01_solutions_pandas.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## IPython Notebooks\n",
    "\n",
    "* You can run a cell by pressing ``[shift] + [Enter]`` or by pressing the \"play\" button in the menu.\n",
    "* You can get help on a function or object by pressing ``[shift] + [tab]`` after the opening parenthesis ``function(``\n",
    "* You can also get help by executing: ``function?``\n",
    "\n",
    "We'll use the following standard imports.  Execute this cell first:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercise: are first-borns more likely to be late?\n",
    "\n",
    "This exercise is based on [lecture material by Allen Downey](https://github.com/AllenDowney/CompStats.git).\n",
    "\n",
    "License: [Creative Commons Attribution 4.0 International](http://creativecommons.org/licenses/by/4.0/)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# this future import makes this code mostly compatible with Python 2 and 3\n",
    "from __future__ import print_function, division\n",
    "\n",
    "import random\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Are first babies more likely to be late?\n",
    "----------------------------------------\n",
    "\n",
    "Allen Downey wrote a popular blog post about this topic:\n",
    "\n",
    "http://allendowney.blogspot.com/2011/02/are-first-babies-more-likely-to-be-late.html\n",
    "\n",
    "We are going to investigate the question for ourselves, based on data from the National Survey of Family Growth (NSFG)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use the Pandas ``read_csv`` command to load ``data/2002FemPreg.csv.gz``."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "preg = pd.read_csv('data/2002FemPreg.csv.gz')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- The variable **`outcome`** encodes the outcome of the pregnancy.  Outcome 1 is a live birth.\n",
    "- The variable **`pregordr`** encodes for first pregnancies (==1) and others (>1).\n",
    "- The variables **`prglngth`** encodes for the length of pregnancy up to birth."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1    9148\n",
       "2    1862\n",
       "3     120\n",
       "4    1921\n",
       "5     190\n",
       "6     352\n",
       "dtype: int64"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "preg.outcome.value_counts().sort_index()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1     5033\n",
       "2     3766\n",
       "3     2334\n",
       "4     1224\n",
       "5      613\n",
       "6      308\n",
       "7      158\n",
       "8       78\n",
       "9       38\n",
       "10      17\n",
       "11       8\n",
       "12       5\n",
       "13       3\n",
       "14       3\n",
       "15       1\n",
       "16       1\n",
       "17       1\n",
       "18       1\n",
       "19       1\n",
       "dtype: int64"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "preg.pregordr.value_counts().sort_index()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's visualize the number of births over different weeks:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f640acf8cf8>"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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5v3/rnhoefXYLQ4ojfO4jZ1IUDbe+durEYZSXRFi9pZJUun/SQLWNcb720Bs8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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f640acfb6a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "preg.prglngth.value_counts().sort_index().plot(title='Number of births for week')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And here is the total number of babies born up to a certain week:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f640b92ac50>"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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XEZNC0KtQMLMbgF3u/qSZ3RYtzv6PqQdqgDhwIGt5A1DbZXn7uiJHFAQBqXSG\n1mSG1rY0jamALdv2hSN4mpLvG8mzftt+WtvCqRwm1FVz9qljOXvqWEZrzn+RQ+ptS+GzQMbMLib8\n5v9zoC7r+Tiwn/B4QU2X5fui5fEu6x5RXV38yCsViHysiyAIaGpJ0dKWorUtTWsyTUtrmtZk2Mff\n0JQk0dga7tQb2jgQ3U80ttESHQdobUuR6Wbfz9iRVcydOZ55MycwcVxhfO/Ix7+L/qK66J1ehYK7\nz2u/b2ZPA18AvmNmc939OeBS4GlgGXCHmZUBlcAUYBWwFLiM8CD1ZcBiukEn5oTq6uJ5Vxebtid4\n4In1bNqe6NHriotiDKsspaKsmHhlKWVlxZSXtv8UMaK2ktKiWDhqp6o0ug1H8FSUFXcc5M23+uqN\nfPy76C+qi049Dce+HJL6VeDHZlYKrAUecvfAzO4GlhAed7jN3dvMbAFwn5ktBlqB6/qwHDKINDQn\n+e2zb/Lsa+8SAFOOH07tsHLKSoooKy2mrLSI8tJiykqKqaoIx+LHq8rC28oyKsuLDzt6R//8In0r\nFnT3DJrcC/TPH8qHHWEmCFiycjsP/fFNGpqTHDu6mk9ffApTJvbtHPz5UBcDRXXRSXXRqa4u3qMx\n0Tp5Tfrclh313P+E89a7CcrLivnUhScx/8wJumSjSB5QKEi3pdIZ6puSHGhs5UBDG/sbWtlX38r+\nrPv76ltpaE4CMHvqGK6+6GRGxMtzXHIR6S6FQoHLBAGb3k2QaGyjsaX9wizhxVnaz+Q9EI0Gat/Z\nH0p5WTEjhpVzwrg4l8w+nlNPGDlAWyEifUWhUMDSmQw/fHg1y9fvPux61RUl1FSXMaGuumNuntrq\nMoYPK2d4vJwRw8oZES/XfP0iQ4D+iwtUJgj42e/XsXz9bk4aX8usU+qorixhWEV4Bm/7xVl0Jq9I\nYVEoFKAgCPjVkxtYumoHJx5bw19/arq+5YsI8P6pKaRALFz8Fn94dRsT6qr5q6sUCCLSSaFQYBa9\nuIVHlm5hzIhKvnL1DIZVlua6SCIyiCgUCsgzK97hN398kxHxcr56zQxqh2moqIi8n0KhQLy4egcP\nPO7Eq0r56jUzGF2rmUJF5E+pM3kIS2cyrNy4hz++9i6r3tpDRXkJX7l6BuNGVee6aCIySCkUhqC9\niRaee/1dFq/czr76VgAmj6/huvmncPxYTScsIoemUBgigiBgzeZ9PP3qNl7b+B5BABVlxVw4azwX\nzBjPcWOxMzRdAAAKMUlEQVSG5bqIIpIHFAp5LhMEvLbhPR5ZupnNO8JZISceE+fCmeOZPXUMFWX6\nFYtI92mPkafSmQzL1u7i0Re28M57jcSAM6yOy86ZyKQCucqYiPQ9hUKeSabSPP7iFh580tm1v5mi\nWIw5px3D5XMmcuxoHUAWkaOjUMgDrW1p3nhrD6/4Ll5/cw+tbWlKimNcMONYLjlnImN0IXoR6SMK\nhUGquTXF62++x3LfzRtv7qEtlQFgdG0FHz1vEueeOlbXKRCRPqdQGIQ2bjvAdx98jda2NABjR1Zx\nptVxpo3h+LHDGDOmRpcaFJF+oVAYZJpaUvzoP1fTlkzzsXNP4KypYxg/uvqwF68XEekrCoVB5hdP\nrue9Ay189NwTuHLuibkujogUGM19NIi8vHYnL6zewaRxNXz8vBNyXRwRKUAKhUFib6KFnz/mlJcW\nc9PHTqWkWL8aERl42vMMAplMwD2PrKGpNcW1809m7MiqXBdJRApUr44pmFkJ8FPgBKAMuANYA9wL\nZIBV7n5LtO6NwE1AErjD3R81swrgAWAMkACud/c9R7Uleezxl99m3dv7mXnyaD74gXG5Lo6IFLDe\nthQ+Dbzn7nOBS4DvA3cBt7n7PKDIzK4ws7HArcCcaL07zawUuBlYGb3+fuD2o9yOvLVlRz2/fe4t\naqvLuOHSKRplJCI51dtQeJDOHXkxkAJmufviaNki4GJgNrDE3VPungA2ANOB84HHstad38ty5LXW\nZJof/edq0pmAz10+lXhVWa6LJCIFrlfdR+7eBGBmceA3wN8C/5i1Sj1QA8SBA1nLG4DaLsvb1y0o\nQRDw66c3sn1PE/PPmMDpJ47KdZFERHp/noKZHQf8Fvi+u/+bmf1D1tNxYD/h8YKaLsv3RcvjXdY9\norq6oXGBmCAIuH/RWv644h0mHhPnC1fNoLy0uEfvMVTqoi+oLjqpLjqpLnqntweaxwKPA7e4+zPR\n4hVmNtfdnwMuBZ4GlgF3mFkZUAlMAVYBS4HLgFei28V0w1CY2qG9hfDEsq2MHVHJrZ+cRmJ/U4/e\no64uPiTqoi+oLjqpLjqpLjr1NBx721L4BjAcuN3M/hcQAF8G/l90IHkt8JC7B2Z2N7AEiBEeiG4z\nswXAfWa2GGgFrutlOfJKJgj41ZMb+MOr2xg3qoqvXTuT4cM0qZ2IDB6xIAhyXYbuCvI5+TNBwM8f\nc557/V3G11Xz1WtmUlvduwPL+hbUSXXRSXXRSXXRqa4u3qMhjZr7aABkMgE/+/1anl+1g+PHDOMr\n18zQSCMRGZQUCv0sncnwk0fW8uKanUwaF+dvrp5BdUVproslInJQCoV+0pZM89Lanfxh+Tbe3tnA\nSeNr+aurplNVoSoXkcFLe6g+tmtfE8+seIclK7fT2JIiFoPZU8dw/SVTqCxXdYvI4Ka9VB8IgoA3\n3trDU8u3seqtvQDEq0q5fM5ELpgxnlG1FTkuoYhI9ygU+sAjSzezcPEmAE4aX8tFs8Zzho2htEST\n0IpIflEoHKVVm/bw8OJNjKop5y8/+QEmHqOzKEUkf+mr7FHYc6CFH/1uDcXFMb545TQFgojkPYVC\nLyVTGX7w8CoampNcO/8UJo0ruDn9RGQIUij00r89vYFN2xPMOe0YLphxbK6LIyLSJxQKvfDCqh08\n8+o7TKir5jOXmC6MIyJDhkKhh7btauC+x9ZRWV7MLVdO6/GU1yIig5lCoQeaW1P8y8I3aEtl+Nzl\npzJ2ZFWuiyQi0qc0JLWb9tW3ct9j69i5r5lLzz6eWafU5bpIIiJ9TqFwGEEQ8Na7CZ58ZSvLfTfp\nTMCU44fzyXkn5rpoIiL9QqFwEKl0hmVrd/HU8q1s2h7OyT5+dDXzz5zAnNOOobhIvW4iMjQpFLp4\n7vV3WfjcWxxobCMGzDx5NPPPmMCUiSM0ykhEhjyFQpZFL23hN8+8SWV5MR8+6zguOmMCY4ZX5rpY\nIiIDRqEQeWTpZn773FuMiJfz9WtnamSRiBQkhQLwuyWbeHhJOKnd166bpdaBiBSsgg6FIAhYuHgT\njyzdzOjaCr5+7UxGKxBEpIAVbCgEQcC/P/sWv39xC2OGV/L162YyskYXwxGRwlaQoRAEAQ8+s5HH\nX97K2JFVfP3amYyIl+e6WCIiOVdQofDe/mZeXLOTF1bvYPueJsaNquJr185k+DAFgogI5DAUzCwG\n/ACYDrQAn3f3t/r6cxpbkixbt4sXV+1g/bYDAJQUFzF76hiunX8KtdVlff2RIiJ5K5cthU8A5e5+\nrpmdDdwVLeu1IAjYk2hh684Gtu5qYNP2BKs37yWVDogBUyeO4JxTx3KGjaGqoqAaSSIi3ZLLPeP5\nwGMA7v6SmZ15uJVfXr2D3XsaSKUzpNIB6UxAKp0hnQ7Ym2hh664wCJpaU+973fi6as497RjOPnWs\nDiSLiBxBLkOhBjiQ9ThlZkXunjnYyt/66UuHfbMYMGZkFadNGslxY4Zx/NhhHDcmrgPIIiI9kMtQ\nSADZV7o/ZCAA/Od3r9DEQ1nq6uJHXqlAqC46qS46qS56J5fTfT4PXAZgZucAb+SwLCIiQm5bCguB\ni83s+ejxZ3NYFhERAWJBEOS6DCIiMkjoajEiItJBoSAiIh0UCiIi0mHQn9Y7UNNhDHbRWd/fdvcL\nzWwycC+QAVa5+y05LdwAMbMS4KfACUAZcAewhsKsiyLgx4ARbvsXgFYKsC7amdkY4BVgPpCmQOvC\nzJbTeQ7YJuDv6UFd5ENLoWM6DOAbhNNhFBQz+xrhDqD9TLy7gNvcfR5QZGZX5KxwA+vTwHvuPhe4\nBPg+hVsXHwMCdz8fuJ3wH79Q66L9C8MPgaZoUUHWhZmVA7j7RdHP5+hhXeRDKLxvOgzgsNNhDFEb\ngSuzHp/h7ouj+4sIvxkVggcJd4AAxUAKmFWIdeHu/wHcFD2cCOyjQOsi8o/AAuBdwgkOCrUupgPV\nZva4mT0V9TD0qC7yIRQOOh1GrgqTC+6+kHAH2C777O56oHZgS5Qb7t7k7o1mFgd+A/wtBVoXAO6e\nMbOfAXcDv6RA68LMbgB2ufuTdNZB9j6iYOqCsKX0HXf/CHAz8At6+HeRDzvXHk2HUSCytz8O7M9V\nQQaamR0HPA3c5+7/RgHXBYC7fxY4BbgHyL6WbCHVxWcJT4R9hvCb8s+BuqznC6ku1hMGAe6+AdgD\njM16/oh1kQ+hoOkw/tSrZjY3un8psPhwKw8VZjYWeBz4urvfFy1eUaB18Wdm9o3oYQvhgdVXzGxe\ntKxg6sLd57n7he5+IfAa8GfAokL8uyAMyO8CmNmxhD0tT/Tk72LQjz5C02EczFeBH5tZKbAWeCjH\n5Rko3wCGA7eb2f8CAuDLwP8rwLp4CLjXzJ4l/D/+ErAOuKcA6+JgCvV/5CfAT83sOcL/jxsIWwvd\n/rvQNBciItIhH7qPRERkgCgURESkg0JBREQ6KBRERKSDQkFERDooFEREpINCQUREOigURESkw/8H\n5eQD2HK4ShkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f640ace0780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "preg.prglngth.value_counts().sort_index().cumsum().plot(title='Total nr of births up to week')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, create a Pandas dataframe containing *only* the three columns of interest.  **Hint:** ``loc``"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>outcome</th>\n",
       "      <th>pregordr</th>\n",
       "      <th>prglngth</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>39</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>39</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>39</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>39</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>39</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   outcome  pregordr  prglngth\n",
       "0        1         1        39\n",
       "1        1         2        39\n",
       "2        1         1        39\n",
       "3        1         2        39\n",
       "4        1         3        39"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pp = preg.loc[:, ['outcome', 'pregordr', 'prglngth']]\n",
    "pp.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, select only entries where ``outcome`` is 1 (i.e., live births)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "pp = pp[pp.outcome == 1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Also, we are only interested in whether babies are first born or not, so set any entries for ``pregordr`` that are  !=1 to the value 2.  *Hint:* Use ``.loc`` with two indices."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>outcome</th>\n",
       "      <th>pregordr</th>\n",
       "      <th>prglngth</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>39</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>39</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>39</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>39</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>39</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   outcome  pregordr  prglngth\n",
       "0        1         1        39\n",
       "1        1         2        39\n",
       "2        1         1        39\n",
       "3        1         2        39\n",
       "4        1         2        39"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pp.loc[pp.pregordr != 1, 'pregordr'] = 2\n",
    "pp.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>outcome</th>\n",
       "      <th>prglngth</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>pregordr</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"8\" valign=\"top\">1</th>\n",
       "      <th>count</th>\n",
       "      <td>3368</td>\n",
       "      <td>3368.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>1</td>\n",
       "      <td>38.584323</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0</td>\n",
       "      <td>2.681048</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>1</td>\n",
       "      <td>17.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>1</td>\n",
       "      <td>39.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>1</td>\n",
       "      <td>39.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>1</td>\n",
       "      <td>40.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1</td>\n",
       "      <td>48.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"8\" valign=\"top\">2</th>\n",
       "      <th>count</th>\n",
       "      <td>5780</td>\n",
       "      <td>5780.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>1</td>\n",
       "      <td>38.546713</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0</td>\n",
       "      <td>2.714811</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>1</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>1</td>\n",
       "      <td>39.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>1</td>\n",
       "      <td>39.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>1</td>\n",
       "      <td>39.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1</td>\n",
       "      <td>50.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                outcome     prglngth\n",
       "pregordr                            \n",
       "1        count     3368  3368.000000\n",
       "         mean         1    38.584323\n",
       "         std          0     2.681048\n",
       "         min          1    17.000000\n",
       "         25%          1    39.000000\n",
       "         50%          1    39.000000\n",
       "         75%          1    40.000000\n",
       "         max          1    48.000000\n",
       "2        count     5780  5780.000000\n",
       "         mean         1    38.546713\n",
       "         std          0     2.714811\n",
       "         min          1     0.000000\n",
       "         25%          1    39.000000\n",
       "         50%          1    39.000000\n",
       "         75%          1    39.000000\n",
       "         max          1    50.000000"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pp.groupby('pregordr').describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create two dataframes.  One with first pregnancies, and one with all the rest."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "firsts = pp[pp.pregordr == 1]\n",
    "others = pp[pp.pregordr != 1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Computer the mean difference in weeks:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(38.584323040380049, 38.54671280276817)"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "firsts.prglngth.mean(), others.prglngth.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The difference is very small--a few hours!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Let's see if we can visualize the difference in the histograms.\n",
    "\n",
    "1. From the first pregnancy table, select column ``prglngth``, then call ``hist`` on it.\n",
    "2. You will get better results if you specify bins to ``hist``, with ``bins=range(50)``.\n",
    "3. Do the same for other births.\n",
    "4. To optimally compare the two histograms, set the x-axis to be the same with ``plt.xlim(30, 45)``"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(30, 45)"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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KzG9FxB11c/OHxjSwFGgAe5va9wPLOlmmpN6aOXqU5557jt2793d97HPOeRsnnXRS18dV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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f640c543550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "firsts.prglngth.hist(bins=range(50))\n",
    "plt.xlim(30, 45)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(30, 45)"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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eTX3vfjQzjwD7I2IX8C+Bx06ubElSu2Y7R38A+Exm/hvgOuDLwLyG1yeAZUCNl6Z3ACaB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\no20HJwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f640c41b8d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "others.prglngth.hist(bins=range(50))\n",
    "plt.xlim(30, 45)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I wrote a little utility function to help us plot the distributions side-by-side.  See if you can read the code below and figure out what it does:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "LILAC = '#998ec3'\n",
    "ORANGE = '#f1a340'\n",
    "\n",
    "\n",
    "def hist_two(series_A, series_B,\n",
    "             labels=['series_A', 'series_B'],\n",
    "             normalize=False, cumulative=False, bar_or_line='bar'):\n",
    "\n",
    "    fig, ax = plt.subplots(figsize=(10, 5))\n",
    "    \n",
    "    a_heights, a_bins = np.histogram(series_A, bins=range(45), normed=normalize)\n",
    "    b_heights, b_bins = np.histogram(series_B, bins=a_bins, normed=normalize)\n",
    "    \n",
    "    if cumulative:\n",
    "        a_heights = np.cumsum(a_heights)\n",
    "        b_heights = np.cumsum(b_heights)\n",
    "\n",
    "    width = (a_bins[1] - a_bins[0])/2.5\n",
    "\n",
    "    if bar_or_line == 'bar':\n",
    "        ax.bar(a_bins[:-1], a_heights, width=width, facecolor=LILAC, label=labels[0])\n",
    "        ax.bar(b_bins[:-1] + width, b_heights, width=width, facecolor=ORANGE, label=labels[1])\n",
    "    else:\n",
    "        plt.plot(a_bins[:-1], a_heights, linewidth=4, color=LILAC, label=labels[0])\n",
    "        plt.plot(b_bins[:-1], b_heights, linewidth=4, color=ORANGE, label=labels[1])\n",
    "\n",
    "    plt.legend(loc='upper left')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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1uxt4hMp8rrljtg9Wt3ePaTuhwcFttTRrej093fT3b230MDSGdWk+1mR8AwNDzJyifmt5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\nSZJU0P8H2NQVkJmMX9IAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f640b6fd4a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hist_two(firsts.prglngth, others.prglngth, labels=['firsts', 'others'])\n",
    "plt.xlim(33, 44);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Remember that the vertical axis is counts.  In this case, we are comparing counts with different totals, which might be misleading.\n",
    "\n",
    "An alternative is to compute a probability mass function (PMF), which divides the counts by the totals, yielding a map from each element to its probability.\n",
    "\n",
    "The probabilities are \"normalized\" to add up to 1.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can compare histograms fairly."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f640baa49e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hist_two(firsts.prglngth, others.prglngth, labels=['firsts', 'others'], normalize=True)\n",
    "plt.xlim(33, 44);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see here that some of the difference at 39 weeks was an artifact of the different samples sizes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Even so, it is not easy to compare histograms.  One more alternative is the cumulative histogram, which shows, for each $t$, the total probability up to and including $t$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "pp = live.loc[:, ['birthord','prglngth']]\n",
    "not_firsts = pp['birthord'] != 1\n",
    "pp.loc[not_firsts, 'birthord'] = 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ZOmNxBHPufK7tugZX4rcCMHBAa1uJyPbQIqIismuZo/+a1x5PDrLkNNHSVkdT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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f640bb99898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hist_two(firsts.prglngth, others.prglngth, labels=['firsts', 'others'], normalize=True, cumulative=True, bar_or_line='line')\n",
    "plt.xlim(33, 44);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The cumulative histograms are similar up to week 38.  After that, first babies are more likely to be born late. \n",
    "\n",
    "*Can you read this from the plot above?*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One other thought: cumulative curves are often a good option for visualizing noisy series.  For example, the graphic below works pretty well despite some questionable aesthetic choices. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"figures/cumulative_snowfall.png\"/>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.4.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}