Hypothesis_2.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "08e6e294",
   "metadata": {},
   "source": [
    "## <span style = \"color:#1A237E;\">Hypothesis Two</span>\n",
    "### <span style = \"color:green;\">Null Hypothesis</span>\n",
    "Households in counties with higher poverty gaps are more likely to access credit.\n",
    "### <span style = \"color:green;\">Alternative Hypothesis</span>\n",
    "Households in counties with higher poverty gaps are less likely to access credit.\n",
    "### <span style = \"color:green;\">Relevance</span>\n",
    "Poverty gaps measure the depth of poverty, indicating how far the poor are from the poverty line. If households are far from the poverty line, they may face more difficulties accessing credit, thereby exacerbating their poverty situation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "08503d9c",
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# Import required libraries\n",
    "import pandas as pd\n",
    "from scipy.stats import pearsonr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "6bc7d8d7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>residence_county</th>\n",
       "      <th>Headcount Rate (%)</th>\n",
       "      <th>Distribution of the Poor (%)</th>\n",
       "      <th>Poverty Gap (%)</th>\n",
       "      <th>Severity of Poverty (%)</th>\n",
       "      <th>Population (ths)</th>\n",
       "      <th>Number of Poor (ths)</th>\n",
       "      <th>Proportion of households that sought credit (%)</th>\n",
       "      <th>Number of Households (ths)</th>\n",
       "      <th>Proportion of households that sought and accessed credit (%)</th>\n",
       "      <th>Number of Households that sought credit (ths)</th>\n",
       "      <th>Distribution of the Poor (%).1</th>\n",
       "      <th>Poverty Gap (%).1</th>\n",
       "      <th>Severity of Poverty (%).1</th>\n",
       "      <th>Population (ths).1</th>\n",
       "      <th>Number of Poor (ths).1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Baringo</td>\n",
       "      <td>39.6</td>\n",
       "      <td>1.7</td>\n",
       "      <td>9.7</td>\n",
       "      <td>4.2</td>\n",
       "      <td>704</td>\n",
       "      <td>278</td>\n",
       "      <td>44.4</td>\n",
       "      <td>152</td>\n",
       "      <td>98.6</td>\n",
       "      <td>68</td>\n",
       "      <td>2.0</td>\n",
       "      <td>10.8</td>\n",
       "      <td>4.1</td>\n",
       "      <td>704</td>\n",
       "      <td>291</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Bomet</td>\n",
       "      <td>48.8</td>\n",
       "      <td>2.7</td>\n",
       "      <td>9.3</td>\n",
       "      <td>2.8</td>\n",
       "      <td>916</td>\n",
       "      <td>447</td>\n",
       "      <td>19.5</td>\n",
       "      <td>179</td>\n",
       "      <td>83.8</td>\n",
       "      <td>35</td>\n",
       "      <td>2.1</td>\n",
       "      <td>5.6</td>\n",
       "      <td>1.6</td>\n",
       "      <td>916</td>\n",
       "      <td>300</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Bungoma</td>\n",
       "      <td>35.7</td>\n",
       "      <td>3.4</td>\n",
       "      <td>9.5</td>\n",
       "      <td>3.6</td>\n",
       "      <td>1,553</td>\n",
       "      <td>555</td>\n",
       "      <td>32.8</td>\n",
       "      <td>321</td>\n",
       "      <td>58.0</td>\n",
       "      <td>105</td>\n",
       "      <td>3.5</td>\n",
       "      <td>9.5</td>\n",
       "      <td>3.9</td>\n",
       "      <td>1,553</td>\n",
       "      <td>503</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Busia</td>\n",
       "      <td>69.3</td>\n",
       "      <td>3.6</td>\n",
       "      <td>22.3</td>\n",
       "      <td>9.3</td>\n",
       "      <td>840</td>\n",
       "      <td>583</td>\n",
       "      <td>5.5</td>\n",
       "      <td>177</td>\n",
       "      <td>62.2</td>\n",
       "      <td>10</td>\n",
       "      <td>3.4</td>\n",
       "      <td>17.5</td>\n",
       "      <td>7.2</td>\n",
       "      <td>840</td>\n",
       "      <td>500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Elgeyo/Marakwet</td>\n",
       "      <td>43.4</td>\n",
       "      <td>1.2</td>\n",
       "      <td>13.4</td>\n",
       "      <td>5.6</td>\n",
       "      <td>469</td>\n",
       "      <td>204</td>\n",
       "      <td>43.1</td>\n",
       "      <td>99</td>\n",
       "      <td>98.7</td>\n",
       "      <td>43</td>\n",
       "      <td>1.4</td>\n",
       "      <td>10.8</td>\n",
       "      <td>4.0</td>\n",
       "      <td>469</td>\n",
       "      <td>210</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  residence_county  Headcount Rate (%)  Distribution of the Poor (%)  \\\n",
       "0          Baringo                39.6                           1.7   \n",
       "1            Bomet                48.8                           2.7   \n",
       "2          Bungoma                35.7                           3.4   \n",
       "3            Busia                69.3                           3.6   \n",
       "4  Elgeyo/Marakwet                43.4                           1.2   \n",
       "\n",
       "   Poverty Gap (%)  Severity of Poverty (%) Population (ths)  \\\n",
       "0              9.7                      4.2              704   \n",
       "1              9.3                      2.8              916   \n",
       "2              9.5                      3.6            1,553   \n",
       "3             22.3                      9.3              840   \n",
       "4             13.4                      5.6              469   \n",
       "\n",
       "   Number of Poor (ths)  Proportion of households that sought credit (%)  \\\n",
       "0                   278                                             44.4   \n",
       "1                   447                                             19.5   \n",
       "2                   555                                             32.8   \n",
       "3                   583                                              5.5   \n",
       "4                   204                                             43.1   \n",
       "\n",
       "   Number of Households (ths)  \\\n",
       "0                         152   \n",
       "1                         179   \n",
       "2                         321   \n",
       "3                         177   \n",
       "4                          99   \n",
       "\n",
       "   Proportion of households that sought and accessed credit (%)  \\\n",
       "0                                               98.6              \n",
       "1                                               83.8              \n",
       "2                                               58.0              \n",
       "3                                               62.2              \n",
       "4                                               98.7              \n",
       "\n",
       "   Number of Households that sought credit (ths)  \\\n",
       "0                                             68   \n",
       "1                                             35   \n",
       "2                                            105   \n",
       "3                                             10   \n",
       "4                                             43   \n",
       "\n",
       "   Distribution of the Poor (%).1  Poverty Gap (%).1  \\\n",
       "0                             2.0               10.8   \n",
       "1                             2.1                5.6   \n",
       "2                             3.5                9.5   \n",
       "3                             3.4               17.5   \n",
       "4                             1.4               10.8   \n",
       "\n",
       "   Severity of Poverty (%).1 Population (ths).1  Number of Poor (ths).1  \n",
       "0                        4.1                704                     291  \n",
       "1                        1.6                916                     300  \n",
       "2                        3.9              1,553                     503  \n",
       "3                        7.2                840                     500  \n",
       "4                        4.0                469                     210  "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Read data into pandas dataframe\n",
    "data = pd.read_csv(\"overall_poverty_est.csv\")\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "a59aa438",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(47, 16)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Display number of rows and columns\n",
    "data.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "6e0f8685",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Headcount Rate (%)</th>\n",
       "      <th>Distribution of the Poor (%)</th>\n",
       "      <th>Poverty Gap (%)</th>\n",
       "      <th>Severity of Poverty (%)</th>\n",
       "      <th>Number of Poor (ths)</th>\n",
       "      <th>Proportion of households that sought credit (%)</th>\n",
       "      <th>Number of Households (ths)</th>\n",
       "      <th>Proportion of households that sought and accessed credit (%)</th>\n",
       "      <th>Number of Households that sought credit (ths)</th>\n",
       "      <th>Distribution of the Poor (%).1</th>\n",
       "      <th>Poverty Gap (%).1</th>\n",
       "      <th>Severity of Poverty (%).1</th>\n",
       "      <th>Number of Poor (ths).1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>47.000000</td>\n",
       "      <td>47.000000</td>\n",
       "      <td>47.000000</td>\n",
       "      <td>47.000000</td>\n",
       "      <td>47.000000</td>\n",
       "      <td>47.000000</td>\n",
       "      <td>47.000000</td>\n",
       "      <td>47.000000</td>\n",
       "      <td>47.000000</td>\n",
       "      <td>47.000000</td>\n",
       "      <td>47.000000</td>\n",
       "      <td>47.000000</td>\n",
       "      <td>47.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>40.557447</td>\n",
       "      <td>2.129787</td>\n",
       "      <td>12.085106</td>\n",
       "      <td>5.306383</td>\n",
       "      <td>349.042553</td>\n",
       "      <td>33.082979</td>\n",
       "      <td>242.808511</td>\n",
       "      <td>85.814894</td>\n",
       "      <td>81.851064</td>\n",
       "      <td>2.127660</td>\n",
       "      <td>10.314894</td>\n",
       "      <td>4.463830</td>\n",
       "      <td>309.297872</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>16.291085</td>\n",
       "      <td>1.109429</td>\n",
       "      <td>8.496751</td>\n",
       "      <td>5.254911</td>\n",
       "      <td>182.080125</td>\n",
       "      <td>16.187170</td>\n",
       "      <td>225.060343</td>\n",
       "      <td>16.561138</td>\n",
       "      <td>79.732972</td>\n",
       "      <td>1.142404</td>\n",
       "      <td>6.053852</td>\n",
       "      <td>3.569827</td>\n",
       "      <td>166.793795</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>16.700000</td>\n",
       "      <td>0.200000</td>\n",
       "      <td>2.400000</td>\n",
       "      <td>0.500000</td>\n",
       "      <td>36.000000</td>\n",
       "      <td>5.500000</td>\n",
       "      <td>30.000000</td>\n",
       "      <td>33.900000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>0.200000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>0.800000</td>\n",
       "      <td>25.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>28.800000</td>\n",
       "      <td>1.400000</td>\n",
       "      <td>7.350000</td>\n",
       "      <td>2.500000</td>\n",
       "      <td>231.000000</td>\n",
       "      <td>21.300000</td>\n",
       "      <td>127.000000</td>\n",
       "      <td>84.050000</td>\n",
       "      <td>39.500000</td>\n",
       "      <td>1.300000</td>\n",
       "      <td>6.750000</td>\n",
       "      <td>2.550000</td>\n",
       "      <td>192.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>35.800000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>9.400000</td>\n",
       "      <td>3.500000</td>\n",
       "      <td>321.000000</td>\n",
       "      <td>32.900000</td>\n",
       "      <td>210.000000</td>\n",
       "      <td>92.500000</td>\n",
       "      <td>69.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>9.100000</td>\n",
       "      <td>3.500000</td>\n",
       "      <td>287.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>47.450000</td>\n",
       "      <td>2.750000</td>\n",
       "      <td>13.400000</td>\n",
       "      <td>5.800000</td>\n",
       "      <td>455.500000</td>\n",
       "      <td>43.100000</td>\n",
       "      <td>277.500000</td>\n",
       "      <td>97.550000</td>\n",
       "      <td>108.500000</td>\n",
       "      <td>2.650000</td>\n",
       "      <td>11.750000</td>\n",
       "      <td>4.950000</td>\n",
       "      <td>385.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>79.400000</td>\n",
       "      <td>5.200000</td>\n",
       "      <td>46.000000</td>\n",
       "      <td>30.800000</td>\n",
       "      <td>860.000000</td>\n",
       "      <td>66.100000</td>\n",
       "      <td>1503.000000</td>\n",
       "      <td>99.200000</td>\n",
       "      <td>510.000000</td>\n",
       "      <td>4.900000</td>\n",
       "      <td>32.900000</td>\n",
       "      <td>20.400000</td>\n",
       "      <td>717.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Headcount Rate (%)  Distribution of the Poor (%)  Poverty Gap (%)  \\\n",
       "count           47.000000                     47.000000        47.000000   \n",
       "mean            40.557447                      2.129787        12.085106   \n",
       "std             16.291085                      1.109429         8.496751   \n",
       "min             16.700000                      0.200000         2.400000   \n",
       "25%             28.800000                      1.400000         7.350000   \n",
       "50%             35.800000                      2.000000         9.400000   \n",
       "75%             47.450000                      2.750000        13.400000   \n",
       "max             79.400000                      5.200000        46.000000   \n",
       "\n",
       "       Severity of Poverty (%)  Number of Poor (ths)  \\\n",
       "count                47.000000             47.000000   \n",
       "mean                  5.306383            349.042553   \n",
       "std                   5.254911            182.080125   \n",
       "min                   0.500000             36.000000   \n",
       "25%                   2.500000            231.000000   \n",
       "50%                   3.500000            321.000000   \n",
       "75%                   5.800000            455.500000   \n",
       "max                  30.800000            860.000000   \n",
       "\n",
       "       Proportion of households that sought credit (%)  \\\n",
       "count                                        47.000000   \n",
       "mean                                         33.082979   \n",
       "std                                          16.187170   \n",
       "min                                           5.500000   \n",
       "25%                                          21.300000   \n",
       "50%                                          32.900000   \n",
       "75%                                          43.100000   \n",
       "max                                          66.100000   \n",
       "\n",
       "       Number of Households (ths)  \\\n",
       "count                   47.000000   \n",
       "mean                   242.808511   \n",
       "std                    225.060343   \n",
       "min                     30.000000   \n",
       "25%                    127.000000   \n",
       "50%                    210.000000   \n",
       "75%                    277.500000   \n",
       "max                   1503.000000   \n",
       "\n",
       "       Proportion of households that sought and accessed credit (%)  \\\n",
       "count                                          47.000000              \n",
       "mean                                           85.814894              \n",
       "std                                            16.561138              \n",
       "min                                            33.900000              \n",
       "25%                                            84.050000              \n",
       "50%                                            92.500000              \n",
       "75%                                            97.550000              \n",
       "max                                            99.200000              \n",
       "\n",
       "       Number of Households that sought credit (ths)  \\\n",
       "count                                      47.000000   \n",
       "mean                                       81.851064   \n",
       "std                                        79.732972   \n",
       "min                                         4.000000   \n",
       "25%                                        39.500000   \n",
       "50%                                        69.000000   \n",
       "75%                                       108.500000   \n",
       "max                                       510.000000   \n",
       "\n",
       "       Distribution of the Poor (%).1  Poverty Gap (%).1  \\\n",
       "count                       47.000000          47.000000   \n",
       "mean                         2.127660          10.314894   \n",
       "std                          1.142404           6.053852   \n",
       "min                          0.200000           3.000000   \n",
       "25%                          1.300000           6.750000   \n",
       "50%                          2.000000           9.100000   \n",
       "75%                          2.650000          11.750000   \n",
       "max                          4.900000          32.900000   \n",
       "\n",
       "       Severity of Poverty (%).1  Number of Poor (ths).1  \n",
       "count                  47.000000               47.000000  \n",
       "mean                    4.463830              309.297872  \n",
       "std                     3.569827              166.793795  \n",
       "min                     0.800000               25.000000  \n",
       "25%                     2.550000              192.000000  \n",
       "50%                     3.500000              287.000000  \n",
       "75%                     4.950000              385.500000  \n",
       "max                    20.400000              717.000000  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Display statistical summary\n",
    "data.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "6b8d9349",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['residence_county', 'Headcount Rate (%)',\n",
       "       'Distribution of the Poor (%)', 'Poverty Gap (%)',\n",
       "       'Severity of Poverty (%)', 'Population (ths)', 'Number of Poor (ths)',\n",
       "       'Proportion of households that sought credit (%)',\n",
       "       'Number of Households (ths)',\n",
       "       'Proportion of households that sought and accessed credit (%)',\n",
       "       'Number of Households that sought credit (ths)',\n",
       "       'Distribution of the Poor (%).1', 'Poverty Gap (%).1',\n",
       "       'Severity of Poverty (%).1', 'Population (ths).1',\n",
       "       'Number of Poor (ths).1'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Display column headers\n",
    "data.columns"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "02fce0dd",
   "metadata": {},
   "source": [
    "### <span style = \"color:green;\">Pearson correlation coefficient and p-value</span>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "19574d1f",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calculate Pearson correlation coefficient and p-value\n",
    "corr, pval = pearsonr(data[\"Poverty Gap (%)\"], data[\"Proportion of households that sought credit (%)\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "83ec67f9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pearson correlation coefficient: -0.4777136954992022\n",
      "p-value: 0.0006844717800419033\n"
     ]
    }
   ],
   "source": [
    "# Print results\n",
    "print(\"Pearson correlation coefficient:\", corr)\n",
    "print(\"p-value:\", pval)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "79072f6c",
   "metadata": {},
   "source": [
    "### <span style = \"color:green;\">Observations and Inferences</span>\n",
    "1. The Pearson correlation coefficient between the `Poverty Gap (%)` and `Proportion of households that \n",
    "sought credit (%)` is `-0.4777`, which means that there is a moderate negative correlation between \n",
    "these two variables. This indicates that as the `Poverty Gap (%)` increases, the `Proportion of \n",
    "households that sought credit (%)` _decreases_, and vice versa.\n",
    "2. The `p-value` is `0.000684`, which is less than the commonly used threshold of `0.05`. This suggests \n",
    "that the observed correlation between the two variables _is statistically significant_, and not \n",
    "likely to have occurred by chance."
   ]
  }
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