DS_Lecture4.ipynb

{
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   "source": [
    "# AB Testing\n",
    "\n",
    "1. Permutation Tests\n",
    "2. Binary Processes\n",
    "    * AB Tests\n",
    "    * Binomial Distribution"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Importing Our Functions**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'%.3f'"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%run ./ourFunctions.py\n",
    "%precision 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# %load ../ourFunctions.py\n",
    "import numpy as np\n",
    "import matplotlib as matplt\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "from scipy.stats import norm\n",
    "from scipy import stats\n",
    "\n",
    "from numpy import random \n",
    "#random.seed(42)\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "## Permutation 2-sample test\n",
    "\n",
    "We have used the bootstrap to compare two sets of data, both of which are samples. In particular, we can test two-sample hypotheses such as  \n",
    "\n",
    "$H_0: \\mu_m = \\mu_f, H_A: \\mu_m \\neq \\mu_f$\n",
    "\n",
    "or the one-sided versions:\n",
    "\n",
    "$H_0: \\mu_m = \\mu_f, H_A: \\mu_m > \\mu_f$\n",
    "\n",
    "$H_0: \\mu_m = \\mu_f, H_A: \\mu_m < \\mu_f$\n",
    "\n",
    "\n",
    "Another way to compare 2 distributions (in some ways much more straightforward than the bootstrap) is **permutation sampling**. It directly simulates the hypothesis that two variables have identical probability distributions.\n",
    "\n",
    "A permutation sample of two arrays having respectively $n_1$ and $n_2$ entries is constructed by concatenating the arrays together, scrambling the contents of the concatenated array, and then taking the first $n_1$ entries as the permutation sample of the first array and the last $n_2$ entries as the permutation sample of the second array.\n",
    "\n",
    "At DataCamp the first example offers a nice visualization of this process:\n",
    "\n",
    "<div>\n",
    "<img src=\"./figures/PennsylvaniaOhioDataCamp.png\" width=\"400\"/>\n",
    "</div>\n",
    "\n",
    "Take a look at the code in *ourFunctions.py* to run a permutation test"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "------\n",
    "\n",
    "**Let us apply our first permutation sampling on the Titanic data. (First, we explore the data a bit)**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>survived</th>\n",
       "      <th>pclass</th>\n",
       "      <th>sex</th>\n",
       "      <th>age</th>\n",
       "      <th>sibsp</th>\n",
       "      <th>parch</th>\n",
       "      <th>fare</th>\n",
       "      <th>embarked</th>\n",
       "      <th>class</th>\n",
       "      <th>who</th>\n",
       "      <th>adult_male</th>\n",
       "      <th>deck</th>\n",
       "      <th>embark_town</th>\n",
       "      <th>alive</th>\n",
       "      <th>alone</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>male</td>\n",
       "      <td>22.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>7.2500</td>\n",
       "      <td>S</td>\n",
       "      <td>Third</td>\n",
       "      <td>man</td>\n",
       "      <td>True</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Southampton</td>\n",
       "      <td>no</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>female</td>\n",
       "      <td>38.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>71.2833</td>\n",
       "      <td>C</td>\n",
       "      <td>First</td>\n",
       "      <td>woman</td>\n",
       "      <td>False</td>\n",
       "      <td>C</td>\n",
       "      <td>Cherbourg</td>\n",
       "      <td>yes</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>female</td>\n",
       "      <td>26.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>7.9250</td>\n",
       "      <td>S</td>\n",
       "      <td>Third</td>\n",
       "      <td>woman</td>\n",
       "      <td>False</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Southampton</td>\n",
       "      <td>yes</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>female</td>\n",
       "      <td>35.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>53.1000</td>\n",
       "      <td>S</td>\n",
       "      <td>First</td>\n",
       "      <td>woman</td>\n",
       "      <td>False</td>\n",
       "      <td>C</td>\n",
       "      <td>Southampton</td>\n",
       "      <td>yes</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>male</td>\n",
       "      <td>35.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>8.0500</td>\n",
       "      <td>S</td>\n",
       "      <td>Third</td>\n",
       "      <td>man</td>\n",
       "      <td>True</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Southampton</td>\n",
       "      <td>no</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   survived  pclass     sex   age  sibsp  parch     fare embarked  class  \\\n",
       "0         0       3    male  22.0      1      0   7.2500        S  Third   \n",
       "1         1       1  female  38.0      1      0  71.2833        C  First   \n",
       "2         1       3  female  26.0      0      0   7.9250        S  Third   \n",
       "3         1       1  female  35.0      1      0  53.1000        S  First   \n",
       "4         0       3    male  35.0      0      0   8.0500        S  Third   \n",
       "\n",
       "     who  adult_male deck  embark_town alive  alone  \n",
       "0    man        True  NaN  Southampton    no  False  \n",
       "1  woman       False    C    Cherbourg   yes  False  \n",
       "2  woman       False  NaN  Southampton   yes   True  \n",
       "3  woman       False    C  Southampton   yes  False  \n",
       "4    man        True  NaN  Southampton    no   True  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "titanic = sns.load_dataset('titanic')\n",
    "titanic.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "pclass  survived\n",
       "1       0            80\n",
       "        1           136\n",
       "2       0            97\n",
       "        1            87\n",
       "3       0           372\n",
       "        1           119\n",
       "dtype: int64"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "PclassSurv = titanic.groupby(['pclass', 'survived'])\n",
    "PclassSurv.size()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>survived</th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>All</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>pclass</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>80</td>\n",
       "      <td>136</td>\n",
       "      <td>216</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>97</td>\n",
       "      <td>87</td>\n",
       "      <td>184</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>372</td>\n",
       "      <td>119</td>\n",
       "      <td>491</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>All</th>\n",
       "      <td>549</td>\n",
       "      <td>342</td>\n",
       "      <td>891</td>\n",
       "    </tr>\n",
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      "text/plain": [
       "survived    0    1  All\n",
       "pclass                 \n",
       "1          80  136  216\n",
       "2          97   87  184\n",
       "3         372  119  491\n",
       "All       549  342  891"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.crosstab(titanic.pclass, titanic.survived,margins=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>survived</th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>All</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>pclass</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3</td>\n",
       "      <td>91</td>\n",
       "      <td>94</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>6</td>\n",
       "      <td>70</td>\n",
       "      <td>76</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>72</td>\n",
       "      <td>72</td>\n",
       "      <td>144</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>All</th>\n",
       "      <td>81</td>\n",
       "      <td>233</td>\n",
       "      <td>314</td>\n",
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      "text/plain": [
       "survived   0    1  All\n",
       "pclass                \n",
       "1          3   91   94\n",
       "2          6   70   76\n",
       "3         72   72  144\n",
       "All       81  233  314"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "WomenOnly = titanic[titanic[\"sex\"]==\"female\"]\n",
    "pd.crosstab(WomenOnly.pclass, WomenOnly.survived,margins=True)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "------\n",
    "\n",
    "**Test the claim that the survival chances of women in 1st and 2nd class were pretty much the same.**\n",
    "\n",
    "1. Write down the Null hypothesis and test statistic\n",
    "2. Write code that generates permutation samples from two data sets\n",
    "3. Generate many **permutation replicates** for the relevant Titanic subset\n",
    "4. Compute a p-value"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We could choose alpha = 0.05, but keep in mind the following\n",
    "- would you step into a plane that has a 5% crash probability ?\n",
    "- Would you buy a drug that has a 5% chance of severe side effects ?\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**What is the difference between these two methods (bootstrap, permutation) ?**\n",
    "\n",
    "Testing the hypothesis that two samples have the same distribution may be done with a bootstrap test, but a permutation test is preferred because it is more accurate (exact, in fact). But a permutation test is not as versatile as the bootstrap. \n",
    "\n",
    "We often want to test the hypothesis that population A and population B have the same mean, but not necessarily the same distribution. This is difficult with a permutation test as it assumes **exchangeability**.\n",
    "\n",
    "We will get back to this topic!\n",
    "\n",
    "[More info..](https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20150001882.pdf)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "------\n",
    "\n",
    "## 2-sample t test\n",
    "\n",
    "Of course there is an equivalent fully parametric 2-sample test, the t-test.\n",
    "\n",
    "We first read in the [The National Survey of Family Growth](https://greenteapress.com/thinkstats2/html/thinkstats2002.html#sec7) data from the [think stats book](https://greenteapress.com/wp/think-stats-2e/).\n",
    "\n",
    "Look at section 1.7 for a description of the variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "#preg = pd.read_hdf('data/pregNSFG.h5', 'df')\n",
    "preg = pd.read_csv('data/pregNSFG.csv.gz', compression='gzip')\n",
    "#only look at live births\n",
    "live = preg[preg.outcome == 1]\n",
    "\n",
    "#define first babies\n",
    "firsts = live[live.birthord == 1]\n",
    "\n",
    "#and all others\n",
    "others = live[live.birthord != 1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "p-value:           0.167554\n",
       "test statistic:    1.380215\n",
       "dtype: float64"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tRes = stats.ttest_ind(firsts.prglngth.values, others.prglngth.values)\n",
    "p = pd.Series([tRes.pvalue,tRes.statistic], index = ['p-value:', 'test statistic:'])\n",
    "p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "p-value:           0.168528\n",
       "test statistic:    1.377059\n",
       "dtype: float64"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#ttest_ind often underestimates p for unequal variances:\n",
    "tRes = stats.ttest_ind(firsts.prglngth.values, others.prglngth.values, equal_var = False)\n",
    "p = pd.Series([tRes.pvalue,tRes.statistic], index = ['p-value:', 'test statistic:'])\n",
    "p"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Can you reproduce the first p-value from the [test statistic](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.t.html) ?**"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "--------------------------------------------------------\n",
    "\n",
    "## Random Walks\n",
    "\n",
    "An illustrative application of basic stochastic concepts in binary processes is the simulation of random walks. Let’s first consider a simple random walk starting at 0 with steps of 1 and -1 occurring with equal probability ($p = 0.5$)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nsteps = 10000\n",
    "draws = np.random.randint(0, 2, size=nsteps)\n",
    "steps = np.where(draws > 0, 1, -1)\n",
    "walk = steps.cumsum() # random walk !\n",
    "fig = plt.figure(); ax = fig.add_subplot(1, 1, 1)\n",
    "ax.plot(walk, linewidth=0.5)\n",
    "ax.grid()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Extra Credit**\n",
    "\n",
    "A more complicated statistic is the first crossing time, the step at which the random walk reaches a particular value. Here we might want to know how long it took the random walk to get at least 10 steps away from the origin 0 in either direction.\n",
    "np.abs(walk) >= 10 gives us a boolean array indicating where the walk has reached or exceeded 10, but we want the index of the first 10 or -10. This can be computed using argmax, which returns the first index of the maximum value in the boolean array (True is the maximum value):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "57"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(np.abs(walk) >= 10).argmax()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "-------\n",
    "\n",
    "### Simulating Many Random Walks at Once\n",
    "\n",
    "If your goal was to simulate many random walks, say 5,000 of them, you can generate all of the random walks with minor modifications to the above code. The numpy.random functions if passed a 2-tuple will generate a 2D array of draws, and we can compute the cumulative sum across the rows to compute all 5,000 random walks in one shot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "nwalks = 5000\n",
    "nsteps = 10000\n",
    "draws = np.random.randint(0, 2, size=(nwalks, nsteps)) # 0 or 1\n",
    "steps = np.where(draws > 0, 1, -1)\n",
    "walks = steps.cumsum(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5000, 10000)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "walks.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "nwalks = 5000\n",
    "nsteps = 10000\n",
    "steps = random.choice([-1,1], size=(nwalks, nsteps), p=(0.52,0.48)) # 0 or 1\n",
    "#steps = np.where(draws > 0, 1, 0)\n",
    "#steps = np.where(np.random.rand() <= 0.1,1,-1)\n",
    "\n",
    "walks = steps.cumsum(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5000, 10000)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "walks.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n = 100: 9.813276720851196\n",
      "n = 200: 13.944520449266085\n",
      "n = 400: 20.019379666712954\n",
      "n = 1600: 39.25214456510624\n"
     ]
    }
   ],
   "source": [
    "#compute stdevs at n= 100, 200, 400, 1600:\n",
    "print(\"n = 100:\", str(np.std(walks[:,99])))\n",
    "print(\"n = 200:\", str(np.std(walks[:,199])))\n",
    "print(\"n = 400:\", str(np.std(walks[:,399])))\n",
    "print(\"n = 1600:\", str(np.std(walks[:,1599])))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(1, 1, 1)\n",
    "\n",
    "ax.plot(walks[1,:], 'k', label='one', linewidth=0.25)\n",
    "ax.plot(walks[2,:], label='two', linestyle ='--', linewidth=0.25)\n",
    "ax.plot(walks[3,:],  label='three', linestyle ='--', linewidth=0.25)\n",
    "ax.plot(walks[4,:],  label='four', linestyle ='--', linewidth=0.25)\n",
    "ax.grid()\n",
    "\n",
    "#a very useless legend just because we can\n",
    "ax.legend(loc='best');"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "-------\n",
    "\n",
    "### The $\\sqrt{n}$ law again !\n",
    "\n",
    "Compute the variance and/or standard deviation at times $1000, 4000, 9000$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "std_1000: 18.920595808800524\n",
      "std_4000: 38.202094719530756\n",
      "std_9000: 55.862619130864246\n"
     ]
    }
   ],
   "source": [
    "print('std_1000:', np.std(walks[:,1000]))\n",
    "print('std_4000:', np.std(walks[:,4000]))\n",
    "print('std_9000:', np.std(walks[:,9000]))"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Extra Credit**\n",
    "\n",
    "Out of these walks, let’s compute the minimum crossing time to 30 or -30. This is slightly tricky because not all 5,000 of them reach 30. We can check this using the *any* method.\n",
    "\n",
    "We can then use this boolean array to select out the rows of walks that actually cross the absolute 30 level and call argmax across axis 1 to get the crossing times:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "36.620"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hits30 = (np.abs(walks) >= 30).any(1)\n",
    "hits30\n",
    "hits30.sum() # Number that hit 30 or -30\n",
    "\n",
    "crossing_times = (np.abs(walks[hits30]) >= 30).argmax(1)\n",
    "crossing_times.mean()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "-------\n",
    "\n",
    "## Tasks\n",
    "\n",
    "1. Compute the stdev for multiples of 100 iterations and find a pattern\n",
    "2. Repeat for \"biased\" random walks, where $p \\neq 0.5$. Try $p = 0.1$ and $p = 0.9$\n",
    "3. Learn\n",
    "    * the analytic formular for variance/stdev of coin flips\n",
    "    * the actual distribution (chap 3.4 in https://www.openintro.org/stat/)\n",
    "    * its approximation \n",
    "4. Complete the labeling of the two axis (with the help of https://codeandstats.shinyapps.io/binomialtails/)\n",
    " ![BinomialTails](figures/BinomialTails.png)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "--------\n",
    "\n",
    "### Binomial Probability Distribution\n",
    "\n",
    "1. Explore the *binom* function from scipy.stats\n",
    "\n",
    "2. Size matters: insurance company A insures 100 cars, company B 400 cars. The probability of a car being stolen is 10%. Compute the probabilities that more than 15% of the respective fleets are stolen.\n",
    "\n",
    "4. Faced with a mutliple choice test containing 20 question with 4 choices each you decide in desparation to just guess all answers. What is the probability that you will pass, i.e. get at least 10 correct answers?\n",
    "\n",
    "5. Think about nonparametric versions of the above answers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    " from scipy.stats import binom"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "--------\n",
    "\n",
    "### A/B Testing\n",
    "\n",
    "1. Perform a permutation test on the DataCamp example:\n",
    "\n",
    "<div>\n",
    "<img src=\"figures/DC_ABtest.png\" width=\"400\"/>\n",
    "</div>"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "------\n",
    "\n",
    "**What does A/B testing have to do with random walks?**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Construct arrays of data: campaigns A and B\n",
    "clickthroughA = np.array([True] * 45 + [False] * (500-45))\n",
    "clickthroughB = np.array([True] * 67 + [False] * (500-67))\n",
    "\n",
    "obsDiff = np.mean(clickthroughB)-np.mean(clickthroughA)\n",
    "\n",
    "# Acquire permutation samples: perm_replicates\n",
    "perm_replicates = draw_perm_reps(clickthroughB, clickthroughA, diff_of_means, 10000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.016"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#p-value:\n",
    "np.mean(perm_replicates >= obsDiff)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Construct arrays of data: campaigns A and B\n",
    "clickthroughA = np.array([True] * 45 + [False] * (500-45))\n",
    "clickthroughB = np.array([True] * 67 + [False] * (500-67))\n",
    "\n",
    "obsDiff = np.mean(clickthroughB)-np.mean(clickthroughA)\n",
    "\n",
    "# Acquire permutation samples: perm_replicates\n",
    "perm_replicates = draw_perm_reps(clickthroughB, clickthroughA, diff_of_means, 10000)\n",
    "\n",
    "plt.hist(perm_replicates)\n",
    "plt.vlines(obsDiff,0,3000,colors=\"red\")\n",
    "plt.vlines(-obsDiff,0,3000, colors=\"red\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "hide_input": false,
  "kernelspec": {
   "display_name": "Python 3.9.0 64-bit",
   "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": "3.9.0"
  },
  "varInspector": {
   "cols": {
    "lenName": 16,
    "lenType": 16,
    "lenVar": 40
   },
   "kernels_config": {
    "python": {
     "delete_cmd_postfix": "",
     "delete_cmd_prefix": "del ",
     "library": "var_list.py",
     "varRefreshCmd": "print(var_dic_list())"
    },
    "r": {
     "delete_cmd_postfix": ") ",
     "delete_cmd_prefix": "rm(",
     "library": "var_list.r",
     "varRefreshCmd": "cat(var_dic_list()) "
    }
   },
   "types_to_exclude": [
    "module",
    "function",
    "builtin_function_or_method",
    "instance",
    "_Feature"
   ],
   "window_display": false
  },
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