{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Inf2 – Foundations of Data Science\n",
    "\n",
    "# A/B testing\n",
    "\n",
    "David Sterratt 2020-2024"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from scipy.stats import t\n",
    "from scipy.stats import binom\n",
    "from scipy.stats import norm\n",
    "from scipy.stats import beta\n",
    "\n",
    "plt.rcParams['figure.dpi'] = 200\n",
    "plt.rcParams['figure.figsize'] = [3, 2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Click-through A/B test"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Estimation approach: confidence intervals with the bootstrap method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 1000 # Numbers in group A and group B\n",
    "\n",
    "# Observed proportions\n",
    "pAhat = 0.70\n",
    "pBhat = 0.72\n",
    "B = 10000\n",
    "\n",
    "def bootstrap_prop(pAhat, pBhat, n, B=10000):\n",
    "    dhat = pAhat - pBhat\n",
    "        \n",
    "    # Difference in numbers\n",
    "    dstar = pd.Series(np.zeros(B))\n",
    "    for j in range(B):\n",
    "        fAstar = binom.rvs(n, pAhat)/n\n",
    "        fBstar = binom.rvs(n, pBhat)/n\n",
    "        dstar[j] = fAstar - fBstar\n",
    "        \n",
    "    ci95 = dstar.quantile([0.025, 0.975])\n",
    "    return(dstar, dhat, ci95)\n",
    "\n",
    "dstar_1000, dhat_1000, ci95_1000 = bootstrap_prop(pAhat, pBhat, 1000, B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Proportion of simulations in which the fraction clikcing through in Group A is bigger than the fraction clicking through in Group B is 0.1574\n"
     ]
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 1200x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print('Proportion of simulations in which the fraction clikcing through in Group A is bigger than the fraction clicking through in Group B is %2.4f'%(np.sum(dstar_1000>0)/B))\n",
    "\n",
    "plt.figure(figsize=(6,3))\n",
    "\n",
    "def plot_bootstrap(dstar, dhat, ci95, ymax=25, xann=-0.01, type=\"estimate\"):\n",
    "    # type can also be hypothesis_test\n",
    "    plt.hist(dstar, 20, density=True)\n",
    "    plt.xlabel('$p_A - p_B$')\n",
    "    plt.ylim([0, ymax])\n",
    "    plt.vlines(dhat, 0, ymax/5, color='red')\n",
    "    plt.vlines(dstar.quantile([0.025, 0.975]), 0, ymax/5, color='orange')\n",
    "    plt.vlines(0, 0, ymax/5, color='magenta')\n",
    "\n",
    "    plt.annotate('$\\hat{d}$ = %2.2f'%(dhat), (xann, ymax*.85), color='red')\n",
    "    plt.annotate('95% CI' if type=='estimate' else 'Rejection region boundaries' + ' = (%2.2f, %2.2f)'%(ci95.loc[0.025], ci95.loc[0.975]), (xann, ymax*.75), color='orange')\n",
    "    if type == 'estimate':\n",
    "        plt.annotate('$p(p_A - p_B)>0$ = (%2.4f)'%(np.sum(dstar > 0)/B), (xann, ymax*.65), color='magenta')\n",
    "\n",
    "\n",
    "plot_bootstrap(dstar_1000, dhat_1000, ci95_1000)\n",
    "plt.tight_layout()\n",
    "plt.savefig('ab-boot.png')\n",
    "plt.savefig('ab-boot.pdf')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Bootstrap estimate of sample size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0014\n"
     ]
    }
   ],
   "source": [
    "dstar_10000, dhat_10000, ci95_10000 = bootstrap_prop(pAhat, pBhat, 10000, B)\n",
    "print(np.sum(dstar_10000 > 0)/B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0143\n"
     ]
    }
   ],
   "source": [
    "dstar_5000, dhat_5000, ci95_5000 = bootstrap_prop(pAhat, pBhat, 5000, B)\n",
    "print(np.sum(dstar_5000 > 0)/B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1200x1200 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(6, 6))\n",
    "plt.subplot(3, 1, 1)\n",
    "plot_bootstrap(dstar_1000, dhat_1000, ci95_1000, ymax=70)\n",
    "plt.xlim([-0.1, 0.06])\n",
    "plt.annotate(\"n=1000\", (-0.08, 70*.85))\n",
    "\n",
    "plt.subplot(3, 1, 2)\n",
    "plot_bootstrap(dstar_5000, dhat_5000, ci95_5000, ymax=70)\n",
    "plt.annotate(\"n=5000\", (-0.08, 70*.85))\n",
    "plt.xlim([-0.1, 0.06])\n",
    "\n",
    "plt.subplot(3, 1, 3)\n",
    "plot_bootstrap(dstar_10000, dhat_10000, ci95_10000, ymax=70)\n",
    "plt.annotate(\"n=10000\", (-0.08, 70*.85))\n",
    "plt.xlim([-0.1, 0.06])\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.savefig('ab-boot-n.pdf')\n",
    "plt.savefig('ab-boot-n.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Estimation approach: confidence intervals obtained theoretically"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "See the lecture notes for this worked example, which gives the same result as for the bootstrap"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\\hat d = -0.02\n",
      "Standard error of estimator of d (\\hat\\sigma_{\\hat d}) = 0.020\n",
      "Value of z which has 2.5% of z-distribution to its right, z_0.025 = 1.959964\n",
      "Theoretical 95% CI: (-0.05976, 0.01976)\n"
     ]
    }
   ],
   "source": [
    "n = 1000\n",
    "# The variances of nA and nB (not actually needed)\n",
    "sigma_nA2 = n*pAhat*(1-pAhat)\n",
    "sigma_nB2 = n*pBhat*(1-pBhat)\n",
    "\n",
    "# The squared standard error of the estimators of pA and pB\n",
    "se_pA2 = pAhat*(1-pAhat)/n\n",
    "se_pB2 = pBhat*(1-pBhat)/n\n",
    "\n",
    "# The squared standard error the estimator of d\n",
    "se_d2  = se_pA2 + se_pB2\n",
    "\n",
    "# The standard error of the estimator of d\n",
    "se_d   = np.sqrt(se_d2)\n",
    "\n",
    "# The estimator of d\n",
    "dhat = pAhat - pBhat\n",
    "\n",
    "# The z-critical value z_{0.025}\n",
    "z0025 = norm.isf(0.025)\n",
    "\n",
    "print('\\hat d = %2.2f'%(dhat))\n",
    "print('Standard error of estimator of d (\\hat\\sigma_{\\hat d}) = %1.3f'%(se_d))\n",
    "print('Value of z which has 2.5%% of z-distribution to its right, z_0.025 = %1.6f'%(z0025)) \n",
    "print(\"Theoretical 95%% CI: (%2.5f, %2.5f)\"%(d - se_d*z0025, d + se_d*z0025))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Null hypothesis approach\n",
    "\n",
    "H<sub>0</sub>: proportions in population A and B are the same\n",
    "\n",
    "H<sub>a</sub>: proportions in population A and B differ\n",
    "\n",
    "1. Test statistic: difference in population proportions $\\hat d = \\hat p_A - \\hat p_B$\n",
    "2. Sampling distribution of null hypothesis: difference $d = p_A - p_B$ where $p_A$ and $p_B$ are generated from binomial distribution with $n$ samples and parameter $p$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.025   -0.04\n",
      "0.975    0.04\n",
      "dtype: float64\n",
      "p-value = 0.3175\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def H0_simulations(pAhat, pBhat, n, B=10000):\n",
    "    p = (pAhat + pBhat)/2\n",
    "\n",
    "    # Difference in numbers\n",
    "    dstar = pd.Series(np.zeros(B))\n",
    "    for j in range(B):\n",
    "        fAstar = binom.rvs(n, p)/n\n",
    "        fBstar = binom.rvs(n, p)/n\n",
    "        dstar[j] = fAstar - fBstar\n",
    "        \n",
    "    reject5 = dstar.quantile([0.025, 0.975])\n",
    "    p_value = (np.sum(dstar > abs(pAhat - pBhat)) + np.sum(dstar < -abs(pAhat - pBhat)))/B\n",
    "    return(dstar, reject5, p_value)\n",
    "\n",
    "H0_dstar_1000, H0_reject5, p_value = H0_simulations(pAhat, pBhat, n=1000)\n",
    "print(H0_reject5)\n",
    "plot_bootstrap(H0_dstar_1000, pAhat - pBhat, H0_reject5, ymax=70, type='hypothesis_test')\n",
    "print('p-value = %2.4f'%(p_value))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.025   -0.0124\n",
      "0.975    0.0126\n",
      "dtype: float64\n",
      "p-value = 0.002\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## H0_dstar_1000, H0_reject5, p_value = H0_simulations(pAhat, pBhat, n=10000)\n",
    "print(H0_reject5)\n",
    "plot_bootstrap(H0_dstar_1000, pAhat - pBhat, H0_reject5, ymax=70, type='hypothesis_test')\n",
    "print('p-value = %2.3f'%(p_value))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Hypothesis testing approach: confidence intervals obtained theoretically\n",
    "\n",
    "H_<sub>0</sub>: The probability of click through is the same for both groups: $p_\\mathrm{A} = p_\\mathrm{B} = p$; alternatively that $d = p_\\mathrm{A} - p_\\mathrm{B} = 0$.\n",
    "\n",
    "Test statistic: $d = \\frac{n_\\mathrm{A}}{n} - \\frac{n_\\mathrm{B}}{n}$.\n",
    "\n",
    "Distribution of test statistic: $n_A$ and $n_B$ are generated by $n$ draws from a binomial distribution with $p= \\frac{n_\\mathrm{A} + n_\\mathrm{B}}{2n}$. The variance $\\sigma^2_{n_A} = \\sigma^2_{n_B} = n p (1-p)$. The variance of a sum of random numbers is equal to the sums of the variances so $\\sigma^2_d = \\frac{1}{n^2}(\\sigma^2_{n_A} + \\sigma^2_{n_B})=\\frac{1}{n}2p(1-p)$\n",
    "\n",
    "Since $p= 1/2(p_A + p_B)$, we can write:\n",
    "$\\sigma^2_d = \\frac{1}{n}2p(1-p) = \\frac{1}{n}(p_A+ p_B)(1-\\frac{p_A-p_B}{2}) = \\frac{1}{n}(p_A(1-p_A/2) + p_B(1-p_B/2))$\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Value of z which has 2.5% of z-distribution to its right, z_0.025 = 1.959964\n",
      "Boudnaries of 5% rejection region: (0.03977, 0.03977)\n"
     ]
    }
   ],
   "source": [
    "n = 1000\n",
    "\n",
    "phat = (pAhat + pBhat)/2\n",
    "sigma_d2 = 2*phat*(1-phat)/n\n",
    "sigma_d = np.sqrt(sigma_d2)\n",
    "\n",
    "# The z-critical value z_{0.025}\n",
    "z0025 = norm.isf(0.025)\n",
    "\n",
    "print('Value of z which has 2.5%% of z-distribution to its right, z_0.025 = %1.6f'%(z0025)) \n",
    "print(\"Boudnaries of 5%% rejection region: (%2.5f, %2.5f)\"%(sigma_d*z0025, sigma_d*z0025))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8378863161044898"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Z = (pAhat-pBhat)/sepd\n",
    "norm.sf(Z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Theoretical CI: (-0.060, 0.020)\n"
     ]
    }
   ],
   "source": [
    "print(\"Theoretical 95% CI: (%2.3f, %2.3f)\"%(d - sepd*1.96, d + sepd*1.96))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bayesian\n",
    "\n",
    "One variable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f8be0169eb0>]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 100\n",
    "nA = n*pAhat\n",
    "nB = n*pBhat\n",
    "pA = np.linspace(0, 1, 2000)\n",
    "pB = pA\n",
    "pA_nA = beta.pdf(pA, a=nA+1, b=n-nA+1)\n",
    "pB_nB = beta.pdf(pB, a=nB+1, b=n-nB+1)\n",
    "\n",
    "plt.plot(pA, pA_nA)\n",
    "plt.plot(pB, pB_nB)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "72.0"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nB"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Numeric samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "dat = pd.read_csv('exmp10-05.txt')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "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>ACTmath</th>\n",
       "      <th>semester</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>27</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>29</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>30</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>34</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>29</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>149</th>\n",
       "      <td>15</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>150</th>\n",
       "      <td>28</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>151</th>\n",
       "      <td>27</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>152</th>\n",
       "      <td>28</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>153</th>\n",
       "      <td>32</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>154 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     ACTmath  semester\n",
       "0         27         1\n",
       "1         29         1\n",
       "2         30         1\n",
       "3         34         1\n",
       "4         29         1\n",
       "..       ...       ...\n",
       "149       15         2\n",
       "150       28         2\n",
       "151       27         2\n",
       "152       28         2\n",
       "153       32         2\n",
       "\n",
       "[154 rows x 2 columns]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.boxplot(x='semester', y='ACTmath', data=dat, color='white')\n",
    "plt.xlabel('Semester')\n",
    "plt.tight_layout()\n",
    "plt.savefig('maths.pdf')\n",
    "plt.savefig('maths.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.371621621621621"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = dat.loc[dat['semester']==1,'ACTmath']\n",
    "y = dat.loc[dat['semester']==2,'ACTmath']\n",
    "\n",
    "x.mean() - y.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bootstrap"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "B = 10000\n",
    "m = len(x)\n",
    "n = len(y)\n",
    "dstar = pd.Series(B)\n",
    "for j in range(B):\n",
    "    xstar = x.sample(n, replace=True)\n",
    "    ystar = y.sample(n, replace=True)\n",
    "    dstar.loc[j] = xstar.mean() - ystar.mean()\n",
    "\n",
    "ci95 = dstar.quantile([0.025, 0.975])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(4,2))\n",
    "plt.hist(dstar, 20, density=True)\n",
    "plt.xlabel('$\\overline{x^*}-\\overline{y^*}$')\n",
    "plt.vlines(x.mean()-y.mean(), 0, 0.4, color='red')\n",
    "plt.annotate('Mean = %2.2f'%(x.mean()-y.mean()), (3, 0.55), color='red')\n",
    "plt.annotate('95%% CI = (%2.2f, %2.2f)'%(ci95.loc[0.025], ci95.loc[0.975]), (3, 0.45), color='orange')\n",
    "\n",
    "plt.vlines(dstar.quantile([0.025, 0.975]), 0, 0.4, color='orange')\n",
    "plt.xlim([0, 6]) \n",
    "plt.tight_layout()\n",
    "plt.savefig('maths-bootstrap.pdf')\n",
    "plt.savefig('maths-bootstrap.png')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Theory"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "m = len(x)\n",
    "n = len(y)\n",
    "semx = x.std()/np.sqrt(m)\n",
    "semy = y.std()/np.sqrt(n)\n",
    "\n",
    "Z = (x.mean() - y.mean())/(np.sqrt(np.power(semx, 2) + np.power(semy, 2)))\n",
    "nu = np.power((np.power(semx,2) + np.power(semy,2)), 2)/\\\n",
    "              (np.power(semx, 2)/(m-1) + np.power(semy, 2)/(n-1))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0004461152829789135"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t.sf(Z, nu)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "delta = t.isf(0.025, nu)*np.sqrt(np.power(semx,2)+np.power(semy,2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1.055114619953228, 3.688128623290014]"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[x.mean()-y.mean() - delta, x.mean()-y.mean() + delta]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.arange(100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2.475, 96.525])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.quantile(x, [0.025, 0.975])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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