notebooks/moe_demo.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Introduction to cenpy American Community Survey margin of error tools"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "The Census Bureau publishes a margin of error (MOE) alongside each American Community (ACS) estimte. These MOEs give an understanding of how reliable that particulare estimate is. In this demonstration we show how to compute an MOE when multiple ACS estimates are combined. \n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import cenpy as cen\n",
    "from cenpy.moe import analytic_utils\n",
    "from cenpy.moe import pseudo_utils\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Pull data from the Census API"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Identify some variables for the demonstration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "cols_raw = ['B01003_001', # Total Population\n",
    "            'B03001_003', # Hispanic\n",
    "            'B19313_001', # Aggregate Income\n",
    "            'B15002_012', # Males with Some College, Less Than 1 Year\n",
    "            'B15002_013', # Males with Some College, 1 Or More Years, No Degree\n",
    "            'B15002_014'] # Males with Associate's Degree"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will need the published estimates and margins of error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['B01003_001E',\n",
       " 'B03001_003E',\n",
       " 'B19313_001E',\n",
       " 'B15002_012E',\n",
       " 'B15002_013E',\n",
       " 'B15002_014E']"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Estimates end in an \"E\" and MOEs end in an \"M\"\n",
    "cols_E = [i+'E' for i in cols_raw]\n",
    "cols_M = [i+'M' for i in cols_raw]\n",
    "\n",
    "cols_E"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['B01003_001M',\n",
       " 'B03001_003M',\n",
       " 'B19313_001M',\n",
       " 'B15002_012M',\n",
       " 'B15002_013M',\n",
       " 'B15002_014M']"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cols_M"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will pull data from the 2014-2018 detailed tables from the ACS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'American Community Survey: 1-Year Estimates: Detailed Tables 5-Year': 'The American Community Survey (ACS) is an ongoing survey that provides data every year -- giving communities the current information they need to plan investments and services. The ACS covers a broad range of topics about social, economic, demographic, and housing characteristics of the U.S. population.  Summary files include the following geographies: nation, all states (including DC and Puerto Rico), all metropolitan areas, all congressional districts (114th congress), all counties, all places, and all tracts and block groups.  Summary files contain the most detailed cross-tabulations, many of which are published down to block groups. The data are population and housing counts. There are over 64,000 variables in this dataset.'}"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "api_database = 'ACSDT5Y2018'\n",
    "api_conn = cen.remote.APIConnection(api_database)\n",
    "cen.explorer.explain(api_database)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The demostration will be for all census tracts in Coconino County, Arizona"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "g_unit = 'tract'\n",
    "g_filter = {'state':'04', 'county':'005'} # Coconino County, Arizona"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With all the pieces in place, we can now pull the data from the Census API"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_E = api_conn.query(cols_E, geo_unit=g_unit, geo_filter=g_filter)\n",
    "data_M = api_conn.query(cols_M, geo_unit=g_unit, geo_filter=g_filter)\n",
    "\n",
    "data_E[cols_E] = data_E[cols_E].astype('int') # convert downloaded data to ints\n",
    "data_M[cols_M] = data_M[cols_M].astype('int') # convert downloaded data to ints"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is what the estimates look like"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>B01003_001E</th>\n",
       "      <th>B03001_003E</th>\n",
       "      <th>B19313_001E</th>\n",
       "      <th>B15002_012E</th>\n",
       "      <th>B15002_013E</th>\n",
       "      <th>B15002_014E</th>\n",
       "      <th>state</th>\n",
       "      <th>county</th>\n",
       "      <th>tract</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>4611</td>\n",
       "      <td>618</td>\n",
       "      <td>155911000</td>\n",
       "      <td>63</td>\n",
       "      <td>201</td>\n",
       "      <td>101</td>\n",
       "      <td>04</td>\n",
       "      <td>005</td>\n",
       "      <td>001101</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>8339</td>\n",
       "      <td>1989</td>\n",
       "      <td>200765900</td>\n",
       "      <td>197</td>\n",
       "      <td>390</td>\n",
       "      <td>198</td>\n",
       "      <td>04</td>\n",
       "      <td>005</td>\n",
       "      <td>001102</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>5193</td>\n",
       "      <td>598</td>\n",
       "      <td>182234100</td>\n",
       "      <td>205</td>\n",
       "      <td>297</td>\n",
       "      <td>90</td>\n",
       "      <td>04</td>\n",
       "      <td>005</td>\n",
       "      <td>001301</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>5633</td>\n",
       "      <td>845</td>\n",
       "      <td>162323000</td>\n",
       "      <td>170</td>\n",
       "      <td>419</td>\n",
       "      <td>97</td>\n",
       "      <td>04</td>\n",
       "      <td>005</td>\n",
       "      <td>001302</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>6735</td>\n",
       "      <td>824</td>\n",
       "      <td>322765600</td>\n",
       "      <td>49</td>\n",
       "      <td>262</td>\n",
       "      <td>337</td>\n",
       "      <td>04</td>\n",
       "      <td>005</td>\n",
       "      <td>002200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>5891</td>\n",
       "      <td>641</td>\n",
       "      <td>186444600</td>\n",
       "      <td>305</td>\n",
       "      <td>838</td>\n",
       "      <td>169</td>\n",
       "      <td>04</td>\n",
       "      <td>005</td>\n",
       "      <td>002300</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>3795</td>\n",
       "      <td>58</td>\n",
       "      <td>56610200</td>\n",
       "      <td>28</td>\n",
       "      <td>139</td>\n",
       "      <td>56</td>\n",
       "      <td>04</td>\n",
       "      <td>005</td>\n",
       "      <td>942201</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>3467</td>\n",
       "      <td>55</td>\n",
       "      <td>42392000</td>\n",
       "      <td>38</td>\n",
       "      <td>106</td>\n",
       "      <td>15</td>\n",
       "      <td>04</td>\n",
       "      <td>005</td>\n",
       "      <td>942202</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>4726</td>\n",
       "      <td>24</td>\n",
       "      <td>75087400</td>\n",
       "      <td>43</td>\n",
       "      <td>221</td>\n",
       "      <td>123</td>\n",
       "      <td>04</td>\n",
       "      <td>005</td>\n",
       "      <td>944900</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>4438</td>\n",
       "      <td>108</td>\n",
       "      <td>47734200</td>\n",
       "      <td>64</td>\n",
       "      <td>147</td>\n",
       "      <td>76</td>\n",
       "      <td>04</td>\n",
       "      <td>005</td>\n",
       "      <td>945000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>3943</td>\n",
       "      <td>67</td>\n",
       "      <td>52120200</td>\n",
       "      <td>44</td>\n",
       "      <td>144</td>\n",
       "      <td>64</td>\n",
       "      <td>04</td>\n",
       "      <td>005</td>\n",
       "      <td>945100</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>4499</td>\n",
       "      <td>72</td>\n",
       "      <td>71813000</td>\n",
       "      <td>35</td>\n",
       "      <td>245</td>\n",
       "      <td>103</td>\n",
       "      <td>04</td>\n",
       "      <td>005</td>\n",
       "      <td>945200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>6959</td>\n",
       "      <td>1076</td>\n",
       "      <td>257579300</td>\n",
       "      <td>31</td>\n",
       "      <td>476</td>\n",
       "      <td>311</td>\n",
       "      <td>04</td>\n",
       "      <td>005</td>\n",
       "      <td>000900</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>3850</td>\n",
       "      <td>636</td>\n",
       "      <td>153190500</td>\n",
       "      <td>70</td>\n",
       "      <td>261</td>\n",
       "      <td>73</td>\n",
       "      <td>04</td>\n",
       "      <td>005</td>\n",
       "      <td>000200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>6438</td>\n",
       "      <td>2440</td>\n",
       "      <td>155474100</td>\n",
       "      <td>149</td>\n",
       "      <td>291</td>\n",
       "      <td>248</td>\n",
       "      <td>04</td>\n",
       "      <td>005</td>\n",
       "      <td>000300</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>6122</td>\n",
       "      <td>1302</td>\n",
       "      <td>99347200</td>\n",
       "      <td>172</td>\n",
       "      <td>237</td>\n",
       "      <td>158</td>\n",
       "      <td>04</td>\n",
       "      <td>005</td>\n",
       "      <td>000800</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>3517</td>\n",
       "      <td>390</td>\n",
       "      <td>159329400</td>\n",
       "      <td>46</td>\n",
       "      <td>170</td>\n",
       "      <td>93</td>\n",
       "      <td>04</td>\n",
       "      <td>005</td>\n",
       "      <td>000100</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>2720</td>\n",
       "      <td>256</td>\n",
       "      <td>112123900</td>\n",
       "      <td>59</td>\n",
       "      <td>120</td>\n",
       "      <td>74</td>\n",
       "      <td>04</td>\n",
       "      <td>005</td>\n",
       "      <td>001200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>2903</td>\n",
       "      <td>254</td>\n",
       "      <td>109610200</td>\n",
       "      <td>73</td>\n",
       "      <td>206</td>\n",
       "      <td>45</td>\n",
       "      <td>04</td>\n",
       "      <td>005</td>\n",
       "      <td>001500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>3706</td>\n",
       "      <td>647</td>\n",
       "      <td>129996900</td>\n",
       "      <td>44</td>\n",
       "      <td>144</td>\n",
       "      <td>97</td>\n",
       "      <td>04</td>\n",
       "      <td>005</td>\n",
       "      <td>000700</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>5414</td>\n",
       "      <td>993</td>\n",
       "      <td>142256900</td>\n",
       "      <td>111</td>\n",
       "      <td>115</td>\n",
       "      <td>144</td>\n",
       "      <td>04</td>\n",
       "      <td>005</td>\n",
       "      <td>000400</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>3619</td>\n",
       "      <td>916</td>\n",
       "      <td>90293300</td>\n",
       "      <td>108</td>\n",
       "      <td>209</td>\n",
       "      <td>130</td>\n",
       "      <td>04</td>\n",
       "      <td>005</td>\n",
       "      <td>000500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>3475</td>\n",
       "      <td>1054</td>\n",
       "      <td>85740300</td>\n",
       "      <td>149</td>\n",
       "      <td>213</td>\n",
       "      <td>110</td>\n",
       "      <td>04</td>\n",
       "      <td>005</td>\n",
       "      <td>001700</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>7547</td>\n",
       "      <td>707</td>\n",
       "      <td>160342600</td>\n",
       "      <td>163</td>\n",
       "      <td>483</td>\n",
       "      <td>155</td>\n",
       "      <td>04</td>\n",
       "      <td>005</td>\n",
       "      <td>002100</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>12368</td>\n",
       "      <td>2344</td>\n",
       "      <td>55454100</td>\n",
       "      <td>7</td>\n",
       "      <td>37</td>\n",
       "      <td>32</td>\n",
       "      <td>04</td>\n",
       "      <td>005</td>\n",
       "      <td>001000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>5262</td>\n",
       "      <td>302</td>\n",
       "      <td>218984700</td>\n",
       "      <td>111</td>\n",
       "      <td>583</td>\n",
       "      <td>29</td>\n",
       "      <td>04</td>\n",
       "      <td>005</td>\n",
       "      <td>000600</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>3180</td>\n",
       "      <td>276</td>\n",
       "      <td>157001500</td>\n",
       "      <td>89</td>\n",
       "      <td>125</td>\n",
       "      <td>140</td>\n",
       "      <td>04</td>\n",
       "      <td>005</td>\n",
       "      <td>001600</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>1867</td>\n",
       "      <td>174</td>\n",
       "      <td>57021800</td>\n",
       "      <td>38</td>\n",
       "      <td>189</td>\n",
       "      <td>40</td>\n",
       "      <td>04</td>\n",
       "      <td>005</td>\n",
       "      <td>002000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    B01003_001E  B03001_003E  B19313_001E  B15002_012E  B15002_013E  \\\n",
       "0          4611          618    155911000           63          201   \n",
       "1          8339         1989    200765900          197          390   \n",
       "2          5193          598    182234100          205          297   \n",
       "3          5633          845    162323000          170          419   \n",
       "4          6735          824    322765600           49          262   \n",
       "5          5891          641    186444600          305          838   \n",
       "6          3795           58     56610200           28          139   \n",
       "7          3467           55     42392000           38          106   \n",
       "8          4726           24     75087400           43          221   \n",
       "9          4438          108     47734200           64          147   \n",
       "10         3943           67     52120200           44          144   \n",
       "11         4499           72     71813000           35          245   \n",
       "12         6959         1076    257579300           31          476   \n",
       "13         3850          636    153190500           70          261   \n",
       "14         6438         2440    155474100          149          291   \n",
       "15         6122         1302     99347200          172          237   \n",
       "16         3517          390    159329400           46          170   \n",
       "17         2720          256    112123900           59          120   \n",
       "18         2903          254    109610200           73          206   \n",
       "19         3706          647    129996900           44          144   \n",
       "20         5414          993    142256900          111          115   \n",
       "21         3619          916     90293300          108          209   \n",
       "22         3475         1054     85740300          149          213   \n",
       "23         7547          707    160342600          163          483   \n",
       "24        12368         2344     55454100            7           37   \n",
       "25         5262          302    218984700          111          583   \n",
       "26         3180          276    157001500           89          125   \n",
       "27         1867          174     57021800           38          189   \n",
       "\n",
       "    B15002_014E state county   tract  \n",
       "0           101    04    005  001101  \n",
       "1           198    04    005  001102  \n",
       "2            90    04    005  001301  \n",
       "3            97    04    005  001302  \n",
       "4           337    04    005  002200  \n",
       "5           169    04    005  002300  \n",
       "6            56    04    005  942201  \n",
       "7            15    04    005  942202  \n",
       "8           123    04    005  944900  \n",
       "9            76    04    005  945000  \n",
       "10           64    04    005  945100  \n",
       "11          103    04    005  945200  \n",
       "12          311    04    005  000900  \n",
       "13           73    04    005  000200  \n",
       "14          248    04    005  000300  \n",
       "15          158    04    005  000800  \n",
       "16           93    04    005  000100  \n",
       "17           74    04    005  001200  \n",
       "18           45    04    005  001500  \n",
       "19           97    04    005  000700  \n",
       "20          144    04    005  000400  \n",
       "21          130    04    005  000500  \n",
       "22          110    04    005  001700  \n",
       "23          155    04    005  002100  \n",
       "24           32    04    005  001000  \n",
       "25           29    04    005  000600  \n",
       "26          140    04    005  001600  \n",
       "27           40    04    005  002000  "
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_E"
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  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "...and the MOEs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
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       "      <th></th>\n",
       "      <th>B01003_001M</th>\n",
       "      <th>B03001_003M</th>\n",
       "      <th>B19313_001M</th>\n",
       "      <th>B15002_012M</th>\n",
       "      <th>B15002_013M</th>\n",
       "      <th>B15002_014M</th>\n",
       "      <th>state</th>\n",
       "      <th>county</th>\n",
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       "      <th>0</th>\n",
       "      <td>406</td>\n",
       "      <td>170</td>\n",
       "      <td>22714480</td>\n",
       "      <td>42</td>\n",
       "      <td>64</td>\n",
       "      <td>52</td>\n",
       "      <td>04</td>\n",
       "      <td>005</td>\n",
       "      <td>001101</td>\n",
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       "      <th>1</th>\n",
       "      <td>615</td>\n",
       "      <td>345</td>\n",
       "      <td>25521201</td>\n",
       "      <td>129</td>\n",
       "      <td>170</td>\n",
       "      <td>118</td>\n",
       "      <td>04</td>\n",
       "      <td>005</td>\n",
       "      <td>001102</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>599</td>\n",
       "      <td>255</td>\n",
       "      <td>22397589</td>\n",
       "      <td>95</td>\n",
       "      <td>114</td>\n",
       "      <td>52</td>\n",
       "      <td>04</td>\n",
       "      <td>005</td>\n",
       "      <td>001301</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>681</td>\n",
       "      <td>200</td>\n",
       "      <td>18576594</td>\n",
       "      <td>86</td>\n",
       "      <td>140</td>\n",
       "      <td>66</td>\n",
       "      <td>04</td>\n",
       "      <td>005</td>\n",
       "      <td>001302</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>635</td>\n",
       "      <td>209</td>\n",
       "      <td>63593535</td>\n",
       "      <td>57</td>\n",
       "      <td>128</td>\n",
       "      <td>141</td>\n",
       "      <td>04</td>\n",
       "      <td>005</td>\n",
       "      <td>002200</td>\n",
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       "      <th>5</th>\n",
       "      <td>740</td>\n",
       "      <td>234</td>\n",
       "      <td>23082343</td>\n",
       "      <td>132</td>\n",
       "      <td>221</td>\n",
       "      <td>87</td>\n",
       "      <td>04</td>\n",
       "      <td>005</td>\n",
       "      <td>002300</td>\n",
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       "      <th>6</th>\n",
       "      <td>304</td>\n",
       "      <td>37</td>\n",
       "      <td>5737985</td>\n",
       "      <td>16</td>\n",
       "      <td>35</td>\n",
       "      <td>23</td>\n",
       "      <td>04</td>\n",
       "      <td>005</td>\n",
       "      <td>942201</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>321</td>\n",
       "      <td>38</td>\n",
       "      <td>4566029</td>\n",
       "      <td>17</td>\n",
       "      <td>29</td>\n",
       "      <td>13</td>\n",
       "      <td>04</td>\n",
       "      <td>005</td>\n",
       "      <td>942202</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>517</td>\n",
       "      <td>28</td>\n",
       "      <td>10494052</td>\n",
       "      <td>35</td>\n",
       "      <td>101</td>\n",
       "      <td>58</td>\n",
       "      <td>04</td>\n",
       "      <td>005</td>\n",
       "      <td>944900</td>\n",
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       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>302</td>\n",
       "      <td>60</td>\n",
       "      <td>5082556</td>\n",
       "      <td>33</td>\n",
       "      <td>44</td>\n",
       "      <td>35</td>\n",
       "      <td>04</td>\n",
       "      <td>005</td>\n",
       "      <td>945000</td>\n",
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       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>316</td>\n",
       "      <td>33</td>\n",
       "      <td>4527569</td>\n",
       "      <td>22</td>\n",
       "      <td>37</td>\n",
       "      <td>22</td>\n",
       "      <td>04</td>\n",
       "      <td>005</td>\n",
       "      <td>945100</td>\n",
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       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>505</td>\n",
       "      <td>61</td>\n",
       "      <td>8895939</td>\n",
       "      <td>32</td>\n",
       "      <td>92</td>\n",
       "      <td>52</td>\n",
       "      <td>04</td>\n",
       "      <td>005</td>\n",
       "      <td>945200</td>\n",
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       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>575</td>\n",
       "      <td>318</td>\n",
       "      <td>45061154</td>\n",
       "      <td>37</td>\n",
       "      <td>233</td>\n",
       "      <td>195</td>\n",
       "      <td>04</td>\n",
       "      <td>005</td>\n",
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       "      <th>13</th>\n",
       "      <td>410</td>\n",
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       "      <td>19648625</td>\n",
       "      <td>41</td>\n",
       "      <td>91</td>\n",
       "      <td>56</td>\n",
       "      <td>04</td>\n",
       "      <td>005</td>\n",
       "      <td>000200</td>\n",
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       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>603</td>\n",
       "      <td>543</td>\n",
       "      <td>22955692</td>\n",
       "      <td>79</td>\n",
       "      <td>92</td>\n",
       "      <td>132</td>\n",
       "      <td>04</td>\n",
       "      <td>005</td>\n",
       "      <td>000300</td>\n",
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       "      <th>15</th>\n",
       "      <td>646</td>\n",
       "      <td>255</td>\n",
       "      <td>13744500</td>\n",
       "      <td>91</td>\n",
       "      <td>99</td>\n",
       "      <td>68</td>\n",
       "      <td>04</td>\n",
       "      <td>005</td>\n",
       "      <td>000800</td>\n",
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       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>277</td>\n",
       "      <td>167</td>\n",
       "      <td>17873519</td>\n",
       "      <td>37</td>\n",
       "      <td>59</td>\n",
       "      <td>50</td>\n",
       "      <td>04</td>\n",
       "      <td>005</td>\n",
       "      <td>000100</td>\n",
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       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>202</td>\n",
       "      <td>134</td>\n",
       "      <td>14820577</td>\n",
       "      <td>41</td>\n",
       "      <td>87</td>\n",
       "      <td>67</td>\n",
       "      <td>04</td>\n",
       "      <td>005</td>\n",
       "      <td>001200</td>\n",
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       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>394</td>\n",
       "      <td>160</td>\n",
       "      <td>20598280</td>\n",
       "      <td>58</td>\n",
       "      <td>98</td>\n",
       "      <td>40</td>\n",
       "      <td>04</td>\n",
       "      <td>005</td>\n",
       "      <td>001500</td>\n",
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       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>372</td>\n",
       "      <td>237</td>\n",
       "      <td>17359157</td>\n",
       "      <td>34</td>\n",
       "      <td>60</td>\n",
       "      <td>68</td>\n",
       "      <td>04</td>\n",
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       "      <td>15198039</td>\n",
       "      <td>69</td>\n",
       "      <td>53</td>\n",
       "      <td>78</td>\n",
       "      <td>04</td>\n",
       "      <td>005</td>\n",
       "      <td>000400</td>\n",
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       "      <th>21</th>\n",
       "      <td>400</td>\n",
       "      <td>237</td>\n",
       "      <td>12601177</td>\n",
       "      <td>76</td>\n",
       "      <td>95</td>\n",
       "      <td>68</td>\n",
       "      <td>04</td>\n",
       "      <td>005</td>\n",
       "      <td>000500</td>\n",
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       "      <th>22</th>\n",
       "      <td>131</td>\n",
       "      <td>165</td>\n",
       "      <td>9039383</td>\n",
       "      <td>66</td>\n",
       "      <td>67</td>\n",
       "      <td>56</td>\n",
       "      <td>04</td>\n",
       "      <td>005</td>\n",
       "      <td>001700</td>\n",
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       "      <th>23</th>\n",
       "      <td>19</td>\n",
       "      <td>380</td>\n",
       "      <td>19269569</td>\n",
       "      <td>106</td>\n",
       "      <td>164</td>\n",
       "      <td>114</td>\n",
       "      <td>04</td>\n",
       "      <td>005</td>\n",
       "      <td>002100</td>\n",
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       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>1302</td>\n",
       "      <td>362</td>\n",
       "      <td>8854217</td>\n",
       "      <td>10</td>\n",
       "      <td>37</td>\n",
       "      <td>30</td>\n",
       "      <td>04</td>\n",
       "      <td>005</td>\n",
       "      <td>001000</td>\n",
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       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>455</td>\n",
       "      <td>135</td>\n",
       "      <td>36625917</td>\n",
       "      <td>96</td>\n",
       "      <td>216</td>\n",
       "      <td>31</td>\n",
       "      <td>04</td>\n",
       "      <td>005</td>\n",
       "      <td>000600</td>\n",
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       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>152</td>\n",
       "      <td>177</td>\n",
       "      <td>33347773</td>\n",
       "      <td>59</td>\n",
       "      <td>57</td>\n",
       "      <td>98</td>\n",
       "      <td>04</td>\n",
       "      <td>005</td>\n",
       "      <td>001600</td>\n",
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       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>413</td>\n",
       "      <td>132</td>\n",
       "      <td>14479669</td>\n",
       "      <td>48</td>\n",
       "      <td>86</td>\n",
       "      <td>39</td>\n",
       "      <td>04</td>\n",
       "      <td>005</td>\n",
       "      <td>002000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    B01003_001M  B03001_003M  B19313_001M  B15002_012M  B15002_013M  \\\n",
       "0           406          170     22714480           42           64   \n",
       "1           615          345     25521201          129          170   \n",
       "2           599          255     22397589           95          114   \n",
       "3           681          200     18576594           86          140   \n",
       "4           635          209     63593535           57          128   \n",
       "5           740          234     23082343          132          221   \n",
       "6           304           37      5737985           16           35   \n",
       "7           321           38      4566029           17           29   \n",
       "8           517           28     10494052           35          101   \n",
       "9           302           60      5082556           33           44   \n",
       "10          316           33      4527569           22           37   \n",
       "11          505           61      8895939           32           92   \n",
       "12          575          318     45061154           37          233   \n",
       "13          410          252     19648625           41           91   \n",
       "14          603          543     22955692           79           92   \n",
       "15          646          255     13744500           91           99   \n",
       "16          277          167     17873519           37           59   \n",
       "17          202          134     14820577           41           87   \n",
       "18          394          160     20598280           58           98   \n",
       "19          372          237     17359157           34           60   \n",
       "20          409          284     15198039           69           53   \n",
       "21          400          237     12601177           76           95   \n",
       "22          131          165      9039383           66           67   \n",
       "23           19          380     19269569          106          164   \n",
       "24         1302          362      8854217           10           37   \n",
       "25          455          135     36625917           96          216   \n",
       "26          152          177     33347773           59           57   \n",
       "27          413          132     14479669           48           86   \n",
       "\n",
       "    B15002_014M state county   tract  \n",
       "0            52    04    005  001101  \n",
       "1           118    04    005  001102  \n",
       "2            52    04    005  001301  \n",
       "3            66    04    005  001302  \n",
       "4           141    04    005  002200  \n",
       "5            87    04    005  002300  \n",
       "6            23    04    005  942201  \n",
       "7            13    04    005  942202  \n",
       "8            58    04    005  944900  \n",
       "9            35    04    005  945000  \n",
       "10           22    04    005  945100  \n",
       "11           52    04    005  945200  \n",
       "12          195    04    005  000900  \n",
       "13           56    04    005  000200  \n",
       "14          132    04    005  000300  \n",
       "15           68    04    005  000800  \n",
       "16           50    04    005  000100  \n",
       "17           67    04    005  001200  \n",
       "18           40    04    005  001500  \n",
       "19           68    04    005  000700  \n",
       "20           78    04    005  000400  \n",
       "21           68    04    005  000500  \n",
       "22           56    04    005  001700  \n",
       "23          114    04    005  002100  \n",
       "24           30    04    005  001000  \n",
       "25           31    04    005  000600  \n",
       "26           98    04    005  001600  \n",
       "27           39    04    005  002000  "
      ]
     },
     "execution_count": 10,
     "metadata": {},
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   ],
   "source": [
    "data_M"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Computing margins of error on combined estimates "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Three options are available in cenpy:\n",
    "\n",
    "a. Analytic\n",
    "\n",
    "b. Pseudo\n",
    "\n",
    "c. Replicate"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### a. Analytic"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The analytic approach uses classic statistical theory to compute the MOEs. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this first example, we sum three columns to get the unpublished value for males with more than high school diploma, but less than a bachelors degree."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
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       "      <td>365</td>\n",
       "      <td>92.541882</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>785</td>\n",
       "      <td>243.854465</td>\n",
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       "      <th>2</th>\n",
       "      <td>592</td>\n",
       "      <td>157.241852</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>686</td>\n",
       "      <td>177.064960</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>648</td>\n",
       "      <td>198.781287</td>\n",
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       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1312</td>\n",
       "      <td>271.724125</td>\n",
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       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>223</td>\n",
       "      <td>44.833024</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>159</td>\n",
       "      <td>36.041643</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>387</td>\n",
       "      <td>121.614144</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>287</td>\n",
       "      <td>65.192024</td>\n",
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       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>252</td>\n",
       "      <td>48.342528</td>\n",
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       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>383</td>\n",
       "      <td>110.417390</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>818</td>\n",
       "      <td>306.076788</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>404</td>\n",
       "      <td>114.446494</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>688</td>\n",
       "      <td>179.245642</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>567</td>\n",
       "      <td>150.685102</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>309</td>\n",
       "      <td>85.732141</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>253</td>\n",
       "      <td>117.213480</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>324</td>\n",
       "      <td>120.697970</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>285</td>\n",
       "      <td>96.850400</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>370</td>\n",
       "      <td>116.850332</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>447</td>\n",
       "      <td>139.373599</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>472</td>\n",
       "      <td>109.457754</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>801</td>\n",
       "      <td>226.115015</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>76</td>\n",
       "      <td>48.672374</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>723</td>\n",
       "      <td>238.396728</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>354</td>\n",
       "      <td>127.804538</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>267</td>\n",
       "      <td>105.929222</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     est         moe\n",
       "0    365   92.541882\n",
       "1    785  243.854465\n",
       "2    592  157.241852\n",
       "3    686  177.064960\n",
       "4    648  198.781287\n",
       "5   1312  271.724125\n",
       "6    223   44.833024\n",
       "7    159   36.041643\n",
       "8    387  121.614144\n",
       "9    287   65.192024\n",
       "10   252   48.342528\n",
       "11   383  110.417390\n",
       "12   818  306.076788\n",
       "13   404  114.446494\n",
       "14   688  179.245642\n",
       "15   567  150.685102\n",
       "16   309   85.732141\n",
       "17   253  117.213480\n",
       "18   324  120.697970\n",
       "19   285   96.850400\n",
       "20   370  116.850332\n",
       "21   447  139.373599\n",
       "22   472  109.457754\n",
       "23   801  226.115015\n",
       "24    76   48.672374\n",
       "25   723  238.396728\n",
       "26   354  127.804538\n",
       "27   267  105.929222"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Summing values\n",
    "results_sum = analytic_utils.analytic_sum(data_E[['B15002_012E','B15002_013E','B15002_014E']], \n",
    "                                          data_M[['B15002_012M','B15002_013M','B15002_014M']])\n",
    "results_sum"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Second, we compute per capita income, which is a _ratio_ of aggregate income to total population."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>est</th>\n",
       "      <th>moe</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>33812.838864</td>\n",
       "      <td>5755.941612</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>24075.536635</td>\n",
       "      <td>3538.230172</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>35092.258810</td>\n",
       "      <td>5914.981952</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>28816.438843</td>\n",
       "      <td>4797.096911</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>47923.622866</td>\n",
       "      <td>10467.668017</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>31649.057885</td>\n",
       "      <td>5581.939327</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>14917.048748</td>\n",
       "      <td>1927.167003</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>12227.285838</td>\n",
       "      <td>1736.695411</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>15888.150656</td>\n",
       "      <td>2819.843781</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>10755.790897</td>\n",
       "      <td>1359.142260</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>13218.412376</td>\n",
       "      <td>1562.277944</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>15961.991554</td>\n",
       "      <td>2668.317933</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>37013.838195</td>\n",
       "      <td>7161.150235</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>39789.740260</td>\n",
       "      <td>6633.342759</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>24149.440820</td>\n",
       "      <td>4222.569512</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>16227.899379</td>\n",
       "      <td>2823.603357</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>45302.644299</td>\n",
       "      <td>6209.514257</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>41222.022059</td>\n",
       "      <td>6249.847617</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>37757.561144</td>\n",
       "      <td>8752.544168</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>35077.415003</td>\n",
       "      <td>5859.853587</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>26275.748061</td>\n",
       "      <td>3438.087137</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>24949.792760</td>\n",
       "      <td>4441.686777</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>24673.467626</td>\n",
       "      <td>2762.555735</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>21245.872532</td>\n",
       "      <td>2553.835527</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>4483.675614</td>\n",
       "      <td>857.494397</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>41616.248575</td>\n",
       "      <td>7835.640446</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>49371.540881</td>\n",
       "      <td>10748.973683</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>30541.938939</td>\n",
       "      <td>10285.681097</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             est           moe\n",
       "0   33812.838864   5755.941612\n",
       "1   24075.536635   3538.230172\n",
       "2   35092.258810   5914.981952\n",
       "3   28816.438843   4797.096911\n",
       "4   47923.622866  10467.668017\n",
       "5   31649.057885   5581.939327\n",
       "6   14917.048748   1927.167003\n",
       "7   12227.285838   1736.695411\n",
       "8   15888.150656   2819.843781\n",
       "9   10755.790897   1359.142260\n",
       "10  13218.412376   1562.277944\n",
       "11  15961.991554   2668.317933\n",
       "12  37013.838195   7161.150235\n",
       "13  39789.740260   6633.342759\n",
       "14  24149.440820   4222.569512\n",
       "15  16227.899379   2823.603357\n",
       "16  45302.644299   6209.514257\n",
       "17  41222.022059   6249.847617\n",
       "18  37757.561144   8752.544168\n",
       "19  35077.415003   5859.853587\n",
       "20  26275.748061   3438.087137\n",
       "21  24949.792760   4441.686777\n",
       "22  24673.467626   2762.555735\n",
       "23  21245.872532   2553.835527\n",
       "24   4483.675614    857.494397\n",
       "25  41616.248575   7835.640446\n",
       "26  49371.540881  10748.973683\n",
       "27  30541.938939  10285.681097"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Ratio\n",
    "results_ratio = analytic_utils.analytic_ratio(data_E[['B19313_001E','B01003_001E']],\n",
    "                                              data_M[['B19313_001M','B01003_001M']])\n",
    "results_ratio"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we compute the _proportion_ Hispanic residents are of the total population."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>est</th>\n",
       "      <th>moe</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.134027</td>\n",
       "      <td>0.034929</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.238518</td>\n",
       "      <td>0.037446</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.115155</td>\n",
       "      <td>0.047274</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.150009</td>\n",
       "      <td>0.030524</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.122346</td>\n",
       "      <td>0.028808</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.108810</td>\n",
       "      <td>0.037296</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.015283</td>\n",
       "      <td>0.009672</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.015864</td>\n",
       "      <td>0.010862</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.005078</td>\n",
       "      <td>0.005899</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.024335</td>\n",
       "      <td>0.013418</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0.016992</td>\n",
       "      <td>0.008258</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>0.016004</td>\n",
       "      <td>0.013439</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>0.154620</td>\n",
       "      <td>0.043874</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>0.165195</td>\n",
       "      <td>0.063046</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>0.379000</td>\n",
       "      <td>0.076509</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>0.212676</td>\n",
       "      <td>0.035091</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>0.110890</td>\n",
       "      <td>0.046674</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>0.094118</td>\n",
       "      <td>0.048766</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>0.087496</td>\n",
       "      <td>0.053821</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>0.174582</td>\n",
       "      <td>0.061502</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>0.183413</td>\n",
       "      <td>0.050594</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>0.253109</td>\n",
       "      <td>0.059212</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>0.303309</td>\n",
       "      <td>0.046085</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>0.093680</td>\n",
       "      <td>0.050351</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>0.189521</td>\n",
       "      <td>0.021416</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>0.057393</td>\n",
       "      <td>0.025171</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>0.086792</td>\n",
       "      <td>0.055506</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>0.093198</td>\n",
       "      <td>0.067629</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         est       moe\n",
       "0   0.134027  0.034929\n",
       "1   0.238518  0.037446\n",
       "2   0.115155  0.047274\n",
       "3   0.150009  0.030524\n",
       "4   0.122346  0.028808\n",
       "5   0.108810  0.037296\n",
       "6   0.015283  0.009672\n",
       "7   0.015864  0.010862\n",
       "8   0.005078  0.005899\n",
       "9   0.024335  0.013418\n",
       "10  0.016992  0.008258\n",
       "11  0.016004  0.013439\n",
       "12  0.154620  0.043874\n",
       "13  0.165195  0.063046\n",
       "14  0.379000  0.076509\n",
       "15  0.212676  0.035091\n",
       "16  0.110890  0.046674\n",
       "17  0.094118  0.048766\n",
       "18  0.087496  0.053821\n",
       "19  0.174582  0.061502\n",
       "20  0.183413  0.050594\n",
       "21  0.253109  0.059212\n",
       "22  0.303309  0.046085\n",
       "23  0.093680  0.050351\n",
       "24  0.189521  0.021416\n",
       "25  0.057393  0.025171\n",
       "26  0.086792  0.055506\n",
       "27  0.093198  0.067629"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Proportion\n",
    "results_prop = analytic_utils.analytic_prop(data_E[['B03001_003E','B01003_001E']],\n",
    "                                            data_M[['B03001_003M','B01003_001M']])\n",
    "results_prop"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### b. Pseudo "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The pseudo approach generates random draws from a distribution around each published estimate built using the published estimate and MOE. These random draws are used to compute the MOEs on the combined estimates."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Following the example using the analytic approach, we again compute the sum of the number of males with more than a high school diploma but less than a college degree. First, we need to construct a function returning the sum of the `ests` arguement in the `pseudo` function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_sum(ests):\n",
    "    return ests.sum(axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we pass our `get_sum` function to the `func` parameter along with the published estiamtes and margains of error we used above to `pseudo`. This will return the margain of errors for the summed estimates derived usign the pseudo method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>est</th>\n",
       "      <th>moe</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>365</td>\n",
       "      <td>84.735357</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>785</td>\n",
       "      <td>250.007884</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>592</td>\n",
       "      <td>140.238331</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>686</td>\n",
       "      <td>167.853122</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>648</td>\n",
       "      <td>181.748614</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1312</td>\n",
       "      <td>272.964043</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>223</td>\n",
       "      <td>41.073046</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>159</td>\n",
       "      <td>37.448461</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>387</td>\n",
       "      <td>120.257335</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>287</td>\n",
       "      <td>64.421342</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>252</td>\n",
       "      <td>48.405048</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>383</td>\n",
       "      <td>106.709926</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>818</td>\n",
       "      <td>295.366184</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>404</td>\n",
       "      <td>122.884843</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>688</td>\n",
       "      <td>187.736771</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>567</td>\n",
       "      <td>150.526368</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>309</td>\n",
       "      <td>89.161340</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>253</td>\n",
       "      <td>121.917382</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>324</td>\n",
       "      <td>123.955399</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>285</td>\n",
       "      <td>89.015580</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>370</td>\n",
       "      <td>116.621658</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>447</td>\n",
       "      <td>148.584868</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>472</td>\n",
       "      <td>116.897372</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>801</td>\n",
       "      <td>253.655756</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>76</td>\n",
       "      <td>42.377793</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>723</td>\n",
       "      <td>229.177557</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>354</td>\n",
       "      <td>128.139737</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>267</td>\n",
       "      <td>106.464339</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     est         moe\n",
       "0    365   84.735357\n",
       "1    785  250.007884\n",
       "2    592  140.238331\n",
       "3    686  167.853122\n",
       "4    648  181.748614\n",
       "5   1312  272.964043\n",
       "6    223   41.073046\n",
       "7    159   37.448461\n",
       "8    387  120.257335\n",
       "9    287   64.421342\n",
       "10   252   48.405048\n",
       "11   383  106.709926\n",
       "12   818  295.366184\n",
       "13   404  122.884843\n",
       "14   688  187.736771\n",
       "15   567  150.526368\n",
       "16   309   89.161340\n",
       "17   253  121.917382\n",
       "18   324  123.955399\n",
       "19   285   89.015580\n",
       "20   370  116.621658\n",
       "21   447  148.584868\n",
       "22   472  116.897372\n",
       "23   801  253.655756\n",
       "24    76   42.377793\n",
       "25   723  229.177557\n",
       "26   354  128.139737\n",
       "27   267  106.464339"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Summing\n",
    "pseudo_results_sum = pseudo_utils.pseudo(get_sum,\n",
    "                                         ests=data_E[['B15002_012E','B15002_013E','B15002_014E']],\n",
    "                                         moes=data_M[['B15002_012M','B15002_013M','B15002_014M']])\n",
    "pseudo_results_sum"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we will demonstrate how to derive the pseudo MOEs for a ratio calculation. Again, we create a function, `get_div`, to pass to `pseudo`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_div(ests):\n",
    "    return ests.iloc[:,0] / (ests.iloc[:,1]*1.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now pass the function to `pseudo` as done in the summing example."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
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       "      <th></th>\n",
       "      <th>est</th>\n",
       "      <th>moe</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>33812.838864</td>\n",
       "      <td>5588.264669</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>24075.536635</td>\n",
       "      <td>3486.556631</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>35092.258810</td>\n",
       "      <td>5461.779371</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>28816.438843</td>\n",
       "      <td>5061.058406</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>47923.622866</td>\n",
       "      <td>9465.400697</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>31649.057885</td>\n",
       "      <td>5534.522928</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>14917.048748</td>\n",
       "      <td>2043.322715</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>12227.285838</td>\n",
       "      <td>1854.067618</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>15888.150656</td>\n",
       "      <td>2823.545890</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>10755.790897</td>\n",
       "      <td>1287.138719</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>13218.412376</td>\n",
       "      <td>1464.332840</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>15961.991554</td>\n",
       "      <td>2871.830815</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>37013.838195</td>\n",
       "      <td>6493.285858</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>39789.740260</td>\n",
       "      <td>6507.534991</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>24149.440820</td>\n",
       "      <td>4240.028495</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>16227.899379</td>\n",
       "      <td>2787.390325</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>45302.644299</td>\n",
       "      <td>5949.813275</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>41222.022059</td>\n",
       "      <td>6104.126699</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>37757.561144</td>\n",
       "      <td>7763.523896</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>35077.415003</td>\n",
       "      <td>5580.745826</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>26275.748061</td>\n",
       "      <td>3703.960585</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>24949.792760</td>\n",
       "      <td>4134.406837</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>24673.467626</td>\n",
       "      <td>2625.090636</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>21245.872532</td>\n",
       "      <td>2858.229990</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>4483.675614</td>\n",
       "      <td>907.514745</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>41616.248575</td>\n",
       "      <td>8763.624949</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>49371.540881</td>\n",
       "      <td>9494.487316</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>30541.938939</td>\n",
       "      <td>10340.741340</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             est           moe\n",
       "0   33812.838864   5588.264669\n",
       "1   24075.536635   3486.556631\n",
       "2   35092.258810   5461.779371\n",
       "3   28816.438843   5061.058406\n",
       "4   47923.622866   9465.400697\n",
       "5   31649.057885   5534.522928\n",
       "6   14917.048748   2043.322715\n",
       "7   12227.285838   1854.067618\n",
       "8   15888.150656   2823.545890\n",
       "9   10755.790897   1287.138719\n",
       "10  13218.412376   1464.332840\n",
       "11  15961.991554   2871.830815\n",
       "12  37013.838195   6493.285858\n",
       "13  39789.740260   6507.534991\n",
       "14  24149.440820   4240.028495\n",
       "15  16227.899379   2787.390325\n",
       "16  45302.644299   5949.813275\n",
       "17  41222.022059   6104.126699\n",
       "18  37757.561144   7763.523896\n",
       "19  35077.415003   5580.745826\n",
       "20  26275.748061   3703.960585\n",
       "21  24949.792760   4134.406837\n",
       "22  24673.467626   2625.090636\n",
       "23  21245.872532   2858.229990\n",
       "24   4483.675614    907.514745\n",
       "25  41616.248575   8763.624949\n",
       "26  49371.540881   9494.487316\n",
       "27  30541.938939  10340.741340"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Ratio\n",
    "pseudo_results_ratio = pseudo_utils.pseudo(get_div,\n",
    "                                           ests=data_E[['B19313_001E','B01003_001E']],\n",
    "                                           moes=data_M[['B19313_001M','B01003_001M']])\n",
    "pseudo_results_ratio"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To produce replicable results, the seed option can be set. This parameter makes a call to `numpy.random.seed`. The default setting is `seed=None` and will produce variable results for the MOEs with each call."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
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       "      <th></th>\n",
       "      <th>est</th>\n",
       "      <th>moe</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>33812.838864</td>\n",
       "      <td>5199.547268</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>24075.536635</td>\n",
       "      <td>3099.242861</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>35092.258810</td>\n",
       "      <td>5456.081228</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>28816.438843</td>\n",
       "      <td>5159.557118</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>47923.622866</td>\n",
       "      <td>10679.994625</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>31649.057885</td>\n",
       "      <td>5280.682360</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>14917.048748</td>\n",
       "      <td>2124.933063</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>12227.285838</td>\n",
       "      <td>1743.989476</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>15888.150656</td>\n",
       "      <td>2542.562317</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>10755.790897</td>\n",
       "      <td>1277.229939</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>13218.412376</td>\n",
       "      <td>1603.675747</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>15961.991554</td>\n",
       "      <td>2730.129336</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>37013.838195</td>\n",
       "      <td>7144.187530</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>39789.740260</td>\n",
       "      <td>6695.631941</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>24149.440820</td>\n",
       "      <td>4223.362927</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>16227.899379</td>\n",
       "      <td>2663.508198</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>45302.644299</td>\n",
       "      <td>5497.257798</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>41222.022059</td>\n",
       "      <td>5937.705580</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>37757.561144</td>\n",
       "      <td>8643.619015</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>35077.415003</td>\n",
       "      <td>5431.386916</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>26275.748061</td>\n",
       "      <td>3082.989079</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>24949.792760</td>\n",
       "      <td>4105.625732</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>24673.467626</td>\n",
       "      <td>2643.484526</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>21245.872532</td>\n",
       "      <td>3141.699151</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>4483.675614</td>\n",
       "      <td>780.529335</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>41616.248575</td>\n",
       "      <td>7669.268454</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>49371.540881</td>\n",
       "      <td>11278.086226</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>30541.938939</td>\n",
       "      <td>9370.148160</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             est           moe\n",
       "0   33812.838864   5199.547268\n",
       "1   24075.536635   3099.242861\n",
       "2   35092.258810   5456.081228\n",
       "3   28816.438843   5159.557118\n",
       "4   47923.622866  10679.994625\n",
       "5   31649.057885   5280.682360\n",
       "6   14917.048748   2124.933063\n",
       "7   12227.285838   1743.989476\n",
       "8   15888.150656   2542.562317\n",
       "9   10755.790897   1277.229939\n",
       "10  13218.412376   1603.675747\n",
       "11  15961.991554   2730.129336\n",
       "12  37013.838195   7144.187530\n",
       "13  39789.740260   6695.631941\n",
       "14  24149.440820   4223.362927\n",
       "15  16227.899379   2663.508198\n",
       "16  45302.644299   5497.257798\n",
       "17  41222.022059   5937.705580\n",
       "18  37757.561144   8643.619015\n",
       "19  35077.415003   5431.386916\n",
       "20  26275.748061   3082.989079\n",
       "21  24949.792760   4105.625732\n",
       "22  24673.467626   2643.484526\n",
       "23  21245.872532   3141.699151\n",
       "24   4483.675614    780.529335\n",
       "25  41616.248575   7669.268454\n",
       "26  49371.540881  11278.086226\n",
       "27  30541.938939   9370.148160"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Ratio w/ set seed\n",
    "pseudo_results_ratio_w_seed = pseudo_utils.pseudo(get_div,\n",
    "                                                  ests=data_E[['B19313_001E','B01003_001E']],\n",
    "                                                  moes=data_M[['B19313_001M','B01003_001M']],\n",
    "                                                  seed=123)\n",
    "pseudo_results_ratio_w_seed"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The number of simulations run to produce the results is also adjustable through the `sims` parameter. Increasing the number of simulations results in more stable MOE values if the algorithm is run multiple times, but takes longer to run. The default setting is `sims=100`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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       "\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>est</th>\n",
       "      <th>moe</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>33812.838864</td>\n",
       "      <td>5920.022199</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>24075.536635</td>\n",
       "      <td>3486.954777</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>35092.258810</td>\n",
       "      <td>5891.939088</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>28816.438843</td>\n",
       "      <td>4746.521858</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>47923.622866</td>\n",
       "      <td>10589.112366</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>31649.057885</td>\n",
       "      <td>5628.217362</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>14917.048748</td>\n",
       "      <td>1951.230050</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>12227.285838</td>\n",
       "      <td>1748.012442</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>15888.150656</td>\n",
       "      <td>2898.571655</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>10755.790897</td>\n",
       "      <td>1359.418504</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>13218.412376</td>\n",
       "      <td>1594.214628</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>15961.991554</td>\n",
       "      <td>2683.506220</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>37013.838195</td>\n",
       "      <td>7080.390284</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>39789.740260</td>\n",
       "      <td>6418.354355</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>24149.440820</td>\n",
       "      <td>4211.844071</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>16227.899379</td>\n",
       "      <td>2791.605432</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>45302.644299</td>\n",
       "      <td>6148.847893</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>41222.022059</td>\n",
       "      <td>6114.515450</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>37757.561144</td>\n",
       "      <td>8853.231000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>35077.415003</td>\n",
       "      <td>5962.098206</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>26275.748061</td>\n",
       "      <td>3413.756703</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>24949.792760</td>\n",
       "      <td>4305.782054</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>24673.467626</td>\n",
       "      <td>2653.020760</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>21245.872532</td>\n",
       "      <td>2623.506060</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>4483.675614</td>\n",
       "      <td>870.426504</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>41616.248575</td>\n",
       "      <td>8172.820273</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>49371.540881</td>\n",
       "      <td>10552.436291</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>30541.938939</td>\n",
       "      <td>10801.993313</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             est           moe\n",
       "0   33812.838864   5920.022199\n",
       "1   24075.536635   3486.954777\n",
       "2   35092.258810   5891.939088\n",
       "3   28816.438843   4746.521858\n",
       "4   47923.622866  10589.112366\n",
       "5   31649.057885   5628.217362\n",
       "6   14917.048748   1951.230050\n",
       "7   12227.285838   1748.012442\n",
       "8   15888.150656   2898.571655\n",
       "9   10755.790897   1359.418504\n",
       "10  13218.412376   1594.214628\n",
       "11  15961.991554   2683.506220\n",
       "12  37013.838195   7080.390284\n",
       "13  39789.740260   6418.354355\n",
       "14  24149.440820   4211.844071\n",
       "15  16227.899379   2791.605432\n",
       "16  45302.644299   6148.847893\n",
       "17  41222.022059   6114.515450\n",
       "18  37757.561144   8853.231000\n",
       "19  35077.415003   5962.098206\n",
       "20  26275.748061   3413.756703\n",
       "21  24949.792760   4305.782054\n",
       "22  24673.467626   2653.020760\n",
       "23  21245.872532   2623.506060\n",
       "24   4483.675614    870.426504\n",
       "25  41616.248575   8172.820273\n",
       "26  49371.540881  10552.436291\n",
       "27  30541.938939  10801.993313"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Ratio w/ set number of sims\n",
    "pseudo_results_ratio_w_sims = pseudo_utils.pseudo(get_div,\n",
    "                                                  ests=data_E[['B19313_001E','B01003_001E']],\n",
    "                                                  moes=data_M[['B19313_001M','B01003_001M']],\n",
    "                                                  sims=1000)\n",
    "pseudo_results_ratio_w_sims"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The internal algorithm used to compute the MOE simulates estimates from a normal distribution, which means that fractions of people (or housing units) will be simulated. Since this is not realisitc, `whole=True` can be set to always generate whole values. Setting `whole=False` (the default) means that the distribution of simulated values we more closely match the normal distibution from which the simulatations were drawn."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>est</th>\n",
       "      <th>moe</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>365</td>\n",
       "      <td>95.561324</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>785</td>\n",
       "      <td>263.578440</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>592</td>\n",
       "      <td>150.353658</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>686</td>\n",
       "      <td>173.452135</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>648</td>\n",
       "      <td>213.159069</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1312</td>\n",
       "      <td>289.587681</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>223</td>\n",
       "      <td>45.635722</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>159</td>\n",
       "      <td>34.752764</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>387</td>\n",
       "      <td>109.892965</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>287</td>\n",
       "      <td>64.969844</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>252</td>\n",
       "      <td>50.101928</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>383</td>\n",
       "      <td>110.514091</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>818</td>\n",
       "      <td>336.864738</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>404</td>\n",
       "      <td>107.684536</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>688</td>\n",
       "      <td>181.048703</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>567</td>\n",
       "      <td>148.519262</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>309</td>\n",
       "      <td>89.188083</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>253</td>\n",
       "      <td>115.830401</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>324</td>\n",
       "      <td>130.379528</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>285</td>\n",
       "      <td>109.033326</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>370</td>\n",
       "      <td>98.904817</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>447</td>\n",
       "      <td>125.572913</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>472</td>\n",
       "      <td>104.921034</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>801</td>\n",
       "      <td>236.569068</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>76</td>\n",
       "      <td>50.355092</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>723</td>\n",
       "      <td>223.743146</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>354</td>\n",
       "      <td>130.769898</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>267</td>\n",
       "      <td>109.245031</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     est         moe\n",
       "0    365   95.561324\n",
       "1    785  263.578440\n",
       "2    592  150.353658\n",
       "3    686  173.452135\n",
       "4    648  213.159069\n",
       "5   1312  289.587681\n",
       "6    223   45.635722\n",
       "7    159   34.752764\n",
       "8    387  109.892965\n",
       "9    287   64.969844\n",
       "10   252   50.101928\n",
       "11   383  110.514091\n",
       "12   818  336.864738\n",
       "13   404  107.684536\n",
       "14   688  181.048703\n",
       "15   567  148.519262\n",
       "16   309   89.188083\n",
       "17   253  115.830401\n",
       "18   324  130.379528\n",
       "19   285  109.033326\n",
       "20   370   98.904817\n",
       "21   447  125.572913\n",
       "22   472  104.921034\n",
       "23   801  236.569068\n",
       "24    76   50.355092\n",
       "25   723  223.743146\n",
       "26   354  130.769898\n",
       "27   267  109.245031"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Sum MOE generated from whole people\n",
    "pseudo_results_sum_w_whole = pseudo_utils.pseudo(get_sum, \n",
    "                                                  ests=data_E[['B15002_012E','B15002_013E','B15002_014E']],\n",
    "                                                  moes=data_M[['B15002_012M','B15002_013M','B15002_014M']],\n",
    "                                                  whole=True)\n",
    "pseudo_results_sum_w_whole"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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