      "\n",
      "5.0% kritická hodnota rozdělení t:\n",
      "t(0.05)=1.7531\n",
      "\n",
      "Levostranný IS:  [  -inf 10.702]\n",
      "Oboustranný IS:  [ 9.774 10.826]\n"
     ]
    }
   ],
   "source": [
    "Xbar = 10.3\n",
    "sn = 1.2\n",
    "n = 16\n",
    "alpha = 0.1\n",
    "\n",
    "kriticka_hodnota_jedno = t.isf(alpha, df=n-1)\n",
    "kriticka_hodnota_obou = t.isf(alpha/2, df=n-1)\n",
    "print('{0}% kritická hodnota rozdělení t:\\nt({1})={2:.4f}'\n",
    "      .format(100*alpha, alpha, kriticka_hodnota_jedno))\n",
    "print('\\n{0}% kritická hodnota rozdělení t:\\nt({1})={2:.4f}'\n",
    "      .format(100*alpha/2, alpha/2, kriticka_hodnota_obou))\n",
    "delta = kriticka_hodnota_jedno * s / np.sqrt(n)\n",
    "delta_obou = kriticka_hodnota_obou * s / np.sqrt(n)\n",
    "ISlevy = np.array([-np.inf, Xn + delta])\n",
    "IS = np.array([Xn - delta_obou, Xn + delta_obou])\n",
    "print('\\nLevostranný IS: ', ISlevy)\n",
    "print('Oboustranný IS: ', IS)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**b) Najděte oboustranný a levý (dolní) interval 90% spolehlivosti pro rozptyl $\\sigma^2$.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Levostranný IS:  [0.    2.527]\n",
      "Oboustranný IS:  [0.864 2.975]\n"
     ]
    }
   ],
   "source": [
    "sn = 1.2\n",
    "s2 = sn**2\n",
    "n = 16\n",
    "alpha = 0.1\n",
    "\n",
    "kriticka_hodnota_levy = chi2.isf(1-alpha, df=n-1)\n",
    "kriticka_hodnota_oboustr = chi2.isf([alpha/2, 1-alpha/2], df=n-1)\n",
    "\n",
    "IS_levy = np.array([0, (n-1) * s2 / kriticka_hodnota_levy])\n",
    "IS = (n - 1) * s2 / kriticka_hodnota_oboustr\n",
    "\n",
    "print('Levostranný IS: ', IS_levy)\n",
    "print('Oboustranný IS: ', IS)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Příklad 10.2\n",
    "\n",
    "**Potřebujeme odhadnout průměrnou délku transakce databázového serveru (v jednotkách ms). Předpokládejme, že délky transakcí jsou nezávislé a stejně rozdělené $X_1, X_2, \\dotsc$ s konečnými $\\mu = \\mathrm E X_i$ a $\\sigma^2 = \\operatorname{var} X_i$.**\n",
    "\n",
    "**Z $50$ náhodně vybraných transakcí jsme spočetli:**\n",
    "\n",
    "$$\n",
    "            \\sum_{i=1}^{50} X_i = 684.199\\quad\\text{a}\\quad \\sum_{i=1}^{50} X_i^2 = 18651.3.\n",
    "$$\n",
    "\n",
    "**a) Najděte bodový odhad střední hodnoty $\\mu$ a rozptylu $\\sigma^2$.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Průměr - odhad střední hodnoty: 13.68\n",
      "Výběrová variance s2 = 189.5660\n",
      "(Bez Besselovy korekce: s2 = 185.7747)\n"
     ]
    }
   ],
   "source": [
    "sum_x = 684.199\n",
    "sum_x2 = 18651.3\n",
    "n = 50\n",
    "\n",
    "mean_x = sum_x / n\n",
    "mean_x2 = sum_x2 / n\n",
    "varX = mean_x2 - mean_x**2\n",
    "varXc = varX * n/(n-1)\n",
    "\n",
    "print('Průměr - odhad střední hodnoty: {0:.2f}'.format(mean_x))\n",
    "print('Výběrová variance s2 = {0:.4f}'.format(varXc))\n",
    "print('(Bez Besselovy korekce: s2 = {0:.4f})'.format(varX))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**b) Najděte jedno a oboustranné $99\\%$ intervalové odhady $\\mu$.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Levostranný IS:  [  -inf 18.367]\n",
      "Pravostranný IS:  [9.001   inf]\n",
      "Oboustranný IS:  [ 8.466 18.902]\n"
     ]
    }
   ],
   "source": [
    "s = np.sqrt(varXc)\n",
    "alpha = 0.01\n",
    "\n",
    "kriticka_hodnota_jedno = t.isf(alpha, df=n-1)\n",
    "kriticka_hodnota_obou = t.isf(alpha/2, df=n-1)\n",
    "\n",
    "delta = kriticka_hodnota_jedno * s / np.sqrt(n)\n",
    "delta_obou = kriticka_hodnota_obou * s / np.sqrt(n)\n",
    "\n",
    "ISpravy = np.array([mean_x - delta, np.inf])\n",
    "ISlevy = np.array([-np.inf, mean_x + delta])\n",
    "IS = np.array([mean_x - delta_obou, mean_x + delta_obou])\n",
    "\n",
    "print('\\nLevostranný IS: ', ISlevy)\n",
    "print('Pravostranný IS: ', ISpravy)\n",
    "print('Oboustranný IS: ', IS)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**c) Proč je třeba předpokládat konečný rozptyl $\\sigma^2$?**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Centrální limitní věta, již používáme při aproximacích, má tuto nutnou podmínku."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**d) Proč nemůžeme zkonstruovat intervalový odhad $\\sigma^2$?**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Uvedený intervalový odhad pro rozptyl předpokládá normálně rozdělenou veličinu. Tou doba odezvy serveru není."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Příklad 10.3\n",
    "\n",
    "**Uvažujme náhodnou veličinu $Y$ s normálním rozdělením. Chceme odhadnout její střední hodnotu  pomocí 95% konfidenčního intervalu šířky 0.01.**\n",
    "       \n",
    "**Z předběžného výběru jsme odhadli rozptyl jako $s^2 = 4.23$.**\n",
    "\n",
    "**a) Odhadněte, jak veliký náhodný výběr budeme potřebovat.**\n",
    "\n",
    "Nejjednodušší bude využít odhad pomocí kvantilů/kritických hodnot normálního rozdělení a pak případně zpřesnit v okolí pohledem na Studentovo t rozdělení. V normálním rozdělení hledáme oboustranný interval,\n",
    "\n",
    "$$\n",
    "\\left(\\bar{X}_n - \\frac{z_{0.05/2} \\cdot \\sigma}{\\sqrt{n}}, \\bar{X}_n + \\frac{z_{0.05/2} \\cdot \\sigma}{\\sqrt{n}}\\right)\n",
    "=\n",
    "\\left(\\bar{X}_n - \\frac{0.01}{2}, \\bar{X}_n + \\frac{0.01}{2}\\right),\n",
    "$$\n",
    "\n",
    "kde nahradíme za $\\sigma$ výběrovou směrodatnou odchylku $s$ a řešíme pro $n$,\n",
    "\n",
    "$$\n",
    "n = \\left( \\frac{z_{0.05/2} \\cdot \\sigma}{\\frac{0.01}{2}} \\right)\n",
    "$$\n",
    "\n",
    "Pro jednoduchost můžeme položit $\\bar{X}_n = 0$, neboť poloha průměru o potřebném $n$ nerozhoduje.\n",
    "\n",
    "Níže je výpočet z normality:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Z normálního rozdělení před zaokrouhlením:  649974.8324614464\n"
     ]
    }
   ],
   "source": [
    "s2 = 4.23\n",
    "\n",
    "n_norm = 0.01/2 * np.sqrt(n)\n",
    "n_norm = (norm.isf(0.05/2) * np.sqrt(s2) / (0.01/2))**2\n",
    "print('Z normálního rozdělení před zaokrouhlením: ', n_norm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "a numerická optimalizace ve Studentovi pro nalezení optimální hodnoty. Funkce `fminbound()` hledá minimum, omezili jsme se na výsledek z předchozího kroku plus mínus 100 a hledáme minimum\n",
    "\n",
    "$$\n",
    "\\left| \\frac{t_{n-1}(0.05/2) \\cdot \\sigma}{\\sqrt{n}} - \\frac{0.01}{2} \\right|,\n",
    "$$\n",
    "\n",
    "neboť víme, že by se měly hodnota před mínusem by se měla rovnat hodnotě za mínusem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimalizací v t rozdělení před zaokrouhlením:  649977.2476477955\n"
     ]
    }
   ],
   "source": [
    "from scipy.optimize import fminbound\n",
    "def target_func(n, tol=1e-10):\n",
    "    return np.abs(t.isf(0.05/2, df=n-1) * np.sqrt(s2) / np.sqrt(n) - 0.01/2)\n",
    "\n",
    "res = fminbound(target_func, n_norm-100, n_norm+100)\n",
    "print('Optimalizací v t rozdělení před zaokrouhlením: ', res)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**b) Jak se požadovaná velikost výběru změní, pokud by nám stačila šířka intervalu jen $0.1$?**\n",
    "\n",
    "Postup bude stejný."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Z normálního rozdělení před zaokrouhlením:  6499.748324614463\n",
      "Optimalizací v t rozdělení před zaokrouhlením:  6502.169188003062\n"
     ]
    }
   ],
   "source": [
    "s2 = 4.23\n",
    "\n",
    "n_norm = (norm.isf(0.05/2) * np.sqrt(s2) / (0.1/2))**2\n",
    "print('Z normálního rozdělení před zaokrouhlením: ', n_norm)\n",
    "\n",
    "from scipy.optimize import fminbound\n",
    "\n",
    "def target_func(n, tol=1e-10):\n",
    "    return np.abs(t.isf(0.05/2, df=n-1) * np.sqrt(s2) / np.sqrt(n) - 0.1/2)\n",
    "\n",
    "res = fminbound(target_func, n_norm-100, n_norm+100)\n",
    "print('Optimalizací v t rozdělení před zaokrouhlením: ', res)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Příklad 11.1\n",
    "\n",
    "**Výrobce deklaruje, že při daném napětí mají jeho kruhové oscilátory frekvenci 50MHz se standardní směrodatnou odchylkou menší než 1.3MHz. Na substrátovém disku jsme otestovali 8 oscilátorů a naměřili tyto hodnoty frekvence:**\n",
    "\n",
    "\t\t47.4; 51.7; 53.6; 49.5; 51.7; 48.6; 50.2; 50.1\n",
    "\n",
    "**Tj. $\\bar{X}_n=50.35, s_n\\doteq 1.96$.**\n",
    "\t\t\n",
    "**Na hladinách významnosti 5% a 1% otestujte, zda oscilátory splňují parametry výrobce, tj.,**\n",
    "\n",
    "**a) zda střední hodnota frekvencí je rovna 50MHz,**\n",
    "\n",
    "Máme-li testovat \"rovna versus nerovna\", jedná se o oboustranný test s oboustranným intervalem spolehlivosti. V tomto případě s výběrovým rozptylem (resp. směrodatnou odchylkou), tedy **t test**, neboť použijeme Studentovo rozdělení na konstrukci intervalu spolehlivosti. Hypotézy tedy jsou:\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "&H_0: \\mu = 50 \\\\\n",
    "&H_A: \\mu \\ne 50.\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "Zkonstruujeme příslušné intervaly pro $\\mu$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Oboustranný IS, hladina 0.05:  [48.711 51.989]\n",
      "Oboustranný IS, hladina 0.01:  [47.925 52.775]\n"
     ]
    }
   ],
   "source": [
    "Xn = 50.35\n",
    "n = 8\n",
    "s = 1.96\n",
    "\n",
    "alpha_0_05 = 0.05\n",
    "alpha_0_01 = 0.01\n",
    "\n",
    "kriticka_hodnota_0_05 = t.isf(alpha_0_05/2, df=n-1)\n",
    "kriticka_hodnota_0_01 = t.isf(alpha_0_01/2, df=n-1)\n",
    "\n",
    "delta_0_05 = kriticka_hodnota_0_05 * s / np.sqrt(n)\n",
    "delta_0_01 = kriticka_hodnota_0_01 * s / np.sqrt(n)\n",
    "\n",
    "IS_0_05 = np.array([Xn - delta_0_05, Xn + delta_0_05])\n",
    "IS_0_01 = np.array([Xn - delta_0_01, Xn + delta_0_01])\n",
    "\n",
    "print('Oboustranný IS, hladina 0.05: ', IS_0_05)\n",
    "print('Oboustranný IS, hladina 0.01: ', IS_0_01)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Jelikož testovaná hodnota $\\mu_0 = 50$ leží v obou intervalech spolehlivosti, nezamítáme $H_0$, že střední hodnota frekvencí je 50MHz. **Ale tím neříkáme, že opravdu je - nezamítnutí hypotézy neříká nic o její pravdivosti či pravdivosti alternativy!** Zamyslete se - stačilo by spočítat interval jen pro jednu hladinu významnosti? Pro kterou? Nápověda - vemte v úvahu šířky intervalů. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**b) zda směrodatná odchylka je menší než 1.3MHz.**\n",
    "\n",
    "**Předpokládejte normální rozdělení frekvencí.**\n",
    "\n",
    "Testujeme chí-kvadrát testem - pozor, předpoklad normality je zde silný. Máme testovat proti alternativě, že je větší, půjde tedy o pravostranný interval spolehlivosti,\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "&H_0: \\sigma^2 = 1.3^2 \\\\\n",
    "&H_A: \\sigma^2 > 1.3^2 = 1.69.\n",
    "\\end{align}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pravostranný IS, hladina 0.01:  [1.456   inf]\n",
      "Pravostranný IS, hladina 0.05:  [1.912   inf]\n"
     ]
    }
   ],
   "source": [
    "s2 = 1.96**2\n",
    "\n",
    "kriticka_hodnota_0_01 = chi2.isf(alpha_0_01, df=n-1)\n",
    "kriticka_hodnota_0_05 = chi2.isf(alpha_0_05, df=n-1)\n",
    "\n",
    "IS_pravy_0_01 = np.array([(n-1) * s2 / kriticka_hodnota_0_01, np.inf])\n",
    "IS_pravy_0_05 = np.array([(n-1) * s2 / kriticka_hodnota_0_05, np.inf])\n",
    "\n",
    "print('Pravostranný IS, hladina 0.01: ', IS_pravy_0_01)\n",
    "print('Pravostranný IS, hladina 0.05: ', IS_pravy_0_05)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "V případě hladiny 0.05 nulovou hypotézu zamítneme, neboť testovaná hodnota neleží v příslušném intervalu spolehlivosti. V případě hladiny 0.01 nulovou hypotézu nezamítáme."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Příklad 11.2\n",
    "\n",
    "**Výrobce aut uvádí, že průměrná spotřeba nového modelu je 6 l/100 km. Provedli jsme test na dvaceti vozech a naměřili jsme průměrnou spotřebu a její výběrový rozptyl jako:**\n",
    "        \n",
    "$$\\bar X_n=6.8, s_n^2=2.56.$$\n",
    "        \n",
    "**Otestujte, zda je tvrzení výrobce pravdivé, nebo zda je průměrná spotřeba významně vyšší. Uvažujte**\n",
    "\n",
    "**a) $\\alpha=5\\%$,**\n",
    "\n",
    "**b) $\\alpha=1\\%$.**\n",
    "\n",
    "V obou případech budeme testovat pravostranným intervalem spolehlivosti, neboť\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "&H_0: \\mu = 6 \\\\\n",
    "&H_A: \\mu > 6.\n",
    "\\end{align}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pravostranný 95% IS:  [6.181   inf]\n",
      "Pravostranný 99% IS:  [5.891   inf]\n"
     ]
    }
   ],
   "source": [
    "Xn = 6.8\n",
    "n = 20\n",
    "s = np.sqrt(2.56)\n",
    "\n",
    "kriticka_hodnota_0_05 = t.isf(0.05, df=n-1)\n",
    "kriticka_hodnota_0_01 = t.isf(0.01, df=n-1)\n",
    "\n",
    "delta_0_05 = kriticka_hodnota_0_05 * s / np.sqrt(n)\n",
    "delta_0_01 = kriticka_hodnota_0_01 * s / np.sqrt(n)\n",
    "\n",
    "ISpravy_0_05 = np.array([Xn - delta_0_05, np.inf])\n",
    "ISpravy_0_01 = np.array([Xn - delta_0_01, np.inf])\n",
    "\n",
    "print('Pravostranný 95% IS: ', ISpravy_0_05)\n",
    "print('Pravostranný 99% IS: ', ISpravy_0_01)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$H_0$ tedy na hladině 5% zamítáme, zatímco na hladině 1% nezamítáme."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Příklad 11.3\n",
    "\n",
    "**Před bouřkou typicky vzroste rozptyl rychlosti větru. Předpokládejme, že jestliže se blíží bouřka, rozptyl $\\sigma^2$ překročí hodnotu 4.5. Z 200 měření jsme určili konfidenční intervaly pro $\\sigma^2$ jako**\n",
    "\n",
    "- **99% konfidenční interval: $(2.64, 4.43)$,**\n",
    "- **98% konfidenční interval: $(2.7, 4.31)$.**\n",
    " \n",
    "**Přichází bouřka?        \n",
    "Otestujte hypotézu $H_0:\\sigma^2\\leq 4.5$ proti alternativě $H_A:\\sigma^2>4.5$ na hladině významnosti 1%.**\n",
    "\n",
    "Nejprve si spočteme výběrový rozptyl. K tomu nám poslouží libovolný ze vzorců určujících některou z mezí některého z intervalů spolehlivosti, např. pro dolní hranici $L$:\n",
    "\n",
    "$$\n",
    "\\frac{(n-1)s^2}{\\chi_{n-1}^2\\left(\\frac{\\alpha}{2}\\right)} = L \\qquad \\Longrightarrow s^2 = \\frac{L\\cdot \\chi_{n-1}^2\\left(\\frac{\\alpha}{2}\\right) }{n-1}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Výběrový rozptyl s2 = 3.37\n"
     ]
    }
   ],
   "source": [
    "n = 200\n",
    "\n",
    "s2 = 2.7 * chi2.isf(0.02/2, df=n-1) / (n-1)\n",
    "print(\"Výběrový rozptyl s2 = {0:.2f}\".format(s2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Následně můžeme otestovat hypotézu..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pravostranný IS, hladina 0.01:  [2.7 inf]\n"
     ]
    }
   ],
   "source": [
    "kriticka_hodnota_0_01 = chi2.isf(alpha_0_01, df=n-1)\n",
    "\n",
    "IS_pravy_0_01 = np.array([(n-1) * s2 / kriticka_hodnota_0_01, np.inf])\n",
    "\n",
    "print('Pravostranný IS, hladina 0.01: ', IS_pravy_0_01)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Jelikož interval obsahuje testovanou hodnotu 4.5, nulovou hypotézu nezamítáme."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Příklad 11.4\n",
    "\n",
    "**Bezpečnostní senzor pravidelně kontroluje počítačovou učebnu. Jestliže není v učebně detekován žádný pohyb, senzor vrací signál $X=W$, kde $W$ je náhodná veličina se střední hodnotou 0 a malým rozptylem. V případě detekce pohybu vrací senzor signál $X=W+\\theta$, kde $\\theta>0$ je neznámá konstanta. Po 35 pozorováních jsme určili konfidenční intervaly pro $\\mu=\\mathrm{E} X$ jako**\n",
    "\n",
    "- **90% konfidenční interval: $(0.405, 5.394)$,**\n",
    "- **95% konfidenční interval: $(-0.072, 5.872)$.**\n",
    "\n",
    "**Zvolte nulovou hypotézu $H_0$ a alternativní hypotézu $H_A$, chceme-li otestovat přítomnost pohybu v učebně.**\n",
    "\n",
    "**S touto volbou proveďte testování tak, aby pravděpodobnost chyby prvního druhu byla:**\n",
    "\n",
    "**a) 5%,**\n",
    "\n",
    "**b) 2.5%.**\n",
    "\n",
    "Postup bude stejný jako v předchozím případě, jen musíme najít dvě neznámé - průměr $\\bar{X}_n$ a směrodatnou odchylku $\\sigma$. Je více způsobů, jak to udělat. Buď\n",
    "\n",
    "- vyjádříme horní a dolní mez jednoho z intervalů příslušnou rovnicí a dostaneme 2 rovnice pro 2 neznámé.\n",
    "- jednodušší: uvědomíme si, kde leží průměr v intervalu spolehlivosti a jak velká je vzdálenost od něj ke kraji intervalu. Zkuste sami :)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Průměr: 2.899\n",
      "Směrodatná odchylka: 8.972\n"
     ]
    }
   ],
   "source": [
    "n = 35\n",
    "l = 0.405 #-0.072 \n",
    "u = 5.394 #5.872\n",
    "alpha = 0.1\n",
    "\n",
    "delta = (u - l)/2\n",
    "Xn = l + delta\n",
    "\n",
    "kriticka_hodnota = norm.isf(alpha/2)\n",
    "s = delta * np.sqrt(n) / kriticka_hodnota\n",
    "\n",
    "print('Průměr: {0:.3f}'.format(Xn))\n",
    "print('Směrodatná odchylka: {0:.3f}'.format(s))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A můžeme testovat. Má-li být v učebně pohyb, bude alternativní hypotéza $H_A: \\mu > 0$. Test bude pravostranný, stejně jako interval spolehlivosti."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pravostranný 95% IS:  [0.405   inf]\n",
      "Pravostranný 97.5% IS:  [-0.073    inf]\n"
     ]
    }
   ],
   "source": [
    "kriticka_hodnota_0_05 = norm.isf(0.05)\n",
    "kriticka_hodnota_0_025 = norm.isf(0.025)\n",
    "\n",
    "delta_0_05 = kriticka_hodnota_0_05 * s / np.sqrt(n)\n",
    "delta_0_025 = kriticka_hodnota_0_025 * s / np.sqrt(n)\n",
    "\n",
    "ISpravy_0_05 = np.array([Xn - delta_0_05, np.inf])\n",
    "ISpravy_0_025 = np.array([Xn - delta_0_025, np.inf])\n",
    "\n",
    "print('Pravostranný 95% IS: ', ISpravy_0_05)\n",
    "print('Pravostranný 97.5% IS: ', ISpravy_0_025)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Na hladině 5% nulovou hypotézu zamítneme, neboť testovaná hodnota do intervalu nepatří. Na hladině 2.5% ji ale nezamítáme."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Příklad 11.5\n",
    "\n",
    "**Servírovaný objem nápoje dle jídelního lístku by měl být 0.5 litru. Provedli jsme měření na deseti vzorcích a získali jsme data:**\n",
    "\n",
    "    0.510; 0.462; 0.491; 0.466; 0.451; 0.503; 0.475; 0.487; 0.512; 0.505.\n",
    "\n",
    "**Otestujte, zda je míra dodržena, nebo zda nás obsluha šidí.**\n",
    "  \n",
    "**a)** $\\alpha=5\\%$,\n",
    "\n",
    "**b)** $\\alpha=1\\%$.\n",
    "\n",
    "\n",
    "V obou případech budeme testovat\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "&H_0: \\mu = 0.5 \\\\\n",
    "&H_A: \\mu < 0.5.\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "Spočítáme průměr a rozptyl a použijeme levostranný interval spolehlivosti pro $\\mu$ na příslušných hladinách 0.05 a 0.01:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Průměr: 0.486\n",
      "Výběrová směrodatná odchylka: 0.021\n",
      "Levostranný IS:  [ -inf 0.498]\n"
     ]
    }
   ],
   "source": [
    "Xi = np.array([0.510, 0.462, 0.491, 0.466, 0.451, 0.503, 0.475, 0.487, 0.512, 0.505])\n",
    "mean_x = Xi.mean()\n",
    "s = Xi.std()\n",
    "n = Xi.size\n",
    "\n",
    "alpha = 0.05\n",
    "\n",
    "kriticka_hodnota = t.isf(alpha, df=n-1)\n",
    "delta = kriticka_hodnota * s / np.sqrt(n)\n",
    "ISlevy = np.array([-np.inf, mean_x + delta])\n",
    "\n",
    "print('Průměr: {0:.3f}'.format(mean_x))\n",
    "print('Výběrová směrodatná odchylka: {0:.3f}'.format(s))\n",
    "print('Levostranný IS: ', ISlevy)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Na hladině 5% tedy $H_0$ zamítneme se závěrem, že nás obsluha šidí, neboť testovaná hodnota $\\mu_0 = 0.5$ neleží v přislušném levostranném intervalu spolehlivosti. Zkusíme ještě hladinu 1%:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Levostranný IS:  [ -inf 0.505]\n"
     ]
    }
   ],
   "source": [
    "alpha = 0.01\n",
    "\n",
    "kriticka_hodnota = t.isf(alpha, df=n-1)\n",
    "delta = kriticka_hodnota * s / np.sqrt(n)\n",
    "ISlevy = np.array([-np.inf, mean_x + delta])\n",
    "\n",
    "print('Levostranný IS: ', ISlevy)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Na hladině 1% je interval spolehlivosti širší a pokrývá testovanou hodnotu $\\mu_0 = 0.5$.\n",
    "\n",
    "Abychom to uzavřeli:\n",
    "\n",
    "- jsme-li s pravděpodobností 5% ochotni připustit chybné zamítnutí $H_0$, pak tuto hypotézu opravdu zamítneme.\n",
    "- jsme-li ochotni se chybného zamítnutí $H_0$ dopustit pouze s pravděpodobností 1%, pak hypotézu o správné míře nezamítneme. **Tím ale současně neříkáme vůbec nic o její platnosti či platnosti alternativy!**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Hacky aby se centrovaly buňky tabulky..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
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       "var marked = require('components/marked/lib/marked');\n",
       "\n",
       "if (marked.Renderer.name !== 'NonExtensibleTableRenderer') {\n",
       "    function tablecell(content, flags) {\n",
       "        var type = flags.header ? 'th' : 'td';\n",
       "        var style = flags.align == null ? '' : ' style=\"text-align: ' + flags.align + '\"';\n",
       "        var start_tag = '<' + type + style + '>';\n",
       "        var end_tag = '</' + type + '>\\n';\n",
       "        return start_tag + content + end_tag;\n",
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       "\n",
       "    var DefaultRenderer = marked.Renderer;\n",
       "    function NonExtensibleTableRenderer(options) {\n",
       "        DefaultRenderer.call(this, options);\n",
       "        Object.defineProperty(this, 'tablecell', {\n",
       "            get: function () { return tablecell; },\n",
       "            set: function () { } // No-op, sorry for this hack but we must prevent it from being redefined\n",
       "        });\n",
       "    }\n",
       "    NonExtensibleTableRenderer.prototype = Object.create(DefaultRenderer.prototype);\n",
       "    NonExtensibleTableRenderer.prototype.constructor = NonExtensibleTableRenderer;\n",
       "\n",
       "    marked.setOptions({\n",
       "        renderer: new NonExtensibleTableRenderer()\n",
       "    });\n",
       "    // Look away... it has to be done as newer versions of the notebook build a custom\n",
       "    // renderer rather than extending the default.\n",
       "    marked.Renderer = NonExtensibleTableRenderer;\n",
       "}\n",
       "\n",
       "var Jupyter = require('base/js/namespace');\n",
       "Jupyter.notebook.get_cells()\n",
       "   .filter(cell => cell.cell_type === 'markdown' && cell.rendered)\n",
       "   .forEach(mdcell => {\n",
       "       mdcell.unrender();\n",
       "       mdcell.render();\n",
       "   });"
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   "source": [
    "%%javascript\n",
    "var marked = require('components/marked/lib/marked');\n",
    "\n",
    "if (marked.Renderer.name !== 'NonExtensibleTableRenderer') {\n",
    "    function tablecell(content, flags) {\n",
    "        var type = flags.header ? 'th' : 'td';\n",
    "        var style = flags.align == null ? '' : ' style=\"text-align: ' + flags.align + '\"';\n",
    "        var start_tag = '<' + type + style + '>';\n",
    "        var end_tag = '</' + type + '>\\n';\n",
    "        return start_tag + content + end_tag;\n",
    "    }\n",
    "\n",
    "    var DefaultRenderer = marked.Renderer;\n",
    "    function NonExtensibleTableRenderer(options) {\n",
    "        DefaultRenderer.call(this, options);\n",
    "        Object.defineProperty(this, 'tablecell', {\n",
    "            get: function () { return tablecell; },\n",
    "            set: function () { } // No-op, sorry for this hack but we must prevent it from being redefined\n",
    "        });\n",
    "    }\n",
    "    NonExtensibleTableRenderer.prototype = Object.create(DefaultRenderer.prototype);\n",
    "    NonExtensibleTableRenderer.prototype.constructor = NonExtensibleTableRenderer;\n",
    "\n",
    "    marked.setOptions({\n",
    "        renderer: new NonExtensibleTableRenderer()\n",
    "    });\n",
    "    // Look away... it has to be done as newer versions of the notebook build a custom\n",
    "    // renderer rather than extending the default.\n",
    "    marked.Renderer = NonExtensibleTableRenderer;\n",
    "}\n",
    "\n",
    "var Jupyter = require('base/js/namespace');\n",
    "Jupyter.notebook.get_cells()\n",
    "   .filter(cell => cell.cell_type === 'markdown' && cell.rendered)\n",
    "   .forEach(mdcell => {\n",
    "       mdcell.unrender();\n",
    "       mdcell.render();\n",
    "   });"
   ]
  }
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