Ch13-multiple-lab-b.ipynb

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    "\n",
    "# Chapter 13\n",
    "\n",
    "# Lab: Multiple Testing\n",
    " "
   ]
  },
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    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import statsmodels.api as sm\n",
    "from ISLP import load_data\n"
   ]
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   "source": [
    "from scipy.stats import \\\n",
    "    (ttest_1samp,\n",
    "     ttest_rel,\n",
    "     ttest_ind,\n",
    "     t as t_dbn)\n",
    "from statsmodels.stats.multicomp import \\\n",
    "     pairwise_tukeyhsd\n",
    "from statsmodels.stats.multitest import \\\n",
    "     multipletests as mult_test\n"
   ]
  },
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    "## Review of Hypothesis Tests\n",
    "We begin by performing some one-sample $t$-tests.\n",
    "\n",
    "First we create 100 variables, each consisting of 10 observations. The\n",
    "first 50 variables have mean $0.5$ and variance $1$, while the others\n",
    "have mean $0$ and variance $1$."
   ]
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   "source": [
    "rng = np.random.default_rng(12)\n",
    "X = rng.standard_normal((10, 100))\n",
    "true_mean = np.array([0.5]*50 + [0]*50)\n",
    "X += true_mean[None,:]\n"
   ]
  },
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    "To begin, we use `ttest_1samp()`  from the\n",
    "`scipy.stats` module to test $H_{0}: \\mu_1=0$, the null\n",
    "hypothesis that the first variable has mean zero."
   ]
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   "source": [
    "### 1-sample t-test\n"
   ]
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   "source": [
    "result = ttest_1samp(X[:,0], 0)\n",
    "result.pvalue\n"
   ]
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    "The $p$-value comes out to 0.931, which is not low enough to\n",
    "reject the null hypothesis at level $\\alpha=0.05$.  In this case,\n",
    "$\\mu_1=0.5$, so the null hypothesis is false. Therefore, we have made\n",
    "a Type II error by failing to reject the null hypothesis when the null\n",
    "hypothesis is false. \n",
    "\n",
    "We now test $H_{0,j}: \\mu_j=0$ for $j=1,\\ldots,100$. We compute the\n",
    "100 $p$-values, and then construct a vector recording whether the\n",
    "$j$th $p$-value is less than or equal to 0.05, in which case we reject\n",
    "$H_{0j}$, or greater than 0.05, in which case we do not reject\n",
    "$H_{0j}$, for $j=1,\\ldots,100$."
   ]
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   "source": [
    "p_values = np.empty(100)\n",
    "for i in range(100):\n",
    "   p_values[i] = ttest_1samp(X[:,i], 0).pvalue\n",
    "decision = pd.cut(p_values,\n",
    "                  [0, 0.05, 1],\n",
    "                  labels=['Reject H0',\n",
    "                          'Do not reject H0'])\n",
    "truth = pd.Categorical(true_mean == 0,\n",
    "                       categories=[True, False], #specify order: True < False\n",
    "                       ordered=True)\n"
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "Since this is a simulated data set, we can create a $2 \\times 2$ table\n",
    "similar to  Table 13.2."
   ]
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   "source": [
    "`pd.crosstab()` is a function provided by the pandas library in Python, and it is used for cross-tabulation of two or more factors. Cross-tabulation is a method of summarizing and analyzing the relationship between two or more categorical variables. The result of pd.crosstab() is a table that shows the frequency distribution of variables in a matrix format."
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       "      <th>H0</th>\n",
       "      <th>True</th>\n",
       "      <th>False</th>\n",
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       "      <th>Decision</th>\n",
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       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Reject H0</th>\n",
       "      <td>5</td>\n",
       "      <td>15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Do not reject H0</th>\n",
       "      <td>45</td>\n",
       "      <td>35</td>\n",
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       "H0                True  False\n",
       "Decision                     \n",
       "Reject H0            5     15\n",
       "Do not reject H0    45     35"
      ]
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   "source": [
    "pd.crosstab(decision, #row\n",
    "            truth, # col\n",
    "     rownames=['Decision'],\n",
    "     colnames=['H0'])\n"
   ]
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    "Therefore, at level $\\alpha=0.05$, we reject 15 of the 50 false\n",
    "null hypotheses, and we incorrectly reject 5 of the true null\n",
    "hypotheses. Using the notation from Section 13.3, we have\n",
    "$V=5$, $S=15$, $U=45$ and $W=35$.\n",
    "We have set $\\alpha=0.05$, which means that we expect to reject around\n",
    "5% of the true null hypotheses. This is in line with the $2 \\times 2$\n",
    "table above, which indicates that we rejected $V=5$ of the $50$ true\n",
    "null hypotheses.\n",
    "\n",
    "In the simulation above, for the false null hypotheses, the ratio of\n",
    "the mean to the standard deviation was only $0.5/1 = 0.5$. This\n",
    "amounts to quite a weak signal, and it resulted in a high number of\n",
    "Type II errors.  Let’s instead simulate data with a stronger signal,\n",
    "so that the ratio of the mean to the standard deviation for the false\n",
    "null hypotheses equals $1$. We make only 10 Type II errors.\n",
    " "
   ]
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       "    <tr>\n",
       "      <th>Reject H0</th>\n",
       "      <td>2</td>\n",
       "      <td>40</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Do not reject H0</th>\n",
       "      <td>48</td>\n",
       "      <td>10</td>\n",
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      "text/plain": [
       "H0                True  False\n",
       "Decision                     \n",
       "Reject H0            2     40\n",
       "Do not reject H0    48     10"
      ]
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   "source": [
    "true_mean = np.array([1]*50 + [0]*50)\n",
    "X = rng.standard_normal((10, 100))\n",
    "X += true_mean[None,:]\n",
    "for i in range(100):\n",
    "   p_values[i] = ttest_1samp(X[:,i], 0).pvalue\n",
    "decision = pd.cut(p_values,\n",
    "                  [0, 0.05, 1],\n",
    "                  labels=['Reject H0',\n",
    "                          'Do not reject H0'])\n",
    "truth = pd.Categorical(true_mean == 0,\n",
    "                       categories=[True, False],\n",
    "                       ordered=True)\n",
    "pd.crosstab(decision,\n",
    "            truth,\n",
    "            rownames=['Decision'],\n",
    "            colnames=['H0'])\n"
   ]
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    "    "
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    "## Family-Wise Error Rate\n",
    "Recall from  (13.5)  that if the null hypothesis is true\n",
    "for each of $m$ independent hypothesis tests, then the FWER is equal\n",
    "to $1-(1-\\alpha)^m$. We can use this expression to compute the FWER\n",
    "for $m=1,\\ldots, 500$ and $\\alpha=0.05$, $0.01$, and $0.001$.\n",
    "We plot the FWER for these values of $\\alpha$ in order to\n",
    "reproduce  Figure 13.2."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `linspace` function takes three main arguments:\n",
    "\n",
    "- start: The starting value of the sequence.\n",
    "- stop: The end value of the sequence.\n",
    "- num: The number of evenly spaced values to generate between the start and stop.\n",
    "If the num parameter is not provided, it defaults to 50."
   ]
  },
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "m = np.linspace(1, 501)\n",
    "fig, ax = plt.subplots()\n",
    "[ax.plot(m,\n",
    "         1 - (1 - alpha)**m,\n",
    "         label=r'$\\alpha=%s$' % str(alpha))\n",
    "         for alpha in [0.05, 0.01, 0.001]]\n",
    "ax.set_xscale('log')\n",
    "ax.set_xlabel('Number of Hypotheses')\n",
    "ax.set_ylabel('Family-Wise Error Rate')\n",
    "ax.legend()\n",
    "ax.axhline(0.05, c='k', ls='--');\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fecaca9e",
   "metadata": {},
   "source": [
    "As discussed previously, even for moderate values of $m$ such as $50$,\n",
    "the FWER exceeds $0.05$ unless $\\alpha$ is set to a very low value,\n",
    "such as $0.001$.  Of course, the problem with setting $\\alpha$ to such\n",
    "a low value is that we are likely to make a number of Type II errors:\n",
    "in other words, our power is very low.\n",
    "\n",
    "We now conduct a one-sample $t$-test for each of the first five\n",
    "managers in the  \n",
    "`Fund`   dataset, in order to test the null\n",
    "hypothesis that the $j$th fund manager’s mean return equals zero,\n",
    "$H_{0,j}: \\mu_j=0$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "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>Manager1</th>\n",
       "      <th>Manager2</th>\n",
       "      <th>Manager3</th>\n",
       "      <th>Manager4</th>\n",
       "      <th>Manager5</th>\n",
       "      <th>Manager6</th>\n",
       "      <th>Manager7</th>\n",
       "      <th>Manager8</th>\n",
       "      <th>Manager9</th>\n",
       "      <th>Manager10</th>\n",
       "      <th>...</th>\n",
       "      <th>Manager1991</th>\n",
       "      <th>Manager1992</th>\n",
       "      <th>Manager1993</th>\n",
       "      <th>Manager1994</th>\n",
       "      <th>Manager1995</th>\n",
       "      <th>Manager1996</th>\n",
       "      <th>Manager1997</th>\n",
       "      <th>Manager1998</th>\n",
       "      <th>Manager1999</th>\n",
       "      <th>Manager2000</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-3.341992</td>\n",
       "      <td>-4.167469</td>\n",
       "      <td>9.389223</td>\n",
       "      <td>8.417220</td>\n",
       "      <td>0.997863</td>\n",
       "      <td>7.191473</td>\n",
       "      <td>-10.767592</td>\n",
       "      <td>4.072425</td>\n",
       "      <td>1.575264</td>\n",
       "      <td>-0.798505</td>\n",
       "      <td>...</td>\n",
       "      <td>-2.948706</td>\n",
       "      <td>10.350706</td>\n",
       "      <td>-2.855337</td>\n",
       "      <td>-4.431786</td>\n",
       "      <td>0.739544</td>\n",
       "      <td>0.198044</td>\n",
       "      <td>1.752188</td>\n",
       "      <td>-1.534710</td>\n",
       "      <td>-3.359419</td>\n",
       "      <td>6.585654</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3.759627</td>\n",
       "      <td>12.525254</td>\n",
       "      <td>3.403366</td>\n",
       "      <td>0.143944</td>\n",
       "      <td>-7.222227</td>\n",
       "      <td>0.067747</td>\n",
       "      <td>-10.737053</td>\n",
       "      <td>-1.138185</td>\n",
       "      <td>-7.166604</td>\n",
       "      <td>4.778522</td>\n",
       "      <td>...</td>\n",
       "      <td>24.003150</td>\n",
       "      <td>-1.966606</td>\n",
       "      <td>-1.609109</td>\n",
       "      <td>1.405325</td>\n",
       "      <td>4.717175</td>\n",
       "      <td>1.540359</td>\n",
       "      <td>-12.218233</td>\n",
       "      <td>-0.073008</td>\n",
       "      <td>-8.547683</td>\n",
       "      <td>-2.382629</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>12.970091</td>\n",
       "      <td>-2.581061</td>\n",
       "      <td>-0.824734</td>\n",
       "      <td>6.584604</td>\n",
       "      <td>17.050241</td>\n",
       "      <td>1.857130</td>\n",
       "      <td>3.196942</td>\n",
       "      <td>-7.981362</td>\n",
       "      <td>-1.214148</td>\n",
       "      <td>2.338250</td>\n",
       "      <td>...</td>\n",
       "      <td>-2.926914</td>\n",
       "      <td>6.420147</td>\n",
       "      <td>8.946921</td>\n",
       "      <td>3.449013</td>\n",
       "      <td>1.009957</td>\n",
       "      <td>1.481369</td>\n",
       "      <td>14.203314</td>\n",
       "      <td>0.005562</td>\n",
       "      <td>-5.105035</td>\n",
       "      <td>2.292429</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-4.874630</td>\n",
       "      <td>7.981743</td>\n",
       "      <td>-4.026743</td>\n",
       "      <td>-4.731946</td>\n",
       "      <td>0.503276</td>\n",
       "      <td>0.740187</td>\n",
       "      <td>-28.969410</td>\n",
       "      <td>4.683751</td>\n",
       "      <td>-0.568840</td>\n",
       "      <td>-4.000547</td>\n",
       "      <td>...</td>\n",
       "      <td>-3.112208</td>\n",
       "      <td>3.173581</td>\n",
       "      <td>-6.017109</td>\n",
       "      <td>-1.984873</td>\n",
       "      <td>1.022525</td>\n",
       "      <td>-2.261927</td>\n",
       "      <td>19.345970</td>\n",
       "      <td>-1.048299</td>\n",
       "      <td>-0.016154</td>\n",
       "      <td>1.196832</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2.019279</td>\n",
       "      <td>-5.370236</td>\n",
       "      <td>-4.854669</td>\n",
       "      <td>10.594432</td>\n",
       "      <td>-6.891574</td>\n",
       "      <td>9.877838</td>\n",
       "      <td>1.430033</td>\n",
       "      <td>9.840311</td>\n",
       "      <td>5.311455</td>\n",
       "      <td>18.365094</td>\n",
       "      <td>...</td>\n",
       "      <td>7.173653</td>\n",
       "      <td>-9.157211</td>\n",
       "      <td>7.643125</td>\n",
       "      <td>-1.022339</td>\n",
       "      <td>-1.325865</td>\n",
       "      <td>2.848785</td>\n",
       "      <td>-6.642081</td>\n",
       "      <td>2.488612</td>\n",
       "      <td>0.032060</td>\n",
       "      <td>-7.510032</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 2000 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "    Manager1   Manager2  Manager3   Manager4   Manager5  Manager6   Manager7  \\\n",
       "0  -3.341992  -4.167469  9.389223   8.417220   0.997863  7.191473 -10.767592   \n",
       "1   3.759627  12.525254  3.403366   0.143944  -7.222227  0.067747 -10.737053   \n",
       "2  12.970091  -2.581061 -0.824734   6.584604  17.050241  1.857130   3.196942   \n",
       "3  -4.874630   7.981743 -4.026743  -4.731946   0.503276  0.740187 -28.969410   \n",
       "4   2.019279  -5.370236 -4.854669  10.594432  -6.891574  9.877838   1.430033   \n",
       "\n",
       "   Manager8  Manager9  Manager10  ...  Manager1991  Manager1992  Manager1993  \\\n",
       "0  4.072425  1.575264  -0.798505  ...    -2.948706    10.350706    -2.855337   \n",
       "1 -1.138185 -7.166604   4.778522  ...    24.003150    -1.966606    -1.609109   \n",
       "2 -7.981362 -1.214148   2.338250  ...    -2.926914     6.420147     8.946921   \n",
       "3  4.683751 -0.568840  -4.000547  ...    -3.112208     3.173581    -6.017109   \n",
       "4  9.840311  5.311455  18.365094  ...     7.173653    -9.157211     7.643125   \n",
       "\n",
       "   Manager1994  Manager1995  Manager1996  Manager1997  Manager1998  \\\n",
       "0    -4.431786     0.739544     0.198044     1.752188    -1.534710   \n",
       "1     1.405325     4.717175     1.540359   -12.218233    -0.073008   \n",
       "2     3.449013     1.009957     1.481369    14.203314     0.005562   \n",
       "3    -1.984873     1.022525    -2.261927    19.345970    -1.048299   \n",
       "4    -1.022339    -1.325865     2.848785    -6.642081     2.488612   \n",
       "\n",
       "   Manager1999  Manager2000  \n",
       "0    -3.359419     6.585654  \n",
       "1    -8.547683    -2.382629  \n",
       "2    -5.105035     2.292429  \n",
       "3    -0.016154     1.196832  \n",
       "4     0.032060    -7.510032  \n",
       "\n",
       "[5 rows x 2000 columns]"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Fund = load_data('Fund')\n",
    "Fund.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "406e59a8",
   "metadata": {
    "execution": {}
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.00620236, 0.91827115, 0.01160098, 0.6005396 , 0.75578151])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "fund_mini = Fund.iloc[:,:5]\n",
    "fund_mini_pvals = np.empty(5)\n",
    "for i in range(5):\n",
    "    fund_mini_pvals[i] = ttest_1samp(fund_mini.iloc[:,i], 0).pvalue\n",
    "fund_mini_pvals\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "14d64aac",
   "metadata": {},
   "source": [
    "### Multiple Testing"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "87bab88b",
   "metadata": {},
   "source": [
    "The $p$-values are low for Managers One and Three, and high for the\n",
    "other three managers.  However, we cannot simply reject $H_{0,1}$ and\n",
    "$H_{0,3}$, since this would fail to account for the multiple testing\n",
    "that we have performed. Instead, we will conduct Bonferroni’s method\n",
    "and Holm’s method to control the FWER.\n",
    "\n",
    "To do this, we use the `multipletests()`  function from the\n",
    "`statsmodels` module (abbreviated to `mult_test()`). Given the $p$-values,\n",
    "for methods like Holm and Bonferroni the function outputs\n",
    "adjusted $p$-values,  which\n",
    "can be thought of as a new set of $p$-values that have been corrected\n",
    "for multiple testing. If the adjusted $p$-value for a given hypothesis\n",
    "is less than or equal to $\\alpha$, then that hypothesis can be\n",
    "rejected while maintaining a FWER of no more than $\\alpha$. In other\n",
    "words, for such methods, the adjusted $p$-values resulting from the `multipletests()`\n",
    "function can simply be compared to the desired FWER in order to\n",
    "determine whether or not to reject each hypothesis. We will later\n",
    "see that we can use the same function to control FDR as well."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d0c7a2a0",
   "metadata": {},
   "source": [
    "The `mult_test()` function takes $p$-values and a `method` argument, as well as an optional\n",
    "`alpha` argument. It returns the  decisions (`reject` below)\n",
    "as well as the adjusted $p$-values (`bonf`)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "d4f6a247",
   "metadata": {
    "execution": {},
    "lines_to_next_cell": 2
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True, False, False, False, False])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reject, bonf = mult_test(fund_mini_pvals, method = \"bonferroni\")[:2]\n",
    "reject\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4d5bc7e7",
   "metadata": {},
   "source": [
    "The $p$-values `bonf` are simply the `fund_mini_pvalues` multiplied by 5 and truncated to be less than\n",
    "or equal to 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "01a29d71",
   "metadata": {
    "execution": {}
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([0.03101178, 1.        , 0.05800491, 1.        , 1.        ]),\n",
       " array([0.03101178, 1.        , 0.05800491, 1.        , 1.        ]))"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bonf, np.minimum(fund_mini_pvals * 5, 1)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e68c9051",
   "metadata": {},
   "source": [
    "Therefore, using Bonferroni’s method, we are able to reject the null hypothesis only for Manager\n",
    "One while controlling FWER at $0.05$.\n",
    "\n",
    "By contrast, using Holm’s method, the adjusted $p$-values indicate\n",
    "that we can  reject the null\n",
    "hypotheses for Managers One and Three at a FWER of $0.05$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "95454eb4",
   "metadata": {
    "execution": {},
    "lines_to_next_cell": 2
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ True, False,  True, False, False]),\n",
       " array([0.03101178, 1.        , 0.04640393, 1.        , 1.        ]))"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mult_test(fund_mini_pvals, method = \"holm\", alpha=0.05)[:2]\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "587b5b48",
   "metadata": {},
   "source": [
    "As discussed previously, Manager One seems to perform particularly\n",
    "well, whereas Manager Two has poor performance.\n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "1f1ac764",
   "metadata": {
    "execution": {},
    "lines_to_next_cell": 2
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Manager1    3.0\n",
       "Manager2   -0.1\n",
       "Manager3    2.8\n",
       "Manager4    0.5\n",
       "Manager5    0.3\n",
       "dtype: float64"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fund_mini.mean()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e3c4b716",
   "metadata": {},
   "source": [
    "Is there evidence of a meaningful difference in performance between\n",
    "these two managers?  We can check this by performing a  paired $t$-test  using the `ttest_rel()` function\n",
    "from `scipy.stats`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "298d975d",
   "metadata": {
    "execution": {}
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.038391072368079586"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ttest_rel(fund_mini['Manager1'],\n",
    "          fund_mini['Manager2']).pvalue\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dab4c69a",
   "metadata": {},
   "source": [
    "ttest_rel() is used for the paired t-test. It's used when you have two related observations (i.e., measurements of the same subject at different times) and you want to see if the means of these two observations are significantly different.\n",
    "\n",
    "ttest_ind() is used for the independent t-test. It's used when you have two independent observations (i.e., measurements of two different subjects) and you want to see if the means of these two observations are significantly different."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "69facec9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.03238986961450353"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ttest_ind(fund_mini['Manager1'],fund_mini['Manager2'],equal_var=True).pvalue"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3908d7d2",
   "metadata": {},
   "source": [
    "The test results in a $p$-value of 0.038,\n",
    "suggesting a statistically significant difference.\n",
    "\n",
    "### Turkey’s Honest Significant Differences\n",
    "\n",
    "However, we decided to perform this test only after examining the data\n",
    "and noting that Managers One and Two had the highest and lowest mean\n",
    "performances.  In a sense, this means that we have implicitly\n",
    "performed ${5 \\choose 2} = 5(5-1)/2=10$ hypothesis tests, rather than\n",
    "just one, as discussed in  Section 13.3.2.  Hence, we use the\n",
    "`pairwise_tukeyhsd()`  function from\n",
    "`statsmodels.stats.multicomp` to apply Tukey’s method\n",
    "  in order to adjust for multiple testing.  This function takes\n",
    "as input a fitted *ANOVA*  regression model, which is\n",
    "essentially just a linear regression in which all of the predictors\n",
    "are qualitative.  In this case, the response consists of the monthly\n",
    "excess returns achieved by each manager, and the predictor indicates\n",
    "the manager to which each return corresponds."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`pairwise_tukeyhsd()` is a function provided by the statsmodels library in Python, specifically in the statsmodels.stats.multicomp module. This function is used to perform Tukey's Honestly Significant Difference (HSD) test for multiple comparisons of means.\n",
    "\n",
    "Tukey's HSD is a statistical test that is applied after an Analysis of Variance (ANOVA) to determine which group means are significantly different from each other. It helps identify specific pairs of groups that have statistically significant differences in their means."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(50, 5)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fund_mini.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(250,)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "returns = np.hstack([fund_mini.iloc[:,i] for i in range(5)])\n",
    "returns.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
       "       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
       "       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,\n",
       "       3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,\n",
       "       3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4,\n",
       "       4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,\n",
       "       4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,\n",
       "       4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,\n",
       "       5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,\n",
       "       5, 5, 5, 5, 5, 5, 5, 5])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "managers = np.hstack([[i+1]*50 for i in range(5)])\n",
    "managers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "be117713",
   "metadata": {
    "execution": {},
    "lines_to_next_cell": 2
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Multiple Comparison of Means - Tukey HSD, FWER=0.05\n",
      "===================================================\n",
      "group1 group2 meandiff p-adj   lower  upper  reject\n",
      "---------------------------------------------------\n",
      "     1      2     -3.1 0.1862 -6.9865 0.7865  False\n",
      "     1      3     -0.2 0.9999 -4.0865 3.6865  False\n",
      "     1      4     -2.5 0.3948 -6.3865 1.3865  False\n",
      "     1      5     -2.7 0.3152 -6.5865 1.1865  False\n",
      "     2      3      2.9 0.2453 -0.9865 6.7865  False\n",
      "     2      4      0.6 0.9932 -3.2865 4.4865  False\n",
      "     2      5      0.4 0.9986 -3.4865 4.2865  False\n",
      "     3      4     -2.3  0.482 -6.1865 1.5865  False\n",
      "     3      5     -2.5 0.3948 -6.3865 1.3865  False\n",
      "     4      5     -0.2 0.9999 -4.0865 3.6865  False\n",
      "---------------------------------------------------\n"
     ]
    }
   ],
   "source": [
    "\n",
    "\n",
    "tukey = pairwise_tukeyhsd(returns, managers)\n",
    "print(tukey.summary())\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0fdf963f",
   "metadata": {},
   "source": [
    "The `pairwise_tukeyhsd()` function provides confidence intervals\n",
    "for the difference between each pair of managers (`lower` and\n",
    "`upper`), as well as a $p$-value. All of these quantities have\n",
    "been adjusted for multiple testing. Notice that the $p$-value for the\n",
    "difference between Managers One and Two has increased from $0.038$ to\n",
    "$0.186$, so there is no longer clear evidence of a difference between\n",
    "the managers’ performances.  We can plot the confidence intervals for\n",
    "the pairwise comparisons using the `plot_simultaneous()` method\n",
    "of `tukey`. Any pair of intervals that don’t overlap indicates a significant difference at the nominal level of 0.05. In this case,\n",
    "no differences are considered significant as reported in the table above."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " `plot_simultaneous()` method\n",
    "\n",
    "Plot a universal confidence interval of each group mean\n",
    "\n",
    "Visualize significant differences in a plot with one confidence interval per group instead of all pairwise confidence intervals."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "537c4ea8",
   "metadata": {
    "execution": {}
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8,8))\n",
    "tukey.plot_simultaneous(ax=ax);\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8590f246",
   "metadata": {},
   "source": [
    "## False Discovery Rate\n",
    "Now we perform hypothesis tests for all 2,000 fund managers in the\n",
    "`Fund`  dataset. We perform a one-sample $t$-test\n",
    "of   $H_{0,j}: \\mu_j=0$, which states that the\n",
    "$j$th fund manager’s mean return is zero."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "2c88ec87",
   "metadata": {
    "execution": {}
   },
   "outputs": [],
   "source": [
    "fund_pvalues = np.empty(2000)\n",
    "for i, manager in enumerate(Fund.columns):\n",
    "    fund_pvalues[i] = ttest_1samp(Fund[manager], 0).pvalue\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "80e77fab",
   "metadata": {},
   "source": [
    "There are far too many managers to consider trying to control the FWER.\n",
    "Instead, we focus on controlling the FDR: that is, the expected fraction of rejected null hypotheses that are actually false positives.\n",
    "The `multipletests()` function (abbreviated `mult_test()`) can be used to carry out the Benjamini--Hochberg procedure."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([False, False, False, ..., False, False, False]),\n",
       " array([0.08988921, 0.991491  , 0.12211561, ..., 0.18369843, 0.85233743,\n",
       "        0.96814414]),\n",
       " 2.564631832135955e-05,\n",
       " 2.5e-05)"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mult_test(fund_pvalues, method = \"fdr_bh\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "b6d56819",
   "metadata": {
    "execution": {}
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.08988921, 0.991491  , 0.12211561, 0.92342997, 0.95603587,\n",
       "       0.07513802, 0.0767015 , 0.07513802, 0.07513802, 0.07513802])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fund_qvalues = mult_test(fund_pvalues, method = \"fdr_bh\")[1]\n",
    "fund_qvalues[:10]\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b4662444",
   "metadata": {},
   "source": [
    "The  *q-values* output by the\n",
    "Benjamini--Hochberg procedure can be interpreted as the smallest FDR\n",
    "threshold at which we would reject a particular null hypothesis. For\n",
    "instance, a $q$-value of $0.1$ indicates that we can reject the\n",
    "corresponding null hypothesis at an FDR of 10% or greater, but that\n",
    "we cannot reject the null hypothesis at an FDR below 10%.\n",
    "\n",
    "If we control the FDR at 10%, then for how many of the fund managers can we reject $H_{0,j}: \\mu_j=0$?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "b00da3a1",
   "metadata": {
    "execution": {},
    "lines_to_next_cell": 0
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "146"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(fund_qvalues <= 0.1).sum()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fdccb808",
   "metadata": {},
   "source": [
    "We find that 146 of the 2,000 fund managers have a $q$-value below\n",
    "0.1; therefore, we are able to conclude that 146 of the fund managers\n",
    "beat the market at an FDR of 10%.  Only about 15 (10% of 146) of\n",
    "these fund managers are likely to be false discoveries.\n",
    "\n",
    "By contrast, if we had instead used Bonferroni’s method to control the\n",
    "FWER at level $\\alpha=0.1$, then we would have failed to reject any\n",
    "null hypotheses!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "1c230117",
   "metadata": {
    "execution": {},
    "lines_to_next_cell": 2
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(fund_pvalues <= 0.1 / 2000).sum()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6112239d",
   "metadata": {},
   "source": [
    "### Manually perform Benjamini-Hochberg Procedure\n",
    "Figure 13.6 displays the ordered\n",
    "$p$-values, $p_{(1)} \\leq p_{(2)} \\leq \\cdots \\leq p_{(2000)}$, for\n",
    "the  `Fund`  dataset, as well as the threshold for rejection by the\n",
    "Benjamini--Hochberg procedure.  Recall that the Benjamini--Hochberg\n",
    "procedure identifies the largest $p$-value such that $p_{(j)}<qj/m$,\n",
    "and rejects all hypotheses for which the $p$-value is less than or\n",
    "equal to $p_{(j)}$. In the code below, we implement the\n",
    "Benjamini--Hochberg procedure ourselves, in order to illustrate how it\n",
    "works. We first order the $p$-values. We then identify all $p$-values\n",
    "that satisfy $p_{(j)}<qj/m$ (`sorted_set_`).  Finally, `selected_`\n",
    "is a boolean array indicating which $p$-values\n",
    " are less than or equal to the largest\n",
    "$p$-value in `sorted_[sorted_set_]`. Therefore, `selected_` indexes the\n",
    "$p$-values rejected by the Benjamini--Hochberg procedure."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.33065861e-04, 1.90940191e-04, 3.75994953e-04, ...,\n",
       "       9.98521142e-01, 9.98748664e-01, 9.99473032e-01])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sorted_ = np.sort(fund_pvalues) # sorted p-values\n",
    "sorted_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "m = fund_pvalues.shape[0]\n",
    "q = 0.1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`numpy.where(condition, x, y)`\n",
    "\n",
    "condition: This is the condition that you want to check for each element of the array. It can be a boolean array or any other expression that can be evaluated to a boolean array.\n",
    "\n",
    "`x`, `y` (optional): If provided, these are the values from which to choose. The elements of the output array will be taken from x where the condition is True, and from y where it is False. If not provided, the function returns the indices where the condition is True."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "# set of indices where sorted p-values < qj/m\n",
    "sorted_set_ = np.where(sorted_ < q * np.linspace(1, m, m) / m)[0] # index [0] extracts the array in the returned tuple by where()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.007201079307124033"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sorted_[sorted_set_].max() #p_L=max sorted p-value where it is < qj/m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True, False, False, ..., False, False, False])"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fund_pvalues < sorted_[sorted_set_].max() #boolean array of where p-values < p_L"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "62289650",
   "metadata": {
    "execution": {}
   },
   "outputs": [],
   "source": [
    "\n",
    "if sorted_set_.shape[0] > 0:\n",
    "    selected_ = fund_pvalues < sorted_[sorted_set_].max() #boolean array of where p-values<p_L\n",
    "    sorted_set_ = np.arange(sorted_set_.max()) # note the sorted_set is redefined as [0,1, ..., L-1] \n",
    "else:\n",
    "    selected_ = []\n",
    "    sorted_set_ = []\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "4ff08a86",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,  10,  11,  12,\n",
       "        13,  14,  15,  16,  17,  18,  19,  20,  21,  22,  23,  24,  25,\n",
       "        26,  27,  28,  29,  30,  31,  32,  33,  34,  35,  36,  37,  38,\n",
       "        39,  40,  41,  42,  43,  44,  45,  46,  47,  48,  49,  50,  51,\n",
       "        52,  53,  54,  55,  56,  57,  58,  59,  60,  61,  62,  63,  64,\n",
       "        65,  66,  67,  68,  69,  70,  71,  72,  73,  74,  75,  76,  77,\n",
       "        78,  79,  80,  81,  82,  83,  84,  85,  86,  87,  88,  89,  90,\n",
       "        91,  92,  93,  94,  95,  96,  97,  98,  99, 100, 101, 102, 103,\n",
       "       104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116,\n",
       "       117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129,\n",
       "       130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142,\n",
       "       143, 144], dtype=int64)"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sorted_set_"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c36b13b7",
   "metadata": {},
   "source": [
    "We now reproduce  the middle panel of Figure 13.6."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "18b3c0ed",
   "metadata": {
    "execution": {},
    "lines_to_next_cell": 2
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.scatter(np.arange(0, sorted_.shape[0]) + 1,\n",
    "           sorted_, s=10) # sorted_: sorted p-values\n",
    "ax.set_yscale('log')\n",
    "ax.set_xscale('log')\n",
    "ax.set_ylabel('P-Value')\n",
    "ax.set_xlabel('Index')\n",
    "ax.scatter(sorted_set_+1, sorted_[sorted_set_], c='r', s=20)\n",
    "ax.axline((0, 0), (1,q/m), c='k', ls='--', linewidth=3);\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d87198e4",
   "metadata": {},
   "source": [
    "## A Re-Sampling Approach\n",
    "Here, we implement the re-sampling approach to hypothesis testing\n",
    "using the  `Khan`  dataset, which we investigated in\n",
    "Section 13.5.  First, we merge the training and\n",
    "testing data, which results in observations on 83 patients for\n",
    "2,308 genes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "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>G0001</th>\n",
       "      <th>G0002</th>\n",
       "      <th>G0003</th>\n",
       "      <th>G0004</th>\n",
       "      <th>G0005</th>\n",
       "      <th>G0006</th>\n",
       "      <th>G0007</th>\n",
       "      <th>G0008</th>\n",
       "      <th>G0009</th>\n",
       "      <th>G0010</th>\n",
       "      <th>...</th>\n",
       "      <th>G2299</th>\n",
       "      <th>G2300</th>\n",
       "      <th>G2301</th>\n",
       "      <th>G2302</th>\n",
       "      <th>G2303</th>\n",
       "      <th>G2304</th>\n",
       "      <th>G2305</th>\n",
       "      <th>G2306</th>\n",
       "      <th>G2307</th>\n",
       "      <th>V2308</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.773344</td>\n",
       "      <td>-2.438405</td>\n",
       "      <td>-0.482562</td>\n",
       "      <td>-2.721135</td>\n",
       "      <td>-1.217058</td>\n",
       "      <td>0.827809</td>\n",
       "      <td>1.342604</td>\n",
       "      <td>0.057042</td>\n",
       "      <td>0.133569</td>\n",
       "      <td>0.565427</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.238511</td>\n",
       "      <td>-0.027474</td>\n",
       "      <td>-1.660205</td>\n",
       "      <td>0.588231</td>\n",
       "      <td>-0.463624</td>\n",
       "      <td>-3.952845</td>\n",
       "      <td>-5.496768</td>\n",
       "      <td>-1.414282</td>\n",
       "      <td>-0.647600</td>\n",
       "      <td>-1.763172</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.078178</td>\n",
       "      <td>-2.415754</td>\n",
       "      <td>0.412772</td>\n",
       "      <td>-2.825146</td>\n",
       "      <td>-0.626236</td>\n",
       "      <td>0.054488</td>\n",
       "      <td>1.429498</td>\n",
       "      <td>-0.120249</td>\n",
       "      <td>0.456792</td>\n",
       "      <td>0.159053</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.657394</td>\n",
       "      <td>-0.246284</td>\n",
       "      <td>-0.836325</td>\n",
       "      <td>-0.571284</td>\n",
       "      <td>0.034788</td>\n",
       "      <td>-2.478130</td>\n",
       "      <td>-3.661264</td>\n",
       "      <td>-1.093923</td>\n",
       "      <td>-1.209320</td>\n",
       "      <td>-0.824395</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-0.084469</td>\n",
       "      <td>-1.649739</td>\n",
       "      <td>-0.241308</td>\n",
       "      <td>-2.875286</td>\n",
       "      <td>-0.889405</td>\n",
       "      <td>-0.027474</td>\n",
       "      <td>1.159300</td>\n",
       "      <td>0.015676</td>\n",
       "      <td>0.191942</td>\n",
       "      <td>0.496585</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.696352</td>\n",
       "      <td>0.024985</td>\n",
       "      <td>-1.059872</td>\n",
       "      <td>-0.403767</td>\n",
       "      <td>-0.678653</td>\n",
       "      <td>-2.939352</td>\n",
       "      <td>-2.736450</td>\n",
       "      <td>-1.965399</td>\n",
       "      <td>-0.805868</td>\n",
       "      <td>-1.139434</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.965614</td>\n",
       "      <td>-2.380547</td>\n",
       "      <td>0.625297</td>\n",
       "      <td>-1.741256</td>\n",
       "      <td>-0.845366</td>\n",
       "      <td>0.949687</td>\n",
       "      <td>1.093801</td>\n",
       "      <td>0.819736</td>\n",
       "      <td>-0.284620</td>\n",
       "      <td>0.994732</td>\n",
       "      <td>...</td>\n",
       "      <td>0.259746</td>\n",
       "      <td>0.357115</td>\n",
       "      <td>-1.893128</td>\n",
       "      <td>0.255107</td>\n",
       "      <td>0.163309</td>\n",
       "      <td>-1.021929</td>\n",
       "      <td>-2.077843</td>\n",
       "      <td>-1.127629</td>\n",
       "      <td>0.331531</td>\n",
       "      <td>-2.179483</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.075664</td>\n",
       "      <td>-1.728785</td>\n",
       "      <td>0.852626</td>\n",
       "      <td>0.272695</td>\n",
       "      <td>-1.841370</td>\n",
       "      <td>0.327936</td>\n",
       "      <td>1.251219</td>\n",
       "      <td>0.771450</td>\n",
       "      <td>0.030917</td>\n",
       "      <td>0.278313</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.200404</td>\n",
       "      <td>0.061753</td>\n",
       "      <td>-2.273998</td>\n",
       "      <td>-0.039365</td>\n",
       "      <td>0.368801</td>\n",
       "      <td>-2.566551</td>\n",
       "      <td>-1.675044</td>\n",
       "      <td>-1.082050</td>\n",
       "      <td>-0.965218</td>\n",
       "      <td>-1.836966</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 2308 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      G0001     G0002     G0003     G0004     G0005     G0006     G0007  \\\n",
       "0  0.773344 -2.438405 -0.482562 -2.721135 -1.217058  0.827809  1.342604   \n",
       "1 -0.078178 -2.415754  0.412772 -2.825146 -0.626236  0.054488  1.429498   \n",
       "2 -0.084469 -1.649739 -0.241308 -2.875286 -0.889405 -0.027474  1.159300   \n",
       "3  0.965614 -2.380547  0.625297 -1.741256 -0.845366  0.949687  1.093801   \n",
       "4  0.075664 -1.728785  0.852626  0.272695 -1.841370  0.327936  1.251219   \n",
       "\n",
       "      G0008     G0009     G0010  ...     G2299     G2300     G2301     G2302  \\\n",
       "0  0.057042  0.133569  0.565427  ... -0.238511 -0.027474 -1.660205  0.588231   \n",
       "1 -0.120249  0.456792  0.159053  ... -0.657394 -0.246284 -0.836325 -0.571284   \n",
       "2  0.015676  0.191942  0.496585  ... -0.696352  0.024985 -1.059872 -0.403767   \n",
       "3  0.819736 -0.284620  0.994732  ...  0.259746  0.357115 -1.893128  0.255107   \n",
       "4  0.771450  0.030917  0.278313  ... -0.200404  0.061753 -2.273998 -0.039365   \n",
       "\n",
       "      G2303     G2304     G2305     G2306     G2307     V2308  \n",
       "0 -0.463624 -3.952845 -5.496768 -1.414282 -0.647600 -1.763172  \n",
       "1  0.034788 -2.478130 -3.661264 -1.093923 -1.209320 -0.824395  \n",
       "2 -0.678653 -2.939352 -2.736450 -1.965399 -0.805868 -1.139434  \n",
       "3  0.163309 -1.021929 -2.077843 -1.127629  0.331531 -2.179483  \n",
       "4  0.368801 -2.566551 -1.675044 -1.082050 -0.965218 -1.836966  \n",
       "\n",
       "[5 rows x 2308 columns]"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Khan = load_data('Khan')      \n",
    "D = pd.concat([Khan['xtrain'], Khan['xtest']])\n",
    "D.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "eb79e606",
   "metadata": {
    "execution": {},
    "lines_to_next_cell": 2
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2    29\n",
       "4    25\n",
       "3    18\n",
       "1    11\n",
       "Name: Y, dtype: int64"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "D['Y'] = pd.concat([Khan['ytrain'], Khan['ytest']])\n",
    "D['Y'].value_counts()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "659ee2b8",
   "metadata": {},
   "source": [
    "There are four classes of cancer. For each gene, we compare the mean\n",
    "expression in the second class (rhabdomyosarcoma) to the mean\n",
    "expression in the fourth class (Burkitt’s lymphoma).  Performing a\n",
    "standard two-sample $t$-test  \n",
    "using `ttest_ind()`  from `scipy.stats` on the $11$th\n",
    "gene produces a test-statistic of -2.09 and an associated $p$-value\n",
    "of 0.0412, suggesting modest evidence of a difference in mean\n",
    "expression levels between the two cancer types."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `ttest_ind()` function is part of the scipy.stats module in Python, and it is used to perform an independent two-sample t-test. The independent two-sample t-test is a statistical test that assesses whether the means of two independent samples are significantly different from each other.\n",
    "\n",
    "Here's a brief explanation of the parameters and usage of ttest_ind():\n",
    "\n",
    "```\n",
    "scipy.stats.ttest_ind(a, b, axis=0, equal_var=True, nan_policy='propagate')\n",
    "```\n",
    "\n",
    "- `a` and `b`: These are the two sets of sample data that you want to compare. They can be one-dimensional arrays or lists representing the samples.\n",
    "\n",
    "- `axis`: This parameter specifies the axis along which the test is applied when comparing multi-dimensional arrays. The default is axis=0, which means the test is applied along the first axis (rows). If your data is in two-dimensional arrays, you can choose the axis along which the test is applied.\n",
    "\n",
    "- `equal_var`: This parameter determines whether to assume equal variances between the two samples. If True, the function performs a standard independent two-sample t-test with equal variances. If False, it performs Welch's t-test, which does not assume equal variances. The default is True.\n",
    "\n",
    "- `nan_policy`: This parameter specifies how to handle NaN (Not a Number) values in the input data. The options are 'propagate' (default), 'raise', or 'omit'. If 'propagate', NaN values in the input data will result in NaN values in the output. If 'raise', an error is raised if there are NaN values. If 'omit', NaN values are omitted from the calculations.\n",
    "\n",
    "The function returns a tuple containing the t-statistic and the p-value for the test. The t-statistic measures the difference between the means of the two samples relative to the variance in the samples. The p-value is the probability of observing a t-statistic as extreme as the one computed from the samples, assuming the null hypothesis that the means of the two samples are equal."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "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>G0001</th>\n",
       "      <th>G0002</th>\n",
       "      <th>G0003</th>\n",
       "      <th>G0004</th>\n",
       "      <th>G0005</th>\n",
       "      <th>G0006</th>\n",
       "      <th>G0007</th>\n",
       "      <th>G0008</th>\n",
       "      <th>G0009</th>\n",
       "      <th>G0010</th>\n",
       "      <th>...</th>\n",
       "      <th>G2300</th>\n",
       "      <th>G2301</th>\n",
       "      <th>G2302</th>\n",
       "      <th>G2303</th>\n",
       "      <th>G2304</th>\n",
       "      <th>G2305</th>\n",
       "      <th>G2306</th>\n",
       "      <th>G2307</th>\n",
       "      <th>V2308</th>\n",
       "      <th>Y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.773344</td>\n",
       "      <td>-2.438405</td>\n",
       "      <td>-0.482562</td>\n",
       "      <td>-2.721135</td>\n",
       "      <td>-1.217058</td>\n",
       "      <td>0.827809</td>\n",
       "      <td>1.342604</td>\n",
       "      <td>0.057042</td>\n",
       "      <td>0.133569</td>\n",
       "      <td>0.565427</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.027474</td>\n",
       "      <td>-1.660205</td>\n",
       "      <td>0.588231</td>\n",
       "      <td>-0.463624</td>\n",
       "      <td>-3.952845</td>\n",
       "      <td>-5.496768</td>\n",
       "      <td>-1.414282</td>\n",
       "      <td>-0.647600</td>\n",
       "      <td>-1.763172</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.078178</td>\n",
       "      <td>-2.415754</td>\n",
       "      <td>0.412772</td>\n",
       "      <td>-2.825146</td>\n",
       "      <td>-0.626236</td>\n",
       "      <td>0.054488</td>\n",
       "      <td>1.429498</td>\n",
       "      <td>-0.120249</td>\n",
       "      <td>0.456792</td>\n",
       "      <td>0.159053</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.246284</td>\n",
       "      <td>-0.836325</td>\n",
       "      <td>-0.571284</td>\n",
       "      <td>0.034788</td>\n",
       "      <td>-2.478130</td>\n",
       "      <td>-3.661264</td>\n",
       "      <td>-1.093923</td>\n",
       "      <td>-1.209320</td>\n",
       "      <td>-0.824395</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-0.084469</td>\n",
       "      <td>-1.649739</td>\n",
       "      <td>-0.241308</td>\n",
       "      <td>-2.875286</td>\n",
       "      <td>-0.889405</td>\n",
       "      <td>-0.027474</td>\n",
       "      <td>1.159300</td>\n",
       "      <td>0.015676</td>\n",
       "      <td>0.191942</td>\n",
       "      <td>0.496585</td>\n",
       "      <td>...</td>\n",
       "      <td>0.024985</td>\n",
       "      <td>-1.059872</td>\n",
       "      <td>-0.403767</td>\n",
       "      <td>-0.678653</td>\n",
       "      <td>-2.939352</td>\n",
       "      <td>-2.736450</td>\n",
       "      <td>-1.965399</td>\n",
       "      <td>-0.805868</td>\n",
       "      <td>-1.139434</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.965614</td>\n",
       "      <td>-2.380547</td>\n",
       "      <td>0.625297</td>\n",
       "      <td>-1.741256</td>\n",
       "      <td>-0.845366</td>\n",
       "      <td>0.949687</td>\n",
       "      <td>1.093801</td>\n",
       "      <td>0.819736</td>\n",
       "      <td>-0.284620</td>\n",
       "      <td>0.994732</td>\n",
       "      <td>...</td>\n",
       "      <td>0.357115</td>\n",
       "      <td>-1.893128</td>\n",
       "      <td>0.255107</td>\n",
       "      <td>0.163309</td>\n",
       "      <td>-1.021929</td>\n",
       "      <td>-2.077843</td>\n",
       "      <td>-1.127629</td>\n",
       "      <td>0.331531</td>\n",
       "      <td>-2.179483</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.075664</td>\n",
       "      <td>-1.728785</td>\n",
       "      <td>0.852626</td>\n",
       "      <td>0.272695</td>\n",
       "      <td>-1.841370</td>\n",
       "      <td>0.327936</td>\n",
       "      <td>1.251219</td>\n",
       "      <td>0.771450</td>\n",
       "      <td>0.030917</td>\n",
       "      <td>0.278313</td>\n",
       "      <td>...</td>\n",
       "      <td>0.061753</td>\n",
       "      <td>-2.273998</td>\n",
       "      <td>-0.039365</td>\n",
       "      <td>0.368801</td>\n",
       "      <td>-2.566551</td>\n",
       "      <td>-1.675044</td>\n",
       "      <td>-1.082050</td>\n",
       "      <td>-0.965218</td>\n",
       "      <td>-1.836966</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 2309 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      G0001     G0002     G0003     G0004     G0005     G0006     G0007  \\\n",
       "0  0.773344 -2.438405 -0.482562 -2.721135 -1.217058  0.827809  1.342604   \n",
       "1 -0.078178 -2.415754  0.412772 -2.825146 -0.626236  0.054488  1.429498   \n",
       "2 -0.084469 -1.649739 -0.241308 -2.875286 -0.889405 -0.027474  1.159300   \n",
       "3  0.965614 -2.380547  0.625297 -1.741256 -0.845366  0.949687  1.093801   \n",
       "4  0.075664 -1.728785  0.852626  0.272695 -1.841370  0.327936  1.251219   \n",
       "\n",
       "      G0008     G0009     G0010  ...     G2300     G2301     G2302     G2303  \\\n",
       "0  0.057042  0.133569  0.565427  ... -0.027474 -1.660205  0.588231 -0.463624   \n",
       "1 -0.120249  0.456792  0.159053  ... -0.246284 -0.836325 -0.571284  0.034788   \n",
       "2  0.015676  0.191942  0.496585  ...  0.024985 -1.059872 -0.403767 -0.678653   \n",
       "3  0.819736 -0.284620  0.994732  ...  0.357115 -1.893128  0.255107  0.163309   \n",
       "4  0.771450  0.030917  0.278313  ...  0.061753 -2.273998 -0.039365  0.368801   \n",
       "\n",
       "      G2304     G2305     G2306     G2307     V2308  Y  \n",
       "0 -3.952845 -5.496768 -1.414282 -0.647600 -1.763172  2  \n",
       "1 -2.478130 -3.661264 -1.093923 -1.209320 -0.824395  2  \n",
       "2 -2.939352 -2.736450 -1.965399 -0.805868 -1.139434  2  \n",
       "3 -1.021929 -2.077843 -1.127629  0.331531 -2.179483  2  \n",
       "4 -2.566551 -1.675044 -1.082050 -0.965218 -1.836966  2  \n",
       "\n",
       "[5 rows x 2309 columns]"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "D2 = D[lambda df:df['Y'] == 2]\n",
    "D4 = D[lambda df:df['Y'] == 4]\n",
    "gene_11 = 'G0011'\n",
    "D2.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "c9bde0f7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((29, 2309), (25, 2309))"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "D2.shape, D4.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "1afbcf47",
   "metadata": {
    "execution": {},
    "lines_to_next_cell": 2
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-2.0936330736768185, 0.04118643782678394)"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "observedT, pvalue = ttest_ind(D2[gene_11],\n",
    "                              D4[gene_11],\n",
    "                              equal_var=True) #ttest_ind allows two vectors with different lengths\n",
    "observedT, pvalue\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "5bad036c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.006797218800136647"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ttest_rel(D2[gene_11][0:25],\n",
    "                              D4[gene_11],).pvalue  #ttest_rel requires two vectors of the same length"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-2.0936330736768185"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ttest_ind(D2[gene_11],\n",
    "                              D4[gene_11],\n",
    "                              equal_var=True).statistic"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "61f24919",
   "metadata": {},
   "source": [
    "However, this $p$-value relies on the assumption that under the null\n",
    "hypothesis of no difference between the two groups, the test statistic\n",
    "follows a $t$-distribution with $29+25-2=52$ degrees of freedom.\n",
    "Instead of using this theoretical null distribution, we can randomly\n",
    "split the 54 patients into two groups of 29 and 25, and compute a new\n",
    "test statistic.  Under the null hypothesis of no difference between\n",
    "the groups, this new test statistic should have the same distribution\n",
    "as our original one.  Repeating this process 10,000 times allows us to\n",
    "approximate the null distribution of the test statistic.  We compute\n",
    "the fraction of the time that our observed test statistic exceeds the\n",
    "test statistics obtained via re-sampling."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(54,)"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B = 10000\n",
    "Tnull = np.empty(B) #empty uninitialized array of size B\n",
    "D_ = np.hstack([D2[gene_11], D4[gene_11]])\n",
    "D_.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "29"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n_ = D2[gene_11].shape[0]\n",
    "n_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fisher-Yates shuffle algorithm\n",
    "\n",
    "The random.shuffle function in Python operates on a sequence by applying the Fisher-Yates shuffle algorithm, also known as the Knuth shuffle. This algorithm shuffles a sequence randomly by iteratively swapping each element with a randomly chosen element that comes after it in the sequence, or including itself.\n",
    "\n",
    "Here's a step-by-step explanation of the Fisher-Yates shuffle algorithm:\n",
    "\n",
    "Start from the last element of the sequence.\n",
    "Select a random index from the elements before or including the current element.\n",
    "Swap the current element with the one at the randomly chosen index.\n",
    "Move to the previous element and repeat steps 2-3.\n",
    "Continue this process until you reach the first element of the sequence.\n",
    "The Fisher-Yates shuffle ensures that each element has an equal probability of ending up in any position in the shuffled sequence. This makes the shuffle unbiased and truly random.\n",
    "\n",
    "Mathematically, let's denote the original sequence as $a_1, a_2, \\cdots, a_n$, where \n",
    "n is the length of the sequence. After applying the Fisher-Yates shuffle, each permutation of the original sequence is equally likely.\n",
    "\n",
    "The probability of any specific permutation occurring is \n",
    "$1/n!$,  This ensures that, on average, each element has an equal chance of ending up in any position.\n",
    "\n",
    "In summary, the Fisher-Yates shuffle provides an unbiased and efficient way to generate random permutations of a sequence. The randomness is achieved by iteratively swapping elements, ensuring that the final arrangement is uniformly distributed among all possible permutations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "f73f4c6d",
   "metadata": {
    "execution": {},
    "lines_to_next_cell": 2
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0398"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "D_null = D_.copy()\n",
    "for b in range(B):\n",
    "    rng.shuffle(D_null)\n",
    "    ttest_ = ttest_ind(D_null[:n_],\n",
    "                       D_null[n_:],\n",
    "                       equal_var=True)\n",
    "    Tnull[b] = ttest_.statistic  # test statistic\n",
    "(np.abs(Tnull) > np.abs(observedT)).mean()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a97f74af",
   "metadata": {},
   "source": [
    "This fraction, 0.0398,\n",
    "is our re-sampling-based $p$-value.\n",
    "It is almost identical to the $p$-value of  0.0412 obtained using the theoretical null distribution.\n",
    "We can plot  a histogram of the re-sampling-based test statistics in order to reproduce  Figure 13.7."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`scipy.stats.t.pdf(x, df, loc=0, scale=1)`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "062daf19",
   "metadata": {
    "execution": {},
    "lines_to_next_cell": 0
   },
   "outputs": [
    {
     "data": {
      "image/png": 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7O5vw8HDOOOOMOq+Pj48HqPP47bffzsMPP0zv3r3p3r079913H0lJScetlyoiEkhaL4PeT0PkTtcjhUee3L8f/vtf+O9/GZUEP94IheeaqFJEpOl5HFAnTJhAYWEhU6dOJT8/n5SUFHJyctyTnLZv305QkGdDW++++27Kysq48cYbKS4u5uyzzyYnJ4dwdWGJiJ+rrzvfVgW9noFOH1j3K+Mg/2LocvsS6NsXbDbYssUKqM8+S8TuAgbeD3vGweY/gCOiZT+DiEhTszmdTqfpIk6X3W4nLi6OkpISYmNjTZcj4rGyMoiOtvZLSyEqymw90vQaGld6rOBSGPRniF8DThvsvAK2XQ81UbVjUI9VVsa2m6LpOhdsDrD3gzUz4Oxf1P+rvb466j2viEgT8ySvNessfhEROXXB5TD4XiucVkfB2r/CD7dY4bRBUVFs+zV8+zhUxULsRki5HSgsPMGLRES8mwKqiIgXsFXDGX+BuHVQFQOrZ8J+D+aJFqfANzOhoi1EbwUuuwx0uWgR8VEKqCIiXqDXLGj9DVRHwrePQmkvz89R3r22JTUaWLwYrr/eWpJKRMTHKKCKiBiWkAOdFlhjTjf8GUr7Nv5c5V1h3YNAq1Ywfz4891xTlSki0mIUUEVEDArfDb2fsva3XQdFZ53+OYuHAjNmWHeysuDbb0//pCIiLUgBVUTElBronw0hh6B4MPz0f0147ttvh0susa48NWkSVGk1fxHxHR6vgyoiIk0j6d8Q95017nTjFCC4CU9us8Err0D//rBmDTz+ONx7r0enOOElV0VEmpFaUEVEDGi1H3q8ZO3/+Bs4nNgMb9KhA/z979b+Aw/ADz80w5uIiDQ9BVQREQN6Pg8hZXCwD+z+RTO+0a9+Benp1pJTHragioiYooAqItLCordAwkJr//s/0rRd+8ey2axW1KAgeOcdYtc243uJiDQRBVQRkRbW/UWwOaHgfDjYrwXe8Iwz4IYbAOj1HKAhpCLi5RRQRURaUPxqaLsMHMGw7dct+MYPPABRUcRugPZ5Lfi+IiKNoIAqItJSnNDjBWt3z8/hUKcWfO+OHeGuuwDo9jrgaMH3FhHxkAKqiEgLab0CYjdATTj8NMlAAbffTnUURG2Ddl8ZeH8RkVOkgCoi0kK6vGVt91wClW0MFBAXx85fWrtd30BjUUXEaymgioi0gNj10Hq1NfZ0x9Xm6th1hdWCG7MZ2iw1V4eIyIkooIqItABX62nBhVDRwVwdVXGw67K6NYmIeBsFVBGR5rZxI+2+AqcNdlxruhjYeaXVkhu/FqK/N12NiMjxFFBFRJrbM88AUHQWlHcxXAtQ2Q4K06z9zv8yWoqISL0UUEVEmpPdDnPmALDzcsO1HGXnFda2w+dAQYHRWkREjqWAKiLSnN54A0pLKesCxcNMF3PEwf5g7w9BVcDzz5suR0SkDgVUEZHm4nS6u/d3jwdsRqs5jqsVleeeg6oqo7WIiBxNAVVEpLl89hls3AjR0eRfZLqY4xWeC5Wtgfx8+O9/TZcjIuKmgCoi0lxeesna/upX1ESZLaU+zhDIz6i946pVRMQLKKCKiDSHAwfgvfes/RtuMFvLCez5We3ORx/Bzp1GaxERcVFAFRFpDvPmQUUFDBoEw7xodtQxDiUDY8eCwwGvvWa6HBERQAFVRKR5vPqqtc3MBJuXzY461m9+Y21fftkKqiIihimgiog0tXXrYPlyCAmBiRNNV3NyV1wBcXGwbRssWmS6GhERBVQRkSbn6iq/5BLo0MFoKackMhKuvNLaf+sts7WIiKCAKiLStKqqrMX5were9xWult533rHGzoqIGKSAKiLSlD791Lp0aPv28LOfnfx4b3HuudCpExQXw4cfmq5GRAKcAqqISFOaP9/aXn01tGplthZPBAXBtdda++rmFxHDFFBFRJpKRcWRtU8nTDBbS2O4uvn//W8oKTFbi4gENAVUEZGmkpMDdrvVVT5mjOlqPDdkCPTvbwXtd981XY2IBDAFVBGRpuLq3r/qKqvL3NfYbEdaUefONVuLiAQ0H/wNKiLihcrL4YMPrP1rrjFby+n4f//P2n7+Oa2KjVYiIgFMAVVEpCl8+CGUlUG3bjBqlOlqGq97d+vSrA4H7b4yXYyIBCoFVBGRpnD07H1vv7TpyVxxBQDtvjBch4gELAVUEZHTVV4O//2vte+Ls/eP9ctfAtB6JYSUGq5FRAKSAqqIyOn65BM4dMjq3h861HQ1p69fPxgwgKBqaLPYdDEiEogUUEVETteCBdZ2/Hjf7953qW1Fba9ufhExQAFVROR0VFfDf/5j7Y8fb7SUJlU7DrXNMgg6ZLgWEQk4CqgiIqfjq6+gqAjatPHNxfkbMmQIhzpCcIUVUkVEWlKI6QJERHyaq3v/0kshxHt+peblneZQA5uNwrHQZb7Vzb/v3KapS0TkVKgFVUSksZzOuuNP/cy+2gbhNsvAVmO2FhEJLAqoIiKNtXYtbNsGERFw0UWmq2ly9gFQFQutDkLsd6arEZFAooAqItJYrtbTCy+EyEijpTSLYChKtXbbarkpEWlB3jNgSkTESzU0njPtg+HWzmWXtWA1LavoTEhcCG2XwI+/M12NiAQKtaCKiDRCq/3AypXWnUsuMVpLczowChzBEPUThO8yXY2IBAoFVBGRRnAvvTRsGCQkGK2lOVVHQ8lga7/tErO1iEjgUEAVEWmEtq6A+rOfGa2jJRSdaW0VUEWkpSigioh4yFYDrZfX3rn4YqO1tISi0dY2fjUElxstRUQChAKqiIiHYtZDq1Ksq0elppoup9kdSobyzhBUfVQwFxFpRgqoIiIearu0dueiiyA42GgtLWV/bQ5vo4AqIi1AAVVExENtAmj8qcv+kda2zQqsK2iJiDQjrYMqIuKB0CKI2Vx7JyOj3mMaWjf1dJk8b/EQcLSC8AJg0ybo169ZahERAQVUEZE6ThbWXK2n9n6wan0CrG+BoryAIxxKBkHrVcAnnyigikizalQX/6xZs+jWrRvh4eGkpqaybNmyBo999913GTFiBPHx8URFRZGSksIbb7xR55jrr78em81W5zZu3LjGlCYi0qza1I4/3T/KbB0muLr5+fhjo3WIiP/zOKDOnz+frKwspk2bxqpVqxgyZAgZGRns3bu33uPbtGnDn//8ZxYvXsyaNWvIzMwkMzOTj4/5BTdu3Dj27Nnjvr399tuN+0QiIs3EVlM7BpMjk4YCyf4RtTt5eVBRYbIUEfFzHgfUJ554gsmTJ5OZmcmAAQOYPXs2kZGRvPLKK/Uen5aWxuWXX07//v3p2bMnt912G4MHD+bLL7+sc1xYWBiJiYnuW+vWrRv3iUREmknMRggpg6oYsPc1XU3LK+sJla2B8nL4+mvT5YiIH/MooFZWVrJy5UrS09OPnCAoiPT0dBYvXnzS1zudTnJzc9m0aRNjx46t81xeXh4dOnSgb9++3HTTTRQVFXlSmohIs2u90toeGAYExupSddmOakVVN7+INCOPAuq+ffuoqakh4ZjrTickJJCfn9/g60pKSoiOjiY0NJRLLrmEp59+mgsvvND9/Lhx43j99dfJzc1lxowZLFq0iIsvvpiampp6z1dRUYHdbq9zExFpbq1XWdsDw8zWYZJ7HOonnxitQ0T8W4vM4o+JiWH16tWUlpaSm5tLVlYWPXr0IC0tDYBrrrnGfeygQYMYPHgwPXv2JC8vjwsuuOC482VnZ/PAAw+0ROkiIgAEHYLYddZ+8XCztZh0wNWC+s03UFAAxzRYiIg0BY9aUNu1a0dwcDAFBQV1Hi8oKCAxMbHhNwkKolevXqSkpHDHHXdw5ZVXkp2d3eDxPXr0oF27dmzZsqXe56dMmUJJSYn7tmPHDk8+hoiIx+LXWpf6PJwAh5JMV2NOVWtg6FDrzqefGq1FRPyXRwE1NDSU4cOHk5ub637M4XCQm5vL6NGjT/k8DoeDihPMAN25cydFRUV07Nix3ufDwsKIjY2tcxMRaU7u8afDgeZZL993XHSRtdU4VBFpJh7P4s/KyuLFF19kzpw5bNiwgZtuuomysjIyMzMBmDRpElOmTHEfn52dzcKFC/nxxx/ZsGEDjz/+OG+88Qb/93//B0BpaSl33XUXS5YsYdu2beTm5nLZZZfRq1cvMhq4SouISEurE1ADnSug5ubqsqci0iw8HoM6YcIECgsLmTp1Kvn5+aSkpJCTk+OeOLV9+3aCgo7k3rKyMm6++WZ27txJREQE/fr1480332TChAkABAcHs2bNGubMmUNxcTFJSUlcdNFFPPTQQ4SFhTXRxxQRabxWByD6B2v/wFCztXiFs86CsDDYvRu+/x769m3wClxpaQqwIuI5m9Pp+3/+2u124uLiKCkpUXe/+KSyMoiOtvZLSyEqymw9gay+oNXhMxjwEJT2hBUvGSjKy6SlOeH88+Hzz+G55+B3v1NAFZGT8iSvNepSpyIigUTd+/U47zxr+9lnZusQEb+kgCoiciLOYxboF8v551vbzz8Hh8NsLSLidxRQRUROIHw3hBeAIwRKBpuuxouMHAmRkbBvH6xbZ7oaEfEzCqgiIifgunqUfQDURJitxauEhsI551j76uYXkSamgCoicgLxq61tcYrJKryUq5tfAVVEmpgCqohIQ5wQv8baVUCth2ui1KJFUGO2FBHxLwqoIiINiNgNYfvA0crq4pdjDB0KcXFQUkJM/VemFhFpFAVUEZEGuLr37f3AoeuGHC8kBMaOBSD+G8O1iIhfUUAVEWlA3LfWtmSI2Tq8Wu04VAVUEWlKCqgiIvVxQnxtQNX40xOoHYcavwZsVYZrERG/oYAqIlKP8HwI3wuOYCjR+NOGDRoEbdoQfBhiNpsuRkT8hQKqiEg9XONPD/YDh9Y/bVhQkHs91Lg1hmsREb+hgCoiUg93977Gn56cAqqINDEFVBGResQpoJ662pn8cWsBh9lSRMQ/KKCKiBwjLB8i8sEZBPYzTFfjA4YOpSYcWpVC1FbTxYiIP1BAFRE5hqt7/2AfqIk0W4tPCAmhpDbIq5tfRJqCAqqIyDG0vJTnSgZZ23gFVBFpAiGmCxAR8TaaIHVieXm24x6LG1y7XQs4geMPERE5ZWpBFRE5SmghROy2xp+6WgXl5A72B0cIhBVZXz8RkdOhgCoicpT4tda2tCfURJmtxZc4wqw1Y0HjUEXk9CmgiogcJa42oJYMNluHLyp2dfMroIrIaVJAFRE5Sux31rZEy0t5zBXqNVFKRE6XAqqIiIvdTvSP1q4CqudKBoLTZo1BDS00XY2I+DIFVBERlyVLsDngUEeobGe6GN9TEw2lvax911heEZHGUEAVEXH58ktAraenw7XygcahisjpUEAVEXH56itAAfV0aKKUiDQFBVQREYCqKliyBAC71j9tNFcLavRWCCk1W4uI+C4FVBERgG+/hfJyqqKhrKvpYnxXVRs4lGTtx643W4uI+C4FVBERcI8/tQ9EvxlPk2uIhGvJLhERT+nXsIgIHBl/qu7901Yy0NrGrTNbh4j4LgVUERGnUzP4m5Dd1YK6HqiuNlqLiPgmBVQRka1bIT8fWrVyX09eGq+sK1RHQfBhYK0WRBURzymgiojUtp4yfDiOMLOl+IVgsPev3f/6a6OliIhvUkAVEakdf8rZZ5utw4+4h0oooIpII4SYLkBExDhXC+qYMcBjRkvxF65xqIc+e4uleW/VeS4tzWmgIhHxJWpBFZHAtn8/rK9dsPOss8zW4kfs/cAZBBH5ELrPdDUi4msUUEUksC1dam179YIOHczW4kdqoqCsu7Ufq+WmRMRDCqgiEthqL2/K6NFm6/BDWg9VRBpLAVVEApsroJ55ptk6/JD7ilIKqCLiIQVUEQlcDseRLn61oDY510SpmO8hqNJsLSLiWxRQRSRwbdwIJSUQEQGDdI3TpnY4ESraQFA1xGwyXY2I+BIFVBEJXK7u/ZEjIUSr7jU5G9hrx6HGfme2FBHxLQqoIhK4NEGq2bnGocYpoIqIBxRQRSRwLV5sbTVBqtm4W1A3AFqfX0ROkQKqiAQmux3W1U4vT001W4sfK+0NjhAIPQDhBaarERFfoYAqIoFp+XJwOqFrV+jY0XQ1fssRCqW9rP2Y9WZrERHfoYAqIoFJ409bjL2/tY3dYLYOEfEdCqgiEpg0/rTFHFRAFREPKaCKSOBxOnUFqRZkH2BtY74HW5XZWkTENyigikjg+eEHKCqCsDAYOtR0NX7vUBJUxUJQFUT/YLoaEfEFCqgiEnhcrafDhkFoqNlaAoFN41BFxDMKqCISeDT+tMW5AmqMAqqInAIFVBEJPJrB3+LcLahaakpEToECqogElvJy+PZba18tqC3GNZM/chfW+F8RkRNQQBWRwLJyJdTUQFISdO5supqAUR0D5cm1d5YuNVqLiHi/ENMFiIi0qNrxp4W9drNukf5Gb0n2/hC5Ayug/uxnpssRES+m384iElhqx5+61uaUluMah6oWVBE5GQVUEQkcTqe7BVUBteXVCagOh9FaRMS7NSqgzpo1i27duhEeHk5qairLli1r8Nh3332XESNGEB8fT1RUFCkpKbzxxht1jnE6nUydOpWOHTsSERFBeno6mzdvbkxpIiIN27ED8vMhJISDfUwXE3jKekJNKFBcDPodLyIn4HFAnT9/PllZWUybNo1Vq1YxZMgQMjIy2Lt3b73Ht2nThj//+c8sXryYNWvWkJmZSWZmJh9//LH7mEceeYSnnnqK2bNns3TpUqKiosjIyODw4cON/2QiIsdavtzaDh6MI8xsKYHIGQKlrj8M1M0vIifgcUB94oknmDx5MpmZmQwYMIDZs2cTGRnJK6+8Uu/xaWlpXH755fTv35+ePXty2223MXjwYL788kvAaj2dOXMmf/nLX7jssssYPHgwr7/+Ort372bBggWn9eFEROpw9faMHGm2jgDm7uZ3rUUrIlIPjwJqZWUlK1euJD09/cgJgoJIT09nsevKLCfgdDrJzc1l06ZNjB07FoCtW7eSn59f55xxcXGkpqY2eM6Kigrsdnudm4hIQ/LybOTl2TjwySMAbIx93nBFgcs99lctqCJyAh4F1H379lFTU0NCQkKdxxMSEsjPz2/wdSUlJURHRxMaGsoll1zC008/zYUXXgjgfp0n58zOziYuLs59S05Orvc4ERG3Goj53tp1LRovLc/dgrpmjXXRBBGRerTILP6YmBhWr17N8uXL+etf/0pWVhZ5eXmNPt+UKVMoKSlx33bs2NF0xYqIX4rcASHlUBMOZV1MVxO4KjoAiYlQXQ2rVpkuR0S8lEcL9bdr147g4GAKCgrqPF5QUEBiYmKDrwsKCqJXr14ApKSksGHDBrKzs0lLS3O/rqCggI4dO9Y5Z0pKSr3nCwsLIyxMMxxE5NTFbrS2B/sAwUZLCWw2rEvMLlhgdfOffbbpikTEC3nUghoaGsrw4cPJzc11P+ZwOMjNzWX06NGnfB6Hw0FFRQUA3bt3JzExsc457XY7S5cu9eicIiInElMbUO3q3jcvNdXaahyqiDTA40udZmVlcd111zFixAhGjRrFzJkzKSsrIzMzE4BJkybRqVMnsrOzAWu86IgRI+jZsycVFRV8+OGHvPHGGzz33HMA2Gw2br/9dh5++GF69+5N9+7due+++0hKSmL8+PFN90lFJKC5AurBvmbrEBRQReSkPA6oEyZMoLCwkKlTp5Kfn09KSgo5OTnuSU7bt28nKOhIw2xZWRk333wzO3fuJCIign79+vHmm28yYcIE9zF33303ZWVl3HjjjRQXF3P22WeTk5NDeHh4E3xEEQl0tkqI/sHa1wQpLzB8ONhssH077N0LHTqYrkhEvIzN6XQ6TRdxuux2O3FxcZSUlBAbG2u6HBGPlZVBdLS1X1oKUVFm6/E3K5+zMfxmqIyHr9/FGgcpxqSlOaF/f9i4Ef7zH7jkEtMliUgL8CSvtcgsfhERk2KP7t5XOPUOrosluK7uJSJyFAVUEfF7MRusrSZIeREFVBE5AQVUEfF7MZus7cF+ZuuQoxwdUH1/pJmINDEFVBHxbyUlRG23dhVQvUhKCoSEQGGhNVlKROQoCqgi4t9WrADgUEeoijNcixwRHg6DBln76uYXkWMooIqIf6sNP1r/1AtpHKqINEABVUT827JlgCZIeSUFVBFpgAKqiPi32oCq8adeyBVQV64Eh8NsLSLiVRRQRcR/7d4Nu3bhDIKDvU0XI8cZOBAiIsBuh++/N12NiHgRBVQR8V+1Xcdl3cARYbYUqUdICAwbZu2rm19EjqKAKiL+S9373s/VzV/7vRIRAQVUEfFnta1yds3g916aKCUi9VBAFRH/5HAcWWJKM/i9lyugrl4NlZVGSxER76GAKiL+acsWKC6G8HDKupsuRhrUqxfEx0NFBXz3nelqRMRLKKCKiH9ydRkPHYozxGwpcgI2G4wYYe2rm19Eaimgioh/ck26GTXKbB1ychqHKiLHUEAVEf+0YoW1dbXOifdSQBWRYyigioj/qa62Jt2AAqovcAXUdeugvNxsLSLiFRRQRcT/bNxoBZ3oaOjTx3Q1cjKdOkFiItTUwDffmK5GRLyAAqqI+J+VK63tsGEQpF9zXs9mUze/iNSh39wi4n80/tT3KKCKyFEUUEXE/7gC6vDhZuuQU6eAKiJHUUAVEf+iCVK+yfW92rzZusCCiAQ0LV8tIv5l/Xo4fBhiYqyrFInXycuz1ft4WvfusHWr1QKent7CVYmIN1ELqoj4F9cEqeHDNUHK17i6+V1DNEQkYOm3t4j4F40/9V2u75kCqkjAU0AVEf/iakHV+FPf4/qeub6HIhKwFFBFxH9UVWmClC8bNszabtsGRUVGSxERsxRQRcR/rF8PFRUQFwc9e5quRjyUt7o15Z2s/W9faUdenq3BCVUi4t8UUEXEfxw9/tSmYOOLDva1tjGbzNYhImYpoIqI/zh6Br/4pNI+1jbme7N1iIhZCqgi4j90iVOf525BVUAVCWgKqCLiHyor4dtvrX21oPqsg7XXVggvgFbFRksREYMUUEXEP6xbZ4XU+Hjo0cN0NdJINdFQnmztqxVVJHApoIqIf9AEKb9xsLe1jVZAFQlYCqgi4h+0QL/f0Ex+EVFAFRH/oEuc+o2DmskvEvAUUEXE91VUwJo11r5aUH1eaW9w2iB8L7Q6YLoaETFBAVVEfN9331mXOW3dGrp1M12NnKaaKDjU2dpXK6pIYFJAFRHfd/T4U02Q8gsahyoS2BRQRcT3afyp39E4VJHApoAqIr5PM/j9jlpQRQKbAqqI+LaKCli71tpXQPUbrolSYfuA/HzT5YhIC1NAFRHftnatNUGqbVvo0sV0NdJEaiKg3PXtdLWQi0jAUEAVEd/mGn+qCVJ+xzUOVQFVJPAooIqIb9MEKb/lDqiu77GIBAwFVBHxbZog5bdKaydKqQVVJPAooIqI7zp82FqkH9SC6odKe4EzCNi9G/bsMV2OiLQgBVQR8V1r1kB1NbRvD8nJpquRJlYTAeWub6taUUUCigKqiPiuo8efaoKUX3Kth6pxqCKBJcR0ASIijXbM+NO8PIVUf3OwDyR+glpQRQKMWlBFxHdpBr/fUwuqSGBSQBUR33ToEKxbZ+1rBr/fKu0FBAVZV5Pavdt0OSLSQhRQRcQ3ffst1NRAhw7QqZPpaqSZOMKBAQOsO2pFFQkYCqgi4puOHn+qCVL+zTWEQ+NQRQKGAqqI+KajL3Eq/s31PVYLqkjAUEAVEd+kCVKB4+gWVKfTbC0i0iIUUEXE95SXw/r11r5aUP3fkCEQHAwFBbBrl+lqRKQFNCqgzpo1i27duhEeHk5qairLli1r8NgXX3yRc845h9atW9O6dWvS09OPO/7666/HZrPVuY0bN64xpYlIIFi9GhwOSEyEpCTT1Uhzi4w8MlFK41BFAoLHAXX+/PlkZWUxbdo0Vq1axZAhQ8jIyGDv3r31Hp+Xl8e1117L559/zuLFi0lOTuaiiy5i1zF/BY8bN449e/a4b2+//XbjPpGI+L9jFuiXAKBxqCIBxeOA+sQTTzB58mQyMzMZMGAAs2fPJjIykldeeaXe4+fOncvNN99MSkoK/fr146WXXsLhcJCbm1vnuLCwMBITE9231q1bN+4TiYj/0/jTwKOZ/CIBxaOAWllZycqVK0lPTz9ygqAg0tPTWbx48Smdo7y8nKqqKtq0aVPn8by8PDp06EDfvn256aabKCoqavAcFRUV2O32OjcRCSBqQQ08R7egaqKUiN/zKKDu27ePmpoaEhIS6jyekJBAfn7+KZ3jnnvuISkpqU7IHTduHK+//jq5ubnMmDGDRYsWcfHFF1NTU1PvObKzs4mLi3PfkpOTPfkYIuLLyspgwwZrXy2ogWPwYGuiVGEh7NxpuhoRaWYhLflm06dPZ968eeTl5REeHu5+/JprrnHvDxo0iMGDB9OzZ0/y8vK44IILjjvPlClTyMrKct+32+0KqSKBwjVBKikJOnY0XY20lIgIOOMM6wpiK1aAfueL+DWPWlDbtWtHcHAwBQUFdR4vKCggMTHxhK997LHHmD59Op988gmDBw8+4bE9evSgXbt2bNmypd7nw8LCiI2NrXMTkQCh8aeBy/U910QpEb/nUUANDQ1l+PDhdSY4uSY8jR49usHXPfLIIzz00EPk5OQw4hTGjO3cuZOioiI6qnVERI6l8aeBy/U910QpEb/n8Sz+rKwsXnzxRebMmcOGDRu46aabKCsrIzMzE4BJkyYxZcoU9/EzZszgvvvu45VXXqFbt27k5+eTn59PaWkpAKWlpdx1110sWbKEbdu2kZuby2WXXUavXr3IyMhooo8pIn5DLaiBS1eUEgkYHo9BnTBhAoWFhUydOpX8/HxSUlLIyclxT5zavn07QUFHcu9zzz1HZWUlV155ZZ3zTJs2jfvvv5/g4GDWrFnDnDlzKC4uJikpiYsuuoiHHnqIsLCw0/x4IuJXSkth40ZrXwE18AweDCEhsG8fbN8OXbuarkhEmonN6fT9P0PtdjtxcXGUlJRoPKr4pLIyiI629ktLISrKbD1e64svYOxY6NSp3pnceXk2A0VJc0tLO+q/qWHD4Jtv4F//gl/+0lxRIuIxT/Jaoy51KiJihKt7X+NPA5cmSokEBAVUEfEdmiAlmiglEhBadB1UEZHToglSUvu9r1ryCV99boNjRnXUGQ4gIj5LLagi4hvsdvj+e2tfATVwDRoErVrRyg7hBSc/XER8kwKqiPiGb76xlhZKToYOHUxXI6aEhVkhFYjZZLgWEWk2Cqgi4hs0/lRcan8Gor83XIeINBsFVBHxDRp/Ki61PwNqQRXxXwqoIuIb1IIqLrU/AzHfA5oTJeKXFFBFxPuVlGiClBxxxhk4WkGrgxC+x3QxItIcFFBFxPt984217doV2rUzW4uYFxpKaQ9rV938Iv5J66CKiPc7ZvypLmkaWOr7fvfpA7GbrG7+wvMMFCUizUotqCLi/XSJUznGwb7WVi2oIv5JAVVEvFpeno3yL+cD8G2rP6n1VAA42MfaaqKUiH9SQBURrxZSCpG7rP2Dvc3WIt6jrBs4WkFIGUTsNl2NiDQ1BVQR8WquxdgPdYTqOLO1iPdwtoLSntZ+tLr5RfyOAqqIeDXXGENXl66IS51ufhHxKwqoIuLVXOHDNSlGxMU9UUoBVcTvKKCKiFdzhY9StaDKMeq0oDqMliIiTUwBVUS814ED7gkw6uKXY5V3g5pQTZQS8UcKqCLivVauBOBQElTHGK5FvI4zBMpqJ0ppPVQR/6KAKiLeq3aBfrWeSkM0DlXEPymgioj3qm1B1QQpaYh7HKpaUEX8igKqiHgvtaDKSbj+eInejCZKifgRBVQR8U5FRbBtG6AZ/NKw8q5QEwYh5RCx03Q1ItJUFFBFxDvVdu+Xd4LqaMO1iNdyBkNpL2tf41BF/IcCqoh4J40/lVOkcagi/kcBVUS8k2v8qQKqnIQueSrifxRQRcQ71bagavypnEydiVI1NUZrEZGmoYAqIt6nsBB++gmAg70N1yJer7wL1IRDyCHgezWjivgDBVQR8T61raf06UNNlNlSxAccNVHK/bMjIj5NAVVEvI8rZIwYYbYO8RnutXJrxy6LiG9TQBUR7+MKGcOHm61DfIZ7Mp1aUEX8ggKqiHgftaCKh9wtqKtWaaKUiB8IMV2AiAhAXp4NgFYHYMwOcNrgy9JzIdJwYeITypOtiVLB5eWwaRMMGOB+zvWzday0NGdLlSciHlJAFRGv4lrLsjwZahRO5VQFWys+xK+FDW8MpCDDdEEicjrUxS8iXsV1NSAt0C+ecv3MaMF+Ed+ngCoiXsUVLrRAv3iqVJc8FfEbCqgi4lXUgiqN5b6i1A9g0zwpEZ+mgCoiXiN0P4TtsyZIuRdeFzlF5Z2hOgKCD0PkdtPViMjpUEAVEa8RXdt6Wt4FaiLM1iI+KAhKay+NG61ufhGfpoAqIl7DNf5U3fvSWK71UDVRSsS3KaCKiNdwB1RNkJJG0kx+Ef+ggCoiXkMTpOR0uSdKbdFEKRFfpoAqIl4hdB+EFYEzSBOkpPEOdYLqSAiugMifTFcjIo2lgCoiXsHVJVvWFRzhZmsRHxZ01DhUTZQS8VkKqCLiFbRAvzSVUk2UEvF5Cqgi4hU0/lSainuilFpQRXyWAqqImOd0HgmoakGV0+T6GYr6AWzVZmsRkcZRQBUR83bvJvRA7QSpnqaLEV93KAmqoyC4EiK3ma5GRBpDAVVEzFuxAoCybpogJU1AE6VEfJ4CqoiYt3IloO59aTq6opSIb1NAFRHzli8HNEFKmo4CqohvU0AVEbOcziMBtZ/hWsRvuK8o9QPYqszWIiKeU0AVEbO2bYOiIhwhUNrDdDHiLw4nQVU0BFVB1DbT1YiIpxRQRcSs2tbT0p7gDDVci/gPmxbsF/FlCqgiYpbGn0oz0Ux+Ed+lgCoiZmn8qTQTXVFKxHcpoIqIOTU17jVQFVClqbl+pqJ+hKBKs7WIiGcaFVBnzZpFt27dCA8PJzU1lWXLljV47Isvvsg555xD69atad26Nenp6ccd73Q6mTp1Kh07diQiIoL09HQ2b97cmNJExJds3AhlZRAVRVkX08WIvzmcAJVxEFQNUVtMVyMinvA4oM6fP5+srCymTZvGqlWrGDJkCBkZGezdu7fe4/Py8rj22mv5/PPPWbx4McnJyVx00UXs2rXLfcwjjzzCU089xezZs1m6dClRUVFkZGRw+PDhxn8yEfF+td37DB8OwWZLET9kO9KKGqtufhGf4nFAfeKJJ5g8eTKZmZkMGDCA2bNnExkZySuvvFLv8XPnzuXmm28mJSWFfv368dJLL+FwOMjNzQWs1tOZM2fyl7/8hcsuu4zBgwfz+uuvs3v3bhYsWHBaH05EvJwroI4cabYO8VuugBqzwWwdIuIZjwJqZWUlK1euJD09/cgJgoJIT09n8eLFp3SO8vJyqqqqaNOmDQBbt24lPz+/zjnj4uJITU1t8JwVFRXY7fY6NxHxQQqo0szsroCqFlQRn+JRQN23bx81NTUkJCTUeTwhIYH8/PxTOsc999xDUlKSO5C6XufJObOzs4mLi3PfkpOTPfkYIuINKivh22+tfQVUaSauFtTIHRBcarYWETl1LTqLf/r06cybN4/33nuP8PDwRp9nypQplJSUuG87duxowipFpEWsWWOF1LZtoXt309WIn6qKh0OJYHNqwX4RX+JRQG3Xrh3BwcEUFBTUebygoIDExMQTvvaxxx5j+vTpfPLJJwwePNj9uOt1npwzLCyM2NjYOjcR8TGu7v0RI8BmM1uL+DWthyriezwKqKGhoQwfPtw9wQlwT3gaPXp0g6975JFHeOihh8jJyWHEiBF1nuvevTuJiYl1zmm321m6dOkJzykiPk7jT6WFuGfya6KUiM8I8fQFWVlZXHfddYwYMYJRo0Yxc+ZMysrKyMzMBGDSpEl06tSJ7OxsAGbMmMHUqVN566236Natm3tcaXR0NNHR0dhsNm6//XYefvhhevfuTffu3bnvvvtISkpi/PjxTfdJRcS7uNZDVkCVZqaJUiK+x+OAOmHCBAoLC5k6dSr5+fmkpKSQk5PjnuS0fft2goKONMw+99xzVFZWcuWVV9Y5z7Rp07j//vsBuPvuuykrK+PGG2+kuLiYs88+m5ycnNMapyoiXqy0FDbUNmcpoEozK+0DThuE74XQ/VDZxnRFInIyNqfT6TRdxOmy2+3ExcVRUlKi8ajik8rKIDra2i8thagos/U0u//9D849Fzp1gp07AcjL0zhUaT4jMyFqG6z9KxSdZT2Wlubz//2J+BRP8lqLzuIXEQE0/lRanLubf6PZOkTk1CigikjLU0CVFuaeKKWAKuITFFBFpOW5AuqoUWbrkIBx8OiJUurZF/F6Cqgi0rKKiuDHH639Y5adE2kupT3A0Qpa2SF8t+lqRORkFFBFpGWtWGFte/eG+HijpUjgcLaC0p7WfqyWmxLxegqoItKyNP5UDHF382vBfhGvp4AqIi1LAVUM0YL9Ir5DAVVEWo7TqStIiTHuFtTvwVZjthYROTEFVBFpObt2QX4+BAfD0KGmq5EAU54M1ZEQXAGR20xXIyInooAqIi3H1b0/cCBERpqtRQJPEBzsa+1qPVQR76aAKiItR+NPxTBXQNUVpUS8mwKqiLQcjT8VwzRRSsQ3KKCKSMtwOI60oKammq1FApZrolT0D8ChQ0ZrEZGGKaCKSMvYuBHsdmvs6RlnmK5GAlRFB6hsDTYHsHq16XJEpAEKqCLSMpYutbYjRkBIiNlaJHDZjnTzu4eciIjXUUAVkZbhCqjq3hfDXN387iEnIuJ11IwhIs0mL8/m3h/xKUQD30U9yhk8Yq4oCXjugOr6o0lEvI5aUEWk2QUdgqit1v7BAWZrEbHXLjXFli1QVGS0FhGpnwKqiDS7mO+tSSkV7aCivelqJNBVx1lXlQI0DlXESymgikizi91gbe39zdYh4uKeKLVkidE6RKR+Cqgi0uwUUMXb2F1DTRRQRbySAqqINLvY9dZWAVW8hTugLltmXURCRLyKZvGLSLMKLYSwfeAMgtLaySlHz+4XMaGsBxAeDsXF8P330K/fyV4iIi1ILagi0qxc3ftl3aAmwmgpIm7OEKyLRoC6+UW8kAKqiDQr9/hTLS8lXmZ7py8B2PVeJnl5NrXsi3gRBVQRaVaaICXeyvUz6RojLSLeQwFVRJqNrQZiNln7CqjibVwXjYj+0bqYhIh4DwVUEWk2kVsh+DBUR0J5F9PViNRV0d66eITNYV1MQkS8hwKqiDQbV/f+wb5AsNFSROrlGhutbn4R76KAKiLNRhOkxNu5x6FuMFuHiNSlgCoizUYTpMTb1WlBdRotRUSOooAqIs3Dbifyp9pdBVTxUgf7WBeRCCuCsELT1YiIiwKqiDSP5cuxOeFwAlS1MV2MSP0c4VDa09rXOFQR76FLnYrIaatvgfMub0MP1Hoq3s/eH2I2K6CKeBO1oIpIs9AEKfEV7nGomigl4jUUUEWk6Tk1QUp8h+tnNPp7oLLSaC0iYlFAFZEmF14AoQfAEQylvU1XI3JihzpDVQwEVwJr1pguR0RQQBWRZuAay1faCxxhZmsROamgo1r6ly41WoqIWBRQRaTJxX5nbe0DzdYhcqoOugLqkiVG6xARiwKqiDS5uHXWtkQBVXyEezKfAqqIV1BAFZEmFXQIordY+2pBFV9h71e7s2ULFBUZrUVEFFBFpInFbAKbAyraQUUH09WInJrqWChPrr2jVlQR4xRQRaRJ1eneP379fhGv5e7mX7zYaB0iooAqIk0stjag2s8wW4eIp9xjpr/+2mgdIqKAKiJNyXlUC6quICU+psT1R9XSpVBVZbQWkUCngCoiTSZiJ7Syg6OVFugX31PeFYiPh/JyLdgvYpgCqog0GVfrqb0fOFuZrUXEY0HA6NHWvrr5RYxSQBWRJqMF+sXnnXWWtf3qK7N1iAQ4BVQRaTLuFlQFVPFVroCqFlQRoxRQRaRJhJRC5E/WviZIic8aNQqCg2HHDusmIkYooIpIk4hZDzYnHEqCqjamqxFppOhoGDLE2lcrqogxCqgi0iTqLNAv4svGjLG2CqgixiigikiTiNX4U/EXmiglYpwCqoicvhqI3WDtqgVVfJ6rBXX1aigrM1qKSKBSQBWR0xa1DULKoToCyrqbrkbkNCUnQ+fOUFMDy5ebrkYkICmgishpc40/PdgfCDZaikjTUDe/iFEKqCJy2lwL9Kt7X/yGJkqJGNWogDpr1iy6detGeHg4qampLFu2rMFj161bxxVXXEG3bt2w2WzMnDnzuGPuv/9+bDZbnVu/fv0aU5qIGBC73trazzBbh0iTOXrBfofDbC0iAcjjgDp//nyysrKYNm0aq1atYsiQIWRkZLB37956jy8vL6dHjx5Mnz6dxMTEBs87cOBA9uzZ4759+eWXnpYmIibs3UvkLmvXrgX6xV8MGQKRkVBcDBs3mq5GJOB4HFCfeOIJJk+eTGZmJgMGDGD27NlERkbyyiuv1Hv8yJEjefTRR7nmmmsICwtr8LwhISEkJia6b+3atfO0NBExoXaMXlk3qI42W4pIk2nVyrqqFKibX8QAjwJqZWUlK1euJD09/cgJgoJIT09n8eLFp1XI5s2bSUpKokePHkycOJHt27ef1vlEpIV88QUAxYMN1yHS1DRRSsQYjwLqvn37qKmpISEhoc7jCQkJ5OfnN7qI1NRUXnvtNXJycnjuuefYunUr55xzDgcPHqz3+IqKCux2e52biBhSG1BLNP5U/I0mSokY4xWz+C+++GKuuuoqBg8eTEZGBh9++CHFxcX84x//qPf47Oxs4uLi3Lfk5OQWrlhEACgthW++AaBELajib84809p+/z0UFpqtRSTAeBRQ27VrR3BwMAUFBXUeLygoOOEEKE/Fx8fTp08ftmzZUu/zU6ZMoaSkxH3bsWNHk723iHhgyRKoqeFwAlQknPxwEZ/Spg0MqJ35p1ZUkRblUUANDQ1l+PDh5Obmuh9zOBzk5uYyevToJiuqtLSUH374gY4dO9b7fFhYGLGxsXVuImKAq3t/kOE6RJpIXp6tzm1399o11LSyjEiL8riLPysrixdffJE5c+awYcMGbrrpJsrKysjMzARg0qRJTJkyxX18ZWUlq1evZvXq1VRWVrJr1y5Wr15dp3X0zjvvZNGiRWzbto2vv/6ayy+/nODgYK699tom+Igi0mxq/9NWQBV/VTKkdud//zNah0igCfH0BRMmTKCwsJCpU6eSn59PSkoKOTk57olT27dvJyjoSO7dvXs3Q4cOdd9/7LHHeOyxxzj33HPJy8sDYOfOnVx77bUUFRXRvn17zj77bJYsWUL79u1P8+OJSLOpqrK6+IFiBVTxU+6f7VWrrDHX0VpLTaQl2JxOp9N0EafLbrcTFxdHSUmJuvvFJ5WVHfl/r7QUoqLM1nNKli61JpG0aUPeP/d7yZRLkaZ35jUQXgAsXAhHLbMoIp7xJK/pvxQRaRzXmLwxY/SbRPyaewhL7ZhrEWl++m9FRBrH9Z/1OeeYrUOkmbkvQqFxqCItRgFVRDzncBxpQVVAFT/nXuN3yRKorDRai0igUEAVEc9t3AhFRRARAcOGma5GpFmVdwHatYPDh2HFCtPliAQEBVQR8Zyr9TQ1FUJDzdYi0txsHOkp0DhUkRahgCointP4Uwk0CqgiLUoBVUQ8p4AqgWbsWGv75ZdQU2O2FpEAoIAqIp7ZsQN++gmCg611UEUCwZAh1mLFJSXw3XemqxHxewqoIuIZ1/jTlBSIiTFaikiLCQmx1vwFLTcl0gIUUEXEM+rel0ClcagiLUYBVUQ8s2iRtT33XLN1iLQ01zjU//0PfP8q4SJeTQFVRE7d3r2wfj3YbEf+sxYJFCNHWsuqFRTAli2mqxHxawqoInLqXK2ngwdDmzZmaxFpaeHhMGqUta9xqCLNSgFVRE5dXp61TUszWYWIOUd384tIswkxXYCI+BAFVAlQeXk2AFrHwRDg8MevsyTvddLSNBZVpDmoBVVETo3Gn4pgHwSOYAgvgPA9pqsR8V8KqCJyajT+VISaCDjYz9qP/8ZsLSL+TAFVRE6NuvdFAChOsbbxq01WIeLfFFBF5NQooIoAUDzU2savRuuhijQTBVQROTmNPxVxKxkIjhAILwR++MF0OSJ+SQFVRE5O409F3BzhYB9Qe+fzz43WIuKvFFBF5ORc3fu6vKkIcGQcqgKqSPNQQBWRk9P4U5E66gRUjUMVaXIKqCJyYq7xp6DxpyK17APB0QrIz4dNm0yXI+J3FFBF5MSOHn/atq3ZWkS8hCPUmiwFqJtfpBnoUqcicmLHdO+7LvkoEuiKU6D1aqyAetNNhqsR8S9qQRWRE9P4U5F6udZDJS9P41BFmpgCqog0LD9f65+KNMDeD4iIgMJCWLfOdDkifkUBVUQalptrbVNSNP5U5BjOUGDMGOuOxqGKNCkFVBFpmCugpqebrUPEW513nrV1DYURkSahSVIiUq+8z22c+V8IB75t9ygH8h41XZKI9zk6oDocEKR2H5GmoH9JIlKviJ0Qvtda67FkkOlqRLzUiBEQFQX798OaNaarEfEbCqgiUq/Wq6xtyUBwRJitRcRrtWp15BLAn35qthYRP6KAKiL1ar3S2hYPM1uHiNdzjdFeuNBsHSJ+RAFVRI5XU0P8amv3wHCjlYh4vwsvtLb/+x8cPmy2FhE/oYAqIsf75htaHYTqKDjY13QxIl5u4EDo2NEKp19/bboaEb+ggCoix6sdS1c8BJzBhmsR8XY2m7r5RZqYAqqIHK92/VN174ucIgVUkSaldVBFpK7Dh+HLLwE4oAlSIieUl2cDIDQSzgKcq1ZiKyrSlddETpNaUEWkrq+/hsOHqWgL5V1NFyPiGyrbQVk3sDmBzz4zXY6Iz1NAFZG6asefHhgG2MyWIuJL9o+o3VE3v8hpU0AVkbqODqgicsrc/2YWLgSn02gtIr5OAVVEjigqghUrAE2QEvFUSQo4QoBt2+DHHw1XI+LbFFBF5AhXy88ZZ1DZ3nQxIr6lJgLsA2rvqJtf5LQooIrIER9/bG3HjTNbh4iPOqBxqCJNQgFVRCxO55GAmpFhthYRH+UeGvPZZ1BTY7QWEV+mgCoilrVrYc8eiIyEs882XY2ITzrYF4iPh+JiWLbMcDUivksBVUQsOTnWNi0NwsONliLiq5zBwEUXWXc++shoLSK+TAFVRMjLs3Fg3j0AbO75ofvqOCLSCK4x3AqoIo2mS52KCMGHIG6ttb9/pNlaRHzd17G/5iyAFSv46j0bVa2tx9PStDaqyKlSC6qIEP8NBFXDoY5wqLPpakR8W2VbONjL2m+zwmwtIr5KAVVEaLPc2u4fiS5vKtIE9o+ytm2Wmq1DxFcpoIoIbWonG6t7X6RpuAPqckCrTYl4TAFVJNBt2ULEbnAEQ/Gwkx8uIidnHwjVUdDKDjHfm65GxPcooIoEutrF+e1nQE2k4VpE/IQz5Mii/W20HKqIxxRQRQJd7fqnri5JEWkaRbX/ptpqHKqIxxRQRQLZoUOQmwsooIo0tQO1/6ZiNkKrErO1iPgaBVSRQPb553DoEIfbQ2lP08WI+JeK9lDaA2xOaL3cdDUivqVRAXXWrFl069aN8PBwUlNTWXaC6w2vW7eOK664gm7dumGz2Zg5c+Zpn1NEmsh//gNA0Wi0vJRIM3DP5td/aSIe8Tigzp8/n6ysLKZNm8aqVasYMmQIGRkZ7N27t97jy8vL6dGjB9OnTycxMbFJzikiTcDpPBJQzzRci4if2p9qba3lprTelMip8jigPvHEE0yePJnMzEwGDBjA7NmziYyM5JVXXqn3+JEjR/Loo49yzTXXEBYW1iTnFJEmsHYt7NgBERFaXkqkmZScYS03FVoMqGdQ5JR5FFArKytZuXIl6enpR04QFER6ejqLFy9uVAGNOWdFRQV2u73OTUQ8VNt6ygUX4Kj/b0cROU3OECiqbUXl3/82WouIL/EooO7bt4+amhoSEhLqPJ6QkEB+fn6jCmjMObOzs4mLi3PfkpOTG/XeIgHNFVAvvdRsHSJ+rmh07c4HHxitQ8SX+OQs/ilTplBSUuK+7dixw3RJIr5l715YssTav+QSs7WI+Ln9qeAMAtatgx9/NF2OiE8I8eTgdu3aERwcTEFBQZ3HCwoKGpwA1RznDAsLa3A8q4icgo8+siZJDR0KnTrBZtMFifiv6hgoHgytV2N18992m/u5vLz6l89IS3O2THEiXsqjFtTQ0FCGDx9Obu3C3gAOh4Pc3FxGjx59gle27DlF5CRc3fs//7nZOkQChLubX+NQRU6JRy2oAFlZWVx33XWMGDGCUaNGMXPmTMrKysjMzARg0qRJdOrUiezsbMCaBLV+/Xr3/q5du1i9ejXR0dH06tXrlM4pIk2oshI+/tjaV0AVaRFFZ0Gv54BFi6CkBOLiTJck4tU8DqgTJkygsLCQqVOnkp+fT0pKCjk5Oe5JTtu3byco6EjD7O7duxk6dKj7/mOPPcZjjz3GueeeS15e3imdU0Sa0BdfwMGD0KEDjBhhuhqRgHCoM5R1gajt1ax7PJ7C801XJOLdbE6n0+cHutjtduLi4igpKSE2NtZ0OSIeKyuD6Ghrv7QUoqKa8c1uvx2efBIyM6F2reGGxsGJSNPpMRu6zIeCdNjw5xMfqzGo4o88yWs+OYtfRBrJ6YQFC6x9LS8l0qKKxljbNkvBpotKiZyQAqpIIFm9Gn76CSIiICPDdDUiAaVkAFTFQquDELvWdDUi3k0BVSSQvPeetR03DiIjzdYiEmiCj1xVql3jLr4oEjAUUEUCiSugXn652TpEApSrm7/dl4CGmYo0SAFVJFBs3gzffQchIVpeSsSQ/aOgJhQidkPUD6arEfFeCqgigcLVepqWBq1bGy1FJFDVRMCBkdZ++/+ZrUXEmymgigQKde+LeIXCsda2/Rdm6xDxZgqoIoFg925YssTav+wys7WIBLiis8ARDFHbIGK76WpEvJMCqkggeP99a5uaCp06ma1FJMBVR0PxMGtf3fwi9VNAFQkEru79X/7SbB0iAhzVza+AKlIvBVQRf3fgAHz+ubWv8aciXmHf2eAMgpjNEL7HdDUi3kcBVcTf/fe/UF0NAwdC796mqxERoCoeigdb++00WUrkOAqoIv7un/+0tureF/Eq+9TNL9IgBVQRf1ZcDDk51v7VVxstRUTqKjzb2satg9B9ZmsR8TYKqCL+7P33obISBgyAM84wXY2IHKWyPZQMsPbVzS9SlwKqiD/7xz+s7YQJZusQkXq5uvk7LDJbh4i3CTFdgIg0k/374ZNPrP3a7v28PJvBgkTkWHvToOdsiFsDoYVWq6qIqAVVxH8tWGDN3h88GPr1M12NiNSjIgFKzgCbU62oIkdTQBXxV/PnW1t174t4tb3nW9sOuWbrEPEmCqgi/qiwEHJr/7fT7H0Rr7b3XGvR/tiNEL7bdDUi3kEBVcQfvfce1NTAsGHQq5fpakTkBKrawIGh1n6Hz8zWIuItFFBF/JG690V8yt7zrG2Hz83WIeItNItfxN/s3Inz88+wAUu63MPhvHtMVyQiJ7FvLDhmQvSPELkVSDNckIhhakEV8Tdvv43NaV3n+3Ci6WJE5FRUx8D+Uda+WlFFFFBF/M+bbwJQkG64DhHxiKubPyEXcDqN1iJimgKqiD9ZswbWrMHRCgrTTBcjIp4oGgM14RCxG1i61HQ5IkYpoIr4k7lzASg60+oyFBHfURMBhefU3nn9daO1iJimgCri4/LybNYt10bFK48AUHCh4aJEpFEKMmp35s2DigqjtYiYpIAq4ifiv4WwfVAVDUWppqsRkcY4kAIV7YADB+A//zFdjogxCqgifiJhobUtTANnqNFSRKSxgo/qAVE3vwQwBVQRPxBUAe3/Z+2re1/Et+VfVLvz4YfWZYtFApACqogfaPc/CCmHQ4lQcobpakTkdJR3A0aMgOpqayyqSABSQBXxAx0/srb549C/ahF/MGmStVU3vwQo/Vcm4uPCd0Hrb8Bpqw2oIuL7rrkGQkJgxQpYt850NSItTgFVxMclfmxtDwyHigSztYhIE2nfHn7+c2v/lVfM1iJigAKqiC+rqSExx9rdc7HZUkSk6eTl2VgzagEAVS89waJPrPWORQKFAqqIL1u4kPBCqIqFfWebLkZEmtKBUdaaqK3s0O5L09WItCwFVBFf9vLLABRcoLVPRfyNM/hIz0jSf83WItLSFFBFfNW+ffD++wDs+ZnhWkSkWeT/zJoA2XqVNSFSJFAooIr4qjfegKoqDvaGsl6mixGR5nA40ZoACUeWkxMJBAqoIr7I4YDnngNgz88N1yIizcr1bzwxB2vxfpEAoIAq4os++ww2b4aYGArSTRcjIs1p31lQGQ9hRcB/NRhVAoMCqogvqm095Ve/oibSbCki0rycrSA/o/bO7NlGaxFpKQqoIr5m1y735ChuuslsLSLSIvZcak2WIicHtmwxXY5Is1NAFfE1L74INTVwzjlwxhmmqxGRFnCoE+wfVXvn2WeN1iLSEhRQRXxEXp6NRZ/aqJj1AADrz/1CV5YRCSC7Lq/deeUVKCszWotIc1NAFfEhbb+CsH1Q2RoKzzFdjYi0pP0jgZ49oaQE5s41XY5Is1JAFfEhnWqHnu65WFeOEgk4QcAtt1j7zzwDTqfRckSakwKqiI+I3gKtvwFnEOz+helqRMSI66+HyEhYuxa++MJ0NSLNRgFVxEd0fsfaFo6FigSztYiIIa1bw//9n7X/9NNmaxFpRgqoIr4gP58On1m7O64yW4qIGObq5n/vPdi2zWgpIs1FAVXEFzz7LEFVUDIQDg4wXYyIGDV4MKSnW8vNPfmk6WpEmkWI6QJE5HhHLx8VVAFnPgWhwM4rzdUkIl7kzjvh00+tdZGnTrW6/kX8iFpQRbxcwqcQWgKHE2CflpYSEYCLLrIu1FFWBi+8YLoakSangCrizZxHJkft/CU4g82WIyJewmazWlHB6uavrDRbj0gTU0AV8WJtl0DUNqiOhD0/M12NiHiVa6+FpCTYswfeftt0NSJNSgFVxFs5ocub1u7uy6Am2mw5IuJlQkPhD3+w9h97TAv3i19RQBXxUvHfQtx6qAmFHZocJSL1+e1vIToavvsOPvzQdDUiTaZRAXXWrFl069aN8PBwUlNTWbZs2QmP/+c//0m/fv0IDw9n0KBBfHjMP6Lrr78em81W5zZu3LjGlCbiN7rUXmo7/2dQ1cZsLSLipeLj4Xe/s/YfekitqOI3PA6o8+fPJysri2nTprFq1SqGDBlCRkYGe/furff4r7/+mmuvvZYbbriBb775hvHjxzN+/Hi+++67OseNGzeOPXv2uG9vazyNBLCYjdBmBTiCYfsE09WIiFe74w4ID4elS62lp0T8gMcB9YknnmDy5MlkZmYyYMAAZs+eTWRkJK+88kq9xz/55JOMGzeOu+66i/79+/PQQw8xbNgwnnnmmTrHhYWFkZiY6L611ppuEsC6vGVt96ZDRaLZWkTEyyUmwo03WvsPPWS2FpEm4lFAraysZOXKlaSnpx85QVAQ6enpLF68uN7XLF68uM7xABkZGccdn5eXR4cOHejbty833XQTRUVFDdZRUVGB3W6vcxPxG+vX0/4LcNpg+7WmixERn3D33dakqS++gEWLTFcjcto8Cqj79u2jpqaGhISEOo8nJCSQn59f72vy8/NPevy4ceN4/fXXyc3NZcaMGSxatIiLL76Ympqaes+ZnZ1NXFyc+5acnOzJxxDxbtnZAOw7G8q7Gq5FRHxDp07w619b+2pFFT/gFZc6veaaa9z7gwYNYvDgwfTs2ZO8vDwuuOCC446fMmUKWVlZ7vt2u10hVfzHe+/itMG2600XIiLe5ujLIB8r7FxIfRGCcnNZNcvGsFs0YUp8l0ctqO3atSM4OJiCgoI6jxcUFJCYWP9AucTERI+OB+jRowft2rVjy5Yt9T4fFhZGbGxsnZuIP9l7HpT1MF2FiPiSikQouMja7/aq2VpETpdHATU0NJThw4eTm5vrfszhcJCbm8vo0aPrfc3o0aPrHA+wcOHCBo8H2LlzJ0VFRXTs2NGT8kT8gy2IbdeZLkJEfNFPk8ARAm1WAsf83yviSzyexZ+VlcWLL77InDlz2LBhAzfddBNlZWVkZmYCMGnSJKZMmeI+/rbbbiMnJ4fHH3+cjRs3cv/997NixQpuvfVWAEpLS7nrrrtYsmQJ27ZtIzc3l8suu4xevXqRkZHRRB9TxIdcey2HupguQkR80eFE2H1p7Z0//UnroorP8jigTpgwgccee4ypU6eSkpLC6tWrycnJcU+E2r59O3v27HEff9ZZZ/HWW2/xwgsvMGTIEN555x0WLFjAGWecAUBwcDBr1qzhF7/4BX369OGGG25g+PDhfPHFF4SFhTXRxxTxcl99dWT/qD/wREQ89dP/QU04sGwZLFhguhyRRrE5nb7/55XdbicuLo6SkhKNRxXf43RSdtaFRC+xFtguLYXlyxueCCEicjLdX4aubwIDBsCaNRAcDDQ8ySotzeejgPgAT/Jaoy51KiJN6N13YUn96wiLiDTGjglA69awfj28+abpckQ8poAqYlJlJdxzj+kqRMTPVEdzZLjQfffBoUNG6xHxlAKqiEnPPgs//AAdEk5+rIiIJ269FZKTYccOePxx09WIeEQBVcSUAwfgwQet/fvuM1uLiPifiAh45BFrPzsbdu0yW4+IBxRQRUx5+GErpA4cCL/6lelqRMTP5OXZyEu4lpKBQHk5+b/ubLokkVOmgCpiwsaN8PTT1v5jj0GIV1x1WET8jQ22WMuOk/gJxGwwW47IqVJAFWlpTqc1NqyqCn72M9AFKUSkGR3sB/m1l0DtNQvQilLiAxRQRVraP/9pXYIwLAyeegpsWvNURJrXj5Otxfvj1kHix6arETk5BVSRlnTwIPzxj9b+lCnQs6fZekQkIFS2g22TrP2ez0GrErP1iJyMAqpIS3rgAdi92wqmWv9URFrQzqugtAe0skOP2aarETkxBVSRlrJ2Lcycae0//TSEhxstR0QCizMEvs8Cpw065kDcatMViTRMAVWkJVRXQ2Ym1NTA5ZfDxRebrkhEApB9IOz5ubXf5+9gqzRbj0hDtLaNSEt4/HFYuZKqaFg+8T0q8+pOjDp0KBIoA+B//4siIsJAjSISEH6cDO2+hKjt0HUubMs0XZHI8dSCKtLcNm6EadMA2HILVLY1XI+IBLTqGNj8e2u/65sQvclsPSL1UUAVaU41NfDrX0NFBUWpUKAlT0XECxSeB3vPBZsD+k8HKipMlyRShwKqSHN68klYvBhiYvg+C9CSpyLiJTb/ESpbQ9Q23L08It5CAVWkuaxeba11CvD441R0MFqNiEgdVXHWrH4AHn3U+mNaxEsooIo0h/JyuPZaqKyEyy6D3/zGdEUiIsfZdzbkXwg4HPB//wd2u+mSRAAFVJHmkZVlTY5KSoKXXtLlTEXEa235A9C1K/z4I9x4IzidpksSUUAVaXLvvQfPP2+F0tdfh3btTFckItKg6mhg3jwICYH5860/qkUM0zqoIo2Ul3d8q2j4bjjz1tbWnbvvhgsuaOGqREQa4cwz4a9/tS7B/Ic/wOjRcMYZpquSAKYWVJEmEnQYBk4DDhyA1FR48EHTJYmInLo774Rx4+DwYbj6aigtNV2RBDAFVJGm4IQ+T0DMFqBDB3jnHQgNNV2ViMipCwqyhiV17AgbNsCkSdbkKRED1MUv0gSSFkDiQnAGgW3+fOjc2XRJIiKn7OghS7F/hpQ/QtB778HDD8PUqQ0ee7S0NE2ukqajFlSR0xS/GnrNsvZ/+C2QlmawGhGR02MfCN//sfbOtGnw/vtG65HApBZUkdMQuR0G3gdBNVBwPuy8CnY20LogIuIr8i+G6M3Q+T2s9VEXL9akKWlRakEVaaRWxTBoCrQqhZKBsOludClTEfEbP9wMnHeeNVnq4oth507TJUkAUUAVaYxDhzjjLxCxGw4lwXcPgyPMdFEiIk3HGYI14bN/fyucXnwxFBebLksChAKqiKeqquD//T/i1kFVDKzJhqp400WJiDSDNm3go4+smf3ffQfjx2OrNF2UBAIFVBFPOByQmQkLFlATCt89BIe6mC5KRKQZde1qhdSYGFi0iAF/BVuN6aLE3ymgipwqpxNuvhnmzoWQENbdDyVDTBclItIChgyxLuMcGkr7/0G/vwEKqdKMFFBFToXTCXfcAc8/by1mPXcu+0ebLkpEpAVdcAG88w6OYEj4DPrNQCFVmo0CqsjJOBzw+9/D3/9u3X/xResygCIigebSS1k/1booSeJC6Ps4CqnSLLQOqsiJ1NTAb34Dr70GNpvVgvrrX5uuSkTEmH1jYf1fYMDD0PEjCD4EG/5U/xWmdHUpaSy1oIo0pLLSWqD6tdcgONi6RvXkyaarEhExrvA8WH8fOEKgQx4M+hMEHTJdlfgTBVSR+hw4AOPGwbx50KoV/OMfVlgVEREACtNg7d+gJhzarIAhd0JIiemqxF+oi1/kWNu2wc9+Bhs2QHQ0vPMOeWHjIM90YSIi3uXASPj2MeuqenHrYfjNsDYbyrX8npwmtaCKHG3JEjjzTCucduoEX34JGRmmqxIR8Vr2gfDNk3Ao0bq63rCbofVy01WJr1NAFQFrGannnoOxY6GgwFrzb+lSaysiIidU3h1WPQslZ0BIGQy+Fzq/g/W7VaQR1MUvcugQ3HQTzJkDQOFY2HjPt9Rs7gybDdcmIuIjqlrD6setpacSP4Fes4D8q+DllyEuznR54mPUgiqB7bvvIDXVCqdBQfzwO1h3P9REmi5MRMT3OENh472w+VZrhj//+hcMHw6rVpkuTXyMWlAlMDkcbP5DMD1fgKAqqGwN6+9zUDzUdGEiIt6jvrVNT8oGu64A+wAYPqMr/PCDNbb//vvh7rshRNFDTk4/JRJ4tm2DG2+k90LrbtGZsPEuqGpjtCoREb9ysD/wzTdwww3w3nvw5z/Dv/8Nc+aQt7tvva/Rwv7ioi5+CRzV1fDEEzBwICxcSE0YfH+7tY6fwqmISDNo3drq5p8zB2JjrZVShgyhy5tgqzRdnHgztaCK32ioKyotzWnNyL/lFli50npw7FhW3PA/DmmtPhGR5mWzwaRJcN551qWiP/2UHi9bE6k23wYHhpsuULyRWlDFr4UVAP/v/1njn1auhPh4ePFF+PxzhVMRkZaUnAyffAJvvklla4jcYV19asADEL7bdHHibdSCKn4ppBSS50HnfwKVb1t/wV9/Pfztb5CYaLo8EZHAZLPBxIksi/s/ur0Cnd6HDnnQ7kvYfSnQvwASEkxXKV5ALajiV0IOQrdX4cxroOtcCK4E0tKs1tNXXlE4FRHxAtXRsOUPsPJ52D8Cgqqh83tAz55w332wb5/pEsUwBVTxD/n5dH8ZzrwWur1uXcmktDt89xDw2WcwVOtHiYh4m9JesOZRa4F/e1+grAwefhi6doXbb4ft202XKIaoi19828qV8OSTMG8eXaush0p7wLZJsO8crD/BbI1Yx09ERE7bqa6jWjwMVj0HaQf+BX/9q7Ww/5NPwqxZMGEC3HwzjB6t3+cBRAFVfI/dDv/4h9Vlv3ix++GSgbDjath3NuobEBHxNTbIa3MFPAatV0GXt6D1qmqYO9e6DR5sXZb6//0/a8mqepxwNRfxKfpvXHxDTQ3k5sKvfmWNI5082QqnISEwcSIsW8Y3z8C+seinWkTEl9mspae+fRxWzMZamio8HNassQJqQoLVqvrBB1CpxVT9lVpQxXtVVsLnn8O778KCBbB3r/upsi6QPw4KLqqmsu1cKJtrrk4REWkWpX2B374Mjz1mLfb//POwcaPVi/aPf0CbNnDllXDZZXD++abLlSakgCreZdcuWLjQWivvo4+guPjIc/Hx1l/NmZksLz8TNBRJRCQwtG5tTZq67TZrfOrcufD225CfDy+8YN2iohg4DIpGWysDVLY3XbScDgVUMauw0Oqq//xzK5SuX1/n6crWUHiONeGpOKUYZ8jzcOh5j8LpqQ7SFxERL2ezwfDh1u3RR4/0sn3wAezaRfsvoP0X1qHlyVCcAgeGAgP2QocOJisXD9mcTqfPjxy22+3ExcVRUlJCbAMDp8ULHD4M69bBihXw9dfWbcuWOoc4g+BgH9g/Eg6MhJIBQLCZclvSoUOR/OxnZQB8+GEUERHlhisSEfFudSY+OZ3wzTdsfXo4bRdDzGawOY55Qa9eMGqUdRs50lp+MCLiuPNqolXz8SSvqQVVmp7DATt2WOOE1qyBb7+F1aut+zU1xx8/YACMGcO6Ti9yYChU628MERHxhM0Gw4bx03Xw03XW1QTjvoX41daKANE/YjWIbNkCb71lvSYkxPr/Z+DAI7czzoAaAqJhxNs1KqDOmjWLRx99lPz8fIYMGcLTTz/NqFGjGjz+n//8J/fddx/btm2jd+/ezJgxg5/97Gfu551OJ9OmTePFF1+kuLiYMWPG8Nxzz9G7d+/GlCctoazMCqE7dlgLKW/eDN9/b922bIGKivpf17at9Vfr6NFw1lmQmmqNLQIK815swQ8gIiK+7ETDt6qjoWiMdQNIG1xk9d4tXw7LlsHSpVBQYDWirFlT57XnhMKhZDiUBIcT4VBHONwRSNwI3bpZKwpIs/O4i3/+/PlMmjSJ2bNnk5qaysyZM/nnP//Jpk2b6FDP+I6vv/6asWPHkp2dzc9//nPeeustZsyYwapVqzjjjDMAmDFjBtnZ2cyZM4fu3btz3333sXbtWtavX0/4Kfwg+FsXf0t3L7jfrwZaHYRWByC0BFI6/cOaOV9YaP1D3rGD0g3/JazQOu6EWrWiLKmKsm7WlUJKe1rbynZoclM91MUvItKCnBC2F0ZHfmANPXPdNmywhqOdSPv20LEjJCUdv+3QAdq25asN/amOBecxLbGBPkzAk7zmcUBNTU1l5MiRPPPMMwA4HA6Sk5P5/e9/z7333nvc8RMmTKCsrIz//Oc/7sfOPPNMUlJSmD17Nk6nk6SkJO644w7uvPNOAEpKSkhISOC1117jmmuuadIP7AtOOaBWV8OhQw3fDh+2WjpLSqzF7RvYlucvJ8QOrexg8+CnoToKKtrD4Q7QdtSt0KfPkVuXLuR9oREkp0oBVUSk5R33/2pNDUvnhRCxHSLyIXyPdYvYA9F7Y+DgyVpn6qqOgqpYqI6xtm16ToCYGIiOtrZH7x/9WFSU1VIbHg5hYUf2Q3z7/9VmG4NaWVnJypUrmTJlivuxoKAg0tPTWXzUFX2OtnjxYrKysuo8lpGRwYIFCwDYunUr+fn5pKenu5+Pi4sjNTWVxYsXn1JANaW+IHncD/vGjdbyF1VVVqCsqqq7X8926D6w1Rx1q4agaiCk65HgeeiQ9ZomEHnM/apYqIqDyK5nW38Ntm9vbTt3Zs2B33K4A1R0gJqooz/3001Si4iIiDHBwRzqBIc61fOc8yCt7BBaCGH7IbQI+sU+DHv2WLfdu60ex6Ii9xKJIWXWjT2151gx/7TKcwaBI/SYWyvr5gyxWmyPux3zeELn662g67q1agWTJkFKymnV1tQ8Cqj79u2jpqaGhISEOo8nJCSwcePGel+Tn59f7/H5+fnu512PNXTMsSoqKqg4aoxjSUkJYCXzllRWdvxjx9WwcSP8/e8endcVe521N7DGbFexveEXHf0XVkTEkW1EhHVJuKNvMTFHtnFxfLt1AtXRUB0HVTHWDzPAOef897i32fHFb4/cOerz1/e1r+/rI/U7fNgJWF/D8nInjmNnn4qISJPz+P+uEKBj7Q1IOuf39R72RV4crcog5CCE2K1tq4PW5K2gwxByCIKPugUdrns/+DCEOqKtBqmjG6McwOHaWz1snHwUnZ3Xjn9wyBDo0eMkrzx9rq/3qXTe+2RbcXZ2Ng888MBxjycnJxuo5lhxZt62osK61Yb1puHJZzH0uf3GIVxfwyuvNFuJiEjgON3/u5rz/77SZjz3Ma6/3rq1kIMHDxIXd+KvnUcBtV27dgQHB1NQUFDn8YKCAhITE+t9TWJi4gmPd20LCgro2LFjnWNSGmhunjJlSp1hAw6Hg/3799O2bVtsNv+YgWO320lOTmbHjh1+Ma5WGk8/C3I0/TzI0fTzIC6+8LPgdDo5ePAgSUlJJz3Wo4AaGhrK8OHDyc3NZfz48YAVDnNzc7n11lvrfc3o0aPJzc3l9ttvdz+2cOFCRo8eDUD37t1JTEwkNzfXHUjtdjtLly7lpptuqvecYWFhhIWF1XksPj7ek4/iM2JjY732B01aln4W5Gj6eZCj6edBXLz9Z+FkLacuHnfxZ2Vlcd111zFixAhGjRrFzJkzKSsrIzMzE4BJkybRqVMnsrOzAbjttts499xzefzxx7nkkkuYN28eK1as4IUXXgDAZrNx++238/DDD9O7d2/3MlNJSUnuECwiIiIigcPjgDphwgQKCwuZOnUq+fn5pKSkkJOT457ktH37doKCgtzHn3XWWbz11lv85S9/4U9/+hO9e/dmwYIF7jVQAe6++27Kysq48cYbKS4u5uyzzyYnJ+eU1kAVEREREf/i8Tqo0jIqKirIzs5mypQpxw1nkMCinwU5mn4e5Gj6eRAXf/tZUEAVEREREa8SdPJDRERERERajgKqiIiIiHgVBVQRERER8SoKqCIiIiLiVRRQfUhFRQUpKSnYbDZWr15tuhwxYNu2bdxwww10796diIgIevbsybRp06isrDRdmrSQWbNm0a1bN8LDw0lNTWXZsmWmS5IWlp2dzciRI4mJiaFDhw6MHz+eTZs2mS5LvMD06dPd68v7OgVUH3L33Xef0uXBxH9t3LgRh8PB888/z7p16/j73//O7Nmz+dOf/mS6NGkB8+fPJysri2nTprFq1SqGDBlCRkYGe/fuNV2atKBFixZxyy23sGTJEhYuXEhVVRUXXXQRZWVlpksTg5YvX87zzz/P4MGDTZfSJLTMlI/46KOPyMrK4l//+hcDBw7km2++cV8aVgLbo48+ynPPPcePP/5ouhRpZqmpqYwcOZJnnnkGsC41nZyczO9//3vuvfdew9WJKYWFhXTo0IFFixYxduxY0+WIAaWlpQwbNoxnn32Whx9+mJSUFGbOnGm6rNOiFlQfUFBQwOTJk3njjTeIjIw0XY54mZKSEtq0aWO6DGlmlZWVrFy5kvT0dPdjQUFBpKens3jxYoOViWklJSUA+j0QwG655RYuueSSOr8ffJ3HlzqVluV0Orn++uv53e9+x4gRI9i2bZvpksSLbNmyhaeffprHHnvMdCnSzPbt20dNTY37stIuCQkJbNy40VBVYprD4eD2229nzJgxdS4hLoFj3rx5rFq1iuXLl5supUmpBdWQe++9F5vNdsLbxo0befrppzl48CBTpkwxXbI0o1P9eTjarl27GDduHFdddRWTJ082VLmImHTLLbfw3XffMW/ePNOliAE7duzgtttuY+7cuYSHh5sup0lpDKohhYWFFBUVnfCYHj16cPXVV/Pvf/8bm83mfrympobg4GAmTpzInDlzmrtUaQGn+vMQGhoKwO7du0lLS+PMM8/ktddeIyhIf2v6u8rKSiIjI3nnnXcYP368+/HrrruO4uJi3n//fXPFiRG33nor77//Pv/73//o3r276XLEgAULFnD55ZcTHBzsfqympgabzUZQUBAVFRV1nvMlCqhebvv27djtdvf93bt3k5GRwTvvvENqaiqdO3c2WJ2YsGvXLs477zyGDx/Om2++6bO/fMRzqampjBo1iqeffhqwune7dOnCrbfeqklSAcTpdPL73/+e9957j7y8PHr37m26JDHk4MGD/PTTT3Uey8zMpF+/ftxzzz0+PexDY1C9XJcuXercj46OBqBnz54KpwFo165dpKWl0bVrVx577DEKCwvdzyUmJhqsTFpCVlYW1113HSNGjGDUqFHMnDmTsrIyMjMzTZcmLeiWW27hrbfe4v333ycmJob8/HwA4uLiiIiIMFydtKSYmJjjQmhUVBRt27b16XAKCqgiPmXhwoVs2bKFLVu2HPcHijpD/N+ECRMoLCxk6tSp5Ofnk5KSQk5OznETp8S/PffccwCkpaXVefzVV1/l+uuvb/mCRJqBuvhFRERExKtoZoWIiIiIeBUFVBERERHxKgqoIiIiIuJVFFBFRERExKsooIqIiIiIV1FAFRERERGvooAqIiIiIl5FAVVEPHL99dfXuRZ8Wloat99+e5OcuynPdbT777+flJQU9/1jP0NzvpdJL7zwAsnJyQQFBTFz5kzT5Ri3bds2bDYbq1evbvQ5mvNnR0SOUEAVCQDXX389NpuN6dOn13l8wYIF2Gy2Zn3v1157DZvNhs1mIzg4mNatW5OamsqDDz5ISUlJnWPfffddHnrooVM6rydh9s477yQ3N9fT0k/KZrOxYMGCFnkvT9ntdm699Vbuuecedu3axY033ljn+aO/Lw3dtm3b1qj3fu2114iPjz/pcTU1NUyfPp1+/foRERFBmzZtSE1N5aWXXnIf09g/WuoLksnJyezZs+eULgHZUJh98sknee211zyuR0Q8o0udigSI8PBwZsyYwW9/+1tat27dou8dGxvLpk2bcDqdFBcX8/XXX5Odnc2rr77KV199RVJSEgBt2rRp0vd1Op3U1NQQHR1NdHR0k567IS35Xieyfft2qqqquOSSS+jYseNxz0+YMIFx48a57//yl7/kjDPO4MEHH3Q/1r59+2at8YEHHuD555/nmWeeYcSIEdjtdlasWMGBAwea5f2Cg4NJTEw8rXPExcU1UTUiciJqQRUJEOnp6SQmJpKdnd3gMfV1T8+cOZNu3bqd1nvbbDYSExPp2LEj/fv354YbbuDrr7+mtLSUu+++233csa1lzz77LL179yY8PJyEhASuvPJKwGodW7RoEU8++WSd1r68vDxsNhsfffQRw4cPJywsjC+//LLBbvcHHniA9u3bExsby+9+9zsqKyvdz3Xr1u24bvGUlBTuv/9+9/MAl19+OTabzX3/2PdyOBw8+OCDdO7cmbCwMFJSUsjJyXE/72qpe/fddznvvPOIjIxkyJAhLF68+IRf0+3bt3PZZZcRHR1NbGwsV199NQUFBYDVgjlo0CAAevToUW9raEREBImJie5baGgokZGR7vvh4eH89re/dX99zj//fL799lv367/99lvOO+88YmJiiI2NZfjw4axYsYK8vDwyMzMpKSlxf29cX7NjffDBB9x8881cddVVdO/enSFDhnDDDTdw5513Ag1/n2tqarjhhhvo3r07ERER9O3blyeffNJ93vvvv585c+bw/vvvu1+Xl5d3XKvogQMHmDhxIu3btyciIoLevXvz6quvAtC9e3cAhg4dis1mc1/3/tiWWYfDwSOPPEKvXr0ICwujS5cu/PWvfz3h905ETk4BVSRABAcH87e//Y2nn36anTt3mi6HDh06MHHiRD744ANqamqOe37FihX84Q9/4MEHH2TTpk3k5OQwduxYwOpmHT16NJMnT2bPnj3s2bOH5ORk92vvvfdepk+fzoYNGxg8eHC975+bm8uGDRvIy8vj7bff5t133+WBBx445fqXL18OwKuvvsqePXvc94/15JNP8vjjj/PYY4+xZs0aMjIy+MUvfsHmzZvrHPfnP/+ZO++8k9WrV9OnTx+uvfZaqqur6z2nw+HgsssuY//+/SxatIiFCxfy448/MmHCBMBqHf30008BWLZs2XFfn1Nx1VVXsXfvXj766CNWrlzJsGHDuOCCC9i/fz8AEydOpHPnzixfvpyVK1dy77330qpVK8466yxmzpxJbGys+3vjCpzHSkxM5LPPPqOwsLDBr11932eHw0Hnzp355z//yfr165k6dSp/+tOf+Mc//gFYwyyuvvpqxo0b537dWWedddz577vvPtavX89HH33Ehg0beO6552jXrp376wbw6aefsmfPHt599916a5wyZQrTp093n+utt94iISHBo6+1iBxPXfwiAeTyyy8nJSWFadOm8fLLL5suh379+nHw4EGKioro0KFDnee2b99OVFQUP//5z4mJiaFr164MHToUsLpZj27xO9aDDz7IhRdeeML3Dg0N5ZVXXiEyMpKBAwfy4IMPctddd/HQQw8RFHTyv91d3d/x8fEn7DZ+7LHHuOeee7jmmmsAmDFjBp9//jkzZ85k1qxZ7uPuvPNOLrnkEsBq2R04cCBbtmyhX79+x50zNzeXtWvXsnXrVnfwfP311xk4cCDLly9n5MiRtG3b1l2np93aX375JcuWLWPv3r2EhYW5P8eCBQt45513uPHGG9m+fTt33XWXu77evXu7Xx8XF+duNT+RJ554giuvvJLExEQGDhzIWWedxWWXXcbFF1/sPk993+fg4OA6f0x0796dxYsX849//IOrr76a6OhoIiIiqKioOGEN27dvZ+jQoYwYMQKgTk+B6/vbtm3bBs9x8OBBnnzySZ555hmuu+46AHr27MnZZ599ws8tIienFlSRADNjxgzmzJnDhg0bTJeC0+kEqHei1oUXXkjXrl3p0aMHv/rVr5g7dy7l5eWndF5X4DiRIUOGEBkZ6b4/evRoSktL2bFjxylWf3J2u53du3czZsyYOo+PGTPmuK//0S29rjGje/furfe8GzZsIDk5uU6r6IABA4iPj2+S7+u3335LaWkpbdu2dY+pjY6OZuvWrfzwww8AZGVl8Zvf/Ib09HSmT5/uftwTAwYM4LvvvmPJkiX8+te/Zu/evVx66aX85je/OelrZ82axfDhw2nfvj3R0dG88MILbN++3aP3v+mmm5g3bx4pKSncfffdfP311x69fsOGDVRUVHDBBRd49DoROTkFVJEAM3bsWDIyMpgyZcpxzwUFBblDo0tVVVWz1bJhwwZiY2PdrX1Hi4mJYdWqVbz99tt07NiRqVOnMmTIEIqLi0963qioqNOuraW/Fq1atXLvuwK7w+Fotvc7kdLSUjp27Mjq1avr3DZt2sRdd90FWOM8161bxyWXXMJnn33GgAEDeO+99zx+r6CgIEaOHMntt9/Ou+++y2uvvcbLL7/M1q1bG3zNvHnzuPPOO7nhhhv45JNPWL16NZmZmXXGEJ+Kiy++mJ9++ok//vGP7N69mwsuuKDB4Qj1iYiI8Oj9ROTUKaCKBKDp06fz73//+7iJOO3btyc/P79OMDudNSNPZO/evbz11luMHz++wS71kJAQ0tPTeeSRR1izZg3btm3js88+A6wu+vrGrp6qb7/9lkOHDrnvL1myhOjoaHerZPv27dmzZ4/7ebvdflxoatWq1QlriI2NJSkpia+++qrO41999RUDBgxodO39+/dnx44ddVp7169fT3Fx8Wmd12XYsGHk5+cTEhJCr1696txcYzQB+vTpwx//+Ec++eQTfvnLX7onGJ3O98ZVf1lZWYPn+uqrrzjrrLO4+eabGTp0KL169TquBfdUa2jfvj3XXXcdb775JjNnzuSFF15wvx444Tl69+5NRESEVywrJuJvNAZVJAANGjSIiRMn8tRTT9V5PC0tjcLCQh555BGuvPJKcnJy+Oijj4iNjT2t93M6ne7gW1xczOLFi/nb3/5GXFzccWuzuvznP//hxx9/ZOzYsbRu3ZoPP/wQh8NB3759AWu84NKlS9m2bRvR0dEeL1FVWVnJDTfcwF/+8he2bdvGtGnTuPXWW91h+fzzz+e1117j0ksvJT4+nqlTpxIcHFznHN26dSM3N5cxY8YQFhZW7/Jdd911F9OmTaNnz56kpKTw6quvsnr1aubOnetRvUdLT093fw9nzpxJdXU1N998M+eee+4pDW84lfOPHj2a8ePH88gjj9CnTx92797Nf//7Xy6//HIGDhzIXXfdxZVXXkn37t3ZuXMny5cv54orrgCsr0tpaSm5ubnuoRRHD6dwufLKKxkzZgxnnXUWiYmJbN26lSlTptCnTx/32Nb6vs+9e/fm9ddf5+OPP6Z79+688cYbLF++3D3z3vW6jz/+mE2bNtG2bdt6l4eaOnUqw4cPZ+DAgVRUVPCf//yH/v37A9YkvoiICHJycujcuTPh4eHHnSM8PJx77rmHu+++m9DQUMaMGUNhYSHr1q3jhhtuOO3vg0ggUwuqSIB68MEHj+tC7t+/P88++yyzZs1iyJAhLFu2zKMuz4bY7XY6duxIp06dGD16NM8//zzXXXcd33zzTb1rdII1+ejdd9/l/PPPp3///syePZu3336bgQMHAtakouDgYAYMGED79u09Hn94wQUX0Lt3b8aOHcuECRP4xS9+UWc5pClTpnDuuefy85//nEsuuYTx48fTs2fPOud4/PHHWbhwIcnJye4JXMf6wx/+QFZWFnfccQeDBg0iJyeHDz74oM6kIk/ZbDbef/99WrduzdixY0lPT6dHjx7Mnz+/0ec89vwffvghY8eOJTMzkz59+nDNNdfw008/kZCQQHBwMEVFRUyaNIk+ffpw9dVXc/HFF7snLp111ln87ne/Y8KECbRv355HHnmk3vfJyMjg3//+N5deeil9+vThuuuuo1+/fnzyySeEhFjtJ/V9n3/729/yy1/+kgkTJpCamkpRURE333xznXNPnjyZvn37MmLECNq3b39cKzZYraRTpkxh8ODBjB07luDgYObNmwdYrfdPPfUUzz//PElJSVx22WX1fob77ruPO+64g6lTp9K/f38mTJjQ4NhhETl1Nuexg6xERERERAxSC6qIiIiIeBUFVBERERHxKgqoIiIiIuJVFFBFRERExKsooIqIiIiIV1FAFRERERGvooAqIiIiIl5FAVVEREREvIoCqoiIiIh4FQVUEREREfEqCqgiIiIi4lUUUEVERETEq/x/kNb13kjXtscAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 800x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8,8))\n",
    "ax.hist(Tnull,\n",
    "        bins=100,\n",
    "        density=True, # show probability density rather than the raw count\n",
    "        facecolor='y',\n",
    "        label='Null')\n",
    "xval = np.linspace(-4.2, 4.2, 1001)\n",
    "ax.plot(xval,\n",
    "        t_dbn.pdf(xval, D_.shape[0]-2), #theoretical null disbribution: t-distr: \n",
    "        c='r')\n",
    "ax.axvline(observedT,\n",
    "           c='b',\n",
    "           label='Observed')\n",
    "ax.legend()\n",
    "ax.set_xlabel(\"Null Distribution of Test Statistic\");\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e81b939b",
   "metadata": {},
   "source": [
    "The re-sampling-based null distribution is almost identical to the theoretical null distribution, which is displayed in red.\n",
    "\n",
    "### Plug-in Re-Sampling FDR\n",
    "Finally, we implement the plug-in re-sampling FDR approach outlined in\n",
    "Algorithm 13.4. Depending on the speed of your\n",
    "computer, calculating the FDR for all 2,308 genes in the `Khan`\n",
    "dataset may take a while.  Hence, we will illustrate the approach on a\n",
    "random subset of 100 genes.  For each gene, we first compute the\n",
    "observed test statistic, and then produce 10,000 re-sampled test\n",
    "statistics. This may take a few minutes to run.  If you are in a rush,\n",
    "then you could set `B` equal to a smaller value (e.g. `B=500`)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "6d14fcad",
   "metadata": {
    "execution": {}
   },
   "outputs": [],
   "source": [
    "m, B = 100, 10000\n",
    "idx = rng.choice(Khan['xtest'].columns, m, replace=False)\n",
    "T_vals = np.empty(m)\n",
    "Tnull_vals = np.empty((m, B))\n",
    "\n",
    "for j in range(m):\n",
    "    col = idx[j]\n",
    "    T_vals[j] = ttest_ind(D2[col],\n",
    "                          D4[col],\n",
    "                          equal_var=True).statistic #observed t-statistic\n",
    "    D_ = np.hstack([D2[col], D4[col]])\n",
    "    D_null = D_.copy()\n",
    "    for b in range(B):\n",
    "        rng.shuffle(D_null)\n",
    "        ttest_ = ttest_ind(D_null[:n_],\n",
    "                           D_null[n_:],\n",
    "                           equal_var=True)\n",
    "        Tnull_vals[j,b] = ttest_.statistic\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "06286699",
   "metadata": {},
   "source": [
    "Next, we compute the number of rejected null hypotheses $R$, the\n",
    "estimated number of false positives $\\widehat{V}$, and the estimated\n",
    "FDR, for a range of threshold values $c$ in\n",
    "Algorithm 13.4. The threshold values are chosen\n",
    "using the absolute values of the test statistics from the 100 genes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [],
   "source": [
    "cutoffs = np.sort(np.abs(T_vals))\n",
    "# cutoffs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((100,), (100,), (100,))"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "FDRs, Rs, Vs = np.empty((3, m))\n",
    "FDRs.shape, Rs.shape, Vs.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "id": "8f0ec909",
   "metadata": {
    "execution": {}
   },
   "outputs": [],
   "source": [
    "for j in range(m):\n",
    "   R = np.sum(np.abs(T_vals) >= cutoffs[j]) # Note cufoffs is sorted and increasing\n",
    "   V = np.sum(np.abs(Tnull_vals) >= cutoffs[j]) / B # sum over all elements in Tnull_vals >= cutoffs[j]\n",
    "   Rs[j] = R\n",
    "   Vs[j] = V\n",
    "   FDRs[j] = V / R\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e26b64c6",
   "metadata": {},
   "source": [
    "Now, for any given FDR, we can find the genes that will be\n",
    "rejected. For example, with FDR controlled at 0.1, we reject 15 of the\n",
    "100 null hypotheses. On average, we would expect about one or two of\n",
    "these genes (i.e. 10% of 15) to be false discoveries.  At an FDR of\n",
    "0.2, we can reject the null hypothesis for 28 genes, of which we\n",
    "expect around six to be false discoveries.\n",
    "\n",
    "The variable `idx` stores which\n",
    "genes were included in our 100 randomly-selected genes. Let’s look at\n",
    "the genes whose estimated FDR is less than 0.1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([False, False, False, False, False, False, False, False, False,\n",
       "       False, False, False, False, False, False, False, False, False,\n",
       "       False, False, False, False, False, False, False, False, False,\n",
       "       False, False, False, False, False, False, False, False, False,\n",
       "       False, False, False, False, False, False, False, False, False,\n",
       "       False, False, False, False, False, False, False, False, False,\n",
       "       False, False, False, False, False, False, False, False, False,\n",
       "       False, False, False, False, False, False, False, False, False,\n",
       "       False, False, False, False, False, False, False, False, False,\n",
       "        True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
       "        True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
       "        True])"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#where FDRs < 0.1\n",
    "FDRs < 0.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.019860476823233383"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cutoffs[FDRs < 0.1].min()  # minimum cutoff (test-statistic value) where FDR < 0.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "id": "f11339e5",
   "metadata": {
    "execution": {}
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['G0017',\n",
       " 'G0022',\n",
       " 'G0097',\n",
       " 'G0129',\n",
       " 'G0158',\n",
       " 'G0182',\n",
       " 'G0193',\n",
       " 'G0206',\n",
       " 'G0224',\n",
       " 'G0242',\n",
       " 'G0250',\n",
       " 'G0286',\n",
       " 'G0304',\n",
       " 'G0401',\n",
       " 'G0428',\n",
       " 'G0451',\n",
       " 'G0452',\n",
       " 'G0459',\n",
       " 'G0461',\n",
       " 'G0479',\n",
       " 'G0487',\n",
       " 'G0522',\n",
       " 'G0552',\n",
       " 'G0592',\n",
       " 'G0597',\n",
       " 'G0679',\n",
       " 'G0691',\n",
       " 'G0714',\n",
       " 'G0751',\n",
       " 'G0773',\n",
       " 'G0812',\n",
       " 'G0830',\n",
       " 'G0831',\n",
       " 'G0908',\n",
       " 'G0941',\n",
       " 'G0982',\n",
       " 'G0988',\n",
       " 'G1020',\n",
       " 'G1022',\n",
       " 'G1053',\n",
       " 'G1059',\n",
       " 'G1090',\n",
       " 'G1192',\n",
       " 'G1232',\n",
       " 'G1240',\n",
       " 'G1244',\n",
       " 'G1257',\n",
       " 'G1282',\n",
       " 'G1320',\n",
       " 'G1329',\n",
       " 'G1350',\n",
       " 'G1360',\n",
       " 'G1368',\n",
       " 'G1381',\n",
       " 'G1391',\n",
       " 'G1396',\n",
       " 'G1457',\n",
       " 'G1480',\n",
       " 'G1482',\n",
       " 'G1503',\n",
       " 'G1514',\n",
       " 'G1534',\n",
       " 'G1547',\n",
       " 'G1605',\n",
       " 'G1634',\n",
       " 'G1648',\n",
       " 'G1650',\n",
       " 'G1697',\n",
       " 'G1715',\n",
       " 'G1736',\n",
       " 'G1753',\n",
       " 'G1768',\n",
       " 'G1769',\n",
       " 'G1853',\n",
       " 'G1854',\n",
       " 'G1877',\n",
       " 'G1902',\n",
       " 'G1907',\n",
       " 'G1918',\n",
       " 'G1965',\n",
       " 'G1966',\n",
       " 'G1975',\n",
       " 'G1989',\n",
       " 'G1994',\n",
       " 'G2017',\n",
       " 'G2028',\n",
       " 'G2044',\n",
       " 'G2067',\n",
       " 'G2115',\n",
       " 'G2134',\n",
       " 'G2135',\n",
       " 'G2138',\n",
       " 'G2160',\n",
       " 'G2193',\n",
       " 'G2226',\n",
       " 'G2231',\n",
       " 'G2246',\n",
       " 'G2269',\n",
       " 'G2279']"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sorted(idx[np.abs(T_vals) >= cutoffs[FDRs < 0.1].min()])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "32e600ff",
   "metadata": {},
   "source": [
    "The next line  generates  Figure 13.11, which is similar\n",
    "to  Figure 13.9,\n",
    "except that it is based on only  a subset of the genes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "id": "924b7705",
   "metadata": {
    "execution": {},
    "lines_to_next_cell": 0
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.plot(Rs, FDRs, 'b', linewidth=3)\n",
    "ax.set_xlabel(\"Number of Rejections\")\n",
    "ax.set_ylabel(\"False Discovery Rate\");\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b9f54695",
   "metadata": {},
   "source": [
    " \n"
   ]
  }
 ],
 "metadata": {
  "jupytext": {
   "cell_metadata_filter": "-all",
   "formats": "Rmd,ipynb",
   "main_language": "python"
  },
  "kernelspec": {
   "display_name": "islp",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}