{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Testování hypotéz\n",
    "============\n",
    "\n",
    "Z předchozího měření (nebo teorie) činíme hypotézu o hodnotě neznámého parametru $\\theta_0$ (**odhad** $\\hat\\theta_0 \\pm \\delta$ s pravděp. obsahem *p*)\n",
    ", ev. o rozdělení měřených hodnot. Následující měření umožní **test** hypotézy *H0*:\n",
    "\n",
    "měření dává statistiku $t(y_1,y_2,..,y_N)$, úkolem je stanovit, jaká je pravděpodobnost \n",
    "pozorování $t$ za předpokladu platnosti/neplatnosti *H0* \n",
    "\n",
    "určujeme tedy, s jakym rizikem nastane jedna ze 2 možných chyb\n",
    "\n",
    "- chyba 1. druhu = hypotéza platí, ale _H0_ zamítneme: $P(t \\in K | H_0)=\\alpha$\n",
    "- chyba 2. druhu = hypotéza neplatí, ale _H0_ přijmeme: $P(t \\notin K | \\mathrm{not} H_0)=\\beta$ \n",
    "\n",
    "kde *K* je kritická oblast \"nepřijatelných\" hodnot $t$ (pokud $t$ zde leží, můžeme *H0* **zamítnout na hladině významnosti** $\\alpha$ - jinak je naše statistika nedostatečná a vyžaduje další měření). Pravděpodobnost $1-\\beta$ je pak **síla (mohutnost) testu** (závisí na $\\alpha$)...\n",
    "\n",
    "> pokud _H0_ neplatí (platí alternativa _H1_, pokud je jediná)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0xb0112a0c>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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d1K2pzHjYPkv2VWXL8S1MXDCR3Y85cV4GO9BL9rkWvWSfVmtG1t/L+PlZnqBdv96+51VK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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xb02a666c>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "M,N=12,10 #velikosti vzorků\n",
    "mu=2.\n",
    "sig=1\n",
    "from matplotlib.pyplot import *\n",
    "from scipy import stats\n",
    "from numpy import r_\n",
    "x=r_[-3:8:0.01]\n",
    "hyp0=stats.t(M+N-2,loc=0)\n",
    "hyp1=stats.t(M+N-2,loc=mu)\n",
    "y1=hyp0.pdf(x)\n",
    "y2=hyp1.pdf(x)\n",
    "plot(x,y1)\n",
    "plot(x,y2)\n",
    "prob=0.05\n",
    "pos=hyp0.ppf(1-prob) # hodnoty mensi nez tato \n",
    "axvline(pos,color='r')\n",
    "fill([pos]+list(x[x>pos]),[0]+list(y1[x>pos]),'b',alpha=0.4,hold=1)\n",
    "fill(list(x[x<pos])+[pos],list(y2[x<pos])+[0],'g',alpha=0.4,hold=1)\n",
    "legend([\"H0 - nul.\",\"H1\",\"prob %.2f\"%prob,\"alpha\",\"beta\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Neyman-Pearsonův test\n",
    "\n",
    "Volba kritické oblasti podle poměru $f_N(X|\\theta_1)/f_N(X|\\theta_0) \\gt c_\\alpha$, hodnota $c_\\alpha$ zvolena podle dané hladiny významnosti; v principu jde o poměr věrohodností.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.8644910008005713"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "-np.log(0.1)*0.1+2.4\n",
    "np.log(0.05)/np.log(0.6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test dobré shody\n",
    "\n",
    "určení stupně shody získaných dat s hypotézou o jejich rozdělení\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Pearsonův test\n",
    "\n",
    "z naměřených hodnot sestavíme histogram o *K* buňkách, do každé z nich padne $n_i$ z měřených hodnot ($\\sum n_i = N$). Hypotéza H0 stanoví distrib. funkci rozdělení F, tedy pro každou buňku pravděpodobnost $p_i=P[x \\in \\lt l_i,m_i)]=F(m_i)-F(l_i)$, kde $l_i, m_i$ jsou hranice i-té buňky (obvykle $l_i=m_{i-1}$). Náhodné proměnné $n_i$ mají binomické rozdělení a očekávanou hodnotu $E(n_i)=N p_i$.\n",
    "\n",
    "**Pearsonova statistika**\n",
    "\n",
    "$$T=\\sum_i^k \\frac{(n_i-N p_i)^2}{N p_i} =  \\frac{1}{N} \\sum_i^k \\left( \\frac{n_i^2}{p_i} - 2 n_iN + N^2 p_i \\right) = \\frac{1}{N} \\sum_i^k \\frac{n_i^2}{p_i} - N$$\n",
    "\n",
    "v limitě $N \\to \\infty$ (kdy rozdělení $n_i$ se blíží normálnímu) má $T$ rozdělení $\\chi_{K-1}^2$ (Pearsonova věta).\n",
    "\n",
    "Podmínkou je malé množství buňek, kde není dostatečné množství měřených hodnot (lze řešit úpravou mezí buňek / slučováním tak, aby $p_i$ byly vyrovnané).\n",
    "\n",
    "Rozdělení může být závislé na parametrech $\\theta_1, ..., \\theta_r$ - pak hledáme hodnotu $\\mathbf{\\theta}$ dávající nejlepší shodu, testovaná statistika má rozdělení s méně stupni volnosti, někde mezi $\\chi_{K-1}^2$ a $\\chi_{K-r-1}^2$ (rozdíl je malý, pokud $K \\gg r$).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0xaf70c4ec>]"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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JBpOZ+S/y8xeQKh809RmEY6dWn6V+dr/5Bh57DJ5+et9mZEtow0PcwgQuYTdV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\nJXcRkQD6f5y8qylj+1FgAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xafbc3a8c>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy import stats\n",
    "import numpy as np\n",
    "%matplotlib inline\n",
    "from matplotlib import pyplot as pl\n",
    "\n",
    "N=1000\n",
    "dx=0.5\n",
    "dset=stats.chi2(5).rvs(N)\n",
    "x=np.r_[0:15:dx]\n",
    "ok=pl.hist(dset,x)\n",
    "pred=stats.chi2(5).pdf(x+0.25)\n",
    "pl.plot(x+0.25,pred*N*dx,'r',lw=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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p9Sywf77jPXmf2mzXyewK4CN3/1VTr1dVVVFaWgpASUkJZWVlVFRUANv+Iot1v7q6Ou/2\ne+8NEybkGD8eli6toFevuPIX477ya7+77OdyOWbMmAHwyc/LNAqdkygHrnL3ymR/MlDn7lMbtJkG\n5Nx9VrJfAxwLDGmpr5lVAecCo9x9cxOf3S3mJOq5Q2UlVFTA5MlZpxGRWHX2nMRzwFAzKzWz3sB4\nYHajNrOBM5Nw5cAmd1/fUl8zqwT+BRjXVIHojsxg+vRwpdOyZVmnEZHuoqAi4e5bgUnA48ArwH3J\n1UkTzWxi0mYO8JqZrQCmA+e11Dd565uBPsB8M3vRzG4pJGcxqj8dTKO0FP71X+Hcc6GurtXmHaot\n+YuJ8mcn5uwQf/60Cp2TwN3nAnMbHZveaH9Svn2T40MLzdVVTZoE994Lt90G3/te1mlEpKvT2k0R\nWrIkzE1UV4flO0RE8qW1m7qB4cPh/PPhvPPChLaISEdRkchIoeOakyfDihXwwAPtkyet2MdllT87\nMWeH+POnpSIRqR13hDvugAsvhLffzjqNiHRVmpOI3IUXwp//HJ5kJyLSmrRzEioSkXv/fRgxIlzt\n9KUvZZ1GRIqdJq4j0V7jmn36wLRpMHFiKBidJfZxWeXPTszZIf78aalIdAGVlfCFL4Qb7URE2pOG\nm7qIjRvDsNNvfgNHHpl1GhEpVhpu6qY+8xm4/no45xz46KOs04hIV6EikZGOGNc8/XT47Gdh6tTW\n2xYq9nFZ5c9OzNkh/vxpqUh0IWZw661w003wyitZpxGRrkBzEl3Q7beHQvHss7DbblmnEZFiovsk\nBPdwSeyGDfDww7CDzhdFJKGJ60h05LimGfzsZ2G5jiuv7JjPiH1cVvmzE3N2iD9/WioSXVTv3vDQ\nQ3D33XD//VmnEZFYabipi6uuhhNOgHnzYOTIrNOISNY03CTbKSuDW26Br34V1q/POo2IxEZFIiOd\nOa556qlw1llw8sntd6Nd7OOyyp+dmLND/PnTUpHoJq66CvbaS0+zE5F0NCfRjbz/Phx1FHz3u3DB\nBVmnEZEspJ2T6NmRYaS49OkDs2eHQnHQQTBqVNaJRKTYabgpI1mNaw4ZArNmwTe+AX/6U9vfJ/Zx\nWeXPTszZIf78aRVcJMys0sxqzGy5mV3WTJubktcXm9nI1vqa2almtsTMPjazQwvNKNurqAg32Y0d\nC++9l3UaESlmBc1JmFkPYBkwGqgFFgFnuPvSBm3GAJPcfYyZHQnc6O7lLfU1s2FAHTAduMTdX2ji\nszUnUQB3+P73Yc0aeOQRLd0h0l109n0SRwAr3H2lu28BZgHjGrUZC9wF4O4LgRIz69dSX3evcfdX\nC8wmLTALiwBu2qQn2olI8wotEgOBVQ32VyfH8mkzII++XVYxjGvWL90xcybcdVe6vsWQvxDKn52Y\ns0P8+dMq9OqmfMd78j61SaOqqorS0lIASkpKKCsro6KiAtj2F1ms+9XV1UWTZ84c+OIXcyxdClOm\nxJe/LfvKr/3usp/L5ZgxYwbAJz8v0yh0TqIcuMrdK5P9yUCdu09t0GYakHP3Wcl+DXAsMCSPvgvQ\nnESnqKmB0aPhRz+C73wn6zQi0lE6e07iOWComZWaWW9gPDC7UZvZwJlJuHJgk7uvz7MvdNBZiGxv\n2DBYsCAUiWnTsk4jIsWioCLh7luBScDjwCvAfcnVSRPNbGLSZg7wmpmtIFytdF5LfQHM7Gtmtgoo\nBx41s7mF5CxG9aeDxWToUMjlYMqU8DyKlhRj/jSUPzsxZ4f486dV8B3X7j4XmNvo2PRG+5Py7Zsc\n/zXw60KzSXr77hsKxfHHw5YtcNFFWScSkSxp7SZp0qpVoVCcey5cemnWaUSkvWjtJmkXgwdvf0Zx\nxRVZJxKRLOg+24zEMK45cGAoFDNnhgnthiduMeRvifJnJ+bsEH/+tHQmIS3q3z9c9TR6dDijuPrq\ncLe2iHQPmpOQvLz1VigUlZXh6icVCpE46RnX0iH22gueegrmz4dLLtHT7US6CxWJjMQ4rrnnnvDk\nk/DMM3DiiTk2b846UdvF+P1vKOb8MWeH+POnpSIhqey+ezij+OADOPZYqK3NOpGIdCTNSUibuG+7\nM/v+++GYY7JOJCL5SDsnoSIhBZk7F846K1z1NHFi1mlEpDWauI5E7OOa9flPPBF+/3u48cZQJD78\nMNtc+eoq3/8YxZwd4s+floqEFGzoUFi4EDZsgOOOg7Vrs04kIu1Fw03Sburq4Mc/hunT4cEHobw8\n60Qi0pjmJCRzv/1teHDRNdfoAUYixUZzEpGIfVyzpfxf+Qo8/TRcdx2cfz589FHn5cpXV/7+F7uY\ns0P8+dNSkZAOccABYZ5i1SoYNUrzFCKx0nCTdKi6Ovj3f4ef/xyuvx7OOEPrPolkSXMSUpSeew6q\nqsKVULfeCv36ZZ1IpHvSnEQkYh/XTJv/sMPg+efhoIPgkEPg3nuzXSSwu33/i0nM2SH+/GmpSEin\n2XHHcInso4+GIaiTT4b167NOJSIt0XCTZOLDD8PT7n7xC7jhBhg/XnMVIp1BcxISlT/8IcxVHHhg\nmKvYe++sE4l0bZqTiETs45rtlf+II+CFF8KE9uc/H1aU7Qz6/mcn5uwQf/60Ci4SZlZpZjVmttzM\nLmumzU3J64vNbGRrfc1sDzObb2avmtk8MyspNKcUr512CsuO/+Y3cOWVcOqpsG5d1qlEBAocbjKz\nHsAyYDRQCywCznD3pQ3ajAEmufsYMzsSuNHdy1vqa2bXAhvd/dqkeOzu7pc3+mwNN3VBmzeHuYrb\nb4eLL4aLLoKdd846lUjX0dnDTUcAK9x9pbtvAWYB4xq1GQvcBeDuC4ESM+vXSt9P+iR/frXAnBKJ\nnXYKaz4tXBgumR02LPvLZUW6s0KLxEBgVYP91cmxfNoMaKFvX3evvzhyPdC3wJxFJ/ZxzY7Ov99+\n8NBDcM898JOfwNFHw//8T/u9v77/2Yk5O8SfP62eBfbP9/e7fE5trKn3c3c3syY/p6qqitLSUgBK\nSkooKyujoqIC2PYXWaz71dXVRZWnmPMvWgRXXJFj7FgYPbqCKVPg9dfjyd8R+7Hn137n7edyOWbM\nmAHwyc/LNAqdkygHrnL3ymR/MlDn7lMbtJkG5Nx9VrJfAxwLDGmub9Kmwt3XmVl/YIG7D2v02ZqT\n6Gb++tewsuzNN4en4F1+OXzqU1mnEolLZ89JPAcMNbNSM+sNjAdmN2ozGzgzCVcObEqGklrqOxs4\nK/n6LOCRAnNKF7DrrnDVVfDSS1BbG1aavf12+PjjrJOJdF0FFQl33wpMAh4HXgHuS65OmmhmE5M2\nc4DXzGwFMB04r6W+yVtPAU4ws1eB45P9LqX+dDBWWeYfOBDuuis83Oiee2DkyPB1mhNLff+zE3N2\niD9/WoXOSeDuc4G5jY5Nb7Q/Kd++yfF3CJfGijTrsMPgd7+DRx6Bf/s3+OEP4YorwppQPXpknU6k\na9CyHNIluMOcOWHhwHffhR/8IDy7olevrJOJFBet3STdmjssWBCKxeuvh8ntqqqwAq2IaO2maMQ+\nrlms+c3g+OPhqadg5kyYPTvcc3HDDfC3v21rV6z58xVz/pizQ/z501KRkC7r6KPDsytmz4ann4Z9\n9w1rRL33XtbJROKh4SbpNpYsCUt+PP44nH02fP/7MGRI1qlEOpeGm0SaMXw4/Od/hnWh6urg8MPh\npJNg7tywLyJ/T0UiI7GPa8acf9994aSTcrz5Jnz96+HS2f33h5/+FN55J+t0+Yn5+x9zdog/f1oq\nEtJt7bILTJgAzz0XzjCqq8Mk94QJYQVaEdGchMh2NmyAO++EadOgf384//zwEKSddso6mUj70H0S\nIu3g44/hv/4Lfv5zWLwYvvENOPNMKCsLl9mKxEoT15GIfVyzq+fv0QPGjYN58+CZZ6BPnzB/cfDB\nMHUqrF7dOTmbE/P3P+bsEH/+tFQkRFoxdChcfTX86U9w662wYgV8/vMwejTcfTe8/37WCUU6joab\nRNrggw+2rUL79NPwla/At78No0ZpcUEpbpqTEOlkGzbArFmhYNTWhvmL8ePDKrWav5BiozmJSMQ+\nrqn82+y9N/zTP8GiRfDkk+FKqG9/Gz77WbjwwrCceXs/GCnm73/M2SH+/GmpSIi0owMPDCvQLl0K\njz0Ge+0FF10EAwbAd78bjn30UdYpRfKn4SaRTvDaa/DrX8PDD4cC8uUvh6ul/vEfw019Ip1FcxIi\nRW7NmvA0vYcfDkNUo0eHNaQqK8MNfCIdSXMSkYh9XFP5227AADjvPHjiiXCG8ZWvhEUGhw8Pz+ue\nPBn++79hy5bm3yPm73/M2SH+/GmpSIhkaM89w5Pz7r8/XCX1s5+FS2gvuihMiJ9ySlgmpLY266TS\nXWm4SaRIrVsXnn0xdy7Mnw+DBsGJJ4btqKOgd++sE0qMNCch0gVt3Qp/+EMoGI89BjU1UF4Oxx0X\ntsMOg169sk4pMdCcRCRiH9dU/s7Vs2d4HOvVV4fJ7nvvzXHBBfDWW+EJe5/5TDjDuO66sPR5e9+X\n0Z5i+943Fnv+tNpcJMxsDzObb2avmtk8Mytppl2lmdWY2XIzu6y1/snxBWb2FzO7ua35RLqyPn1g\n7Fi4/vrwHIzXXoNzz4U33oCzzgpFo+HrxVw0pLi1ebjJzK4FNrr7tckP/93d/fJGbXoAy4DRQC2w\nCDjD3Zc219/MdgFGAiOAEe5+QTOfr+EmkWasXw+5HCxYELZ168Lw1NFHwzHHwJFHwm67ZZ1SstBp\ncxJmVgMc6+7rzawfkHP3YY3aHAVc6e6Vyf7lAO4+pbX+ZlYF/IOKhEjhNm6EZ58N2+9/Dy++GFa3\nrS8aRx8dlhHRWlNdX2fOSfR19/XJ1+uBvk20GQisarC/OjmWT/8uXQFiH9dU/mylzV8//DRlSli1\n9p13wrLn++0HDz0UzjIGDQpP4bv++lBI/va34shebGLPn1bPll40s/lAvyZeuqLhjru7mTX1Q73x\nMWviWEv9W1RVVUVpaSkAJSUllJWVUVFRAWz7iyzW/erq6qLKo/zFla+j8z/7bNi/+OIKLr4YFizI\nsXYt1NVV8OyzMG1ajpUrYdiwCg4/HD71qRwHHABnn11B797Z//drP//9XC7HjBkzAD75eZlGocNN\nFe6+zsz6AwuaGG4qB65qMNw0Gahz96mt9Tezs4DDNNwkko0PP4SXXgpXU9Vvr78OI0bA4YeHy24P\nPxyGDdMzNGLSmXMS1wJvJz/wLwdKmpi47kmYuB4FrAH+wPYT183215yESPF5/3144YVwmW194Vi/\nPjypr6xs2zZiBOy8c9ZppSmdWST2AO4H9gFWAqe5+yYzGwDc7u5fTtqdCNwA9ADudPdrWuqfvLYS\n2A3oDbwLfMndaxp9ftRFIpfLfXJqGCPlz1Yx5X/3XVi8OFxqW78tWwb77rt94SgrC0unF1P2tog9\nf9oi0eKcREvc/R3Cpa2Nj68Bvtxgfy4wN9/+yWulbc0lIp1r992hoiJs9T78MCyJXl80Hn00/Lnr\nrmGCvKIiLGg4YkR4BofOOoqXluUQkU7hHm72q66GJUvC9vLLsHw5DB68rWiMGBG+3n9/rU/VEbR2\nk4hEZcuWUCjqi0b99uab4RLd4cPD5Hj9tv/+4YxE2kZFIhKxj2sqf7Zizp9v9s2bw0KGS5aEP+u3\nFSugb9/tC0f91rdvx98QGPP3HjpxTkJEpCPttNO2Ce+GPv4YVq7cVjSefx5mzgxfb9kCBxwQ7iav\n3z73ufDn7rtn8p8RPZ1JiEiXsXFjuLJqxYowhNVw23HH7YtGwyJS0uTypF2ThptERBpxD0/+a1w4\nVqwIW69e4ZLdprbBg7vWszpUJCIR+7im8mcr5vzFlt09nIG89lrT27p1MHDgtqLhnuO44yooLQ2L\nIvbvDztE9GQezUmIiKRgFm7y22uvsIR6Yx99FK60qi8auRz85jfhct6VK2HTpnDvx2c/yyeFo+HX\ngwaFh0bFSmcSIiIF+OADWLUqFIw33thWPOq/XrcO9t47DFs1t/Xt23lnIxpuEhEpIlu2wNq1oZC8\n+Wb4s/H25z/DgAHbisbAgX+/9e/fPnMjKhKRKLZx2bSUP1sx5485O3RM/s2bYfXqbUWjtvbvt7fe\ngj32CMMUX3p/AAAF3ElEQVRXDYvHgAFh698/bHvu2fJZieYkREQis9NO4VLcz32u+TZbt4YVdxsX\nj1wunKnUb++9F4avGhaO+m3AgPTZdCYhItKFfPhhmAepLxpr1mxfRObO1XCTiIg0ozOfcS0FqH+8\nYKyUP1sx5485O8SfPy0VCRERaZaGm0REuhENN4mISLtRkchI7OOayp+tmPPHnB3iz5+WioSIiDRL\ncxIiIt2I5iRERKTdtLlImNkeZjbfzF41s3lm1uSzncys0sxqzGy5mV3WWn8zO8HMnjOzl5I/j2tr\nxmIW+7im8mcr5vwxZ4f486dVyJnE5cB8d98feDLZ346Z9QB+BlQCBwFnmNmBrfR/CzjJ3T8PnAXc\nU0DGolVdXZ11hIIof7Zizh9zdog/f1qFFImxwF3J13cBX22izRHACndf6e5bgFnAuJb6u3u1u69L\njr8C7GxmXejhgcGmTZuyjlAQ5c9WzPljzg7x50+rkCLR193XJ1+vB/o20WYgsKrB/urkWL79Twae\nTwqMiIh0shaXCjez+UC/Jl66ouGOu7uZNXWpUeNj1sSxJvub2XBgCnBCSxljtXLlyqwjFET5sxVz\n/pizQ/z5U3P3Nm1ADdAv+bo/UNNEm3LgsQb7k4HLWusPDAKWAUe18PmuTZs2bdrSb2l+1hfy0KHZ\nhInlqcmfjzTR5jlgqJmVAmuA8cAZLfVPrnJ6lFBM/qe5D09zna+IiLRNm2+mM7M9gPuBfYCVwGnu\nvsnMBgC3u/uXk3YnAjcAPYA73f2aVvr/kHCl0/IGH3eCu29sU1AREWmzaO+4FhGRjhflHdfN3aAX\nAzMbbGYLzGyJmb1sZv+Udaa0zKyHmb1oZr/NOktaZlZiZg+a2VIze8XMyrPOlIaZTU7+3/mjmf3K\nzHbMOlNLzOwXZrbezP7Y4FheN+IWg2byX5f8/7PYzB42s09nmbElTeVv8NolZlaXjOo0K7oi0coN\nejHYAlzk7sMJE/vnR5Yf4ELCPSwxnobeCMxx9wOBzwNLM86Tt2Ru71zgUHc/mDCEe3qWmfLwS8K/\n1YZavRG3iDSVfx4w3N0PAV4lXJBTrJrKj5kNJlw5+kZrbxBdkaDlG/SKnruvc/fq5Ov3CT+kBmSb\nKn9mNggYA9xBuKQ5GslvfP/H3X8B4O5b3f3PGcdK4z3CLxm7mFlPYBegNttILXP3p4F3Gx3O50bc\notBUfnef7+51ye5CwtWYRamZ7z/AfwCX5vMeMRaJlm7Qi0rym+FIwv9osbge+BegrrWGRWgI8JaZ\n/dLMXjCz281sl6xD5cvd3wF+CrxJuFpwk7s/kW2qNsnnRtpYTADmZB0iDTMbB6x295fyaR9jkYhx\niOPvmFkf4EHgwuSMouiZ2UnABnd/kcjOIhI9gUOBW9z9UOCvFPdQx3bMbD/g/wKlhLPPPmb2zUxD\nFShZ7z/Kf9NmdgXwkbv/Kuss+Up+KfoBcGXDwy31ibFI1AKDG+wPJpxNRCNZi+oh4D/dvan7S4rV\n0cBYM3sduBc43szuzjhTGqsJv0EtSvYfJBSNWBwGPOvub7v7VuBhwt9JbNabWT8AM+sPbMg4T2pm\nVkUYdo2tSO9H+CVjcfLveBDwvJnt3VyHGIvEJzfomVlvwg16szPOlDczM+BO4BV3vyHrPGm4+w/c\nfbC7DyFMmD7l7mdmnStfycKRq8xs/+TQaGBJhpHSqgHKzWzn5P+j0YQLCGJTfyMtNH8jbtEys0rC\nkOs4d9+cdZ403P2P7t7X3Yck/45XEy6EaLZQR1ckkt+gJgGPE/6B3Ofu0VyhAhwDfAs4LrmM9MXk\nf7oYxThMcAEw08wWE65u+n8Z58mbuy8G7ib8olQ/nnxbdolaZ2b3As8CB5jZKjM7m2RNNjN7FTg+\n2S9KTeSfANwM9AHmJ/9+b8k0ZAsa5N+/wfe/oVb/DetmOhERaVZ0ZxIiItJ5VCRERKRZKhIiItIs\nFQkREWmWioSIiDRLRUJERJqlIiEiIs1SkRARkWb9f7g0IYfIKrWwAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xaf5f44cc>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cumpred=stats.chi2(5).cdf(x)\n",
    "pred2=cumpred[1:]-cumpred[:-1]\n",
    "pl.plot(x[1:-1],pred[1:-1]*dx/pred2[1:]-1)\n",
    "pl.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(31.590190917491448, array([ 37.91592254,  41.33713815,  48.27823577]))"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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731nzGIcrqbbtAQaAQWAoWR5P/qtlLWtZy728PA6MJssV4D/jbcxdk1VPfj7wYpJoATrx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\nP587KrKOaGWeAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xaf6222cc>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "resid=ok[0]-pred[:-1]*N*dx\n",
    "pl.plot(x[:-1]+dx/2.,resid,'d')\n",
    "pl.axhline(0)\n",
    "pl.grid()\n",
    "sum(resid**2./(pred[:-1]*N*dx)),stats.chi2(len(ok[0])-1).isf([0.1,0.05,0.01])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(155.49945566272714, 149.73151462190449)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def testN(ndf,dat,dx=0.5):\n",
    "    pred=stats.chi2(ndf).pdf(x[:len(dat)]+dx/2.)\n",
    "    return sum((dat-pred*sum(dat)*dx)**2./(pred*sum(dat)*dx))\n",
    "testN(4,ok[0]),testN(6,ok[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "nulovou hypotézu (teor. křivka a histogram se neliší) nemůžeme zamítnout ani na *hladině spolehlivosti* 90%."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Kolgomorův test\n",
    "\n",
    "sestavení distribuční funkce z *N* naměřených dat $S_N(X)$ = (počet měření<x) / *N*.\n",
    "\n",
    "statistika $D_N=\\max \\|S_N(x)-F(x)\\|$ pro velká *N* (>80) má rozdělení \n",
    "\n",
    "$$F_{Klg}(\\sqrt{N}D_N)=1-2 \\sum_j^\\infty (-1)^{j-1} \\exp(-2j^2 N D_N^2)$$\n",
    "\n",
    "H0 zamítáme s rizikem $\\alpha$, pokud vyšlo $\\sqrt{N}D_N > z_\\alpha$\n",
    "\n",
    "$\\alpha$|$z_\\alpha$ <br/>(Kolgomorov-Smirnovo rozdělení)\n",
    "-|-\n",
    "0.01 | 1.63\n",
    "0.05 | 1.36\n",
    "0.10 | 1.22\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.020252210725574704, 0.64043113546507324)"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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awGJn8SkAvKCUuqu1Xhl3Z506dcLPzw8Ab29vqlWrhr+/P3C/v2X18r11Vv38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\nJEXWAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xaf8129cc>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "edf=np.cumsum(ok[0])\n",
    "edf/=float(N)\n",
    "pred=stats.chi2(5).cdf(x[1:])\n",
    "pl.plot(x[1:]+0.25,edf,x[1:],pred)\n",
    "pl.grid()\n",
    "Dn=max(abs(edf-pred))\n",
    "Dn,Dn*np.sqrt(N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.72901387077572011, 0.25713257574053389)"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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dvbclecks6+lb14LG+abvVddunuO8z+c313He47Ob6xjv+jwuyQ1J7uz6fMd+2vUf61U1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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xb025694c>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "multest=np.array([max(abs(np.cumsum(np.histogram(stats.chi2(5).rvs(N),x)[0])/float(N)-pred)) for i in range(1000)])\n",
    "multest*=np.sqrt(N)\n",
    "pl.hist(multest,30)\n",
    "pl.axvline(1.22,color='r')\n",
    "pl.axvline(1.36,color='r')\n",
    "multest.mean(),multest.std()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.056000000000000001, 0.021999999999999999)"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(multest>1.22)/1000.,sum(multest>1.36)/1000.,\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Test homogenity\n",
    "============\n",
    "\n",
    "## rovnost rozdělení 2 vzorků dat"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Smirnovův test\n",
    "\n",
    "srovnáváme empirické dist. funkce $S_n$, $S_m$: statistika \n",
    "$D_{nm}=\\max \\|S_n(x)-S_m(x)\\|$ má asymptotické rozdělení jako v předchozím případě se \n",
    "$\\sqrt{nm/(n+m)}D_{nm} < z_\\alpha$  \n",
    "\n",
    "nebo jednostranné testy $D_{nm}^{\\pm}=\\max \\{\\pm (S_n(x)-S_m(x))\\}$\n",
    "má jednodušší rozdělení\n",
    "$K^\\pm(z)=\\lim P(\\sqrt{nm/(n+m)}D_{nm}^{\\pm} \\lt z_\\alpha)=1-\\exp(-2 z^2)$\n",
    "pro $n\\rightarrow\\infty, m\\rightarrow\\infty$\n",
    "\n",
    "úpravou vzniká"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Wayneův test\n",
    "\n",
    "$$W_{nm}=\\sqrt{nm/(n+m)}\\ \\max \\{ \\|S_n(x)-S_m(x)\\|/S_m(x) \\}$$ pro $x$ splňující $S(x)\\geq a$ (kde $a>0$ je konstanta) má rozdělení\n",
    "\n",
    "$$\\lim P(W_{nm}^{\\pm} \\lt z_\\alpha)=\\sqrt{\\frac{2}{\\pi}} \\int_0^{z\\sqrt{a/(1-a)}} \\exp\\left(\\frac{t^2}{2}\\right) dt$$ pro $z \\gt 0$.\n",
    "\n",
    "-------------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Wilcoxonův (-Mann-Whitney)  test\n",
    "\n",
    "2 vzorky spojíme, (n+m) čísel uspořádáme podle velikosti a určíme pořadí (pozice) čísel $x_1, .., x_n$ z první sady: jejich součet je $T_n$ a výraz\n",
    "$$U_0=\\frac{\\frac{nm + n(n+1)}{2}-T_n}{\\sqrt{\\frac{nm}{12}(n+m+1)}}$$ má rozdělení N(0,1).\n",
    "\n",
    "-------------------\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## rovnost středních hodnot\n",
    "předpokládáme normální rozdělení N($\\mu_x,\\sigma_x^2$), N($\\mu_y,\\sigma_y^2$)\n",
    "\n",
    "hypotéza H0: $\\mu_x=\\mu_y$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Studentův test\n",
    "\n",
    "testovací statistika\n",
    "$$t=\\frac{\\bar{x}-\\bar{y}}{\\sqrt{\\frac{\\left((n-1)\\widehat{\\sigma_x^2} + (m-1)\\widehat{\\sigma_y^2}\\right)(n+m)}{nm(n+m-2)}}}$$\n",
    "\n",
    "kde $\\bar{x}=\\sum_i{x_i}/n$, $\\widehat{\\sigma_x^2}=\\sum_i{(x_i-\\bar{x})^2}/(n-1)$ (resp. pro *y* a *m*)\n",
    "má Studentovo rozdělení s *n+m-2* stupni volnosti.\n",
    "\n",
    "Pozn.: Disperze rozdílu $\\Delta = \\bar{x} -\\bar{y}$ je odhadnuta jako $$\\widehat{\\sigma_{\\Delta}^2} = \\widehat{\\sigma_{\\bar{x}}^2} + \\widehat{\\sigma_{\\bar{y}}^2} = \\frac{n+m}{nm} \\widehat{\\sigma^2},$$ kde $$\\widehat{\\sigma^2} = \\frac{(n-1)\\widehat{\\sigma_x^2} + (m-1)\\widehat{\\sigma_y^2}}{n+m-2}$$ je společný odhad kombinující odhady disperze vzorků $\\widehat{\\sigma_x^2}$ a $\\widehat{\\sigma_y^2}$.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## rovnost disperzí"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fischerův test\n",
    "\n",
    "hypotéza H0: $\\sigma_x=\\sigma_y$\n",
    "\n",
    "statistika $F=\\widehat{\\sigma_x^2}/\\widehat{\\sigma_y^2}$ (definice viz výše) má [Fischer-Snedecorovo](mmzm_rozdeleni.ipynb/#fischer-snedecorovo_rozd+len+) rozdělení $F_{n-1,m-1}$     "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.3693434492264385, 2.0942743714793242)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from numpy import random\n",
    "N,M=20,30\n",
    "samp1=np.random.normal(3,1.,size=N)\n",
    "samp2=np.random.normal(3,1.4,size=M)\n",
    "sig1=sum((samp1-samp1.mean())**2)/(N-1)\n",
    "sig2=sum((samp2-samp2.mean())**2)/(M-1)\n",
    "sig1,sig2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 1.68490635,  1.95814552,  2.23127383,  2.59874401]),\n",
       " array([ 1.68490635,  1.95814552,  2.23127383,  2.59874401]),\n",
       " 0.65385102729361144)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.f(N-1,M-1).isf([0.1,0.05,0.025,0.01]),1/stats.f(M-1,N-1).ppf([0.1,0.05,0.025,0.01]),sig1/sig2"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}