statkclee/chap14soln.ipynb

## chap14soln.ipynb
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "통계적 사고 (2판) 연습문제 ([thinkstats2.com](thinkstats2.com), [think-stat.xwmooc.org](http://think-stat.xwmooc.org))<br>\n",
    "Allen Downey / 이광춘(xwMOOC)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "from __future__ import print_function, division\n",
    "\n",
    "import numpy as np\n",
    "import random\n",
    "\n",
    "import first\n",
    "import normal\n",
    "import thinkstats2\n",
    "import thinkplot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 연습문제 14.1\n",
    "\n",
    "5.4 절에서, 성인 체중분포는 근사적으로 로그정규분포임을 알아냈다.\n",
    "한가지 가능한 설명은 매년 성인이 느는 체중은 현재 체중에 비례한다는 것이다.\n",
    "이런 경우, 성인 체중은 많은 숫자의 복잡한 요인의 곱이 된다:\n",
    "\n",
    "\n",
    "$ w = w_0 f_1 f_2 ... f_n$\n",
    "\n",
    "\n",
    "여기서, $w$는 성인체중, $w_0$는 출생체중,\n",
    "$f_i$는 $i$ 년도에 대한 체중 증가 요인이다.\n",
    "\n",
    "\n",
    "곱에 대해 로그를 취하면, 요인에 로그를 취한 합으로 바뀐다:\n",
    "\n",
    "$log w = log w_0 + log f_1 + log f_2 + ... + log f_n$\n",
    "\n",
    "\n",
    "그래서, 중심극한정리에 의해서, \n",
    "$\\log w$의 분포는 근사적으로 큰 $n$에 대해 근사적으로 정규분포가 된다.\n",
    "이는 $w$의 분포가 로그정규분포라는 것을 함의를 갖는다.\n",
    "\n",
    "이런 현상을 모형화하는데, $f$에 대한 일리있어 보이는 분포를 고르고 나서,\n",
    "출생체중 분포로 부터 난수를 고르고, $f$ 분포로부터 요인 시퀀스를 고르고,\n",
    "곱을 계산함으로써 성인체중 표본을 생성한다.\n",
    "로그정규 분포로 수렴하는데 $n$ 값이 얼마나 필요할까?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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Dj6BHtzxGHtufkycci9frJS3NSjCbxNPgmYCI/Bd4D3gV+LTmDEBEugCnAVcDr6rqszEP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\naccsCRhjTDv2/wH9vSW7s70mIgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xae95428c>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.figure.Figure at 0xaf4defac>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def GenerateAdultWeight(birth_weights, n):\n",
    "    \"\"\"Generate a random adult weight by simulating annual gain.\n",
    "\n",
    "    birth_weights: sequence of birth weights in lbs\n",
    "    n: number of years to simulate\n",
    "\n",
    "    returns: adult weight in lbs\n",
    "    \"\"\"\n",
    "    bw = random.choice(birth_weights)\n",
    "    factors = np.random.normal(1.09, 0.03, n)\n",
    "    aw = bw * np.prod(factors)\n",
    "    return aw\n",
    "\n",
    "\n",
    "def PlotAdultWeights(live):\n",
    "    \"\"\"Makes a normal probability plot of log10 adult weight.\n",
    "\n",
    "    live: DataFrame of live births\n",
    "\n",
    "    \"\"\"\n",
    "    birth_weights = live.totalwgt_lb.dropna().values\n",
    "    aws = [GenerateAdultWeight(birth_weights, 40) for _ in range(1000)]\n",
    "    log_aws = np.log10(aws)\n",
    "    thinkstats2.NormalProbabilityPlot(log_aws)\n",
    "    thinkplot.Show(xlabel='standard normal values',\n",
    "                   ylabel='adult weight (log10 lbs)')\n",
    "\n",
    "thinkstats2.RandomSeed(17)\n",
    "\n",
    "\n",
    "live, firsts, others = first.MakeFrames()\n",
    "PlotAdultWeights(live)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$n=40$ 표본을 갖는 분포가 가장 작은 체중에 대해서 제외하고 근사적으로 로그정규분포를 따른다.\n",
    "\n",
    "실제 분포는 로그정규분포에서 벗어나는데 이유는 다른 연령에 사람과 섞여있고, 매년 증가하는 체중에 상관관계가 있기 때문이다."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "## 연습문제 14.2 \n",
    "\n",
    "14.6절에서, 중심극한정리를 사용해서 \n",
    "동일 모집단에서 양쪽 표본이 추출되었다는 귀무가설 아래,\n",
    "평균간에 차이, $\\delta$, 표집분포를 알아냈다.\n",
    "\n",
    "이 분포를 사용해서 추정값 표준오차와 신뢰구간도 알아낼 수 있다.\n",
    "하지만, 이 방식은 근사적으로 맞다.\n",
    "좀더 정확성을 기하기 위해서, 표본이 다른 모집단에서 추출되었다는\n",
    "대립가설 아래 $\\delta$ 표집분포를 계산해야 된다.\n",
    "\n",
    "이 분포를 계산하고, 이를 사용해서 평균 사이 차이에 대한 \n",
    "표준오차와 90% 신뢰구간을 계산하시오."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "prglngth example\n",
      "0.0780372667775\n",
      "null hypothesis N(0, 0.00319708)\n",
      "0.0837707042554 0.0837707042554\n",
      "estimated params N(0.0780373, 0.00321144)\n",
      "-0.0151758158699 0.171250349425\n"
     ]
    },
    {
     "data": {
      "image/png": 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/rz+De+goQvmeiGCMOaNL66w+3LQG6CcimSISBNwCLGjYQUQycCWI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\noZRSqkWaJJRSSrVIk4RSSqkW/f/+IEs7ZUg0EQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xae8cb26c>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.figure.Figure at 0xae93656c>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def PlotPregLengths(live, firsts, others):\n",
    "    \"\"\"Plots sampling distributions under the null and alternate hypotheses.\n",
    "    live, firsts, others: DataFrames\n",
    "    \"\"\"\n",
    "    print('prglngth example')\n",
    "    delta = firsts.prglngth.mean() - others.prglngth.mean()\n",
    "    print(delta)\n",
    "\n",
    "    dist1 = normal.SamplingDistMean(live.prglngth, len(firsts))\n",
    "    dist2 = normal.SamplingDistMean(live.prglngth, len(others))\n",
    "    dist = dist1 - dist2\n",
    "    print('null hypothesis', dist)\n",
    "    print(dist.Prob(-delta), 1 - dist.Prob(delta))\n",
    "\n",
    "    thinkplot.PrePlot(2)\n",
    "    thinkplot.Plot(dist, label='null hypothesis')\n",
    "\n",
    "    dist1 = normal.SamplingDistMean(firsts.prglngth, len(firsts))\n",
    "    dist2 = normal.SamplingDistMean(others.prglngth, len(others))\n",
    "    dist = dist1 - dist2\n",
    "    print('estimated params', dist)\n",
    "    print(dist.Percentile(5), dist.Percentile(95))\n",
    "\n",
    "    thinkplot.Plot(dist, label='estimated params')\n",
    "    thinkplot.Show(xlabel='difference in means (weeks)',\n",
    "                   ylabel='CDF')\n",
    "\n",
    "PlotPregLengths(live, firsts, others)    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "귀무가설 아래 표집분포가 0을 중심으로 모여있다.\n",
    "\n",
    "귀무가설아래 표집분포가 관측차이 0.078을 갖고 모여있다.\n",
    "\n",
    "두 분포의 분산은 매우 유사하다."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 연습문제 14.3 \n",
    "최신 논문에서, 스타인과 동료들은 학생공학팀 안에서 성별 고정관념에 따른 작업 배정을 완화하려는 의도로 개입 효과를 조사했다.\n",
    "\n",
    "개입 전과 후에 대해서, 학생들이 7점 척도로 학급 프로젝트 각 측면에 대한 기여도를 \n",
    "평가하는 설문에 응답했다.\n",
    "\n",
    "개입 전에는, 남자 학생이 여자 학생보다 프로젝트의 프로그래밍 측면에 대해서\n",
    "더 높은 점수를 보고했다; 평균적으로 남자가 0.28 표준오차를 갖는 3.57\n",
    "점수를 보고했다. 여자는 평균적으로 0.32 표준오차를 갖는 1.91을 보고했다.\n",
    "\n",
    "성별 격차(평균에 있어 차이)에 대한 표집분포를 계산하고,\n",
    "통계적으로 유의적인지 검정하라.\n",
    "추정한 평균에 대한 표준오차만 주어졌기 때문에,\n",
    "표집분포를 식별하는데 표본크기를 알 필요는 없다.\n",
    "\n",
    "개입후에, 성별격차가 더 적어졌다:\n",
    "남자에 대한 평균점수는 3.44 (표준오차 0.16); 여자에 대한 평균점수 3.18 (표준오차 0.16).\n",
    "다시, 성별격차에 대한 표집분포를 계산하고 검정하라.\n",
    "\n",
    "마지막으로 성별격차에 변화를 추정하라; 이 변화에 대한 표집분포는 무엇이고,\n",
    "통계적으로 유의적인가?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean, p-value -1.66 4.73095323208e-05\n",
      "CI -2.3594013558 -0.960598644196\n",
      "stderr 0.425205832509\n",
      "mean, p-value -0.26 0.125267987207\n",
      "CI -0.632187889177 0.112187889177\n",
      "stderr 0.22627416998\n",
      "mean, p-value 1.4 0.00182694836898\n",
      "CI 0.607733579312 2.19226642069\n",
      "stderr 0.481663783152\n"
     ]
    }
   ],
   "source": [
    "def TestIntervention():\n",
    "    \"\"\"Tests whether reported changes are statistically significant.\n",
    "    \"\"\"\n",
    "    male_before = normal.Normal(3.57, 0.28**2)\n",
    "    male_after = normal.Normal(3.44, 0.16**2)\n",
    "\n",
    "    female_before = normal.Normal(1.91, 0.32**2)\n",
    "    female_after = normal.Normal(3.18, 0.16**2)\n",
    "\n",
    "    diff_before = female_before - male_before\n",
    "    print('mean, p-value', diff_before.mu, 1-diff_before.Prob(0))\n",
    "    print('CI', diff_before.Percentile(5), diff_before.Percentile(95))\n",
    "    print('stderr', diff_before.sigma)\n",
    "\n",
    "    diff_after = female_after - male_after\n",
    "    print('mean, p-value', diff_after.mu, 1-diff_after.Prob(0))\n",
    "    print('CI', diff_after.Percentile(5), diff_after.Percentile(95))\n",
    "    print('stderr', diff_after.sigma)\n",
    "\n",
    "    diff = diff_after - diff_before\n",
    "    print('mean, p-value', diff.mu, diff.Prob(0))\n",
    "    print('CI', diff.Percentile(5), diff.Percentile(95))\n",
    "    print('stderr', diff.sigma)\n",
    "\n",
    "TestIntervention()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
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    "1. 개입전 성별격차는 1.66 점 (p-값 5e-5)\n",
    "1. 개입후 성별격차는 0.26 점 (p-값 유의적이지 않음)\n",
    "1. 성별격차에 변화 1.4점 (p-값 0.002 유의적)"
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   "source": []
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