Chapter07MatchedPairs.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter 7: Matched-Pairs Experiment"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "pandas           : 2.1.1\n",
      "matplotlib       : 3.8.0\n",
      "statsmodels      : 0.13.5\n",
      "numpy            : 1.23.5\n",
      "scipy            : 1.11.3\n",
      "matplotlib_inline: 0.1.6\n",
      "\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import scipy as sp\n",
    "import statsmodels.api as sm\n",
    "import statsmodels.formula.api as smf\n",
    "\n",
    "# viz\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "font = {\"family\": \"IBM Plex Sans Condensed\", \"weight\": \"normal\", \"size\": 10}\n",
    "plt.rc(\"font\", **font)\n",
    "plt.rcParams[\"figure.figsize\"] = (6, 6)\n",
    "%matplotlib inline\n",
    "%config InlineBackend.figure_format = 'retina'\n",
    "%load_ext autoreload\n",
    "%autoreload 1\n",
    "\n",
    "%load_ext watermark\n",
    "%watermark --iversions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def MP_enumerate(i, n_pairs):\n",
    "    if i > 2**n_pairs:\n",
    "        return None\n",
    "    a = 2 ** np.arange(n_pairs)[::-1]\n",
    "    b = 2 * a\n",
    "    return 2 * (i % b >= a) - 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "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>pair</th>\n",
       "      <th>pot</th>\n",
       "      <th>cross</th>\n",
       "      <th>self</th>\n",
       "      <th>diff</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>23.500</td>\n",
       "      <td>17.375</td>\n",
       "      <td>6.125</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>12.000</td>\n",
       "      <td>20.375</td>\n",
       "      <td>-8.375</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>21.000</td>\n",
       "      <td>20.000</td>\n",
       "      <td>1.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>2</td>\n",
       "      <td>22.000</td>\n",
       "      <td>20.000</td>\n",
       "      <td>2.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>2</td>\n",
       "      <td>19.125</td>\n",
       "      <td>18.375</td>\n",
       "      <td>0.750</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   pair  pot   cross    self   diff\n",
       "0     1    1  23.500  17.375  6.125\n",
       "1     2    1  12.000  20.375 -8.375\n",
       "2     3    1  21.000  20.000  1.000\n",
       "3     4    2  22.000  20.000  2.000\n",
       "4     5    2  19.125  18.375  0.750"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# ZeaMays from HistData r package\n",
    "ZeaMays = pd.read_csv(\"ZeaMays.csv\")\n",
    "ZeaMays.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Randomization distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.026337473677785578"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t_obs = ZeaMays[\"diff\"].mean()\n",
    "abs_diff = np.abs(ZeaMays[\"diff\"].values)\n",
    "n_pairs = ZeaMays.shape[0]\n",
    "t_ran = (\n",
    "    np.array([np.sum(MP_enumerate(i, 15) * abs_diff) for i in range(1, 2**15)])\n",
    "    / n_pairs\n",
    ")\n",
    "(p_value := np.mean(t_ran >= t_obs))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.05, 0.9, 'p-value = 0.026')"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 526,
       "width": 524
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(t_ran, bins=50)\n",
    "plt.axvline(t_obs, color=\"red\")\n",
    "plt.title(\"Exact Randomization Distribution: Darwin Data\")\n",
    "plt.annotate(f\"p-value = {p_value:.3f}\", xy=(0.05, 0.9), xycoords=\"axes fraction\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "IR(2015) : Children's TV Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "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>x_control</th>\n",
       "      <th>x_treatment</th>\n",
       "      <th>y_control</th>\n",
       "      <th>y_treatment</th>\n",
       "      <th>diffx</th>\n",
       "      <th>diffy</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>12.9</td>\n",
       "      <td>12.0</td>\n",
       "      <td>54.6</td>\n",
       "      <td>60.6</td>\n",
       "      <td>-0.9</td>\n",
       "      <td>6.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>15.1</td>\n",
       "      <td>12.3</td>\n",
       "      <td>56.5</td>\n",
       "      <td>55.5</td>\n",
       "      <td>-2.8</td>\n",
       "      <td>-1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>16.8</td>\n",
       "      <td>17.2</td>\n",
       "      <td>75.2</td>\n",
       "      <td>84.8</td>\n",
       "      <td>0.4</td>\n",
       "      <td>9.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>15.8</td>\n",
       "      <td>18.9</td>\n",
       "      <td>75.6</td>\n",
       "      <td>101.9</td>\n",
       "      <td>3.1</td>\n",
       "      <td>26.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>13.9</td>\n",
       "      <td>15.3</td>\n",
       "      <td>55.3</td>\n",
       "      <td>70.6</td>\n",
       "      <td>1.4</td>\n",
       "      <td>15.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>14.5</td>\n",
       "      <td>16.6</td>\n",
       "      <td>59.3</td>\n",
       "      <td>78.4</td>\n",
       "      <td>2.1</td>\n",
       "      <td>19.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>17.0</td>\n",
       "      <td>16.0</td>\n",
       "      <td>87.0</td>\n",
       "      <td>84.2</td>\n",
       "      <td>-1.0</td>\n",
       "      <td>-2.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>15.8</td>\n",
       "      <td>20.1</td>\n",
       "      <td>73.7</td>\n",
       "      <td>108.6</td>\n",
       "      <td>4.3</td>\n",
       "      <td>34.9</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   x_control  x_treatment  y_control  y_treatment  diffx  diffy\n",
       "1       12.9         12.0       54.6         60.6   -0.9    6.0\n",
       "2       15.1         12.3       56.5         55.5   -2.8   -1.0\n",
       "3       16.8         17.2       75.2         84.8    0.4    9.6\n",
       "4       15.8         18.9       75.6        101.9    3.1   26.3\n",
       "5       13.9         15.3       55.3         70.6    1.4   15.3\n",
       "6       14.5         16.6       59.3         78.4    2.1   19.1\n",
       "7       17.0         16.0       87.0         84.2   -1.0   -2.8\n",
       "8       15.8         20.1       73.7        108.6    4.3   34.9"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dataxy = np.array(\n",
    "    [\n",
    "        12.9,\n",
    "        12.0,\n",
    "        54.6,\n",
    "        60.6,\n",
    "        15.1,\n",
    "        12.3,\n",
    "        56.5,\n",
    "        55.5,\n",
    "        16.8,\n",
    "        17.2,\n",
    "        75.2,\n",
    "        84.8,\n",
    "        15.8,\n",
    "        18.9,\n",
    "        75.6,\n",
    "        101.9,\n",
    "        13.9,\n",
    "        15.3,\n",
    "        55.3,\n",
    "        70.6,\n",
    "        14.5,\n",
    "        16.6,\n",
    "        59.3,\n",
    "        78.4,\n",
    "        17.0,\n",
    "        16.0,\n",
    "        87.0,\n",
    "        84.2,\n",
    "        15.8,\n",
    "        20.1,\n",
    "        73.7,\n",
    "        108.6,\n",
    "    ]\n",
    ")\n",
    "dataxy = dataxy.reshape(-1, 4)\n",
    "diffx = dataxy[:, 1] - dataxy[:, 0]\n",
    "diffy = dataxy[:, 3] - dataxy[:, 2]\n",
    "dataxy = np.c_[dataxy, diffx, diffy]\n",
    "dataxy = pd.DataFrame(\n",
    "    dataxy,\n",
    "    columns=[\"x_control\", \"x_treatment\", \"y_control\", \"y_treatment\", \"diffx\", \"diffy\"],\n",
    "    index=np.arange(1, 9),\n",
    ")\n",
    "dataxy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((13.425,), 4.6363374553628)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tauhat = (dataxy.diffy.mean(),)\n",
    "sehat = np.sqrt(dataxy.diffy.var(ddof=1) / dataxy.shape[0])\n",
    "tauhat, sehat"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With a regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alal/anaconda3/envs/econometrics/lib/python3.9/site-packages/scipy/stats/_stats_py.py:1806: UserWarning: kurtosistest only valid for n>=20 ... continuing anyway, n=8\n",
      "  warnings.warn(\"kurtosistest only valid for n>=20 ... continuing \"\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "    <td></td>       <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th> <td>   13.4250</td> <td>    4.636</td> <td>    2.896</td> <td> 0.023</td> <td>    2.462</td> <td>   24.388</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.table.SimpleTable'>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "unadj_res = sm.OLS(dataxy.diffy, np.repeat(1, dataxy.shape[0])).fit().summary()\n",
    "unadj_t = float(unadj_res.tables[1].data[1][3])\n",
    "unadj_res.tables[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alal/anaconda3/envs/econometrics/lib/python3.9/site-packages/scipy/stats/_stats_py.py:1806: UserWarning: kurtosistest only valid for n>=20 ... continuing anyway, n=8\n",
      "  warnings.warn(\"kurtosistest only valid for n>=20 ... continuing \"\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "    <td></td>       <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th> <td>    8.9943</td> <td>    1.410</td> <td>    6.381</td> <td> 0.001</td> <td>    5.545</td> <td>   12.443</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>diffx</th> <td>    5.3705</td> <td>    0.599</td> <td>    8.964</td> <td> 0.000</td> <td>    3.904</td> <td>    6.837</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.table.SimpleTable'>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "adj_res = sm.OLS(dataxy.diffy, sm.add_constant(dataxy.diffx)).fit().summary()\n",
    "adj_t = float(adj_res.tables[1].data[1][3])\n",
    "adj_res.tables[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import warnings\n",
    "\n",
    "warnings.simplefilter(\"once\", category=UserWarning)\n",
    "\n",
    "\n",
    "def randist(x):\n",
    "    z_mpe = MP_enumerate(x, 8)\n",
    "    diffy_mpe = dataxy.diffy * z_mpe\n",
    "    diffx_mpe = dataxy.diffx * z_mpe\n",
    "    m0 = sm.OLS(diffy_mpe, np.repeat(1, dataxy.shape[0])).fit().summary()\n",
    "    m1 = sm.OLS(diffy_mpe, sm.add_constant(diffx_mpe)).fit().summary()\n",
    "    return float(m0.tables[1].data[1][3]), float(m1.tables[1].data[1][3])\n",
    "\n",
    "\n",
    "t_randist = np.r_[[randist(i) for i in range(1, 2**8 + 1)]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.03125, 0.0078125)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p_unadjusted = np.mean(np.abs(t_randist[:, 0]) >= np.abs(unadj_t))\n",
    "p_adjusted = np.mean(np.abs(t_randist[:, 1]) >= np.abs(adj_t))\n",
    "p_unadjusted, p_adjusted"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.05, 0.9, 'p-value = 0.008')"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1200x600 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 526,
       "width": 974
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, ax = plt.subplots(1, 2, figsize=(12, 6))\n",
    "ax[0].hist(t_randist[:, 0], bins=50)\n",
    "ax[0].axvline(unadj_t, color=\"red\")\n",
    "ax[0].set_title(\"Unadjusted Randomization Distribution\")\n",
    "ax[0].annotate(\n",
    "    f\"p-value = {p_unadjusted:.3f}\", xy=(0.05, 0.9), xycoords=\"axes fraction\"\n",
    ")\n",
    "ax[1].hist(t_randist[:, 1], bins=50)\n",
    "ax[1].axvline(adj_t, color=\"red\")\n",
    "ax[1].set_title(\"Adjusted Randomization Distribution\")\n",
    "ax[1].annotate(f\"p-value = {p_adjusted:.3f}\", xy=(0.05, 0.9), xycoords=\"axes fraction\")"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "econometrics",
   "language": "python",
   "name": "econometrics"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}