{"nbformat_minor": 0, "cells": [{"source": ["## ThinkStats 9.1 - 9.3 Companion\n", "\n", "This notebook will allow you to practice some of the concepts from ThinkStats2 Chapter 9.\n", "\n", "### Companion to 9.1 - 9.2\n", "\n", "First, we'll start with the question that Allen poses at the beginning of the chapter: \"Suppose we toss a coin 250 times and we see 140 heads.  Is this strong evidence that the coin is biased?\"\n", "\n", "As Allen says, classical hypothesis testing is similar to a proof by contradiction.  First, we assume that the thing we are trying to show is false (that the coin is biased).  Second, we show that this leads to an observed event being excedingly improbable (seeing 140 heads out of 250 tosses).  Finally, we can conclude that our assumption (that the coin is not biased) is unlikely to be true.\n", "\n", "Write a function to simulate n random coin flips of a fair coin (p(heads) = 0.5).  Your function should return the number of heads that occur in those n coin clips."], "cell_type": "markdown", "metadata": {}}, {"execution_count": 10, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["[142, 115, 120, 127, 140, 129, 122, 119, 119, 134, 141, 132, 120, 109, 128, 129, 138, 126, 114, 106, 136, 132, 124, 112, 124, 138, 124, 126, 125, 117, 116, 134, 114, 117, 113, 132, 117, 129, 114, 124, 117, 116, 125, 119, 140, 129, 145, 140, 132, 128, 132, 128, 120, 138, 127, 131, 131, 113, 120, 122, 117, 118, 122, 112, 123, 116, 131, 125, 124, 121, 139, 125, 124, 110, 119, 123, 125, 124, 135, 122, 139, 122, 131, 120, 131, 117, 125, 121, 120, 126, 128, 126, 114, 116, 135, 121, 123, 126, 136, 122, 123, 117, 130, 120, 135, 132, 118, 136, 129, 120, 119, 130, 119, 132, 111, 134, 123, 128, 110, 134, 124, 111, 124, 140, 130, 118, 132, 127, 112, 137, 110, 132, 123, 119, 113, 119, 126, 124, 116, 119, 131, 130, 122, 133, 112, 127, 125, 111, 123, 131, 121, 127, 138, 126, 122, 122, 108, 124, 134, 114, 127, 119, 140, 128, 122, 136, 112, 136, 116, 129, 122, 129, 135, 123, 130, 122, 123, 112, 141, 123, 131, 117, 130, 119, 134, 132, 120, 124, 119, 131, 124, 138, 131, 124, 113, 121, 122, 114, 134, 126, 137, 126, 121, 129, 132, 111, 126, 144, 111, 140, 123, 117, 131, 124, 109, 129, 127, 121, 123, 126, 126, 124, 126, 127, 121, 139, 133, 130, 125, 128, 127, 125, 117, 129, 127, 118, 134, 118, 127, 130, 113, 124, 129, 123, 125, 129, 129, 116, 127, 138, 119, 123, 122, 122, 105, 122, 132, 126, 125, 128, 109, 125, 125, 117, 132, 117, 124, 132, 122, 130, 122, 122, 133, 133, 121, 127, 128, 121, 120, 144, 113, 123, 136, 125, 120, 120, 134, 120, 116, 133, 113, 127, 140, 131, 116, 115, 120, 118, 124, 125, 124, 116, 129, 113, 123, 134, 130, 127, 116, 109, 128, 108, 118, 124, 131, 124, 112, 115, 130, 121, 133, 134, 117, 119, 131, 117, 125, 122, 121, 135, 126, 119, 119, 119, 118, 118, 118, 114, 122, 124, 118, 136, 122, 131, 131, 113, 134, 122, 130, 127, 125, 120, 108, 125, 134, 133, 131, 128, 113, 126, 117, 119, 124, 128, 116, 113, 137, 117, 133, 123, 138, 119, 123, 126, 114, 116, 109, 135, 137, 124, 119, 124, 130, 113, 129, 137, 121, 117, 111, 114, 134, 132, 121, 126, 112, 111, 132, 128, 116, 121, 114, 110, 135, 133, 109, 119, 132, 121, 122, 142, 132, 105, 121, 129, 128, 132, 124, 108, 125, 127, 119, 135, 122, 129, 135, 128, 127, 115, 135, 139, 120, 150, 125, 129, 121, 132, 126, 112, 126, 128, 115, 109, 116, 125, 134, 133, 121, 121, 121, 125, 125, 127, 122, 126, 106, 124, 116, 140, 123, 128, 127, 119, 137, 129, 113, 126, 129, 125, 127, 120, 117, 115, 120, 127, 123, 130, 121, 131, 138, 129, 113, 125, 117, 129, 134, 120, 124, 137, 127, 128, 119, 133, 131, 129, 113, 130, 137, 121, 128, 124, 121, 132, 129, 128, 125, 125, 124, 130, 108, 115, 132, 129, 126, 121, 138, 131, 122, 123, 124, 125, 144, 127, 119, 125, 117, 136, 129, 121, 124, 128, 119, 128, 117, 137, 128, 130, 141, 115, 125, 144, 119, 115, 132, 135, 113, 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138, 131, 115, 124, 112, 116, 132, 115, 124, 134, 120, 133, 126, 114, 122, 137, 123, 139, 121, 127, 133, 131, 120, 127, 129, 109, 131, 133, 107, 126, 106, 115, 114, 129, 121, 117, 126, 123, 118, 130, 124, 140, 113, 120, 129, 131, 111, 128, 135, 119, 129, 118, 123, 122, 124]\n"]}], "source": ["from random import choice\n", "\n", "def simulate_fair_coin_flips(n):\n", "    \"\"\" Return the number of heads that occur in n flips of a\n", "        fair coin p(heads) = 0.5 \"\"\"\n", "    counter = 0\n", "    for i in range(n):\n", "        choices = choice([\"heads\", \"tails\"])\n", "        \n", "        if choices == \"heads\":\n", "            counter += 1\n", "    return counter\n", "\n", "flipData = []\n", "for i in range(1000):\n", "    flipData.append(simulate_fair_coin_flips(250))\n", "print flipData"]}, {"execution_count": 9, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["(136, 114)\n"]}], "source": ["from random import choice\n", "import random\n", "\n", "def simulate_fair_coin_flips(n):\n", "    \"\"\" Return the number of heads that occur in n flips of a\n", "        fair coin p(heads) = 0.5 \"\"\"\n", "    heads = 0\n", "    tails = 0\n", "    for i in range(n):\n", "        coinFlip = random.randint(0, 1)\n", "        if (coinFlip == 0): \n", "            heads +=1; \n", "        elif (coinFlip ==1): \n", "            tails +=1; \n", "    return (heads, tails)\n", "\n", "print simulate_fair_coin_flips(250)"]}, {"execution_count": 16, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["137\n"]}], "source": ["from random import randint\n", "\n", "def simulate_fair_coin_flips(n):\n", "    \"\"\" Return the number of heads that occur in n flips of a\n", "        fair coin p(heads) = 0.5 \"\"\"\n", "    return reduce(lambda heads, _: heads + randint(0, 1), xrange(n))\n", "\n", "print simulate_fair_coin_flips(250)"]}, {"execution_count": 40, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["121\n"]}], "source": ["from random import choice\n", "import itertools\n", "\n", "def simulate_fair_coin_flips(n):\n", "    \"\"\" Return the number of heads that occur in n flips of a\n", "        fair coin p(heads) = 0.5 \"\"\"\n", "    heads = 0\n", "    for _ in itertools.repeat(None, n):\n", "        heads += choice([0,1])\n", "    return heads\n", "\n", "print simulate_fair_coin_flips(250)"]}, {"execution_count": 12, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["126\n"]}], "source": ["from random import choice\n", "\n", "def simulate_fair_coin_flips(n):\n", "    \"\"\" Return the number of heads that occur in n flips of a\n", "        fair coin p(heads) = 0.5 \"\"\"\n", "    return sum([choice([0, 1]) for i in range(n)])\n", "\n", "print simulate_fair_coin_flips(250)"]}, {"execution_count": 1, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["133\n"]}], "source": ["from random import choice\n", "\n", "def simulate_fair_coin_flips(n):\n", "    \"\"\" Return the number of heads that occur in n flips of a\n", "        fair coin p(heads) = 0.5 \"\"\"\n", "    heads = 0\n", "    for i in xrange(n):\n", "        if choice(['heads', 'tails'])=='heads':\n", "            heads += 1\n", "    return heads\n", "\n", "print simulate_fair_coin_flips(250)"]}, {"execution_count": 15, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["116\n"]}], "source": ["from random import choice\n", "import random\n", "import thinkstats2\n", "\n", "def simulate_fair_coin_flips(n):\n", "    \"\"\" Return the number of heads that occur in n flips of a\n", "        fair coin p(heads) = 0.5 \"\"\"\n", "    coin_flips = [random.choice('HT') for _ in range(n)]\n", "    hist = thinkstats2.Hist(coin_flips)\n", "    return hist['H']\n", "\n", "print simulate_fair_coin_flips(250)\n"]}, {"execution_count": 13, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["145\n"]}], "source": ["from random import choice\n", "\n", "def simulate_fair_coin_flips(n):\n", "    \"\"\" Return the number of heads that occur in n flips of a\n", "        fair coin p(heads) = 0.5 \"\"\"\n", "    heads=0\n", "    \n", "    for i in range(n):\n", "        heads += choice([0,1])\n", "    \n", "    return heads\n", "\n", "print simulate_fair_coin_flips(250)"]}, {"execution_count": 1, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["133\n"]}], "source": ["from random import choice\n", "\n", "def simulate_fair_coin_flips(n):\n", "    \"\"\" Return the number of heads that occur in n flips of a\n", "        fair coin p(heads) = 0.5 \"\"\"\n", "    side = [0,1]\n", "    h = 0;\n", "    t = 0;\n", "    for i in range(n):\n", "        if choice(side) == 0:\n", "            h += 1\n", "    return h\n", "        \n", "print simulate_fair_coin_flips(250)"]}, {"execution_count": 5, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["125\n"]}], "source": ["from random import choice\n", "\n", "def simulate_fair_coin_flips(n):\n", "    \"\"\" Return the number of heads that occur in n flips of a\n", "        fair coin p(heads) = 0.5 \"\"\"\n", "    return sum(choice((0,1)) for _ in xrange(n))\n", "\n", "print simulate_fair_coin_flips(250)"]}, {"execution_count": 98, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["132\n"]}], "source": ["from random import choice\n", "\n", "def simulate_fair_coin_flips(n):\n", "    \"\"\" Return the number of heads that occur in n flips of a\n", "        fair coin p(heads) = 0.5 \"\"\"\n", "    \n", "    heads = sum([choice([0,1]) for i in range(0,n)])\n", "            \n", "    return heads\n", "\n", "print simulate_fair_coin_flips(250)"]}, {"execution_count": 14, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["127\n"]}], "source": ["from random import choice\n", "\n", "def simulate_fair_coin_flips(n):\n", "    \"\"\" Return the number of heads that occur in n flips of a\n", "        fair coin p(heads) = 0.5 \"\"\"\n", "    \n", "    toss = [choice([0,1]) for i in xrange(n)]\n", "    return sum(toss)\n", "\n", "print simulate_fair_coin_flips(250)"]}, {"execution_count": 3, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["122\n"]}], "source": ["from random import choice\n", "\n", "def simulate_fair_coin_flips(n):\n", "    \"\"\" Return the number of heads that occur in n flips of a\n", "        fair coin p(heads) = 0.5 \"\"\"\n", "    sample = [choice('HT') for _ in range(n)]\n", "    return sample.count('H')\n", "    \n", "\n", "print simulate_fair_coin_flips(250)"]}, {"execution_count": 4, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["138\n"]}], "source": ["from random import choice\n", "\n", "def simulate_fair_coin_flips(n):\n", "    \"\"\" Return the number of heads that occur in n flips of a\n", "        fair coin p(heads) = 0.5 \"\"\"\n", "    count = 0\n", "    for i in range(0,n):\n", "        if choice([0,1]) == 1:\n", "            count += 1\n", "    return count\n", "\n", "print simulate_fair_coin_flips(250)"]}, {"execution_count": 2, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["137\n"]}], "source": ["from random import choice\n", "\n", "def simulate_fair_coin_flips(n):\n", "    \"\"\" Return the number of heads that occur in n flips of a\n", "        fair coin p(heads) = 0.5 \"\"\"\n", "    count = 0\n", "    for _ in range(n):\n", "        if choice('HT') == 'H':\n", "            count += 1\n", "    return count\n", "\n", "print simulate_fair_coin_flips(250)"]}, {"execution_count": 18, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["122\n"]}], "source": ["from random import choice\n", "import thinkstats2\n", "\n", "def simulate_fair_coin_flips(n):\n", "    \"\"\" Return the number of heads that occur in n flips of a\n", "        fair coin p(heads) = 0.5 \"\"\"\n", "    sample = [choice('HT') for _ in range(n)]\n", "    hist =thinkstats2.Hist(sample)\n", "    return hist['H']\n", "\n", "print simulate_fair_coin_flips(250)"]}, {"execution_count": 26, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["131\n"]}], "source": ["from random import choice\n", "\n", "def simulate_fair_coin_flips(n):\n", "    \"\"\" Return the number of heads that occur in n flips of a\n", "        fair coin p(heads) = 0.5 \"\"\"\n", "    countHeads = 0\n", "    #The options for whether or not the coin is heads\n", "    isHeads = [0, 1]\n", "    for i in range(n):\n", "        countHeads += choice(isHeads)\n", "        \n", "    return countHeads\n", "print simulate_fair_coin_flips(250)"]}, {"execution_count": 18, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"execution_count": 18, "metadata": {}, "data": {"text/plain": ["1"]}, "output_type": "execute_result"}], "source": ["from random import choice\n", "choice([1,2,3])"]}, {"execution_count": 28, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["105\n"]}], "source": ["from random import choice\n", "import numpy as np\n", "\n", "def simulate_fair_coin_flips(n):\n", "    \"\"\" Return the number of heads that occur in n flips of a\n", "        fair coin p(heads) = 0.5 \"\"\"\n", "    return sum(np.random.randint(2, size=n))\n", "\n", "print simulate_fair_coin_flips(250)"]}, {"execution_count": 45, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["132\n"]}], "source": ["from random import choice\n", "import thinkstats2\n", "\n", "def simulate_fair_coin_flips(n):\n", "    \"\"\" Return the number of heads that occur in n flips of a\n", "        fair coin p(heads) = 0.5 \"\"\"\n", "    sample = [choice('HT') for _ in range(n)]\n", "    hist = thinkstats2.Hist(sample)\n", "    return hist['H']\n", "\n", "print simulate_fair_coin_flips(250)"]}, {"execution_count": 2, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["123\n"]}], "source": ["from random import choice\n", "\n", "def simulate_fair_coin_flips(n):\n", "    \"\"\" Return the number of heads that occur in n flips of a\n", "        fair coin p(heads) = 0.5 \"\"\"\n", "    headcount = 0\n", "    for i in range(n):\n", "        if choice([0,1]) == 0:\n", "            headcount+=1\n", "    return headcount\n", "\n", "print simulate_fair_coin_flips(250)"]}, {"execution_count": 65, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["130\n"]}], "source": ["from random import choice\n", "\n", "def simulate_fair_coin_flips(n):\n", "    \"\"\" Return the number of heads that occur in n flips of a\n", "        fair coin p(heads) = 0.5 \"\"\"\n", "    return sum([choice((0,1)) for i in range(n)])\n", "\n", "print simulate_fair_coin_flips(250)"]}, {"source": ["Next, repeat your simulation of 240 coin flips 1000 times.  Create and display a CDF of the number of times heads appears based on  1000 random trials."], "cell_type": "markdown", "metadata": {}}, {"execution_count": 11, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"execution_count": 11, "metadata": {}, "data": {"text/plain": ["{'xscale': 'linear', 'yscale': 'linear'}"]}, "output_type": "execute_result"}, {"output_type": "display_data", "data": {"image/png": 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"text/plain": ["<matplotlib.figure.Figure at 0x7f09b231e190>"]}, "metadata": {}}], "source": ["%matplotlib inline\n", "import thinkstats2\n", "import thinkplot\n", "import matplotlib.pyplot as plt\n", "\n", "\n", "cdf = thinkstats2.Cdf(flipData, label='flipdata')\n", "thinkplot.Cdf(cdf)\n", "# your implementation here (imports included for convenience)"]}, {"execution_count": 24, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [], "source": ["%matplotlib inline\n", "import thinkstats2\n", "import thinkplot\n", "import matplotlib.pyplot as plt\n", "\n", "# your implementation here (imports included for convenience)\n", "headsAppears = [];\n", "for i in range(1000): \n", "    coinFlipResults = simulate_fair_coin_flips(250)\n", "    heads = coinFlipResults[0]\n", "    headsAppears.append(heads)\n", "headsCdf = thinkstats2.Cdf(headsAppears)"]}, {"execution_count": 41, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "display_data", "data": {"image/png": 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"text/plain": ["<matplotlib.figure.Figure at 0x7fcbbd4d0250>"]}, "metadata": {}}, {"output_type": "display_data", "data": {"text/plain": ["<matplotlib.figure.Figure at 0x7fcbbd448fd0>"]}, "metadata": {}}], "source": ["%matplotlib inline\n", "import numpy as np\n", "import thinkstats2\n", "import thinkplot\n", "import matplotlib.pyplot as plt\n", "\n", "iters = 1000\n", "flips = 250\n", "heads = [simulate_fair_coin_flips(flips) for _ in range(iters)]\n", "\n", "cdf = thinkstats2.Cdf(heads, label=('heads per %d flips' % flips))\n", "thinkplot.Cdf(cdf)\n", "thinkplot.show()"]}, {"execution_count": 86, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"execution_count": 86, "metadata": {}, "data": {"text/plain": ["{'xscale': 'linear', 'yscale': 'linear'}"]}, "output_type": "execute_result"}, {"output_type": "display_data", "data": {"image/png": 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XG9gXnwBWVNu3A59v8O/Fz3Ztfxr4YlP7ojq+Gvgm8B3g9OpYE/+O3Ar8/gmuXXJf1Dqi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\nRK5CYII=\n", "text/plain": ["<matplotlib.figure.Figure at 0x7fef99525410>"]}, "metadata": {}}], "source": ["# Simulated for 250 coin flips instead of 240\n", "import thinkstats2\n", "import thinkplot\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "\n", "headlist = []\n", "for _ in itertools.repeat(None, 1000):\n", "    headlist.append(simulate_fair_coin_flips(250))\n", "\n", "headcdf = thinkstats2.Cdf(headlist)\n", "thinkplot.Cdf(headcdf)"]}, {"execution_count": 180, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "display_data", "data": {"image/png": 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"text/plain": ["<matplotlib.figure.Figure at 0x7fae279c24d0>"]}, "metadata": {}}, {"output_type": "display_data", "data": {"text/plain": ["<matplotlib.figure.Figure at 0x7fae273bd1d0>"]}, "metadata": {}}], "source": ["%matplotlib inline\n", "import thinkstats2\n", "import thinkplot\n", "import matplotlib.pyplot as plt\n", "\n", "flips_1000 = [simulate_fair_coin_flips(250) for i in range(1000)]\n", "cdf = thinkstats2.Cdf(flips_1000)\n", "thinkplot.Cdf(cdf)\n", "thinkplot.Show()"]}, {"execution_count": 2, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stderr", "text": ["/home/jsutker/anaconda2/lib/python2.7/site-packages/matplotlib/font_manager.py:273: UserWarning: Matplotlib is building the font cache using fc-list. This may take a moment.\n", "  warnings.warn('Matplotlib is building the font cache using fc-list. This may take a moment.')\n"]}, {"execution_count": 2, "metadata": {}, "data": {"text/plain": ["{'xscale': 'linear', 'yscale': 'linear'}"]}, "output_type": "execute_result"}, {"output_type": "display_data", "data": {"image/png": 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"text/plain": ["<matplotlib.figure.Figure at 0x7f08f2bd6e10>"]}, "metadata": {}}], "source": ["%matplotlib inline\n", "import thinkstats2\n", "import thinkplot\n", "import matplotlib.pyplot as plt\n", "\n", "heads_res = []\n", "for i in xrange(1000):\n", "    heads_res.append(simulate_fair_coin_flips(250))\n", "cdf = thinkstats2.Cdf(heads_res)\n", "thinkplot.Cdf(cdf)"]}, {"execution_count": 35, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"execution_count": 35, "metadata": {}, "data": {"text/plain": ["{'xscale': 'linear', 'yscale': 'linear'}"]}, "output_type": "execute_result"}, {"output_type": "display_data", "data": {"image/png": 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"text/plain": ["<matplotlib.figure.Figure at 0x7f42270a8310>"]}, "metadata": {}}], "source": ["%matplotlib inline\n", "import thinkstats2\n", "import thinkplot\n", "import matplotlib.pyplot as plt\n", "\n", "# your implementation here (imports included for convenience)\n", "coin_flips = [simulate_fair_coin_flips(250) for i in range(1000)]\n", "cdf = thinkstats2.Cdf(coin_flips)\n", "thinkplot.Cdf(cdf)\n"]}, {"execution_count": 24, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"execution_count": 24, "metadata": {}, "data": {"text/plain": ["{'xscale': 'linear', 'yscale': 'linear'}"]}, "output_type": "execute_result"}, {"output_type": "display_data", "data": {"image/png": 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"text/plain": ["<matplotlib.figure.Figure at 0x1035a0490>"]}, "metadata": {}}], "source": ["%matplotlib inline\n", "import thinkstats2\n", "import thinkplot\n", "import matplotlib.pyplot as plt\n", "\n", "flips = [simulate_fair_coin_flips(250) for _ in range(1000)]\n", "\n", "cdf = thinkstats2.Cdf(flips, label=\"flips\")\n", "thinkplot.Cdf(cdf)"]}, {"execution_count": 2, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stderr", "text": ["/home/tj/anaconda2/lib/python2.7/site-packages/matplotlib/font_manager.py:273: UserWarning: Matplotlib is building the font cache using fc-list. This may take a moment.\n", "  warnings.warn('Matplotlib is building the font cache using fc-list. This may take a moment.')\n", "/home/tj/anaconda2/lib/python2.7/site-packages/matplotlib/axes/_axes.py:519: UserWarning: No labelled objects found. Use label='...' kwarg on individual plots.\n", "  warnings.warn(\"No labelled objects found. \"\n"]}, {"output_type": "display_data", "data": {"image/png": 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FnCTMzKyQk4SZmRVykjAzs0JOEmZmVshJwszMCjlJmJlZIScJMzMr9P+EqPmj\n1iTBbQAAAABJRU5ErkJggg==\n", "text/plain": ["<matplotlib.figure.Figure at 0x7f312529b790>"]}, "metadata": {}}, {"output_type": "display_data", "data": {"text/plain": ["<matplotlib.figure.Figure at 0x7f3130be7750>"]}, "metadata": {}}], "source": ["%matplotlib inline\n", "import thinkstats2\n", "import thinkplot\n", "import matplotlib.pyplot as plt\n", "\n", "holder = []\n", "for i in range(1000):\n", "    holder += [simulate_fair_coin_flips(250)]\n", "    \n", "cdf_holder = thinkstats2.Cdf(holder)\n", "thinkplot.Cdf(cdf_holder)\n", "\n", "thinkplot.Show(title='CDF of Coin Flip Head Times',\n", "              xlabel='Number of Time Heads',\n", "              ylabel='CDF')\n"]}, {"execution_count": 8, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "display_data", "data": {"image/png": 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OZmZmmJmZWbHrpapW7GI7XTw5GpiuqvXt6zOAqqqzZ9U7AngfsL6qvt5xreozVo2fDWdu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\nYVcuTQAAAABJRU5ErkJggg==\n", "text/plain": ["<matplotlib.figure.Figure at 0x7fe4d980b950>"]}, "metadata": {}}], "source": ["%matplotlib inline\n", "import thinkstats2\n", "import thinkplot\n", "import matplotlib.pyplot as plt\n", "\n", "results = [simulate_fair_coin_flips(250) for _ in xrange(1000)]\n", "cdf = thinkstats2.Cdf(results)\n", "\n", "thinkplot.Cdf(cdf)\n", "thinkplot.Config(\n", "    title='Coin Flips',\n", "    xlabel='Number of Heads',\n", "    ylabel='CDF'\n", ")"]}, {"execution_count": 99, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "display_data", "data": {"image/png": 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IddeTACAz5wHzSq6LJKnBdLsKrCSpeRkSkqRCPRpukpqBE+akjdmTkKqcMCdtzJCQqpww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\nISFJKvT/AfX0Ln8M88UhAAAAAElFTkSuQmCC\n", "text/plain": ["<matplotlib.figure.Figure at 0x7f5251a1b950>"]}, "metadata": {}}, {"output_type": "display_data", "data": {"text/plain": ["<matplotlib.figure.Figure at 0x7f52519a0dd0>"]}, "metadata": {}}], "source": ["%matplotlib inline\n", "import thinkstats2\n", "import thinkplot\n", "import matplotlib.pyplot as plt\n", "\n", "head_cts = []\n", "\n", "for i in range(1000):\n", "    head_cts.append(simulate_fair_coin_flips(250))\n", "\n", "cdf = thinkstats2.Cdf(head_cts, label='Head Counts')\n", "thinkplot.Cdf(cdf)\n", "thinkplot.Show(xlabel='heads', ylabel='CDF')\n"]}, {"execution_count": 15, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"execution_count": 15, "metadata": {}, "data": {"text/plain": ["{'xscale': 'linear', 'yscale': 'linear'}"]}, "output_type": "execute_result"}, {"output_type": "display_data", "data": {"image/png": 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K6n8YJXwtMRZvBt4E/DPw9r7zv9TCsXgvsK46vgn4RIt/Ln6u7/jDwGfaOhbV+dOArwHf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\nGfSSVLj/B0l+WDZbXM7TAAAAAElFTkSuQmCC\n", "text/plain": ["<matplotlib.figure.Figure at 0x7f409b803110>"]}, "metadata": {}}], "source": ["%matplotlib inline\n", "import thinkstats2\n", "import thinkplot\n", "import matplotlib.pyplot as plt\n", "\n", "flips = [simulate_fair_coin_flips(250) for i in xrange(1000)]\n", "cdf_flips = thinkstats2.Cdf(flips)\n", "thinkplot.Cdf(cdf_flips)"]}, {"execution_count": 21, "cell_type": "code", "metadata": {"scrolled": true, "collapsed": false}, "outputs": [{"execution_count": 21, "metadata": {}, "data": {"text/plain": ["{'xscale': 'linear', 'yscale': 'linear'}"]}, "output_type": "execute_result"}, {"output_type": "display_data", "data": {"image/png": 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Ywo8vyZ4k9yX5yuC2a+i57Y2vqjq/Ac8FbgUeDTyKftnndOBy4C2DNpcB75rE+0/qBrwY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\n", "text/plain": ["<matplotlib.figure.Figure at 0x7f1caf4fa450>"]}, "metadata": {}}], "source": ["%matplotlib inline\n", "import thinkstats2\n", "import thinkplot\n", "import matplotlib.pyplot as plt\n", "\n", "sample = []\n", "for n in range(1000):\n", "    sample.append(simulate_fair_coin_flips(250))\n", "\n", "sample = thinkstats2.Cdf(sample)\n", "thinkplot.Cdf(sample)"]}, {"execution_count": 5, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"execution_count": 5, "metadata": {}, "data": {"text/plain": ["{'xscale': 'linear', 'yscale': 'linear'}"]}, "output_type": "execute_result"}, {"output_type": "display_data", "data": {"image/png": 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v4DhgI3AAsB/tss8RwLXAZ6o2lwPXjOLzR/UFfAQ4HtjYsW/GMQEfAJ6kXR77FeB5qv9B\njeNXj7EdAxwFfBM4oWP/+ydpbLOM76PAkur1NcAXJvFnN8v4fr7j9SeBvy5pfNX+Q4H7gO8BB1X7\nSvn7eRXwhzO0nfP4RjWjfz/waGa+kZm7gIeA84Fzga9Wbb4KnDeizx+JzPwW8MOu3SuZeUznAusz\n86eZ+Z/AFt58/cHYmGlsmflcZm4Buk+ir2SCxgY9x/dAZv6s2nyEdmjAhP3soOf4ftSx+TZg91iL\nGF/lL4BPd+0r4u9nZaYFLHMe36iC/lnglKqs8XPA2cB7gT1Xy2bm94GDR/T5C+ngHmPqdRFZCUoc\n28eBe6vXxYwvIq6OiBeB1cCfVLuLGF9EnAtsy8xnut4qYnyVNVVp8W86ysJzHt9Igj7b98G5FvgG\n7X88TwIzXTZa4pngEsdUtIj4HLAzM29b7L7ULTM/n5nLgb+jXb4pQkQsBa6kXd4o1Y3A+zLzeOD7\nwHXDHmhkJ2Mz85bM/HBmNoDXgOeAVyLiEIDqxNCro/r8BdRrTDto/y9mt0OrfSUoZmwRcRHt/3Gu\n7thdzPg63Eq7fApljO8I2vXppyPie7TH8EREHEx7LMs72k7i+MjM/8qqKA98mb3lmTn//Ea56uaX\nqj+XA79N+y/aPcBFVZPfBe4e1eePULBv3azXmO4BLoyI/SPicOBI4LGF6uSQusfW/d5ukzg26Bpf\ntYrh08C5mdl5o6NSxndkx3vnsfdGhBM/vsx8NjPfnZnvy8zDad+D61cz81Xa47tgkscHeyaOu51P\nuyQOw/z8RngW+aGqY08CjWrfQcADtGf3G4BfWOyz3XMc0620b9X8BvAi7QvD3tlrTMBnaZ8R3wSc\nsdj9H2Js59GuBb5O+6ror0/i2GYZ3xZgK/BE9XVjYeO7A3gGeIr2BOQ9JY2v6/0XqFbdlDI+2ncE\n3lj9/P6e9jnOocbnBVOSVLiRlW4kSePBoJekwhn0klQ4g16SCmfQS1LhDHpJKpxBL0mFM+glqXD/\nD1pafMw9lmwmAAAAAElFTkSuQmCC\n", "text/plain": ["<matplotlib.figure.Figure at 0x7f585ec93250>"]}, "metadata": {}}], "source": ["%matplotlib inline\n", "import thinkstats2\n", "import thinkplot\n", "import matplotlib.pyplot as plt\n", "\n", "total = []\n", "for i in range(0,1000):\n", "    total.append(simulate_fair_coin_flips(240))\n", "cdf = thinkstats2.Cdf(total)\n", "thinkplot.Cdf(cdf)\n", "# your implementation here (imports included for convenience)"]}, {"execution_count": 17, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "display_data", "data": {"image/png": 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B7Ldvd/WdJPYHbhjYv5EmcSxX56a2bCqSxHr9Zb99+451iujWFpPBccc+tpfzS5ptTlyP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\nwgAAAABJRU5ErkJggg==\n", "text/plain": ["<matplotlib.figure.Figure at 0x11129a990>"]}, "metadata": {}}, {"output_type": "display_data", "data": {"text/plain": ["<matplotlib.figure.Figure at 0x10fde6110>"]}, "metadata": {}}], "source": ["%matplotlib inline\n", "import thinkstats2\n", "import thinkplot\n", "import matplotlib.pyplot as plt\n", "\n", "# your implementation here (imports included for convenience)\n", "res = []\n", "for _ in range(1000):\n", "    res.append(simulate_fair_coin_flips(240))\n", "\n", "cdf = thinkstats2.Cdf(res)\n", "thinkplot.Cdf(cdf)\n", "thinkplot.show(xlabel='No of Heads in 240 coin flips', ylabel='CDF')"]}, {"execution_count": 38, "cell_type": "code", "metadata": {"scrolled": true, "collapsed": false}, "outputs": [{"output_type": "display_data", "data": {"image/png": 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"text/plain": ["<matplotlib.figure.Figure at 0x7f5504987350>"]}, "metadata": {}}, {"output_type": "display_data", "data": {"text/plain": ["<matplotlib.figure.Figure at 0x7f5505153690>"]}, "metadata": {}}], "source": ["%matplotlib inline\n", "import thinkstats2\n", "import thinkplot\n", "import matplotlib.pyplot as plt\n", "\n", "# your implementation here (imports included for convenience)\n", "headsCounts= [simulate_fair_coin_flips(240) for i in range(1000)]\n", "cdf = thinkstats2.Cdf(headsCounts)\n", "thinkplot.Cdf(cdf)\n", "thinkplot.Config(title ='Number of times a fair coin toss results in heads')\n", "thinkplot.Show(xlabel = 'Coin toss resulting in heads', ylabel ='CDF')"]}, {"execution_count": 27, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "display_data", "data": {"image/png": 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"text/plain": ["<matplotlib.figure.Figure at 0x1124f9350>"]}, "metadata": {}}, {"output_type": "display_data", "data": {"text/plain": ["<matplotlib.figure.Figure at 0x11231dd90>"]}, "metadata": {}}], "source": ["%matplotlib inline\n", "import thinkstats2\n", "import thinkplot\n", "import matplotlib.pyplot as plt\n", "\n", "flipResults = []\n", "for i in range(1000):\n", "#     The instructions say 240, but everything else says 250, so I'm going with 250\n", "    flipResults.append(simulate_fair_coin_flips(250))\n", "\n", "flipCdf = thinkstats2.Cdf(flipResults, label = 'Coin Flips')\n", "\n", "thinkplot.Cdf(flipCdf)\n", "thinkplot.Show(xlabel = 'Probability of Heads', ylabel='CDF', title='CDF of Coin Flips')"]}, {"execution_count": 50, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [], "source": ["%matplotlib inline\n", "import thinkstats2\n", "import thinkplot\n", "import matplotlib.pyplot as plt\n", "\n", "trials = [simulate_fair_coin_flips(250) for i in range(1000)]"]}, {"execution_count": 98, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "display_data", "data": {"image/png": 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"text/plain": ["<matplotlib.figure.Figure at 0x7f23c50f24d0>"]}, "metadata": {}}, {"output_type": "display_data", "data": {"text/plain": ["<matplotlib.figure.Figure at 0x7f23c4a9ddd0>"]}, "metadata": {}}], "source": ["%matplotlib inline\n", "import thinkstats2\n", "import thinkplot\n", "import matplotlib.pyplot as plt\n", "\n", "resultsList = []\n", "\n", "for i in range(10000):\n", "    resultsList.append(simulate_fair_coin_flips(250))\n", "    \n", "\n", "    \n", "cdf = thinkstats2.Cdf(resultsList)\n", "thinkplot.Cdf(cdf)\n", "thinkplot.Show()\n", "\n", "# your implementation here (imports included for convenience)"]}, {"execution_count": 46, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "display_data", "data": {"image/png": 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ptjQ/A7hS0h1ktY8LyJLID9Oy+WR9LADnpo7zRcCNuRjMhsRDhZuZWSHXJMzM\nrJCThJmZFXKSMDOzQk4SZmZWyEnCzMwKOUmYmVkhJwkzMyvkJGFmZoX+FzKwoAVHGikhAAAAAElF\nTkSuQmCC\n", "text/plain": ["<matplotlib.figure.Figure at 0x109008b10>"]}, "metadata": {}}, {"output_type": "display_data", "data": {"text/plain": ["<matplotlib.figure.Figure at 0x10950ff10>"]}, "metadata": {}}], "source": ["%matplotlib inline\n", "import thinkstats2\n", "import thinkplot\n", "import matplotlib.pyplot as plt\n", "\n", "heads = [simulate_fair_coin_flips(240) for i in range(1000)]\n", "cdf = thinkstats2.Cdf(heads)\n", "\n", "thinkplot.Cdf(cdf)\n", "thinkplot.Config(title ='Number of occurences of heads')\n", "thinkplot.Show(xlabel = 'Heads coin toss', ylabel ='CDF')"]}, {"execution_count": 3, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "display_data", "data": {"image/png": 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jiAjOOussRo0axf333w/AaaedRltbGwCnn346Bx54IA888ABQ+uHxla98hb322ovdd9+d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\nQmCC\n", "text/plain": ["<matplotlib.figure.Figure at 0x7f9a1177ee90>"]}, "metadata": {}}, {"output_type": "display_data", "data": {"text/plain": ["<matplotlib.figure.Figure at 0x7f9a1d53db50>"]}, "metadata": {}}], "source": ["%matplotlib inline\n", "import thinkstats2\n", "import thinkplot\n", "import matplotlib.pyplot as plt\n", "\n", "# your implementation here (imports included for convenience)\n", "hcs = []\n", "for i in range(1000):\n", "    hcs.append(simulate_fair_coin_flips(250))\n", "\n", "cdf = thinkstats2.Cdf(hcs)\n", "thinkplot.Cdf(cdf, label='heads count')\n", "thinkplot.Show(loc='lower right')"]}, {"execution_count": 66, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "display_data", "data": {"image/png": 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kWyetYVaW6q2q9lfV7Rx6KOh24MNVdX9VfR24ncGJXuvWMv1dWVUPdFevYRAUAGfTRn8/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\nyHCXpAb9PwnbU6CI6/CLAAAAAElFTkSuQmCC\n", "text/plain": ["<matplotlib.figure.Figure at 0x7fd3bcf5e0d0>"]}, "metadata": {}}], "source": ["%matplotlib inline\n", "import thinkstats2\n", "import thinkplot\n", "import matplotlib.pyplot as plt\n", "\n", "def coin_flips_trials(n, m):\n", "    head_num_trials = []\n", "    for i in range(n):\n", "        head_num_trials.append(simulate_fair_coin_flips(m))\n", "    hist = thinkstats2.Hist(head_num_trials)\n", "    thinkplot.Hist(hist)\n", "    return head_num_trials\n", "\n", "trials = coin_flips_trials(1000, 250)"]}, {"source": ["The p-value is simply the probability that we would have seen a result as extreme (or greater) as 140 heads out of 250 flips under the hypothesis that the coin is fair (the null hypothesis).  Using the CDF you created in the previous cell, compute the p-value.  If you want to test your learning a bit more: compute the p-value without using the CDF explicitly (instead use the results of the 1000 random trials directly).\n", "\n", "Hint: you should use the PercentileRank function of CDF to compute the p-value, however, there is one important gotcha.  The PercentileRank function returns the percentage of data that is equal to or less than the input value.  When computing the p-value we want the percentage of the data that is equal to or greater than the observed value."], "cell_type": "markdown", "metadata": {"collapsed": true}}, {"execution_count": 13, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["1.7\n"]}], "source": ["percentile = cdf.PercentileRank(140)\n", "#print percentile\n", "print 100 - percentile"]}, {"execution_count": 60, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["Pvalue for percentage of data that is equal to or less than for a one tailed test 97.1\n", "Pvalue for percentage of data that is equal to or greater than for a one tailed test 2.9\n"]}], "source": ["pvalue_of_equal_to_or_less_than_1tailed = headsCdf.PercentileRank(140)\n", "print \"Pvalue for percentage of data that is equal to or less than for a one tailed test\" , pvalue_of_equal_to_or_less_than\n", "pvalue_of_equal_to_or_greater_than_1tailed = 100 -  pvalue_of_equal_to_or_less_than\n", "print \"Pvalue for percentage of data that is equal to or greater than for a one tailed test\",  pvalue_of_equal_to_or_greater_than"]}, {"execution_count": 88, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["pvalue using PercentileRank: 2.700000\n", "pvalue calculated:           2.700000\n"]}], "source": ["observed = 140\n", "\n", "pvalue = 100 - cdf.PercentileRank(observed - 1)\n", "\n", "num_above = sum(h >= observed for h in heads)\n", "pvalue_calculated = 100 * num_above / float(len(heads))\n", "\n", "print 'pvalue using PercentileRank: %f' % pvalue\n", "print 'pvalue calculated:           %f' % pvalue_calculated"]}, {"execution_count": 87, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["p value is 0.025 (one tailed)\n"]}], "source": ["import numpy as np\n", "import scipy.stats as stats\n", "p1 = 1 - 0.01*(stats.percentileofscore(np.array(headlist), 140))\n", "print 'p value is', p1, '(one tailed)'"]}, {"execution_count": 150, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["p-value for 140 heads out of 250 coins:  3.2\n"]}], "source": ["rank = cdf.PercentileRank(140)\n", "p_value = 100 - rank\n", "print \"p-value for 140 heads out of 250 coins: \", p_value"]}, {"execution_count": 3, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["p-value: 3.3%\n"]}], "source": ["print \"p-value:\", str(100-cdf.PercentileRank(140))+\"%\""]}, {"execution_count": 30, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["P-value that 140/250 flips are heads\n", "2.8%\n"]}], "source": ["print \"P-value of data that 140/250 flips are heads\"\n", "print str(100 - cdf.PercentileRank(140)) + \"%\""]}, {"execution_count": 36, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["2.7\n"]}], "source": ["pvalue = 100 - cdf.PercentileRank(140)\n", "print pvalue"]}, {"execution_count": 3, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["3.4 %\n"]}], "source": ["p_val = 100 - cdf_holder.PercentileRank(139)\n", "print p_val, '%'"]}, {"execution_count": 9, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"execution_count": 9, "metadata": {}, "data": {"text/plain": ["0.040000000000000036"]}, "output_type": "execute_result"}], "source": ["1 - cdf[139]"]}, {"execution_count": 100, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["Pvalue:  3.6 %\n"]}], "source": ["pvalue = 100 - cdf.PercentileRank(139)\n", "\n", "print \"Pvalue: \", pvalue, \"%\""]}, {"execution_count": 16, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["P-value calculated with CDF:  3.1 %\n", "P-value calculated without CDF:  3.1 %\n"]}], "source": ["p_value = 100 - cdf_flips.PercentileRank(139)\n", "print 'P-value calculated with CDF: ', p_value, '%'\n", "\n", "flips.sort()\n", "ord_index = flips.index(140)\n", "vals_above = 1 - ord_index/1000.0\n", "\n", "print 'P-value calculated without CDF: ', 100*vals_above, '%'"]}, {"execution_count": 22, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["4.0\n"]}], "source": ["p_val = 100 - sample.PercentileRank(139)\n", "print p_val"]}, {"execution_count": 9, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["P-value:  0.005\n"]}], "source": ["p_value = (100 - cdf.PercentileRank(139))/100\n", "print 'P-value: ', p_value"]}, {"execution_count": 18, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["p-value: 0.4\n"]}], "source": ["print \"p-value:\", float(format(100 - cdf.PercentileRank(139), '.2f'))"]}, {"execution_count": 39, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["P-value using CDF:  0.004\n", "P-value using the results of 1000 random trials directly:  0.004\n"]}], "source": ["percRank = cdf.PercentileRank(139)\n", "pVal = 1 - percRank/100\n", "print \"P-value using CDF: \",pVal\n", "\n", "count = sum(1.0 for x in headsCounts if x>= 140.0)\n", "print \"P-value using the results of 1000 random trials directly: \",count/1000"]}, {"execution_count": 28, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["The p-value is  0.018\n"]}], "source": ["percentileRank = flipCdf.PercentileRank(140)\n", "pValue = 1 - float(percentileRank)/100\n", "print \"The p-value is \", pValue"]}, {"execution_count": 52, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["Percent of data that is equal to or greater than value:\n", "2.5%\n"]}], "source": ["print \"Percent of data that is equal to or greater than value:\"\n", "print str(100 - cdf.PercentileRank(140)) + \"%\""]}, {"execution_count": 99, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"execution_count": 99, "metadata": {}, "data": {"text/plain": ["0.0286"]}, "output_type": "execute_result"}], "source": ["sum(i >= 140 for i in resultsList)/float(len(resultsList))"]}, {"execution_count": 47, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["P value with CDF:  0.011\n", "P-value with the results of 1000 random trials:  0.011\n"]}], "source": ["percRank = cdf.PercentileRank(139)\n", "pVal = 1 - (percRank / 100)\n", "print \"P value with CDF: \", pVal\n", "\n", "count = sum(1.0 for x in heads if x >= 140.0)\n", "print \"P-value with the results of 1000 random trials: \", count / 1000"]}, {"execution_count": 12, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["p-value: 0.033\n"]}], "source": ["print \"p-value:\", 1 - cdf.PercentileRank(139)/100\n", "# 139 because we want to include 140 in our counts"]}, {"execution_count": 67, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["2.0\n"]}], "source": ["trialsCDF = thinkstats2.Cdf(trials)\n", "print 100.0 - trialsCDF.PercentileRank(140)"]}, {"source": ["The p-value we computed above is called a [one-tailed test](https://en.wikipedia.org/wiki/One-_and_two-tailed_tests) in that we only counted simulations of the null-hypothesis that had 140 or more heads (Allen uses the terminology of one versus two-sided tests, see ThinkStats2 9.4).  A two-tailed test would count simulations with 140 or more tails as well (which is what Allen shows in the book).  Whether to use a one-tailed or a two-tailed test mostly has to do with your prior expectations regarding the hypothesis you are testing.  For instance, if you had a reason to suspect that the coin would be biased towards heads (but not tails) you would use a one-tailed test.  If you had no reason to assume a priori that the coin was biased towards heads or tails, you should use a two-tailed test.\n", "\n", "Modify your coin flip simulation code to return the number of heads or tails, whichever is larger, out of n flips."], "cell_type": "markdown", "metadata": {}}, {"execution_count": 18, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["131\n"]}], "source": ["def simulate_fair_coin_flips_two_sided(n):\n", "    \"\"\" Return the number of heads or tails, whichever is larger,\n", "        that occur in n flips of a fair coin p(heads) = 0.5 \"\"\"\n", "    counterh = 0\n", "    countert = 0\n", "    for i in range(n):\n", "        choices = choice([\"heads\", \"tails\"])\n", "        \n", "        if choices == \"heads\":\n", "            counterh += 1\n", "        else:\n", "            countert += 1\n", "    if counterh >= countert:\n", "        #print \"heads\"\n", "        return counterh\n", "    else:\n", "        #print \"tails\"\n", "        return countert\n", "\n", "print simulate_fair_coin_flips_two_sided(250)"]}, {"execution_count": 61, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["128\n"]}], "source": ["def simulate_fair_coin_flips_two_sided(n):\n", "    \"\"\" Return the number of heads or tails, whichever is larger,\n", "        that occur in n flips of a fair coin p(heads) = 0.5 \"\"\"\n", "    heads = 0\n", "    tails = 0\n", "    for i in range(n):\n", "        coinFlip = random.randint(0, 1)\n", "        if (coinFlip == 0): \n", "            heads +=1; \n", "        elif (coinFlip ==1): \n", "            tails +=1; \n", "#     print heads, tails\n", "    if (heads > tails): \n", "        return heads\n", "    elif (tails > heads): \n", "        return tails\n", "    else: \n", "        return heads\n", "    \n", "print simulate_fair_coin_flips_two_sided(250)"]}, {"execution_count": 73, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["141\n"]}], "source": ["def simulate_fair_coin_flips_two_sided(n):\n", "    \"\"\" Return the number of heads or tails, whichever is larger,\n", "        that occur in n flips of a fair coin p(heads) = 0.5 \"\"\"\n", "    heads = simulate_fair_coin_flips(n)\n", "    tails = n - heads\n", "    return max(heads, tails)\n", "\n", "print simulate_fair_coin_flips_two_sided(250)"]}, {"execution_count": 98, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["137\n"]}], "source": ["def simulate_fair_coin_flips_two_sided(n):\n", "    \"\"\" Return the number of heads or tails, whichever is larger,\n", "        that occur in n flips of a fair coin p(heads) = 0.5 \"\"\"\n", "    heads = 0\n", "    for _ in itertools.repeat(None, n):\n", "        heads += choice([0,1])\n", "    return max(heads, n-heads)\n", "\n", "    pass\n", "\n", "print simulate_fair_coin_flips_two_sided(250)"]}, {"execution_count": 133, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["126\n"]}], "source": ["def simulate_fair_coin_flips_two_sided(n):\n", "    \"\"\" Return the number of heads or tails, whichever is larger,\n", "        that occur in n flips of a fair coin p(heads) = 0.5 \"\"\"\n", "    count = sum([choice([0, 1]) for i in range(n)])\n", "    return count if (count>125) else (250-count)\n", "\n", "print simulate_fair_coin_flips_two_sided(250)"]}, {"execution_count": 4, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["131\n"]}], "source": ["def simulate_fair_coin_flips_two_sided(n):\n", "    \"\"\" Return the number of heads or tails, whichever is larger,\n", "        that occur in n flips of a fair coin p(heads) = 0.5 \"\"\"\n", "    heads = 0\n", "    for i in xrange(n):\n", "        if choice(['heads', 'tails'])=='heads':\n", "            heads += 1\n", "    if heads>(n/2):\n", "        return heads\n", "    else:\n", "        return n-heads\n", "\n", "print simulate_fair_coin_flips_two_sided(250)"]}, {"execution_count": 49, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["128\n"]}], "source": ["def simulate_fair_coin_flips_two_sided(n):\n", "    \"\"\" Return the number of heads or tails, whichever is larger,\n", "        that occur in n flips of a fair coin p(heads) = 0.5 \"\"\"\n", "    coin_flips = [random.choice('HT') for _ in range(n)]\n", "    hist = thinkstats2.Hist(coin_flips)\n", "    if(hist['H'] >= hist['T']):\n", "        return hist['H']\n", "    else:\n", "        return hist['T']\n", "\n", "print simulate_fair_coin_flips_two_sided(250)"]}, {"execution_count": 39, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["131\n"]}], "source": ["def simulate_fair_coin_flips_two_sided(n):\n", "    \"\"\" Return the number of heads or tails, whichever is larger,\n", "        that occur in n flips of a fair coin p(heads) = 0.5 \"\"\"\n", "    ht=0\n", "    \n", "    for i in range(n):\n", "        ht += choice([0,1])\n", "    \n", "    if (n-ht)>ht:\n", "        return n-ht\n", "    else:\n", "        return ht\n", "\n", "print simulate_fair_coin_flips_two_sided(250)"]}, {"execution_count": 4, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["136\n"]}], "source": ["def simulate_fair_coin_flips_two_sided(n):\n", "    \"\"\" Return the number of heads or tails, whichever is larger,\n", "        that occur in n flips of a fair coin p(heads) = 0.5 \"\"\"\n", "    side = [0,1]\n", "    h = 0;\n", "    t = 0;\n", "    for i in range(n):\n", "        if choice(side) == 0:\n", "            h += 1\n", "        else:\n", "            t += 1\n", "    if t > h:\n", "        return t\n", "    else:\n", "        return h\n", "\n", "print simulate_fair_coin_flips_two_sided(250)"]}, {"execution_count": 20, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["127\n"]}], "source": ["def simulate_fair_coin_flips_two_sided(n):\n", "    \"\"\" Return the number of heads or tails, whichever is larger,\n", "        that occur in n flips of a fair coin p(heads) = 0.5 \"\"\"\n", "    heads = sum(choice((0,1)) for _ in xrange(n))\n", "    return max(heads, n-heads)\n", "\n", "print simulate_fair_coin_flips_two_sided(250)"]}, {"execution_count": 106, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["130\n"]}], "source": ["def simulate_fair_coin_flips_two_sided(n):\n", "    \"\"\" Return the number of heads or tails, whichever is larger,\n", "        that occur in n flips of a fair coin p(heads) = 0.5 \"\"\"\n", "    \n", "    result = sum([choice([0,1]) for i in range(n)])\n", "    \n", "    if result >= n/2.0:\n", "        return result\n", "    else:\n", "        return n - result\n", "    \n", "\n", "print simulate_fair_coin_flips_two_sided(250)"]}, {"execution_count": 4, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["125\n"]}], "source": ["def simulate_fair_coin_flips_two_sided(n):\n", "    \"\"\" Return the number of heads or tails, whichever is larger,\n", "        that occur in n flips of a fair coin p(heads) = 0.5 \"\"\"\n", "    heads = simulate_fair_coin_flips(n)\n", "    return max(heads, n-heads)\n", "\n", "print simulate_fair_coin_flips_two_sided(250)"]}, {"execution_count": 17, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["130\n"]}], "source": ["def simulate_fair_coin_flips_two_sided(n):\n", "    \"\"\" Return the number of heads or tails, whichever is larger,\n", "        that occur in n flips of a fair coin p(heads) = 0.5 \"\"\"\n", "      \n", "    toss = [choice([0,1]) for i in xrange(n)]\n", "    heads = sum(toss)\n", "    if heads >= n/2.0:\n", "        return heads\n", "    else:\n", "        return n-heads\n", "\n", "\n", "print simulate_fair_coin_flips_two_sided(250)"]}, {"execution_count": 23, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["133\n"]}], "source": ["def simulate_fair_coin_flips_two_sided(n):\n", "    \"\"\" Return the number of heads or tails, whichever is larger,\n", "        that occur in n flips of a fair coin p(heads) = 0.5 \"\"\"\n", "    sample = [choice('HT') for _ in range(n)]\n", "    if sample.count('H') > sample.count('T'):\n", "        return sample.count('H')\n", "    else:\n", "        return sample.count('T')\n", "\n", "print simulate_fair_coin_flips_two_sided(250)"]}, {"execution_count": 10, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["133\n"]}], "source": ["def simulate_fair_coin_flips_two_sided(n):\n", "    \"\"\" Return the number of heads or tails, whichever is larger,\n", "        that occur in n flips of a fair coin p(heads) = 0.5 \"\"\"\n", "    count = 0\n", "    for i in range(0,n):\n", "        if choice([0,1]) == 1:\n", "            count += 1\n", "    if count > n/2:\n", "        return count\n", "    return n-count\n", "\n", "print simulate_fair_coin_flips_two_sided(250)"]}, {"execution_count": 20, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["125\n"]}], "source": ["def simulate_fair_coin_flips_two_sided(n):\n", "    \"\"\" Return the number of heads or tails, whichever is larger,\n", "        that occur in n flips of a fair coin p(heads) = 0.5 \"\"\"\n", "    count_heads = 0\n", "    count_tails = 0\n", "    for _ in range(n):\n", "        if choice('HT') == 'H':\n", "            count_heads += 1\n", "        else:\n", "            count_tails += 1\n", "    return max(count_heads, count_tails)\n", "\n", "print simulate_fair_coin_flips_two_sided(250)"]}, {"execution_count": 44, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["(127, 123)\n"]}], "source": ["def simulate_fair_coin_flips_two_sided(n):\n", "    \"\"\" Return the number of heads or tails, whichever is larger,\n", "        that occur in n flips of a fair coin p(heads) = 0.5 \"\"\"\n", "    sample = [choice('HT') for _ in range(n)]\n", "    hist =thinkstats2.Hist(sample)\n", "    return hist['H'], hist['T']\n", "\n", "print simulate_fair_coin_flips_two_sided(250)"]}, {"execution_count": 29, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["139\n"]}], "source": ["def simulate_fair_coin_flips_two_sided(n):\n", "    \"\"\" Return the number of heads or tails, whichever is larger,\n", "        that occur in n flips of a fair coin p(heads) = 0.5 \"\"\"\n", "    outcomesDict ={\n", "        'heads': 0,\n", "        'tails': 0\n", "    }\n", "    coinOptions = ['heads', 'tails']\n", "    \n", "    for i in range(n):\n", "        outcomesDict[choice(coinOptions)] += 1\n", "        \n", "    if (outcomesDict['heads'] > outcomesDict['tails']):\n", "        return outcomesDict['heads']\n", "    else:\n", "        return outcomesDict['tails']\n", "        \n", "\n", "print simulate_fair_coin_flips_two_sided(250)"]}, {"execution_count": 53, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["125\n"]}], "source": ["def simulate_fair_coin_flips_two_sided(n):\n", "    \"\"\" Return the number of heads or tails, whichever is larger,\n", "        that occur in n flips of a fair coin p(heads) = 0.5 \"\"\"\n", "    count = simulate_fair_coin_flips(n)\n", "    return max(count, abs(n - count))\n", "\n", "print simulate_fair_coin_flips_two_sided(250)"]}, {"execution_count": 91, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["136\n"]}], "source": ["def simulate_fair_coin_flips_two_sided(n):\n", "    \"\"\" Return the number of heads or tails, whichever is larger,\n", "        that occur in n flips of a fair coin p(heads) = 0.5 \"\"\"\n", "    heads= sum(np.random.randint(2, size=n))\n", "    return max(heads, n-heads)\n", "\n", "print simulate_fair_coin_flips_two_sided(250)"]}, {"execution_count": 48, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["(124, 126)\n"]}], "source": ["def simulate_fair_coin_flips_two_sided(n):\n", "    \"\"\" Return the number of heads or tails, whichever is larger,\n", "        that occur in n flips of a fair coin p(heads) = 0.5 \"\"\"\n", "    sample = [choice('HT') for _ in range(n)]\n", "    hist = thinkstats2.Hist(sample)\n", "    return hist['H'], hist['T']\n", "\n", "print simulate_fair_coin_flips_two_sided(250)"]}, {"execution_count": 23, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["132\n"]}], "source": ["def simulate_fair_coin_flips_two_sided(n):\n", "    \"\"\" Return the number of heads or tails, whichever is larger,\n", "        that occur in n flips of a fair coin p(heads) = 0.5 \"\"\"\n", "    res = {\"heads\":0, \"tails\":0}\n", "    for i in range(n):\n", "        if choice([0,1]) == 0:\n", "            res[\"heads\"]+=1\n", "        else:\n", "            res[\"tails\"]+=1\n", "    return max(res.values())\n", "\n", "print simulate_fair_coin_flips_two_sided(250)"]}, {"execution_count": 68, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["130\n"]}], "source": ["def simulate_fair_coin_flips_two_sided(n):\n", "    \"\"\" Return the number of heads or tails, whichever is larger,\n", "        that occur in n flips of a fair coin p(heads) = 0.5 \"\"\"\n", "    heads = sum([choice((0,1)) for i in range(n)])\n", "    return heads if heads > (n-heads) else (n-heads)\n", "\n", "print simulate_fair_coin_flips_two_sided(250)"]}, {"source": ["Using the function `simulate_fair_coin_flips_two_sided`, create and display a CDF of the number of times the most common outcome, heads or tails, appears based on 1000 random trials."], "cell_type": "markdown", "metadata": {}}, {"execution_count": 20, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"execution_count": 20, "metadata": {}, "data": {"text/plain": ["{'xscale': 'linear', 'yscale': 'linear'}"]}, "output_type": "execute_result"}, {"output_type": "display_data", "data": {"image/png": 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Bn+T3geNVtW+46dvAuVX1AuDNwL4kT9io/myWqvqDqjoX+CsGUxZza4mxeJg5Oi6S/Czw\newz+TJ9rS4zFTyvaecyL9wLPrqrLgH8H3rXWN9qQoE/yGuAqBpUbAFV1vKq+N1z+PPA14MKN6M+U\n2AfsHC4fA54xsu+c4bZ5sQ/4VYCq+tGcHRfnM5hnvT/JNxj8t/98kqcyOAbOHWnb+nFxurH4tyRP\nnce8qKr/qOGkPPBBTk3PrDov1iPow8i80vBM8VuAV1bV/45sf8rwzpgkeTZwAfD1dejPZlo8FheM\n7LsaODhcvgO4NsmZSZ7FYCw+t2G93BgrjcWB4fa5Oi6q6ktV9fSqenZVPYvBvaR+oaq+w+C4uGZe\njovlxmLejguA0avyGBSFXxourzovOn04eJJ9QA948nDu9UYGf4qdCXwyCcA9VfUG4EXA25L8iMGJ\nuN1V9f0u+7OZlhiLX0lyEXACOAz8JkBVfSXJ7cBXgOPAG0Z+k8+81YwFc3hcVNWHRpoUp4Jv7o6L\npcaCOTwugBdn8GyPnwDfZHAL+DUdF35hSpIa590rJalxBr0kNc6gl6TGGfSS1DiDXpIaZ9BLUuMM\neklqnEEvSY37P74vRbCNxY4VAAAAAElFTkSuQmCC\n", "text/plain": ["<matplotlib.figure.Figure at 0x7f09af408fd0>"]}, "metadata": {}}], "source": ["flipDataTwo = []\n", "for i in range(1000):\n", "    flipDataTwo.append(simulate_fair_coin_flips_two_sided(250))\n", "\n", "cdf2 = thinkstats2.Cdf(flipDataTwo, label='flipdata')\n", "thinkplot.Cdf(cdf2)"]}, {"execution_count": 72, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [], "source": ["headsOrTailsAppears = [];\n", "for i in range(1000): \n", "    coinFlipResult = simulate_fair_coin_flips_two_sided(250)\n", "    headsOrTailsAppears.append(coinFlipResult)\n", "mostFrequentResultCdf = thinkstats2.Cdf(headsOrTailsAppears)"]}, {"execution_count": 101, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "display_data", "data": {"image/png": 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pGzTQd0leABypqi8tONVK3y3WPmig/wZ2DaaF/yrJmYNjTfTfwHD7fnHo+Ir6b9WCPsnr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\n", "text/plain": ["<matplotlib.figure.Figure at 0x7f7c6c63ad10>"]}, "metadata": {}}, {"output_type": "display_data", "data": {"text/plain": ["<matplotlib.figure.Figure at 0x7f7c6c2fc990>"]}, "metadata": {}}], "source": ["iters = 1000\n", "flips = 250\n", "totals = [simulate_fair_coin_flips_two_sided(flips) for _ in range(iters)]\n", "\n", "two_side_cdf = thinkstats2.Cdf(totals)\n", "thinkplot.Cdf(two_side_cdf)\n", "thinkplot.show()"]}, {"execution_count": 99, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"execution_count": 99, "metadata": {}, "data": {"text/plain": ["{'xscale': 'linear', 'yscale': 'linear'}"]}, "output_type": "execute_result"}, {"output_type": "display_data", "data": {"image/png": 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9Yt2CPskfAKer6sDg0HeAbVX1POCtwIEkj12v+kxKVf1hVW0D/or+lMXMWqQtTjJD/SLJ\nhcDv0/8zfaYt0hY/H9HOYl7cBjyjqq4D/g1472rfaF2CPslvAK+gP3IDoKpOV9X3B9tfBr4OXLke\n9ZkSB4BXD7ZPAE8dOnfp4NisOAD8OkBV/WTG+sXl9OdZH0jyTfr/919O8kT6fWDbUNnW+8X52uK+\nJE+cxbyoqn+vwaQ88GHOTc+sOC/WIujD0LzS4Erx24BXVtX/Dh1/wuDJmCR5BnAF8I01qM8kLWyL\nK4bOvQo4PNi+A7gpyQVJnk6/Lb60brVcH8u1xaHB8ZnqF1X1UFU9uaqeUVVPp/8sqV+uqu/S7xev\nnZV+sVRbzFq/ABi+K4/+oPChwfaK86LTxcGTHAB6wC8O5l5vof+n2AXAZ5MA3FNVbwJeCLwjyU/o\nX4jbU1U/6LI+k7RIW9yY5CrgDHAU+C2Aqvpqkr8GvgqcBt409Jt8w1tJWzCD/aKqPjJUpDgXfDPX\nLxZrC2awXwAvSn9tj58B36L/CPhV9Qu/MCVJjfPplZLUOINekhpn0EtS4wx6SWqcQS9JjTPoJalx\nBr0kNc6gl6TG/R8UgjHB7xd1mQAAAABJRU5ErkJggg==\n", "text/plain": ["<matplotlib.figure.Figure at 0x7fef9baac250>"]}, "metadata": {}}], "source": ["htlist = []\n", "for _ in itertools.repeat(None, 1000):\n", "    htlist.append(simulate_fair_coin_flips_two_sided(250))\n", "\n", "htcdf = thinkstats2.Cdf(htlist)\n", "thinkplot.Cdf(htcdf)"]}, {"execution_count": 179, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stderr", "text": ["/home/yuzhong/anaconda2/lib/python2.7/site-packages/matplotlib/axes/_axes.py:519: UserWarning: No labelled objects found. Use label='...' kwarg on individual plots.\n", "  warnings.warn(\"No labelled objects found. \"\n"]}, {"output_type": "display_data", "data": {"image/png": 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"text/plain": ["<matplotlib.figure.Figure at 0x7fae2741af10>"]}, "metadata": {}}, {"output_type": "display_data", "data": {"text/plain": ["<matplotlib.figure.Figure at 0x7fae273ad4d0>"]}, "metadata": {}}], "source": ["two_flips_1000 = [simulate_fair_coin_flips_two_sided(250) for i in range(1000)]\n", "two_cdf = thinkstats2.Cdf(two_flips_1000)\n", "thinkplot.Cdf(two_cdf)\n", "thinkplot.Show()"]}, {"execution_count": 5, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"execution_count": 5, "metadata": {}, "data": {"text/plain": ["{'xscale': 'linear', 'yscale': 'linear'}"]}, "output_type": "execute_result"}, {"output_type": "display_data", "data": {"image/png": 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eAByqqn9bsKuVvlusfdBA/w3sGkwL/3mS0wbbmui/geH2/dLQ9mX136oFfZI/BI5W1Z7B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\nOINekhpn0EtS4wx6SWqcQS9Jjfs/czJwOgZChV0AAAAASUVORK5CYII=\n", "text/plain": ["<matplotlib.figure.Figure at 0x7f0924162c90>"]}, "metadata": {}}], "source": ["top_res = []\n", "for i in xrange(1000):\n", "    top_res.append(simulate_fair_coin_flips_two_sided(250))\n", "cdf = thinkstats2.Cdf(top_res)\n", "thinkplot.Cdf(cdf)"]}, {"execution_count": 50, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"execution_count": 50, "metadata": {}, "data": {"text/plain": ["{'xscale': 'linear', 'yscale': 'linear'}"]}, "output_type": "execute_result"}, {"output_type": "display_data", "data": {"image/png": 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fNNB/A3sG08J/neS8wbEm+m9guH0/N3R8Rf23ZkGf5I+BU1V14+DQd4FtVfVi4O3AjUme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\nqXEGvSQ17v8AazRtnhLVGWQAAAAASUVORK5CYII=\n", "text/plain": ["<matplotlib.figure.Figure at 0x7f4224a7cdd0>"]}, "metadata": {}}], "source": ["coin_flips = [simulate_fair_coin_flips_two_sided(250) for i in range(1000)]\n", "cdf = thinkstats2.Cdf(coin_flips)\n", "thinkplot.Cdf(cdf)"]}, {"execution_count": 40, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"execution_count": 40, "metadata": {}, "data": {"text/plain": ["{'xscale': 'linear', 'yscale': 'linear'}"]}, "output_type": "execute_result"}, {"output_type": "display_data", "data": {"image/png": 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5D+BNwB/2N/80vZu9zlnu5rC5MDC+36T3V9g5cz9/SfYBp6rqK0O7mpi/VcYHDcwf8I7+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\nrkJggg==\n", "text/plain": ["<matplotlib.figure.Figure at 0x1073c7790>"]}, "metadata": {}}], "source": ["flips = [simulate_fair_coin_flips_two_sided(250) for _ in range(1000)]\n", "\n", "cdf1 = thinkstats2.Cdf(flips, label=\"flips\")\n", "thinkplot.Cdf(cdf1)"]}, {"execution_count": 5, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "display_data", "data": {"image/png": 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ya0FOElaP/wZuBsoPfXuR1BJNO641StNeKA0vLX1eyop/c+XWh1j+ILljI+Kq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\n", "text/plain": ["<matplotlib.figure.Figure at 0x7f314d3c9f90>"]}, "metadata": {}}, {"output_type": "display_data", "data": {"text/plain": ["<matplotlib.figure.Figure at 0x7f31223387d0>"]}, "metadata": {}}], "source": ["holder = []\n", "for i in range(1000):\n", "    holder += [simulate_fair_coin_flips_two_sided(250)]\n", "    \n", "cdf_holder = thinkstats2.Cdf(holder)\n", "thinkplot.Cdf(cdf_holder)\n", "\n", "thinkplot.Show(title='CDF of Coin Flip Two Sided Times',\n", "              xlabel='Number Greater when Flipped',\n", "              ylabel='CDF') \n"]}, {"execution_count": 21, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "display_data", "data": {"image/png": 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VwGFJDk6yJ3AqcPFggyQH0QTEC7sCQpK0PHo93FRV9yY5E7iUJpAurKrNSU5vFtcFwGuB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\nZEhIkjoZEpKkToaEJKnT/wekLfAR8C7SyQAAAABJRU5ErkJggg==\n", "text/plain": ["<matplotlib.figure.Figure at 0x7fe4d9d9a890>"]}, "metadata": {}}], "source": ["results = [simulate_fair_coin_flips_two_sided(250) for _ in xrange(1000)]\n", "cdf = thinkstats2.Cdf(results)\n", "\n", "thinkplot.Cdf(cdf)\n", "thinkplot.Config(\n", "    title='Coin Flips',\n", "    xlabel='Number of Heads',\n", "    ylabel='CDF'\n", ")"]}, {"execution_count": 112, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "display_data", "data": {"image/png": 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pI3c/38xOkPSamZ3q7ruSOxYXF1dOFxUVqaio6IgVCQAtQUlJiUpKSppteZHeT8LMhkoq\ndvfRweMfSXJ3/1lCnz9IutvdlwSPX5d0q7t/mLQs7ieBKrjHA1C3dL+fxDJJhWaWb2ZtJE2Q9HxS\nnzJJoyTJzLpLGiDps4jrAgDUQ6SHm9y93MymS3pV8UB6zN1Xm9n18dk+T9Kdkp40s5XB0/7d3bdF\nWRcAoH4iPyfh7i9LOjGp7ZGE6S2Kn5cAAKQZhuUAAIQiJAAAoQgJAECodLhOAmCwPiBNsSeBtNCU\ngGCgPiA6hATSQlMCgoH6gOhwuAlph6ungfTBngQAIBQhAQAIRUgAAEIREgCAUIQEACAUIQEACEVI\nAABCcZ0EmhXDawCtC3sSaFZNDQiG2ADSCyGBZtXUgGCIDSC9cLgJkWF4DaDlY08CABCKkAAAhCIk\nAAChCAkAQChCAgAQipAAAIQiJAAAoQgJAEAoQgIAEIqQAACEIiQAAKEYuwmhGPYbAHsSCNWUgGDI\nb6B1ICQQqikBwZDfQOvA4SbUC8N+A5mJPQkAQChCAgAQKvKQMLPRZrbGzD4xs1tD+hSZ2UdmtsrM\n3oy6JgBA/UR6TsLMYpIekjRS0mZJy8zsv9x9TUKfjpL+r6QL3H2TmXWJsiYAQP1FvScxRNJady9z\n9wOSFkoam9RnkqRn3X2TJLn7lxHXBACop6hDopekjQmPPw/aEg2QlGtmb5rZMjObEnFNAIB6Soev\nwB4t6QxJ50tqJ+k9M3vP3T9NbVkAgKhDYpOkPgmPewdtiT6X9KW775W018zeknSapGohUVxcXDld\nVFSkoqKiZi4XAFq2kpISlZSUNNvyzN2bbWHVFm52lKT/UfzE9RZJH0ia6O6rE/oMlDRH0mhJbSW9\nL2m8u3+ctCyPslZUN/zi2yqnuZgOaJnMTO5ujX1+pHsS7l5uZtMlvar4+Y/H3H21mV0fn+3z3H2N\nmb0iaaWkcknzkgMCAJAakZ+TcPeXJZ2Y1PZI0uP7Jd0fdS0AgIZJhxPXOAIY9htAYzAsR4Zg2G8A\njUFIZAiG/QbQGBxuykB8UwlAfbEnAQAIRUgAAEIREgCAUIQEACAUIQEACEVIAABCERIAgFC1hoSZ\nPZkwfXXk1QAA0kpdexKnJUz/a5SFAADST10hwQ0cACCD1TUsR28zmy3JEqYrufv3I6sMAJBydYXE\nDxOmP4yyEABA+qk1JNz9qSNVCAAg/dT5FVgzu9rMlpvZ7uDnQzO76kgUBwBIrVr3JIKvvf6bpJsl\nLVf83MQZku4zM3f3X0ZfIhJxhzkAR1JdexLfk3SZu7/p7jvc/St3f0PSP0u6MfrykKypAcFd5gA0\nRF0hke3upcmNQVt2FAWhdk0NCO4yB6Ah6vp2055GzsMRwB3mAEStrpA4ycxW1tBukvpFUA8AII3U\nFRKnSeouaWNSe56kLyKpCACQNuo6J/FzSTvcvSzxR9KOYB4AoBWrKyS6u/tfkhuDtoJIKgIApI26\nQqJTLfOymrMQAED6qSskPjSz65IbzexaSX+KpiQAQLqo68T1v0l6zsy+o8OhcKakNpIui7IwAEDq\n1TXA398kDTOz8yR9PWheHFx1DQBo5erak5Akufubkt6MuBYAQJqpcxRYAEDmIiQAAKEICQBAKEIC\nABCKkAAAhIo8JMxstJmtMbNPzOzWWvoNNrMDZnZ51DUBAOon0pAws5ikhyRdKOlrkiaa2cCQfvdI\neiXKegAADVOv6ySaYIiktcHIsTKzhZLGSlqT1O8mSc9IGhxxPWmF+1UDSHdRH27qpar3ovg8aKtk\nZj0ljXP3Xyh+M6OM0ZSA4F7VAI6EdDhx/Z+SEs9VZExQNCUguFc1gCMh6sNNmyT1SXjcO2hLdKak\nhWZmkrpIGmNmB9z9+eSFFRcXV04XFRWpqKiouetNGe5XDaA5lJSUqKSkpNmWZ+7ebAurtnCzoyT9\nj6SRkrZI+kDSRHdfHdL/CUkvuPvvapjnUdaaCsMvvq1ympAAEAUzk7s3+ghNpHsS7l5uZtMlvar4\noa3H3H21mV0fn+3zkp8SZT0AgIaJ+nCT3P1lSScmtT0S0veaqOsBANRfOpy4BgCkKUICABCKkAAA\nhCIkAAChCAkAQChCAgAQipAAAIQiJAAAoQgJAEAoQgIAEIqQAACEIiQAAKEICQBAqMhHgc0E3Ksa\nQGvFnkQzaGpAcL9qAOmKkGgGTQ0I7lcNIF1xuKmZcRtSAK0JexIAgFCEBAAgFCEBAAhFSAAAQhES\nAIBQhAQAIBQhAQAIRUgAAEIREgCAUIQEACAUIQEACEVIAABCERIAgFCEBAAgFCEBAAhFSAAAQhES\nAIBQ3JkuydO/e7vJ96wGgNaCPYkkTQmIrKy2zVwNAKRW5CFhZqPNbI2ZfWJmt9Ywf5KZ/Tn4ecfM\nTom6pto0JSCmTTq/masBgNSK9HCTmcUkPSRppKTNkpaZ2X+5+5qEbp9JGuHuO8xstKRHJQ2Nsq76\nWrL4rlSXAAApFfWexBBJa929zN0PSFooaWxiB3df6u47godLJfWKuCYAQD1FHRK9JG1MePy5ag+B\nayW9FGlFAIB6S5tvN5nZeZKmSjonrE9xcXHldFFRkYqKiiKvCwBakpKSEpWUlDTb8szdm21h1RZu\nNlRSsbuPDh7/SJK7+8+S+p0q6VlJo919XciyPMpaDxl+8W2V05yTANDSmZnc3Rr7/KgPNy2TVGhm\n+WbWRtIESc8ndjCzPooHxJSwgAAApEakh5vcvdzMpkt6VfFAeszdV5vZ9fHZPk/S7ZJyJT1sZibp\ngLsPibIuAED9RH5Owt1flnRiUtsjCdPXSbou6joAAA3HFdcAgFCEBAAgFCEBAAhFSAAAQhESAIBQ\nhAQAIBQhAQAIRUgAAEKlzQB/UeBWpADQNK16T4JbkQJA07TqkOBWpADQNK36cFMihv0GgIZr1XsS\nAICmISQAAKEICQBAKEICABCKkAAAhCIkAAChCAkAQChCAgAQipAAAIQiJAAAoQgJAEAoQgIAEIqQ\nAACEIiQAAKEICQBAKEICABCKkAAAhGpRd6YbfvFtqS4BADJKRuxJZGW1TXUJANAitfqQyMpqq2mT\nzk91GQDQIrWow02StGTxXakuAQAyRqvfkwAANB4hAQAIFXlImNloM1tjZp+Y2a0hfWab2VozW2Fm\ng6KuCQBQP5GGhJnFJD0k6UJJX5M00cwGJvUZI+kEd+8v6XpJc6OsqTUoKSlJdQlpg3VxGOviMNZF\n84l6T2KIpLXuXubuByQtlDQ2qc9YSfMlyd3fl9TRzLpHXFeLxn+Aw1gXh7EuDmNdNJ+oQ6KXpI0J\njz8P2mrrs6mGPgCAFODENQAglLl7dAs3Gyqp2N1HB49/JMnd/WcJfeZKetPdFwWP10g6193/lrSs\n6AoFgFbM3a2xz436YrplkgrNLF/SFkkTJE1M6vO8pBslLQpC5avkgJCa9iYBAI0TaUi4e7mZTZf0\nquKHth5z99Vmdn18ts9z9xfN7CIz+1TSbklTo6wJAFB/kR5uAgC0bGlz4trMHjOzv5nZyoS2e81s\ndXCR3bNmlh2055vZP8xsefDzcOoqb34h6+I/zOzPZvaRmb1sZj0S5s0ILkZcbWYXpKbqaDRkXWTi\ndpEw7xYzqzCz3IS2jNouEuZVWReZuF2Y2Swz+zzhPY9OmNew7cLd0+JH0jmSBklamdA2SlIsmL5H\n0t3BdH5iv9b2E7Iu2idM3yTpF8H0yZI+UvzQYYGkTxXsIbaGnwaui4zbLoL23pJelrReUm7QdlKm\nbRe1rIuM2y4kzZJ0cw19G7xdpM2ehLu/I2l7Utt/u3tF8HCp4hvAIa32RHbIutiV8LCdpEPr5VJJ\nC939oLuXSlqr+EWMrUID14WUYdtF4OeSfpjUNlYZtl0EaloXUmZuFzW95wZvF2kTEvVwjaSXEh4X\nBLtRb5rZOakq6kgyszvNbIOkSZL+T9CckRcjhqwLKcO2CzO7VNJGd/9L0qyM2y5qWRdShm0XgenB\nofr/Z2Ydg7YGbxctIiTMbKakA+6+IGjaLKmPu58h6RZJC8ysfcoKPELc/cfu3kfSrxU/zJKxQtbF\nFmXQdmFmWZJuU/zQQkYLWReH/pLOxM+LhyX1c/dBkr6Q9EBjF5T2IWFm/yLpIsX/YpQkufsBd98e\nTC+XtE7SgJQUmBoLJF0eTG+SlJcwr3fQlikWSPpnSXL3/Rm2XZyg+HHlP5vZesV/98vNrJvi20Cf\nhL6tfbuoaV38ycy6ZeLnhbv/3YOTEJIe1eFDSg3+vEi3kDAlHEcLzsj/UNKl7r4vob1LMMKszKyf\npEJJnx3hWqOWvC4KE+aNk7QmmH5e0gQza2NmfRVfFx8csSqPjLrWxeqgPaO2C3df5e493L2fu/dV\nfGy00939fxXfLsZnynZR27rItO1CkhK//aj4H5SrgukGf16kze1LzWyBpCJJnYNjzbMU331sI+k1\nM5Okpe5+g6QRkv7DzPYrftLyenf/KiWFRyBkXVxsZidKKpdUJum7kuTuH5vZbyR9LOmApBsS/oJo\n8RqyLpSB24W7P5HQxXX4QzPjtouwdaEM3C4knWfxe/NUSCpV/DYMjdouuJgOABAq3Q43AQDSCCEB\nAAhFSAAAQhESAIBQhAQAIBQhAQAIRUgAgWBI6ZrG/WnqctcnDuENtCSEBFBVFBcOcTESWixCAqjq\naDObZ2arghsatTWzfmb2kpktM7M/mtkASTKzfzKzpWb2JzN71cy6Bu25ZvaKmf3FzB5VcOWvmR1n\nZn+w+M2SVprZFSl8n0C9EBJAVf0lzXH3r0v6StK3Jc2TNN3dBys+ltgvgr5vu/tQd/+GpEWS/j1o\nnxXMO0XSczo80N5oSZvc/XR3P1Xxm+MAaS1txm4C0sRnCfcjWK74yKLDJP3WggHEJB0T/JsXjINz\nfNC2PmgfIekySXL3F83s0A1h/iLpfjO7W9Li4GYxQFpjTwKoal/CdLmkXEnb3f2MYA/g9GAvQ5Lm\nSJod7BV8V9KxIcs8NOjeWklnKB4Wd5rZjyN5B0AzIiSAqpJv+bhT0noz+3ZlB7NTg8lsxW9oI0lX\nJzznLUnfCfqOkdQpmD5e0p7g5ln3KR4YQFojJICqkr+J5Ip/4E8LbgW5SvH7ikvSHZKeMbNlkv6e\n8Jw7JI0Ivk47TtKGoP0USR+Y2UeK33L1zojeA9BsGCocABCKPQkAQChCAgAQipAAAIQiJAAAoQgJ\nAEAoQgIAEIqQAACEIiQAAKH+Pwf7yfhNoP1aAAAAAElFTkSuQmCC\n", "text/plain": ["<matplotlib.figure.Figure at 0x7f5252125a90>"]}, "metadata": {}}, {"output_type": "display_data", "data": {"text/plain": ["<matplotlib.figure.Figure at 0x7f5251a419d0>"]}, "metadata": {}}], "source": ["toss_cts = []\n", "\n", "for i in range(1000):\n", "    toss_cts.append(simulate_fair_coin_flips_two_sided(250))\n", "\n", "cdf = thinkstats2.Cdf(toss_cts, label='Most Common Outcome Counts')\n", "thinkplot.Cdf(cdf)\n", "thinkplot.Show(xlabel='heads', ylabel='CDF')"]}, {"execution_count": 5, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "display_data", "data": {"image/png": 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du0nSpElCVWXU1/d9uOk04F5JdkqyBtgfOHGwQpIdaRLEs7sShCRpefR6uKmqbkpyCHAy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\n", "text/plain": ["<matplotlib.figure.Figure at 0x1bbb590>"]}, "metadata": {}}], "source": ["results = [simulate_fair_coin_flips_two_sided(250) for _ in xrange(1000)]\n", "cdf = thinkstats2.Cdf(results)\n", "thinkplot.Cdf(cdf)\n", "thinkplot.Config(\n", "    title='Coin Flips',\n", "    xlabel='Number of Most Common Outcome',\n", "    ylabel='CDF'\n", ")"]}, {"execution_count": 18, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"execution_count": 18, "metadata": {}, "data": {"text/plain": ["{'xscale': 'linear', 'yscale': 'linear'}"]}, "output_type": "execute_result"}, {"output_type": "display_data", "data": {"image/png": 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Oyt5/nuTCwbEVnxdrFvRJ/gA4XVV3DQ59C7ikql4CvBW4K8lT16o/66Wq/rCqLgH+mn7J\nYmotMhYPM0XnRZKtwO/T/zN9qi0yFj+e0U5jXtwBPK+qrgb+E3jPuC+0JkGf5PXAq+jP3ACoqtNV\n9Z3B9ueBrwIvWIv+bBB3Aa8dbJ8Edgw9dvHg2LS4C/g1gKr64ZSdF5fRr7Pen+Tr9P/vP59kG/1z\n4JKhtq2fFwuNxb8n2TaNeVFVj9WgKA98iHPlmRXnxWoEfRiqKw0+KX4b8Oqq+t+h488crIxJkucB\nlwNfW4X+rKf5Y3H50GOvAY4Mtg8ANyW5IMlz6Y/F59asl2tjubE4PDg+VedFVX2pqp5dVc+rqufS\nX0vqF6rqUfrnxeum5bxYaiym7bwAGL4qj/6k8EuD7RXnxSjfjB29l8ldQA94xqD2eiv9P8UuAD6V\nBODeqnoT8FLgHUl+SP+DuD1V9d0u+7OeFhmLX03yc8AZ4BjwWwBV9eUkfwN8GTgNvGnoN/mmt5Kx\nYArPi6r68FCT4lzwTd15sdhYMIXnBXB9+vf2eAL4Bv0l4Mc6L/zClCQ1ztUrJalxBr0kNc6gl6TG\nGfSS1DiDXpIaZ9BLUuMMeklqnEEvSY37P718OBHXMHjwAAAAAElFTkSuQmCC\n", "text/plain": ["<matplotlib.figure.Figure at 0x7f409b702250>"]}, "metadata": {}}], "source": ["ts_flips = [simulate_fair_coin_flips_two_sided(250) for i in xrange(1000)]\n", "cdf_ts_flips = thinkstats2.Cdf(ts_flips)\n", "thinkplot.Cdf(cdf_ts_flips)"]}, {"execution_count": 24, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"execution_count": 24, "metadata": {}, "data": {"text/plain": ["{'xscale': 'linear', 'yscale': 'linear'}"]}, "output_type": "execute_result"}, {"output_type": "display_data", "data": {"image/png": 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HDfTfwM7BtPBfJTl/cKyJ/hsYbt+vDR1fU/+tW9An+VPgeFXtHhz6LnBxVT0beCOwO8kj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\nvSQ17v8BMs5v2zGkggQAAAAASUVORK5CYII=\n", "text/plain": ["<matplotlib.figure.Figure at 0x7f1caf4fae90>"]}, "metadata": {}}], "source": ["sample = []\n", "for n in range(1000):\n", "    sample.append(simulate_fair_coin_flips_two_sided(250))\n", "\n", "sample = thinkstats2.Cdf(sample)\n", "thinkplot.Cdf(sample)"]}, {"execution_count": 11, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"execution_count": 11, "metadata": {}, "data": {"text/plain": ["{'xscale': 'linear', 'yscale': 'linear'}"]}, "output_type": "execute_result"}, {"output_type": "display_data", "data": {"image/png": 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mvT5zoxpqi4ODQ98BdlTVy4B3AAeTPG1qFVwnVfVHVbUD+Gvmpyxm1hJt8Sgz1C+S/Czw\nB8C7pl2XaVuiLZ4Yxa86L9Yl6JP8BnAl86OVJ5wAnje0f+7gWNMWa4uqOllV3x9sfxn4BnDhVCo4\nHQeBPYPtmewXQw4CvwpQVT+esX5xPvPz7/cn+Rbz//ZfTvJs5vvAjqGyrfeLxdri35I8e5y8WIug\nD0PzR0l2MT/H9Pqq+t+hcrcD1yQ5K8kLgAuAL61BfaZppLZIcs5glVCSvJD5tvjmOtd1rS1siwuG\nzl0FHBlsz2K/WNgWhwfHZ6pfVNVXq+q5VfXCqnoB8+tq/UJVfZf5fnH1rPSL5dpinH4xyjdjR69l\nchDoAc8azDe+i/k/P84CPpcE4J6qemtVfT3JLcDXgZPAW2twSbkFq2kL4BXAu5P8mPkLcfuq6gdT\nqfgaWKItfiXJRcAp4Bjw2wAz2i8WbQtmsF9U1SeGihRngm/m+sVSbcEY/cIvTElS41y9UpIaZ9BL\nUuMMeklqnEEvSY0z6CWpcQa9JDXOoJekxhn0ktS4/wNvEyaHaswAmAAAAABJRU5ErkJggg==\n", "text/plain": ["<matplotlib.figure.Figure at 0x7f585c273d10>"]}, "metadata": {}}], "source": ["total = []\n", "for i in range(0,1000):\n", "    total.append(simulate_fair_coin_flips_two_sided(240))\n", "cdf = thinkstats2.Cdf(total)\n", "thinkplot.Cdf(cdf)\n", "# your implementation here (imports included for convenience)"]}, {"execution_count": 23, "cell_type": "code", "metadata": {"scrolled": true, "collapsed": false}, "outputs": [{"output_type": "display_data", "data": {"image/png": 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CtwOv6DMmSdLc9drdJEkabyNz4TrJqUluSXLZwLq/S3Jle5Pd55Js3a5/dJJ/S3Jx+3Py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\nZJKQJHUySUiSOpkkJEmd/j8eW7ouORRd8QAAAABJRU5ErkJggg==\n", "text/plain": ["<matplotlib.figure.Figure at 0x111025810>"]}, "metadata": {}}, {"output_type": "display_data", "data": {"text/plain": ["<matplotlib.figure.Figure at 0x1117b4390>"]}, "metadata": {}}], "source": ["res = []\n", "for _ in range(1000):\n", "    res.append(simulate_fair_coin_flips_two_sided(250))\n", "\n", "cdf = thinkstats2.Cdf(res)\n", "thinkplot.Cdf(cdf)\n", "thinkplot.show(xlabel='No of Most Common Outcome in 250 coin flips', ylabel='CDF')"]}, {"source": ["I'm not sure if you're asking me to pick either heads or tails, whichever appears in greater number, and then make that CDF or if you want me to compare the CDF of both. So I'm going to do both things"], "cell_type": "markdown", "metadata": {}}, {"execution_count": 30, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "display_data", "data": {"image/png": 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jJX0zk75h6bIdIWkXSc+m+96nZN6iku9HSvp5hbZ7r6RtK7Euqw8OElZtH0TE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\nMDOzXA4SZmaWy0HCzMxyOUiYmVmu/wMwHcT9LVv2cwAAAABJRU5ErkJggg==\n", "text/plain": ["<matplotlib.figure.Figure at 0x1120a9890>"]}, "metadata": {}}, {"output_type": "display_data", "data": {"text/plain": ["<matplotlib.figure.Figure at 0x1120abb10>"]}, "metadata": {}}], "source": ["flipResults = []\n", "for i in range(1000):\n", "#     The instructions say 240, but everything else says 250, so I'm going with 250\n", "    flipResults.append(simulate_fair_coin_flips_two_sided(250))\n", "\n", "flipCdf = thinkstats2.Cdf(flipResults, label = 'Coin Flips')\n", "\n", "thinkplot.Cdf(flipCdf)\n", "thinkplot.Show(xlabel = 'Probability of Heads', ylabel='CDF', title='CDF of Two-Sided Coin Flips')"]}, {"execution_count": 54, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"execution_count": 54, "metadata": {}, "data": {"text/plain": ["{'xscale': 'linear', 'yscale': 'linear'}"]}, "output_type": "execute_result"}, {"output_type": "display_data", "data": {"image/png": 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U1dcXnWql75ZqHzTQf0O7htPCf5PkrOGxJvpvaLR9vz5yfFX9t2ZBn+SPgONVdfPw0APA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\ncQa9JDXOoJekxhn0ktS4/wOvGndgvUXoZgAAAABJRU5ErkJggg==\n", "text/plain": ["<matplotlib.figure.Figure at 0x7f8530948710>"]}, "metadata": {}}], "source": ["trials = [simulate_fair_coin_flips_two_sided(250) for i in range(1000)]\n", "cdf = thinkstats2.Cdf(trials)\n", "thinkplot.Cdf(cdf)"]}, {"execution_count": 95, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "display_data", "data": {"image/png": 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XjcWAtUMDxr7yZ8DHetrWMEFjDwPXD80Z/5nqbNL4zzbOTRj/PwSuy8xXqj4vVu0Dj/9i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\nAAAAAElFTkSuQmCC\n", "text/plain": ["<matplotlib.figure.Figure at 0x7f23c48d57d0>"]}, "metadata": {}}, {"output_type": "display_data", "data": {"text/plain": ["<matplotlib.figure.Figure at 0x7f23c4949610>"]}, "metadata": {}}], "source": ["resultsList = []\n", "\n", "for i in range(10000):\n", "    resultsList.append(simulate_fair_coin_flips_two_sided(250))\n", "    \n", "\n", "    \n", "cdf = thinkstats2.Cdf(resultsList)\n", "thinkplot.Cdf(cdf)\n", "thinkplot.Show()"]}, {"execution_count": 49, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "display_data", "data": {"image/png": 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JScLMzHK5uslsEMneXvTDV95X7XCsDrgkYTaIlN5/uoN7MlkelyTMBqhyU36vLjPlt6fb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\ncpIwM7NcThJmZpbLScLMzHL9f1oGhtOt323MAAAAAElFTkSuQmCC\n", "text/plain": ["<matplotlib.figure.Figure at 0x109756f90>"]}, "metadata": {}}, {"output_type": "display_data", "data": {"text/plain": ["<matplotlib.figure.Figure at 0x108f0e710>"]}, "metadata": {}}], "source": ["results = [simulate_fair_coin_flips_two_sided(250) for _ in range(1000)]\n", "head, tail = zip(*twoSidedResults)\n", "\n", "cdfTwoHeads = thinkstats2.Cdf(head, label = 'heads')\n", "cdfTwoTails = thinkstats2.Cdf(tail, label = 'tails')\n", "\n", "thinkplot.PrePlot(2)\n", "thinkplot.Cdfs([cdfTwoHeads, cdfTwoTails])\n", "thinkplot.Config(title ='Number of occurences in a coin toss')\n", "thinkplot.Show(xlabel = 'Number of each possible toss', ylabel ='CDF')"]}, {"execution_count": 24, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "display_data", "data": {"image/png": 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dXdx6662cc845zJs3j66uLpYsWcKVV17Jxo0bOfroo9m0aRMLFy7kqquuAmD27Nlcc801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\n", "text/plain": ["<matplotlib.figure.Figure at 0x7f9a0f30be90>"]}, "metadata": {}}, {"output_type": "display_data", "data": {"text/plain": ["<matplotlib.figure.Figure at 0x7f9a0ee1b050>"]}, "metadata": {}}], "source": ["counts = []\n", "for i in range(1000):\n", "    counts.append(simulate_fair_coin_flips_two_sided(250))\n", "\n", "cdf = thinkstats2.Cdf(counts)\n", "thinkplot.Cdf(cdf, label='counts')\n", "thinkplot.Show(loc='lower right')"]}, {"execution_count": 69, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "display_data", "data": {"image/png": 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WxuJ8BjXk+5M8wuD7vTfJWczeWFBV36iuyA78NcdKL2sai0mFe/j+3y57gGu65WuA3UPt\nvwlH73B94kj5phGLx2HxuiP2AK9N8oNJXgi8iMFNYC35vrHozvy/Bbiyqr49tN0sjsWLhtZtB448\nSbX14wOGxqKqvlhVZ1fVeVX1QgYhdnFVPc6MjQUcnQgf8Rrgi93y2o6RCZz1/RCD3yLfBg4B1wJn\nAHcyuIP1U8Bzh7Z/D4OzvfczdAXJqf5aZhyuYlAr+z8Gd/H+w9D2N3bjcAB4xXr3/ySMxcPA14B7\nu9d7Z3gsPgbsB/YxmPg8f2j7Jo+P5cZi0fqv0F0tM4tjweAE8gPdz8UngC1D26/6GPEmJklqkP9m\nT5IaZLhLUoMMd0lqkOEuSQ0y3CWpQYa7JDXIcJekBhnuktSg/wdZ7xarJ4nQbgAAAABJRU5ErkJg\ngg==\n", "text/plain": ["<matplotlib.figure.Figure at 0x7fd3bc7ea410>"]}, "metadata": {}}], "source": ["def coin_flips_trials_two_sided(n, m):\n", "    head_num_trials = []\n", "    for i in range(n):\n", "        head_num_trials.append(simulate_fair_coin_flips_two_sided(m))\n", "    hist = thinkstats2.Hist(head_num_trials)\n", "    thinkplot.Hist(hist)\n", "    return head_num_trials\n", "\n", "trials_two_sided = coin_flips_trials(1000, 250)"]}, {"source": ["Use the CDF to compute a two-tailed (or two-sided) p-value for the observed data (140 heads out of 250 flips)."], "cell_type": "markdown", "metadata": {}}, {"execution_count": 24, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["lower\n", "94.9\n", "higher\n", "5.1\n"]}], "source": ["percentile = cdf2.PercentileRank(140)\n", "print \"lower\"\n", "print percentile\n", "print \"higher\"\n", "print 100 - percentile"]}, {"execution_count": 70, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["Percentile rank for percentage of data that is equal to or less than for a two tailed test 97.1\n", "Pvalue for percentage of data that is equal to or greater than for a two tailed test 2.9\n"]}], "source": ["pvalue_of_equal_to_or_less_than_2tailed = mostFrequentResultCdf.PercentileRank(140)\n", "print \"Percentile rank for percentage of data that is equal to or less than for a two tailed test\", pvalue_of_equal_to_or_less_than\n", "pvalue_of_equal_to_or_greater_than_2tailed = 100 -  pvalue_of_equal_to_or_less_than\n", "print \"Pvalue for percentage of data that is equal to or greater than for a two tailed test\",  pvalue_of_equal_to_or_greater_than"]}, {"execution_count": 105, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["pvalue two sided: 5.40\n"]}], "source": ["pvalue_two_side = 100 - two_side_cdf.PercentileRank(observed - 1)\n", "print 'pvalue two sided: %.2f' % pvalue_two_side"]}, {"execution_count": 100, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["p value is 0.052 (two tailed)\n"]}], "source": ["p2 = 1 - 0.01*(stats.percentileofscore(np.array(htlist), 140))\n", "print 'p value is', p2 ,'(two tailed)'"]}, {"execution_count": 177, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["two sided p-value for 140 heads out of 250 coins:  5.4\n"]}], "source": ["two_rank = two_cdf.PercentileRank(140)\n", "two_p_value = 100 - two_rank\n", "print \"two sided p-value for 140 heads out of 250 coins: \", two_p_value"]}, {"execution_count": 6, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["p-value: 4.4%\n"]}], "source": ["print \"p-value:\", str(100-cdf.PercentileRank(140))+\"%\""]}, {"execution_count": 51, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["P-value of data that 140/250 flips are heads\n", "4.1%\n"]}], "source": ["print \"P-value of data that 140/250 flips are heads\"\n", "print str(100 - cdf.PercentileRank(140)) + \"%\""]}, {"execution_count": 41, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["5.4\n"]}], "source": ["pvalue = 100 - cdf1.PercentileRank(140)\n", "print pvalue"]}, {"execution_count": 6, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["7.5 %\n"]}], "source": ["p_val = 100 - cdf_holder.PercentileRank(139)\n", "print p_val, '%'"]}, {"execution_count": 22, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"execution_count": 22, "metadata": {}, "data": {"text/plain": ["0.062000000000000055"]}, "output_type": "execute_result"}], "source": ["1 - cdf[139]"]}, {"execution_count": 115, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["Pvalue:  6.2 %\n"]}], "source": ["pvalue = 100 - cdf.PercentileRank(139)\n", "\n", "print \"Pvalue: \", pvalue, \"%\""]}, {"execution_count": 19, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["Two-sided p_value:  6.3 %\n"]}], "source": ["ts_p_value = 100 - cdf_ts_flips.PercentileRank(139)\n", "print 'Two-sided p_value: ', ts_p_value, '%'"]}, {"execution_count": 25, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["6.7\n"]}], "source": ["p_val = 100 - sample.PercentileRank(139)\n", "print p_val"]}, {"execution_count": 12, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["P-value:  0.009\n"]}], "source": ["p_value = (100 - cdf.PercentileRank(139))/100\n", "print 'P-value: ', p_value"]}, {"execution_count": 24, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["p-value: 5.8\n"]}], "source": ["print \"p-value:\", float(format(100 - cdf.PercentileRank(139), '.2f'))"]}, {"execution_count": 64, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["P-value using CDF:  0.029\n", "P-value using the results of 1000 random trials directly:  0.029\n"]}], "source": ["percRank = cdfTwoHeads.PercentileRank(139)\n", "pVal = 1 - percRank/100\n", "print \"P-value using CDF: \",pVal\n", "\n", "count = sum(1.0 for x in head if x>= 140.0)\n", "print \"P-value using the results of 1000 random trials directly: \",count/1000"]}, {"execution_count": 31, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["The p-value is  0.038\n"]}], "source": ["percentileRank = flipCdf.PercentileRank(140)\n", "pValue = 1 - float(percentileRank)/100\n", "print \"The p-value is \", pValue"]}, {"execution_count": 55, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["Two-sided p-value:\n", "4.7%\n"]}], "source": ["print \"Two-sided p-value:\"\n", "print str(100 - cdf.PercentileRank(140)) + \"%\""]}, {"execution_count": 101, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"execution_count": 101, "metadata": {}, "data": {"text/plain": ["0.0"]}, "output_type": "execute_result"}], "source": ["1-cdf[139]"]}, {"execution_count": 25, "cell_type": "code", "metadata": {"scrolled": true, "collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["p-value: 0.071\n"]}], "source": ["print \"p-value:\", 1 - cdf.PercentileRank(139)/100\n", "# 139 because we want to include 140 in our counts"]}, {"execution_count": 70, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["2.0%\n"]}], "source": ["trials_two_sidedCDF = thinkstats2.Cdf(trials)\n", "print str(100.0 - trials_two_sidedCDF.PercentileRank(140)) + \"%\""]}, {"source": ["This approach (via simulations of the null-hypothesis) to computing p-values has its limitations.  For instance, suppose you observed 180 heads in 250 flips.  If you used your CDF from above to answer this question, what would go wrong?  What would you need to do in order to get a sensible estimate of this p-value?"], "cell_type": "markdown", "metadata": {}}, {"source": ["## Response\n", "What went wrong when I tried to get the p-value of 180 was that it was higher than or equal to all other entries. I would likely need to run many more trials in order to widen the birth of possibilities my model can account for. As it stands, some outcomes are so unlikely that they are never reached with just 1000 trials."], "cell_type": "markdown", "metadata": {}}, {"execution_count": 119, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["Pvalue:  0.0 %\n"]}], "source": ["pvalue = 100 - cdf.PercentileRank(179)\n", "\n", "print \"Pvalue: \", pvalue, \"%\""]}, {"source": ["There were no coin flips that resulted in 180 heads. (Odds are that) We'd have to run orders of magnitude more trials until we actually generated a trial that resulted in 180 heads."], "cell_type": "markdown", "metadata": {}}, {"source": ["In the two-tailed approach, the coin could be biased toward either heads or tails.  The data used to make the CDF could have been all cases where the coin came up tails more often, so comparing an observation of 180 heads to this would just be plain wrong.  It seems like the one-tailed approach would be better for this case where you're specifically testing if the coin is baised in one direction."], "cell_type": "markdown", "metadata": {}}, {"source": ["Well, the data would be an outlier in the set, thus leading to a strange representation. In order to get a better sense of the p-value, it may be better to do a single-sided p-value. Further, it may be better to avoid using a p-value altogether, given that for certain values it does not necessarily lend useful information about the coin."], "cell_type": "markdown", "metadata": {}}, {"execution_count": 76, "cell_type": "code", "metadata": {"collapsed": true}, "outputs": [], "source": ["for element in headsOrTailsAppears: \n", "    if element > 179: \n", "        print element"]}, {"source": ["Using the same cdf, if we compute the percentile rank of 180, we get 100% which means that our calculation of the p-value would be 0. The reason is because in our 1000 trials, we don't have any trials where the most common outcome exceeds 155. You would need to increase the number of trials in order to get a percentile rank of 180 that might not be 100% because you need trials where you actually flipped heads 180 times out of the 250."], "cell_type": "markdown", "metadata": {}}, {"execution_count": 257, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["p value is 0.0 (two tailed)\n"]}], "source": ["p3 = 1 - 0.01*(stats.percentileofscore(np.array(htlist), 180))\n", "print 'p value is', p3 ,'(two tailed)'"]}, {"source": ["The CDF from above doesn't actually include 180 as a viable option, so it would theoretically have a percentile rank over 100% and a negative p-value. I would need to get either a cdf that represents 180 or  a conditional that cuts off at 100% to get a p-value representative of 0 to show the many heads are plausibly explained by more than chance. "], "cell_type": "markdown", "metadata": {}}, {"source": ["The odds of getting 180 heads out of 250 flips are far lower than 1 in 1000, so the p-value of this would be calculated as exactly 0 percent. In order to get a more sensible estimate of the p-value, the simulation would have to be run way more than 1000 times, or a continuous mathematical model, like a Gaussian, can be used."], "cell_type": "markdown", "metadata": {}}, {"source": ["It would likely say the odds were 0 which is wrong (well for all intents and purposes it's fine). You would need to increase the number of iterations sufficiently so that it is likely at least some of them had 180 or more heads. This is problematic since that would require in excess of ~10^13 trials. "], "cell_type": "markdown", "metadata": {}}, {"source": ["180/250 is too unlikely to occur in 1000 tests, we can see from the cdf we did above that 180 will be a 0%. To get a sensible estimate the size would need to dramatically increase."], "cell_type": "markdown", "metadata": {}}, {"source": ["You would get a p-value of 0.0, because within our 1000 trials, we never saw 180 heads, so the CDF would calculate its p-value as there is nothing at or above 180, so the p-value is 0.  A p-value of 0 intuitive suggests that this result is impossible.  You'd need more trials to actually see its real probability"], "cell_type": "markdown", "metadata": {}}, {"source": ["In this two-tailed approach, the coin could theoretically be biased in either direction. The flips used to create it could be all heads, and you might assume that a tails value of 180 is normal, when in reality it might not be normal at all."], "cell_type": "markdown", "metadata": {}}, {"source": ["180 heads in 250 flips does not occur in the random trials. Many many more trials would have to be run and even then fitting a curve to the data to account for values that did not show up in the trials would be the best fit. I know seaborn does a KDE fit to histograms, so that would probably be one way of getting a sensible estimate of the value."], "cell_type": "markdown", "metadata": {}}, {"source": ["Write a function that takes as input a data frame and computes the absolute value of the difference in mean age between men and women."], "cell_type": "markdown", "metadata": {}}, {"execution_count": 102, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["observed age difference 2.81093577935\n"]}], "source": ["import numpy as np\n", "def compute_age_diff(data):\n", "    \"\"\" Compute the absolute value of the difference in mean age\n", "        between men and women on the titanic \"\"\"\n", "    man = []\n", "    woman = []\n", "#     print data.Age\n", "#     newData = pd.Series([data[\"Age\"], data[\"Sex\"]])\n", "#     print newData[\"Age\"]\n", "    \n", "#     data.loc[data[\"Sex\"] == \"male\", \"Sex\"] = data[\"Age\"]\n", "#     data.loc[data[\"Sex\"] == \"female\", \"Sex\"] = data[\"Age\"]\n", "#     print data[\"Sex\"]\n", "#     print data.iterrows()\n", "    \n", "    for index, row in data.iterrows():\n", "        if row.Sex == \"male\":\n", "            man.append(row.Age)\n", "        else:\n", "            woman.append(row.Age)\n", "\n", "#     print man\n", "#     for x in range(len(data.Age)):\n", "# #         print x\n", "        \n", "#         if data.Sex[x] == \"male\":\n", "#             man.append(data.Age[x])\n", "#         else:\n", "#             woman.append(data.Age[x])\n", "    return abs(np.mean(man)-np.mean(woman))\n", "\n", "observed_age_diff = compute_age_diff(data)\n", "print \"observed age difference\", observed_age_diff"]}, {"execution_count": 87, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["observed age difference 2.81093577935\n"]}], "source": ["def compute_age_diff(data):\n", "    \"\"\" Compute the absolute value of the difference in mean age\n", "        between men and women on the titanic \"\"\"\n", "    men = data[data.Sex == 'male']\n", "    women = data[data.Sex == 'female']\n", "    return abs(men.Age.mean() - women.Age.mean())\n", "\n", "observed_age_diff = compute_age_diff(data)\n", "print \"observed age difference\", observed_age_diff"]}, {"execution_count": 22, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["observed age difference 2.81093577935\n"]}], "source": ["def compute_age_diff(data):\n", "    \"\"\" Compute the absolute value of the difference in mean age\n", "        between men and women on the titanic \"\"\"\n", "    men = data[data.Sex == 'male']\n", "    women = data[data.Sex == 'female']\n", "    \n", "    mean_men_age = men.Age.mean()\n", "    mean_women_age = women.Age.mean()\n", "    return abs(mean_men_age - mean_women_age)\n", "\n", "    \n", "observed_age_diff = compute_age_diff(data)\n", "print \"observed age difference\", observed_age_diff"]}, {"execution_count": 240, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["observed age difference 2.81093577935\n"]}], "source": ["def compute_age_diff(data):\n", "    \"\"\" Compute the absolute value of the difference in mean age\n", "        between men and women on the titanic \"\"\"\n", "    agem = []\n", "    agef = []\n", "    for i in data.index:\n", "        if data.Sex[i] == 'male':\n", "            agem.append(data.Age[i])\n", "        elif data.Sex[i] == 'female':\n", "            agef.append(data.Age[i])\n", "        else:\n", "            print 'unknown Sex'\n", "            continue\n", "    diff = abs(np.mean(agem)-np.mean(agef))\n", "    \n", "    return diff\n", "\n", "observed_age_diff = compute_age_diff(data)\n", "print \"observed age difference\", observed_age_diff"]}, {"execution_count": 184, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["observed age difference 2.81093577935\n"]}], "source": ["def compute_age_diff(data):\n", "    \"\"\" Compute the absolute value of the difference in mean age\n", "        between men and women on the titanic \"\"\"\n", "    gender = data.groupby('Sex')\n", "    a, b = gender.Age.mean()\n", "    return abs(a-b)\n", "\n", "observed_age_diff = compute_age_diff(data)\n", "print \"observed age difference\", observed_age_diff"]}, {"execution_count": 8, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["observed age difference 2.81093577935\n"]}], "source": ["def compute_age_diff(data):\n", "    \"\"\" Compute the absolute value of the difference in mean age\n", "        between men and women on the titanic \"\"\"\n", "    return abs(data[data[\"Sex\"]=='male'][\"Age\"].mean()-data[data[\"Sex\"]=='female'][\"Age\"].mean())\n", "\n", "observed_age_diff = compute_age_diff(data)\n", "print \"observed age difference\", observed_age_diff"]}, {"execution_count": 57, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["observed age difference 2.81093577935\n"]}], "source": ["def compute_age_diff(data):\n", "    \"\"\" Compute the absolute value of the difference in mean age\n", "        between men and women on the titanic \"\"\"\n", "    m_age = data[data.Sex == \"male\"].Age.mean() \n", "    f_age = data[data.Sex == \"female\"].Age.mean()\n", "    return abs(m_age - f_age)\n", "\n", "observed_age_diff = compute_age_diff(data)\n", "print \"observed age difference\", observed_age_diff"]}, {"execution_count": 20, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["observed age difference 2.81093577935\n"]}], "source": ["import numpy as np\n", "\n", "def compute_age_diff(data):\n", "    \"\"\" Compute the absolute value of the difference in mean age\n", "        between men and women on the titanic \"\"\"\n", "    men = []\n", "    women = []\n", "    \n", "    for index, row in data.iterrows():\n", "        if row.Sex == \"male\":\n", "            men.append(row.Age)\n", "        else:\n", "            women.append(row.Age)\n", "            \n", "    return abs(np.mean(women)-np.mean(men))\n", "\n", "observed_age_diff = compute_age_diff(data)\n", "print \"observed age difference\", observed_age_diff"]}, {"execution_count": 8, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["observed age difference 2.81093577935\n"]}], "source": ["def compute_age_diff(data):\n", "    \"\"\" Compute the absolute value of the difference in mean age\n", "        between men and women on the titanic \"\"\"\n", "    gender_groupby = data.groupby('Sex')\n", "    a, b = gender_groupby.Age.mean()\n", "    return abs(a-b)\n", "\n", "observed_age_diff = compute_age_diff(data)\n", "print \"observed age difference\", observed_age_diff"]}, {"execution_count": 30, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["observed age difference 2.81093577935\n"]}], "source": ["def compute_age_diff(data):\n", "    \"\"\" Compute the absolute value of the difference in mean age\n", "        between men and women on the titanic \"\"\"\n", "    return abs(data[data.Sex == 'male'].Age.mean() - data[data.Sex == 'female'].Age.mean())\n", "\n", "observed_age_diff = compute_age_diff(data)\n", "print \"observed age difference\", observed_age_diff"]}, {"execution_count": 151, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["male age av:  30.7266445916\n", "female age av:  27.9157088123\n", "observed age difference 2.81093577935\n"]}], "source": ["import math\n", "\n", "def compute_age_diff(data):\n", "    \"\"\" Compute the absolute value of the difference in mean age\n", "        between men and women on the titanic \"\"\"\n", "    \n", "    male_age=  data[data.Sex == 'male'].Age.mean()\n", "    female_age=  data[data.Sex == 'female'].Age.mean()\n", "    print \"male age av: \", male_age\n", "    print \"female age av: \", female_age\n", "    \n", "    return abs(male_age-female_age)\n", "\n", "    \n", "\n", "observed_age_diff = compute_age_diff(data)\n", "print \"observed age difference\", observed_age_diff"]}, {"execution_count": 21, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["observed age difference 2.81093577935\n"]}], "source": ["def compute_age_diff(data):\n", "    \"\"\" Compute the absolute value of the difference in mean age\n", "        between men and women on the titanic \"\"\"\n", "    \n", "    grouped = data.groupby('Sex')\n", "    female, male = grouped.Age.mean()\n", "    return abs(female-male)\n", "\n", "observed_age_diff = compute_age_diff(data)\n", "print \"observed age difference\", observed_age_diff"]}, {"execution_count": 134, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["observed age difference 2.81093577935\n"]}], "source": ["def compute_age_diff(data):\n", "    \"\"\" Compute the absolute value of the difference in mean age\n", "        between men and women on the titanic \"\"\"\n", "    womean = data.Age[data['Sex'] == 'female'].mean()\n", "    mean = data.Age[data['Sex'] == 'male'].mean()\n", "    return abs(mean-womean)\n", "\n", "observed_age_diff = compute_age_diff(data_titanic)\n", "print \"observed age difference\", observed_age_diff"]}, {"execution_count": 30, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["observed age difference 2.81093577935\n"]}], "source": ["def compute_age_diff(data):\n", "    \"\"\" Compute the absolute value of the difference in mean age\n", "        between men and women on the titanic \"\"\"\n", "    men = data[data.Sex == \"male\"]\n", "    women = data[data.Sex == \"female\"]\n", "    return men.Age.mean() - women.Age.mean()\n", "\n", "observed_age_diff = compute_age_diff(data)\n", "print \"observed age difference\", observed_age_diff"]}, {"execution_count": 26, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["observed age difference 2.81093577935\n"]}], "source": ["def compute_age_diff(data):\n", "    \"\"\" Compute the absolute value of the difference in mean age\n", "        between men and women on the titanic \"\"\"\n", "    men_only = data[data.Sex == 'male']\n", "    women_only = data[data.Sex == 'female']\n", "    return abs(men_only.Age.mean() - women_only.Age.mean())\n", "\n", "observed_age_diff = compute_age_diff(data)\n", "print \"observed age difference\", observed_age_diff"]}, {"execution_count": 104, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["observed age difference 2.81093577935\n"]}], "source": ["def compute_age_diff(data):\n", "    \"\"\" Compute the absolute value of the difference in mean age\n", "        between men and women on the titanic \"\"\"\n", "    fem = data[data.Sex == 'female']\n", "    mal = data[data.Sex == 'male']\n", "    ageDiff = abs(fem.Age.mean()-mal.Age.mean())\n", "    return ageDiff\n", "\n", "observed_age_diff = compute_age_diff(data)\n", "print \"observed age difference\", observed_age_diff"]}, {"execution_count": 37, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["observed age difference 2.81093577935\n"]}], "source": ["def compute_age_diff(data):\n", "    \"\"\" Compute the absolute value of the difference in mean age\n", "        between men and women on the titanic \"\"\"\n", "    return (\n", "        abs(data[data.Sex == 'male']['Age'].mean() - \n", "            data[data.Sex == 'female']['Age'].mean()))\n", "\n", "observed_age_diff = compute_age_diff(data)\n", "print \"observed age difference\", observed_age_diff"]}, {"execution_count": 161, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["observed age difference 2.81093577935\n"]}], "source": ["def compute_age_diff(data):\n", "    \"\"\" Compute the absolute value of the difference in mean age\n", "        between men and women on the titanic \"\"\"\n", "    return abs(data[data.Sex == \"male\"].Age.mean() - data[data.Sex == \"female\"].Age.mean())\n", "\n", "observed_age_diff = compute_age_diff(data)\n", "print \"observed age difference\", observed_age_diff"]}, {"execution_count": 108, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["observed age difference 2.81093577935\n"]}], "source": ["def compute_age_diff(data):\n", "    \"\"\" Compute the absolute value of the difference in mean age\n", "        between men and women on the titanic \"\"\"\n", "    return np.mean(data[data['Sex'] == 'male'].Age) - np.mean(data[data['Sex'] == 'female'].Age)\n", "\n", "observed_age_diff = compute_age_diff(data)\n", "print \"observed age difference\", observed_age_diff"]}, {"execution_count": 51, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["observed age difference 2.81093577935\n"]}], "source": ["def compute_age_diff(data):\n", "    \"\"\" Compute the absolute value of the difference in mean age\n", "        between men and women on the titanic \"\"\"\n", "    male = data[data.Sex == 'male']\n", "    female = data[data.Sex == 'female']\n", "    ageDiff = abs(female.Age.mean() - male.Age.mean())\n", "    return ageDiff\n", "\n", "observed_age_diff = compute_age_diff(data)\n", "print \"observed age difference\", observed_age_diff"]}, {"execution_count": 31, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["observed age difference 2.81093577935\n"]}], "source": ["def compute_age_diff(data):\n", "    \"\"\" Compute the absolute value of the difference in mean age\n", "        between men and women on the titanic \"\"\"\n", "    men = data.Age[data.Sex==\"male\"]\n", "    women = data.Age[data.Sex==\"female\"]\n", "    return abs(women.mean() - men.mean())\n", "\n", "observed_age_diff = compute_age_diff(data)\n", "print \"observed age difference\", observed_age_diff"]}, {"execution_count": 72, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["observed age difference 2.81093577935\n"]}], "source": ["def compute_age_diff(data):\n", "    \"\"\" Compute the absolute value of the difference in mean age\n", "        between men and women on the titanic \"\"\"\n", "    male = data['Age'][data['Sex'] == 'male'].mean()\n", "    female = data['Age'][data['Sex'] == 'female'].mean()\n", "    return abs(male-female)\n", "\n", "observed_age_diff = compute_age_diff(data)\n", "print \"observed age difference\", observed_age_diff"]}, {"source": ["Write a function called `shuffle_ages` that returns a copy of the original data frame but where the Ages have been randomly permuted.\n", "\n", "Hint: there are lots of ways to do this, but  `numpy.random.permutation` seems to be an especially succint choice.  Make sure to try this function out on a small, hand-made Pandas series to get the idea of how it works."], "cell_type": "markdown", "metadata": {}}, {"execution_count": 105, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"execution_count": 105, "metadata": {}, "data": {"text/plain": ["1.0720918017812302"]}, "output_type": "execute_result"}], "source": ["from numpy.random import permutation\n", "\n", "def shuffle_ages(data):\n", "    \"\"\" Return a new dataframe (don't modify the original) where\n", "        the values in the Age column have been randomly permuted. \"\"\"\n", "    \n", "    data2 = data\n", "    data2[\"Age\"] = permutation(data[\"Age\"])\n", "#     print data[\"random\"]\n", "    return data2\n", "\n", "compute_age_diff(shuffle_ages(data))"]}, {"execution_count": 112, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"execution_count": 112, "metadata": {}, "data": {"text/plain": ["0.15471898708482357"]}, "output_type": "execute_result"}], "source": ["from numpy.random import permutation\n", "\n", "def shuffle_ages(data):\n", "    \"\"\" Return a new dataframe (don't modify the original) where\n", "        the values in the Age column have been randomly permuted. \"\"\"\n", "    permutedAges = permutation(data.Age)\n", "    data_new = data\n", "#     print data_new.head()\n", "    data_new[\"Age\"] = permutedAges\n", "    return data_new\n", "\n", "compute_age_diff(shuffle_ages(data))"]}, {"execution_count": 28, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"execution_count": 28, "metadata": {}, "data": {"text/plain": ["2.2638128948770664"]}, "output_type": "execute_result"}], "source": ["from numpy.random import permutation\n", "\n", "def shuffle_ages(data):\n", "    \"\"\" Return a new dataframe (don't modify the original) where\n", "        the values in the Age column have been randomly permuted. \"\"\"\n", "    df = data.copy()\n", "    df.Age = np.random.permutation(df.Age)\n", "    return df\n", "\n", "compute_age_diff(shuffle_ages(data))"]}, {"execution_count": 245, "cell_type": "code", "metadata": {"scrolled": true, "collapsed": false}, "outputs": [{"execution_count": 245, "metadata": {}, "data": {"text/plain": ["2.0298046230747779"]}, "output_type": "execute_result"}], "source": ["from numpy.random import permutation\n", "\n", "def shuffle_ages(data):\n", "    \"\"\" Return a new dataframe (don't modify the original) where\n", "        the values in the Age column have been randomly permuted. \"\"\"\n", "    age = []\n", "    for index in data.index:\n", "        age.append(data.Age[index])\n", "    permuted_age = np.random.permutation(age).tolist()\n", "    data.Age = permuted_age\n", "    return data\n", "\n", "compute_age_diff(shuffle_ages(data))"]}, {"execution_count": 191, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"execution_count": 191, "metadata": {}, "data": {"text/plain": ["0.40177133287660993"]}, "output_type": "execute_result"}], "source": ["from numpy.random import permutation\n", "\n", "def shuffle_ages(data):\n", "    \"\"\" Return a new dataframe (don't modify the original) where\n", "        the values in the Age column have been randomly permuted. \"\"\"\n", "    data_copy = data.copy()\n", "    data_copy.Age = permutation(data_copy.Age)\n", "    return data_copy\n", "\n", "compute_age_diff(shuffle_ages(data))"]}, {"execution_count": 9, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"execution_count": 9, "metadata": {}, "data": {"text/plain": ["0.018900053284614415"]}, "output_type": "execute_result"}], "source": ["from numpy.random import permutation\n", "\n", "def shuffle_ages(data):\n", "    \"\"\" Return a new dataframe (don't modify the original) where\n", "        the values in the Age column have been randomly permuted. \"\"\"\n", "    res = data.copy()\n", "    res[\"Age\"] = permutation(res[\"Age\"])\n", "    return res\n", "\n", "compute_age_diff(shuffle_ages(data))"]}, {"execution_count": 28, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"execution_count": 28, "metadata": {}, "data": {"text/plain": ["1.2728859962954502"]}, "output_type": "execute_result"}], "source": ["from numpy.random import permutation\n", "\n", "def shuffle_ages(data):\n", "    \"\"\" Return a new dataframe (don't modify the original) where\n", "        the values in the Age column have been randomly permuted. \"\"\"\n", "    data2 = data\n", "    data2.Age = permutation(data.Age)\n", "    return data2\n", "\n", "compute_age_diff(shuffle_ages(data))"]}, {"execution_count": 9, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"execution_count": 9, "metadata": {}, "data": {"text/plain": ["0.62823095074978852"]}, "output_type": "execute_result"}], "source": ["from numpy.random import permutation\n", "\n", "def shuffle_ages(data):\n", "    \"\"\" Return a new dataframe (don't modify the original) where\n", "        the values in the Age column have been randomly permuted. \"\"\"\n", "    data2 = data.copy()\n", "    shuffle_age = permutation(data.Age.tolist())\n", "    data2.Age = shuffle_age\n", "    return data2\n", "    \n", "compute_age_diff(shuffle_ages(data))"]}, {"execution_count": 144, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"execution_count": 144, "metadata": {}, "data": {"text/plain": ["0.08569409555707708"]}, "output_type": "execute_result"}], "source": ["from numpy.random import permutation\n", "\n", "def shuffle_ages(data):\n", "    \"\"\" Return a new dataframe (don't modify the original) where\n", "        the values in the Age column have been randomly permuted. \"\"\"\n", "    \n", "    shuffled = data.copy()\n", "    shuffled_ages = permutation(shuffled.Age)\n", "    shuffled.Age = shuffled_ages\n", "    \n", "    return shuffled\n", "\n", "compute_age_diff(shuffle_ages(data))"]}, {"execution_count": 9, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"execution_count": 9, "metadata": {}, "data": {"text/plain": ["0.31173098881023265"]}, "output_type": "execute_result"}], "source": ["from numpy.random import permutation\n", "\n", "def shuffle_ages(data):\n", "    \"\"\" Return a new dataframe (don't modify the original) where\n", "        the values in the Age column have been randomly permuted. \"\"\"\n", "    new_data = data.copy()\n", "    new_data.Age = permutation(new_data.Age.values)\n", "    return new_data\n", "\n", "compute_age_diff(shuffle_ages(data))"]}, {"execution_count": 22, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"execution_count": 22, "metadata": {}, "data": {"text/plain": ["0.65757656491842553"]}, "output_type": "execute_result"}], "source": ["from numpy.random import permutation\n", "\n", "def shuffle_ages(data):\n", "    \"\"\" Return a new dataframe (don't modify the original) where\n", "        the values in the Age column have been randomly permuted. \"\"\"\n", "    \n", "    shuffle = data.copy()\n", "    new_ages = permutation(data.Age.tolist())\n", "    shuffle.Age = new_ages\n", "    \n", "    return shuffle\n", "    \n", "compute_age_diff(shuffle_ages(data))"]}, {"execution_count": 135, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["0.371210829464\n"]}], "source": ["from numpy.random import permutation\n", "\n", "def shuffle_ages(data):\n", "    \"\"\" Return a new dataframe (don't modify the original) where\n", "        the values in the Age column have been randomly permuted. \"\"\"\n", "    newframe = data.copy()\n", "    newframe.Age = permutation(newframe.Age)\n", "    return newframe\n", "\n", "random_age_diff = compute_age_diff(shuffle_ages(data_titanic))\n", "\n", "print random_age_diff"]}, {"execution_count": 35, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"execution_count": 35, "metadata": {}, "data": {"text/plain": ["0.9292677171348096"]}, "output_type": "execute_result"}], "source": ["from numpy.random import permutation\n", "\n", "def shuffle_ages(data):\n", "    \"\"\" Return a new dataframe (don't modify the original) where\n", "        the values in the Age column have been randomly permuted. \"\"\"\n", "    \n", "    newdata = data.copy()\n", "    newage = permutation(data.Age.tolist())\n", "    newdata.Age = newage\n", "    return newdata\n", "    \n", "compute_age_diff(shuffle_ages(data))"]}, {"execution_count": 27, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"execution_count": 27, "metadata": {}, "data": {"text/plain": ["2.649336479663038"]}, "output_type": "execute_result"}], "source": ["from numpy.random import permutation\n", "\n", "def shuffle_ages(data):\n", "    \"\"\" Return a new dataframe (don't modify the original) where\n", "        the values in the Age column have been randomly permuted. \"\"\"\n", "    res = data\n", "    res.Age = permutation(res.Age).astype(int)\n", "    return res\n", "\n", "compute_age_diff(shuffle_ages(data))"]}, {"execution_count": 103, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"execution_count": 103, "metadata": {}, "data": {"text/plain": ["1.9901857349470973"]}, "output_type": "execute_result"}], "source": ["from numpy.random import permutation\n", "\n", "def shuffle_ages(data):\n", "    \"\"\" Return a new dataframe (don't modify the original) where\n", "        the values in the Age column have been randomly permuted. \"\"\"\n", "    shuffled_data = data.copy()\n", "    shuffled_data.Age = permutation(shuffled_data.Age)\n", "    return shuffled_data\n", "    \n", "\n", "compute_age_diff(shuffle_ages(data))"]}, {"execution_count": 68, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"execution_count": 68, "metadata": {}, "data": {"text/plain": ["0.12766105909517478"]}, "output_type": "execute_result"}], "source": ["from numpy.random import permutation\n", "\n", "def shuffle_ages(data):\n", "    \"\"\" Return a new dataframe (don't modify the original) where\n", "        the values in the Age column have been randomly permuted. \"\"\"\n", "    shuffledAges = data.copy()\n", "    shuffledAges['Age'] = permutation(shuffledAges['Age'])\n", "    return shuffledAges\n", "\n", "compute_age_diff(shuffle_ages(data))"]}, {"execution_count": 173, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"execution_count": 173, "metadata": {}, "data": {"text/plain": ["0.6840909898251759"]}, "output_type": "execute_result"}], "source": ["from numpy.random import permutation\n", "\n", "def shuffle_ages(data):\n", "    \"\"\" Return a new dataframe (don't modify the original) where\n", "        the values in the Age column have been randomly permuted. \"\"\"\n", "    df = data.copy()\n", "    df = df.apply(permutation)\n", "    return df\n", "\n", "compute_age_diff(shuffle_ages(data))"]}, {"execution_count": 169, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"execution_count": 169, "metadata": {}, "data": {"text/plain": ["0.2272429017279407"]}, "output_type": "execute_result"}], "source": ["from numpy.random import permutation\n", "\n", "def shuffle_ages(data):\n", "    \"\"\" Return a new dataframe (don't modify the original) where\n", "        the values in the Age column have been randomly permuted. \"\"\"\n", "    dataCopy = data.copy(deep=True)\n", "    dataCopy.Age = (np.random.permutation(data.Age))\n", "    return dataCopy\n", "\n", "compute_age_diff(shuffle_ages(data))"]}, {"execution_count": 52, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"execution_count": 52, "metadata": {}, "data": {"text/plain": ["0.70081525462434513"]}, "output_type": "execute_result"}], "source": ["from numpy.random import permutation\n", "\n", "def shuffle_ages(data):\n", "    \"\"\" Return a new dataframe (don't modify the original) where\n", "        the values in the Age column have been randomly permuted. \"\"\"\n", "    new_data = data.copy()\n", "    new_data.Age = permutation(data.Age.values)\n", "    return new_data\n", "\n", "compute_age_diff(shuffle_ages(data))"]}, {"execution_count": 45, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"execution_count": 45, "metadata": {}, "data": {"text/plain": ["0.5950168734617236"]}, "output_type": "execute_result"}], "source": ["from numpy.random import permutation\n", "\n", "def shuffle_ages(data):\n", "    \"\"\" Return a new dataframe (don't modify the original) where\n", "        the values in the Age column have been randomly permuted. \"\"\"\n", "    ages_shuff = np.random.permutation(data.Age)\n", "    data_copy = data\n", "    data_copy.Age = ages_shuff\n", "    return data_copy\n", "\n", "compute_age_diff(shuffle_ages(data))"]}, {"execution_count": 73, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"execution_count": 73, "metadata": {}, "data": {"text/plain": ["0.47985105681154749"]}, "output_type": "execute_result"}], "source": ["from numpy.random import permutation\n", "import numpy as np\n", "\n", "def shuffle_ages(data):\n", "    \"\"\" Return a new dataframe (don't modify the original) where\n", "        the values in the Age column have been randomly permuted. \"\"\"\n", "    d = data\n", "    ages = data['Age'].values\n", "    np.random.shuffle(ages)\n", "    d['Age'] = ages\n", "    return d\n", "\n", "compute_age_diff(shuffle_ages(data))"]}, {"source": ["Using 1000 random simulations, compute the p-value for the hypothesis that the mean ages of men and women were different (you may wish to use Cdf as in the previous section)."], "cell_type": "markdown", "metadata": {}}, {"execution_count": 107, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["63.7\n"]}, {"output_type": "display_data", "data": {"image/png": 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ocsIZ2/IyAGMBrPMfn1UAj6DmDCvHbM9ocsIB2xNAOwCvSM3tyNMAzPNvP0f9\nWY8mJ5yxPYPYsS15MRQRkYvxi1ciIhdjyRMRuRhLnojIxVjyREQuxpInInIxljwRkYux5ImIXIwl\nT0TkYv8HhGbzWMGJKJsAAAAASUVORK5CYII=\n", "text/plain": ["<matplotlib.figure.Figure at 0x7f09afb3e510>"]}, "metadata": {}}], "source": ["randAge = []\n", "for i in range(1000):\n", "    randAge.append(compute_age_diff(shuffle_ages(data)))\n", "\n", "cdf3 = thinkstats2.Cdf(randAge, label='Random_Age')\n", "thinkplot.Cdf(cdf3)\n", "\n", "print cdf3.PercentileRank(1)\n", "#Just in case this makes no sense, I did this because in the event that randomly changing around ages doesn't make\n", "#things come out to be 0 on average, then there must be some bias on either the male or female side.\n"]}, {"execution_count": 113, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [], "source": ["diffAges = [];\n", "for i in range(1000): \n", "    meandiff = compute_age_diff(shuffle_ages(data))\n", "    diffAges.append(meandiff)\n", "meanDiffAgesCdf = thinkstats2.Cdf(diffAges)"]}, {"execution_count": 75, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "display_data", "data": {"image/png": 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D+rqqbhSRDwF8DaAYwOuhBZ5it2PXPluBX/4+H8JNROXHm6EcKHTzsedH3o4Lz29lKA2l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\n", "text/plain": ["<matplotlib.figure.Figure at 0x7fcbbda75310>"]}, "metadata": {}}, {"output_type": "display_data", "data": {"text/plain": ["<matplotlib.figure.Figure at 0x7fcbbd9d5a50>"]}, "metadata": {}}], "source": ["def shuffled_age_diff(data):\n", "    return compute_age_diff(shuffle_ages(data))\n", "    \n", "iters = 1000    \n", "age_diffs = [shuffled_age_diff(data) for _ in range(iters)]\n", "\n", "age_cdf = thinkstats2.Cdf(age_diffs)\n", "\n", "x = observed_age_diff\n", "y = age_cdf.PercentileRank(x) / 100\n", "\n", "thinkplot.Cdf(age_cdf)\n", "plt.axvline(x, 0, y, color='red')\n", "plt.axhline(y, 0, x/4.0, color='red')\n", "plt.plot(x, y, '.', color='green', markersize=30)\n", "plt.xlim((0, 4.0))\n", "thinkplot.show()"]}, {"execution_count": 248, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["p value is 0.074\n"]}, {"output_type": "display_data", "data": {"image/png": 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5yiQRGcaQd0Aqk8D1vJDn1gVE5AYMeQecHH7b0u6KrEZzoM1QNUREH2HIL9B0Ol7QtzTS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\nSUVORK5CYII=\n", "text/plain": ["<matplotlib.figure.Figure at 0x7fef994f8550>"]}, "metadata": {}}], "source": ["agelist = []\n", "for _ in itertools.repeat(None, 1000):\n", "    agelist.append(compute_age_diff(shuffle_ages(data)))\n", "\n", "#plotting cdf\n", "agecdf = thinkstats2.Cdf(agelist)\n", "thinkplot.Cdf(agecdf)\n", "\n", "#Computing p-value for pbserved data 2 years of difference\n", "page = 1 - 0.01*(stats.percentileofscore(np.array(agelist), 2))\n", "print 'p value is', page"]}, {"execution_count": 196, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "display_data", "data": {"image/png": 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MtbnwTENpiChVseQTZMyz74fNPTL0OgNJiCiV8UnRCTJn/heW8ZI5o6MsSUSUONyTT4CX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\n", "text/plain": ["<matplotlib.figure.Figure at 0x7fae2761bc90>"]}, "metadata": {}}, {"output_type": "display_data", "data": {"text/plain": ["<matplotlib.figure.Figure at 0x7fae27647b50>"]}, "metadata": {}}], "source": ["age_diffs = [compute_age_diff(shuffle_ages(data)) for i in range(1000)]\n", "age_diff_cdf = thinkstats2.Cdf(age_diffs)\n", "thinkplot.Cdf(age_diff_cdf)\n", "thinkplot.Show()"]}, {"execution_count": 10, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["p-value: 0.8%\n"]}], "source": ["diff_arr = []\n", "for i in xrange(1000):\n", "    diff_arr.append(compute_age_diff(shuffle_ages(data)))\n", "cdf = thinkstats2.Cdf(diff_arr)\n", "print \"p-value:\", str(100-cdf.PercentileRank(compute_age_diff(data)))+\"%\""]}, {"execution_count": 64, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["0.9%\n"]}, {"output_type": "display_data", "data": {"image/png": 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VlnwSZWfx8BKRWWwhh4x/xnp169/vOsNQEiKiH7HkHbChpBSrv7Xep6Zp41xDaYiIfsSS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\n5GP/D3CFnknsRi1BAAAAAElFTkSuQmCC\n", "text/plain": ["<matplotlib.figure.Figure at 0x7f42246b6e50>"]}, "metadata": {}}], "source": ["\n", "trials = [compute_age_diff(shuffle_ages(data)) for _ in range(1000)]\n", "cdf = thinkstats2.Cdf(trials)\n", "thinkplot.Cdf(cdf)\n", "\n", "print str(100 - cdf.PercentileRank(2.81093577935)) + \"%\""]}, {"execution_count": 44, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"execution_count": 44, "metadata": {}, "data": {"text/plain": ["{'xscale': 'linear', 'yscale': 'linear'}"]}, "output_type": "execute_result"}, {"output_type": "display_data", "data": {"image/png": 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dWGpTNUTkNgx3h4pdo/26SXUJehIRmfEDVYcJq+LZ3YdxvPPCxbbCggJOxxBRRhjuDnNL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\nTkSuQmCC\n", "text/plain": ["<matplotlib.figure.Figure at 0x107673f10>"]}, "metadata": {}}], "source": ["ages = [compute_age_diff(shuffle_ages(data)) for _ in range(1000)]\n", "\n", "cdf2 = thinkstats2.Cdf(ages, label=\"age diff\")\n", "thinkplot.Cdf(cdf2)"]}, {"execution_count": 10, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "display_data", "data": {"image/png": 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Cx1Nn0u+iu2ps0/f4cg7cdxd+2W4jNli/WQNFJhIdJQiRDJxzDL//RT6aMoOPPpmRMr5V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\n", "text/plain": ["<matplotlib.figure.Figure at 0x7f31224ac650>"]}, "metadata": {}}, {"output_type": "stream", "name": "stdout", "text": ["pval: 1.5 %\n"]}, {"output_type": "display_data", "data": {"text/plain": ["<matplotlib.figure.Figure at 0x7f312299fa50>"]}, "metadata": {}}], "source": ["holder = []\n", "for i in range(1000):\n", "    holder += [compute_age_diff(shuffle_ages(data))]\n", "    \n", "cdf_holder = thinkstats2.Cdf(holder)\n", "thinkplot.Cdf(cdf_holder)\n", "\n", "thinkplot.Show(title='CDF of Age difference Average for gender',\n", "              xlabel='Absolute Age Difference',\n", "              ylabel='CDF') \n", "\n", "print 'pval:', 100 - cdf_holder.PercentileRank(observed_age_diff), '%'"]}, {"execution_count": 46, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"execution_count": 46, "metadata": {}, "data": {"text/plain": ["0.014000000000000012"]}, "output_type": "execute_result"}, {"output_type": "display_data", "data": {"image/png": 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YOAGYaWZT0up8DBjv7hOB24AftXbcvl27RxBtYdTW1sYdQl4UZ2GVQpylECMo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\n", "text/plain": ["<matplotlib.figure.Figure at 0x7fe4d9487a10>"]}, "metadata": {}}], "source": ["results = [compute_age_diff(shuffle_ages(data)) for _ in xrange(1000)]\n", "cdf = thinkstats2.Cdf(results)\n", "\n", "thinkplot.Cdf(cdf)\n", "\n", "thinkplot.Config(\n", "    title='Mean Ages',\n", "    xlabel='Mean Age Difference Between \"Males\" and \"Females\"',\n", "    ylabel='CDF'\n", ")\n", "\n", "1-cdf[observed_age_diff]"]}, {"execution_count": 150, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "display_data", "data": {"image/png": 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DOVeqX2JejyBaASudc6uccznABKBr/g7OuQXOuc2BzQWAb7cp//b75qDtGjWq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\nREQiUoEQEZGI/h9Ahqz//Z1G3wAAAABJRU5ErkJggg==\n", "text/plain": ["<matplotlib.figure.Figure at 0x7f52515d9e90>"]}, "metadata": {}}, {"output_type": "stream", "name": "stdout", "text": ["Pvalue:  0.8 %\n"]}, {"output_type": "display_data", "data": {"text/plain": ["<matplotlib.figure.Figure at 0x7f525160ddd0>"]}, "metadata": {}}], "source": ["mean_cts = []\n", "\n", "for i in range(1000):\n", "    mean_cts.append(compute_age_diff(shuffle_ages(data)))\n", "\n", "cdf = thinkstats2.Cdf(mean_cts, label='Abs of Age CDF')\n", "thinkplot.Cdf(cdf)\n", "thinkplot.Show(xlabel='age dif', ylabel='CDF')\n", "\n", "pvalue = 100 - cdf.PercentileRank(compute_age_diff(data))\n", "\n", "print \"Pvalue: \", pvalue, \"%\""]}, {"execution_count": 10, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"execution_count": 10, "metadata": {}, "data": {"text/plain": ["0.009000000000000008"]}, "output_type": "execute_result"}, {"output_type": "display_data", "data": {"image/png": 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js+PKA/t05JYLDokoGhGJihKExFn25YakuuvOGRxBJCISNSUIiZM4M+uTFcMjikREoqYE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\nJSUIERFJSQlCRERS+v+baUHIAoEmSgAAAABJRU5ErkJggg==\n", "text/plain": ["<matplotlib.figure.Figure at 0x49d7b50>"]}, "metadata": {}}], "source": ["results = [compute_age_diff(shuffle_ages(data)) for _ in xrange(1000)]\n", "cdf = thinkstats2.Cdf(results)\n", "thinkplot.Cdf(cdf)\n", "thinkplot.Config(\n", "    title='Mean Ages',\n", "    xlabel='Mean Age Difference Between \"Males\" and \"Females\"',\n", "    ylabel='CDF'\n", ")\n", "# This isn't __quite__ right since it doesn't include the\n", "# values that are exactly the same as the observed difference,\n", "# but the impact of this is pretty negligible since this is\n", "# more continuous than the coin flips example\n", "1 - cdf[observed_age_diff]"]}, {"execution_count": 23, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["P-value of male/female mean age diff:  1.2 %\n"]}, {"output_type": "display_data", "data": {"image/png": 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"text/plain": ["<matplotlib.figure.Figure at 0x7f40d01fdb90>"]}, "metadata": {}}], "source": ["simulation = [compute_age_diff(shuffle_ages(data)) for i in xrange(1000)]\n", "\n", "cdf_sim = thinkstats2.Cdf(simulation)\n", "thinkplot.Cdf(cdf_sim)\n", "\n", "print 'P-value of male/female mean age diff: ', 100 - cdf_sim.PercentileRank(observed_age_diff), '%'"]}, {"execution_count": 136, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["1.3\n"]}, {"output_type": "display_data", "data": {"image/png": 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noioseQc6XlqBGyOUO8BDNET0PZa8A0UqeJ4mSUTBWPIOs3JrUdh5Hp4honBY8g7i9yse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\nTkSuQmCC\n", "text/plain": ["<matplotlib.figure.Figure at 0x7f1caf46f090>"]}, "metadata": {}}], "source": ["sample_raw = []\n", "sample_perm = []\n", "for n in range(1000):\n", "    sample_raw.append(compute_age_diff(data_titanic))\n", "    sample_perm.append(compute_age_diff(shuffle_ages(data_titanic)))\n", "\n", "sample_raw = thinkstats2.Cdf(sample_raw)\n", "sample_perm = thinkstats2.Cdf(sample_perm)\n", "thinkplot.Cdfs([sample_raw, sample_perm])\n", "\n", "\n", "p_val = 100 - sample_perm.PercentileRank(compute_age_diff(data_titanic))\n", "print p_val"]}, {"execution_count": 37, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"execution_count": 37, "metadata": {}, "data": {"text/plain": ["{'xscale': 'linear', 'yscale': 'linear'}"]}, "output_type": "execute_result"}, {"output_type": "display_data", "data": {"image/png": 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353fXRczNemgwb8JFSYdLLpT0lm/53jKeO+ESQ0mIahaP0CmpPTdrvWX88PU9DCUhqnlx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\nWAt0nOCtje8F8Mv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"text/plain": ["<matplotlib.figure.Figure at 0x7f585c099090>"]}, "metadata": {}}], "source": ["total = []\n", "for i in range(0,1000):\n", "    total.append(compute_age_diff(shuffle_ages(data)))\n", "                 \n", "cdf = thinkstats2.Cdf(total)\n", "thinkplot.Cdf(cdf)"]}, {"execution_count": 30, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["p-value: 0.6\n"]}], "source": ["res = []\n", "for _ in range(1000):\n", "    res.append(compute_age_diff(shuffle_ages(data)))\n", "\n", "cdf = thinkstats2.Cdf(res)\n", "print \"p-value:\", float(format(100 - cdf.PercentileRank(observed_age_diff), '.2f'))"]}, {"execution_count": 115, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["P-value using CDF:  1.1 %\n"]}, {"output_type": "display_data", "data": {"image/png": 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AF84eN7R9YeOtyM/JsakiInIbXkLpUNO+RfwkLOABoK64zIZqiMitOJN3qGgBv5f7wRPR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\nrkJggg==\n", "text/plain": ["<matplotlib.figure.Figure at 0x7f5504778c50>"]}, "metadata": {}}], "source": ["import thinkstats2\n", "\n", "ageDiffs= [compute_age_diff(shuffle_ages(data)) for i in range(1000)]\n", "ageCdf = thinkstats2.Cdf(ageDiffs)\n", "thinkplot.Cdf(ageCdf)\n", "#If I'm looking for mean ages that are different, I want anything that's not 0\n", "percentileRank =  ageCdf.PercentileRank(observed_age_diff)\n", "p_Val = 1 - percentileRank/100\n", "print \"P-value using CDF: \",p_Val*100, \"%\""]}, {"execution_count": 64, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["p-value of observed age difference:  0.013\n"]}], "source": ["ageDiffs = []\n", "for i in range(1000):\n", "    ageDiffs.append(compute_age_diff(shuffle_ages(data)))\n", "    \n", "ageCdf = thinkstats2.Cdf(ageDiffs)\n", "\n", "print \"p-value of observed age difference: \", (1 - ageCdf[compute_age_diff(data)])"]}, {"execution_count": 176, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"execution_count": 176, "metadata": {}, "data": {"text/plain": ["{'xscale': 'linear', 'yscale': 'linear'}"]}, "output_type": "execute_result"}, {"output_type": "display_data", "data": {"image/png": 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IPIwlT0TkYSx5IiIPY8kTEXkYS56IyMP+H9GVJ5p/01WuAAAAAElFTkSuQmCC\n", "text/plain": ["<matplotlib.figure.Figure at 0x7f853094cfd0>"]}, "metadata": {}}], "source": ["trials = [compute_age_diff(shuffle_ages(data)) for _ in range(1000)]\n", "cdf = thinkstats2.Cdf(trials)\n", "thinkplot.Cdf(cdf)"]}, {"execution_count": 174, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"execution_count": 174, "metadata": {}, "data": {"text/plain": ["0.0050000000000000044"]}, "output_type": "execute_result"}], "source": ["resultsList = []\n", "for i in range(1000):\n", "    resultsList.append(compute_age_diff(shuffle_ages(data)))\n", "    \n", "cdf = thinkstats2.Cdf(resultsList)\n", "1-cdf[observed_age_diff]"]}, {"execution_count": 53, "cell_type": "code", "metadata": {"collapsed": true}, "outputs": [], "source": ["# not sure whether 1 - cdf[value] vs the implementation at the start (using percentile rank) \n", "# is the right option"]}, {"execution_count": 51, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": 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8AAMAfOL4B+CIa5h7WxARERVNgYGuqudFJBnAYlxYtpguIv1yDuskVV0gIneI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\n", "text/plain": ["<matplotlib.figure.Figure at 0x7f9a0e949390>"]}, "metadata": {}}, {"output_type": "stream", "name": "stdout", "text": ["p-value: 0.016\n"]}, {"output_type": "display_data", "data": {"text/plain": ["<matplotlib.figure.Figure at 0x7f9a0e9938d0>"]}, "metadata": {}}], "source": ["diffs = []\n", "for i in range(1000):\n", "    diffs.append(compute_age_diff(shuffle_ages(data)))\n", "\n", "cdf = thinkstats2.Cdf(diffs)\n", "thinkplot.Cdf(cdf, label='age diffs')\n", "thinkplot.Show(loc='lower right')\n", "\n", "bigger = 0\n", "for x in diffs:\n", "    if x >= observed_age_diff:\n", "        bigger +=1\n", "print \"p-value:\", bigger/1000.0"]}, {"execution_count": 78, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "display_data", "data": {"image/png": "iVBORw0KGgoAAAANSUhEUgAAAXkAAAEACAYAAABWLgY0AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nNez/AOsCatk8AofZAAAAAElFTkSuQmCC\n", "text/plain": ["<matplotlib.figure.Figure at 0x7fd3bc8ca1d0>"]}, "metadata": {}}], "source": ["def age_test(n, data):\n", "    age_trials = []\n", "    for i in range(n):\n", "        age_trials.append(compute_age_diff(shuffle_ages(data)))\n", "    hist = thinkstats2.Hist(age_trials)\n", "    thinkplot.Hist(hist)\n", "    return age_trials\n", "\n", "titanic_age_trials = age_test(1000, data)"]}, {"source": ["Ignoring passengers with missing ages:\n", "\n", "1.  Was the average age of male versus female passengers on the titanic different?\n", "2.  What additional (if any) conclusions can you draw based on the p-value you just computed?  In other words, what does this p-value mean?\n", "\n", "Disclaimer: (1) is a bit of a trick question (sorry!), but I included it to encourage being precise about the definition of the null hypothesis and eactly which population it refers to."], "cell_type": "markdown", "metadata": {}}, {"source": ["## 1\n", "The average was different for all the people, though we can't tell for certain if it is males or females because there is no connection after the age data has been shuffled.\n", "## 2\n", "What I can draw from this is that there is a particular concentration of ages that is higher or lower for males or females. We know that for a value of 1 year in difference, that is a larger gap than 63% of occupants saw, and thereby 37% less than others, but not whether it corresponds to being male or female. We would likely want to leave the ages corresponding with the sex in order to determine that."], "cell_type": "markdown", "metadata": {}}, {"execution_count": 123, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["average male age 29.4970640177\n", "average female age 30.0498084291\n", "diff 0.552744411459\n"]}], "source": ["males = data[data.Sex == 'male']\n", "print \"average male age\", males.Age.mean()\n", "\n", "females = data[data.Sex == 'female']\n", "print \"average female age\", females.Age.mean()\n", "\n", "print \"diff\", abs(males.Age.mean() - females.Age.mean())"]}, {"execution_count": 36, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"output_type": "stream", "name": "stdout", "text": ["Average male age:   30\n", "Average female age: 27\n"]}], "source": ["males = data[data.Sex == 'male']\n", "females = data[data.Sex == 'female']\n", "\n", "avg_male_age = males.Age.mean()\n", "avg_female_age = females.Age.mean()\n", "\n", "print 'Average male age:   %d' % avg_male_age\n", "print 'Average female age: %d' % avg_female_age"]}, {"source": ["The p value is significant (>0.05) when the observed age is 2 years. We can reject the null hypothesis and say that the average male and female age are different.\n", "\n", "When the observed age is 1 year, the p value is insignificant (<0.01) and we cannot reject the null hypothesis and say that the average age of male and female passengers are different."], "cell_type": "markdown", "metadata": {}}, {"source": ["1. Yes, since the p-value of the average age difference is about 1%\n", "2. It means that the difference in average ages was most likely not chance and that there's a reason behind it"], "cell_type": "markdown", "metadata": {}}, {"source": ["The average age was different and the p value of 2.0% we calculated indicates that the 3 year difference we calculated was probably not due to random chance b/c it is so small and most of the values will actually have a differences as we can see from the graph also."], "cell_type": "markdown", "metadata": {}}, {"source": ["1. Yes, it was different. But not by much, and this is a pretty small sample size so that is to be expected.\n", "2. It is more likely to have a larger age difference?"], "cell_type": "markdown", "metadata": {}}, {"source": ["Answers.\n", "\n", "1. Yes, the average age of male verses female were different as proven when finding observed_age_diff, whereas in the null hypothesis has age difference zero.\n", "\n", "2. The p-value is below 5% which implies that it is 'statistically significant'. Here, the chances of the mean age differing that much by chance given the null hypothesis is true is very very low."], "cell_type": "markdown", "metadata": {}}, {"source": ["1. Yes, the average age for males was about 2.8 years older than the average age for females\n", "2. The p-value is statistically significant since it is clearly below 5%. I think this means that it was not random or chance that the average age was older for males. "], "cell_type": "markdown", "metadata": {}}, {"source": ["**1** The average age is definitily different.\n", "\n", "**2** This difference is statistically significant. A random distribution of ages of Titanic passengers is very unlikely to have a observed difference in means for males and females."], "cell_type": "markdown", "metadata": {}}, {"source": ["1. Maybe. The mean age of male passengers in the training set was different from the mean age of female passengers in the training set.\n", "2. The p-value seems to be rather low, so it is unlikely that the difference in mean age is just by chance."], "cell_type": "markdown", "metadata": {}}, {"source": ["Yes, and it appears that the difference may be significant given that the p-value is approximately 0.013. Of course, there are people who did not report their age, and there is a whole testing data set that is not included - thus, it is difficult to actually form a true conclusion."], "cell_type": "markdown", "metadata": {}}, {"source": ["The average age of male versus female passengers on the Titanic was different. Since the p-value we calculated was around 1%, we know that the difference in average age between genders is statistically significant because we tested our null hypothesis by shuffling the ages and the percentage of the shuffled data that is equal to or greater than our observed value is under 1%, which means that this effect is not due to chance. So it follows that the average ages of men vs women on the titanic was actually different, not just due to chance."], "cell_type": "markdown", "metadata": {}}, {"source": ["1. yes the average age is different (medain age difference is about 2.8) \n", "\n", "2. The mean difference in age is plausibly caused by more than chance. A random sample of one age group cannot definitely be male or female. The permutation results also suggest that it is unlikely that a random sample of titanic passengers will exhibt the same age difference. "], "cell_type": "markdown", "metadata": {}}, {"source": ["1. Yes, the average of male versus female passengers on the titanic was different. (The difference in mean ages was about 2.8 years.) This isn't different by that many years in the grand scheme of things, though. \n", "\n", "2. I think that this p-value means that, if the distributions of the ages of male and female passengers weren't different, it would be very unlikely for us to get this particular distribution of ages, which means that there is a (statistically sigificant?) difference between ages of men and women on the titanic. "], "cell_type": "markdown", "metadata": {}}, {"source": ["The average age of male versus female passengers was different, and the low p-value indicates that the age difference of about 3 years was probably not due to random chance. "], "cell_type": "markdown", "metadata": {}}, {"source": ["1. Yes\n", "2. It is unlikley that the age difference is due just to random chance"], "cell_type": "markdown", "metadata": {}}, {"source": ["1. Well, we observed that the average age of male and female passengers was different by about 2 years.  We were testing whether this was expected in a normal distribution of passenger ages or not.\n", "2. We can conclude that, if the ages were the same between male and female passengers, the difference we observed in the data would have a 0.016 chance of occuring."], "cell_type": "markdown", "metadata": {}}, {"source": ["1. The average age of of males was different than the female passengers by about 2.8 years.\n", "2. However, the calculated p-value indicates that the difference in average age of males and females on the Titanic was not significant. 27.4% is a very high p-value indicating that a difference of 2.8 years is not a terribly unexpected difference in means."], "cell_type": "markdown", "metadata": {}}], "metadata": {"kernelspec": {"display_name": "Python 2", "name": "python2", "language": "python"}, "language_info": {"mimetype": "text/x-python", "nbconvert_exporter": "python", "name": "python", "file_extension": ".py", "version": "2.7.11", "pygments_lexer": "ipython2", "codemirror_mode": {"version": 2, "name": "ipython"}}}, "nbformat": 4}