07. AB Testing.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Outline for A/B Tests\n",
    "\n",
    "* Set up the experiment.\n",
    "* Run the test and record the success rate for each group.\n",
    "* Plot the distribution of the difference between the two samples.\n",
    "* Calculate the statistical power.\n",
    "* Evaluate how sample size affects A/B tests."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem Statement\n",
    "\n",
    "We will run an A/B test for a hypothetical company that is trying to increase the amount of users that sign up for a premium account. The goal of running an A/B test is to evaluate if a change in a website will lead to improved performance in a specific metric. You may decide to test very simple alternatives such as changing the look of a single button on a webpage or testing different layouts and headlines. You could also run an A/B test on multi-step processes which may have many differences. Examples of this include the steps required in signing up a new user or processing the sale on an online marketplace"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Baseline Conversion Rate and Lift\n",
    "\n",
    "Before running the test, we will know the baseline conversion rate and the desired lift or increase in signups that we would like to test. The baseline conversion rate is the current rate at which we sign up new users under the existing design.\n",
    "    * For our example, we want to use our test to confirm that the changes we make to our signup process will result in atleast a 2% increase in our sign up rate. We currently sign up 10 out of 100 users who are offered a premium account."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy.stats as scs\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# code in Python\n",
    "\n",
    "# baseline conversion rate\n",
    "bcr = 0.10 \n",
    "\n",
    "# difference between the groups\n",
    "d_hat = 0.02 "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Control Group (A) and Test Group (B)\n",
    "\n",
    "Typically, the total number of users participating in the A/B test make up a small percentage of the total amount of users. Users are randomly selected and assigned to either a control group or a test group. The sample size that you decide on will determine how long you might have to wait until you have collected enough.\n",
    "    * For example, websites with large audiences may be able to collect enough data very quickly, while other websites may have to wait a number of weeks. There are some events that happen rarely even for high-traffic websites, so determining the necessary sample size will inform how soon you can assess your experiment and move on to improving other metrics."
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "Initially, we will collect 1000 users for each group and serve the current signup page to the control group and a new signup page to the test group."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# A is control\n",
    "N_A = 1000\n",
    "\n",
    "# B is test\n",
    "N_B = 1000"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Run the Test\n",
    "Because this is a hypothetical example, we will need “fake” data to work on. So, we will generate some random data for our simulation. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "def generate_data(N_A, N_B, p_A, p_B, days=None, control_label='A',\n",
    "                  test_label='B'):\n",
    "    # initiate empty container\n",
    "    data = []\n",
    "\n",
    "    # total amount of rows in the data\n",
    "    N = N_A + N_B\n",
    "\n",
    "    # distribute events based on proportion of group size\n",
    "    group_bern = scs.bernoulli(N_A / (N_A + N_B))\n",
    "\n",
    "    # initiate bernoulli distributions from which to randomly sample\n",
    "    A_bern = scs.bernoulli(p_A)\n",
    "    B_bern = scs.bernoulli(p_B)\n",
    "\n",
    "    for idx in range(N):\n",
    "        # initite empty row\n",
    "        row = {}\n",
    "        # for 'ts' column\n",
    "        if days is not None:\n",
    "            if type(days) == int:\n",
    "                row['ts'] = idx // (N // days)\n",
    "            else:\n",
    "                raise ValueError(\"Provide an integer for the days parameter.\")\n",
    "                \n",
    "        # assign group based on 50/50 probability\n",
    "        row['group'] = group_bern.rvs()\n",
    "\n",
    "        if row['group'] == 0:\n",
    "            # assign conversion based on provided parameters\n",
    "            row['converted'] = A_bern.rvs()\n",
    "        else:\n",
    "            row['converted'] = B_bern.rvs()\n",
    "        # collect row into data container\n",
    "        data.append(row)\n",
    "\n",
    "    # convert data into pandas dataframe\n",
    "    df = pd.DataFrame(data)\n",
    "\n",
    "    # transform group labels of 0s and 1s to user-defined group labels\n",
    "    df['group'] = df['group'].apply(\n",
    "        lambda x: control_label if x == 0 else test_label)\n",
    "\n",
    "    return df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2000, 2)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# lets use the above function and generate a sample of data for our ab testing\n",
    "ab_data = generate_data(N_A, N_B, bcr, d_hat)\n",
    "\n",
    "# lets check the shape of the data\n",
    "ab_data.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>group</th>\n",
       "      <th>converted</th>\n",
       "    </tr>\n",
       "  </thead>\n",
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       "      <th>0</th>\n",
       "      <td>A</td>\n",
       "      <td>0</td>\n",
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       "      <th>1</th>\n",
       "      <td>A</td>\n",
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       "      <th>2</th>\n",
       "      <td>B</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>B</td>\n",
       "      <td>0</td>\n",
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       "      <th>4</th>\n",
       "      <td>B</td>\n",
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      "text/plain": [
       "  group  converted\n",
       "0     A          0\n",
       "1     A          0\n",
       "2     B          0\n",
       "3     B          0\n",
       "4     B          0"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# lets check the head of the data\n",
    "ab_data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "model_id": "750d5750d00f4fd0a40c906ad826a57d",
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      },
      "text/plain": [
       "interactive(children=(Dropdown(description='column', options=('group', 'converted'), value='group'), Output())…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# lets also check the distribution of values in both the column\n",
    "\n",
    "from ipywidgets import interact\n",
    "from ipywidgets import interact_manual\n",
    "\n",
    "@interact\n",
    "def check(column = ab_data.columns):\n",
    "    return ab_data[column].value_counts()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**The converted column indicates whether a user signed up for the premium service or not with a 1 or 0, respectively. The A group will be used for our control group and the B group will be our test group.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>converted</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>group</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>A</th>\n",
       "      <td>87</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>B</th>\n",
       "      <td>22</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       converted\n",
       "group           \n",
       "A             87\n",
       "B             22"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# using pivot table to check how many people got converted to premium membership\n",
    "\n",
    "ab_summary = ab_data.pivot_table(values='converted', index='group', aggfunc=np.sum)\n",
    "ab_summary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>converted</th>\n",
       "      <th>total</th>\n",
       "      <th>rate</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>group</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "  <tbody>\n",
       "    <tr>\n",
       "      <th>A</th>\n",
       "      <td>87</td>\n",
       "      <td>1023</td>\n",
       "      <td>8.504399</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>B</th>\n",
       "      <td>22</td>\n",
       "      <td>977</td>\n",
       "      <td>2.251791</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       converted  total      rate\n",
       "group                            \n",
       "A             87   1023  8.504399\n",
       "B             22    977  2.251791"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# add additional columns to the pivot table\n",
    "\n",
    "# adding the total number of people\n",
    "ab_summary['total'] = ab_data.pivot_table(values='converted', index='group', aggfunc=lambda x: len(x))\n",
    "\n",
    "# adding the rate of conversion\n",
    "ab_summary['rate'] = ab_data.pivot_table(values='converted', index='group')\n",
    "ab_summary['rate'] = ab_summary['rate'].apply(lambda x: x*100)\n",
    "ab_summary"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* ```It looks like the difference in conversion rates between the two groups is almost 6% which is greater than the lift we initially wanted of 0.02. This is a good sign but this is not enough evidence for us to confidently go with the new design. At this point we have not measured how confident we are in this result. This can be mitigated by looking at the distributions of the two groups.```\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Compare the Two Groups\n",
    "\n",
    "We can compare the two groups by plotting the distribution of the control group and calculating the probability of getting the result from our test group. We can assume that the distribution for our control group is binomial because the data is a series of Bernoulli trials, where each trial only has two possible outcomes (similar to a coin flip)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(12,6))\n",
    "plt.style.use('fivethirtyeight')\n",
    "\n",
    "A_converted = 87\n",
    "A_total = 1023\n",
    "A_cr = 0.085\n",
    "B_cr = 0.0225\n",
    "\n",
    "x = np.linspace(A_converted-49, A_converted+50, 100)\n",
    "y = scs.binom(A_total, A_cr).pmf(x)\n",
    "ax.bar(x, y, alpha=0.5)\n",
    "ax.axvline(x=B_cr * A_total, c='blue', alpha=0.75, linestyle='--')\n",
    "\n",
    "plt.title('Distribution of control group and probability of getting result from test group', fontsize = 12)\n",
    "plt.xlabel('converted')\n",
    "plt.ylabel('probability')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* The distribution for the control group is shown in blue and the result from the test group is indicated by the blue dashed line.\n",
    "\n",
    "* We can see that the probability of getting the result from the test group was very low. \n",
    "\n",
    "* However, the probability does not convey the confidence level of the results.\n",
    "\n",
    "* It does not take the sample size of our test group into consideration. \n",
    "\n",
    "Intuitively, we would feel more confident in our results as our sample sizes grow larger. Let’s continue and plot the test group results as a binomial distribution and compare the distributions against each other."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(12,6))\n",
    "\n",
    "p_A = 0.1 # same as bcr\n",
    "p_B = 0.02 # same as d_hat\n",
    "B_converted = 22\n",
    "B_total = 977\n",
    "\n",
    "xA = np.linspace(A_converted-49, A_converted+50, 100)\n",
    "yA = scs.binom(A_total, p_A).pmf(xA)\n",
    "ax.bar(xA, yA, alpha=0.5)\n",
    "xB = np.linspace(B_converted-49, B_converted+50, 100)\n",
    "yB = scs.binom(B_total, p_B).pmf(xB)\n",
    "ax.bar(xB, yB, alpha=0.5)\n",
    "plt.xlabel('converted')\n",
    "plt.ylabel('probability')\n",
    "plt.suptitle('Binomial Distribution')\n",
    "plt.title('Control Group(red) and Test Group(blue)')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* We can see that the control group converted more users than the test group.\n",
    "* We can also see that the peak of the control group results is lower than the control group. \n",
    "\n",
    "**How do we interpret the difference in peak probability?**\n",
    "\n",
    "    * We should focus instead on the conversion rate so that we have an apples-to-apples comparison. In order to calculate this, we need to standardize the data and compare the probability of successes, p, for each group."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'PDF')"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# standard error of the mean for both groups\n",
    "SE_A = np.sqrt(p_A * (1-p_A)) / np.sqrt(A_total)\n",
    "SE_B = np.sqrt(p_B * (1-p_B)) / np.sqrt(B_total)\n",
    "\n",
    "# plot the null and alternative hypothesis\n",
    "fig, ax = plt.subplots(figsize=(12,6))\n",
    "x = np.linspace(0, .2, 100)\n",
    "yA = scs.norm(p_A, SE_A).pdf(x)\n",
    "\n",
    "ax.plot(xA, yA)\n",
    "ax.axvline(x=p_A, c='red', alpha=0.5, linestyle='--')\n",
    "\n",
    "yB = scs.norm(p_B, SE_B).pdf(x)\n",
    "ax.plot(xB, yB)\n",
    "ax.axvline(x=p_B, c='blue', alpha=0.5, linestyle='--')\n",
    "\n",
    "plt.xlabel('Converted Proportion')\n",
    "plt.ylabel('PDF')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import stats as scs\n",
    "from scipy.stats import sem\n",
    "\n",
    "def abplot(N_a, bcr, d_hat, sig_level=0.05, show_power=False,\n",
    "           show_alpha=False, show_beta=False, show_p_value=False,\n",
    "           show_legend=True):\n",
    "    \"\"\"Example plot of AB test\n",
    "    Example:\n",
    "        abplot(n=4000, bcr=0.11, d_hat=0.03)\n",
    "    Parameters:\n",
    "        n (int): total sample size for both control and test groups (N_A + N_B)\n",
    "        bcr (float): base conversion rate; conversion rate of control\n",
    "        d_hat: difference in conversion rate between the control and test\n",
    "            groups, sometimes referred to as **minimal detectable effect** when\n",
    "            calculating minimum sample size or **lift** when discussing\n",
    "            positive improvement desired from launching a change.\n",
    "    Returns:\n",
    "        None: the function plots an AB test as two distributions for\n",
    "        visualization purposes\n",
    "    \"\"\"\n",
    "    # create a plot object\n",
    "    fig, ax = plt.subplots(figsize=(12, 6))\n",
    "\n",
    "    # define parameters to find pooled standard error\n",
    "    X_A = bcr * N_A\n",
    "    X_B = (bcr + d_hat) * N_B\n",
    "    stderr = sem(N_A, N_B, X_A, X_B)\n",
    "\n",
    "    # plot the distribution of the null and alternative hypothesis\n",
    "    plot_null(ax, stderr)\n",
    "    plot_alt(ax, stderr, d_hat)\n",
    "\n",
    "    # set extent of plot area\n",
    "    ax.set_xlim(-8 * stderr, 8 * stderr)\n",
    "\n",
    "    # shade areas according to user input\n",
    "    if show_power:\n",
    "        show_area(ax, d_hat, stderr, sig_level, area_type='power')\n",
    "    if show_alpha:\n",
    "        show_area(ax, d_hat, stderr, sig_level, area_type='alpha')\n",
    "    if show_beta:\n",
    "        show_area(ax, d_hat, stderr, sig_level, area_type='beta')\n",
    "\n",
    "    # show p_value based on the binomial distributions for the two groups\n",
    "    if show_p_value:\n",
    "        null = ab_dist(stderr, 'control')\n",
    "        p_value = p_val(N_A, N_B, bcr, bcr+d_hat)\n",
    "        ax.text(3 * stderr, null.pdf(0),\n",
    "                'p-value = {0:.3f}'.format(p_value),\n",
    "                fontsize=12, ha='left')\n",
    "\n",
    "    # option to show legend\n",
    "    if show_legend:\n",
    "        plt.legend()\n",
    "\n",
    "    plt.xlabel('d')\n",
    "    plt.ylabel('PDF')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "nan_policy must be one of {'propagate', 'raise', 'omit'}",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-72-554b44cf6f67>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      2\u001b[0m \u001b[0mbcr\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mp_A\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      3\u001b[0m \u001b[0md_hat\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mp_B\u001b[0m \u001b[1;33m-\u001b[0m \u001b[0mp_A\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 4\u001b[1;33m \u001b[0mabplot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mbcr\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0md_hat\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;32m<ipython-input-71-5282bc22557f>\u001b[0m in \u001b[0;36mabplot\u001b[1;34m(n, bcr, d_hat, sig_level, show_power, show_alpha, show_beta, show_p_value, show_legend)\u001b[0m\n\u001b[0;32m     25\u001b[0m     \u001b[0mX_A\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mbcr\u001b[0m \u001b[1;33m*\u001b[0m \u001b[0mN_A\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     26\u001b[0m     \u001b[0mX_B\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mbcr\u001b[0m \u001b[1;33m+\u001b[0m \u001b[0md_hat\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m*\u001b[0m \u001b[0mN_B\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 27\u001b[1;33m     \u001b[0mstderr\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0msem\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mN_A\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mN_B\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mX_A\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mX_B\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     28\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     29\u001b[0m     \u001b[1;31m# plot the distribution of the null and alternative hypothesis\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\users\\roshan\\appdata\\local\\programs\\python\\python36\\lib\\site-packages\\scipy\\stats\\stats.py\u001b[0m in \u001b[0;36msem\u001b[1;34m(a, axis, ddof, nan_policy)\u001b[0m\n\u001b[0;32m   2336\u001b[0m     \u001b[0ma\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0maxis\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0m_chk_asarray\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0ma\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0maxis\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   2337\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 2338\u001b[1;33m     \u001b[0mcontains_nan\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mnan_policy\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0m_contains_nan\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0ma\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mnan_policy\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   2339\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   2340\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[0mcontains_nan\u001b[0m \u001b[1;32mand\u001b[0m \u001b[0mnan_policy\u001b[0m \u001b[1;33m==\u001b[0m \u001b[1;34m'omit'\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\users\\roshan\\appdata\\local\\programs\\python\\python36\\lib\\site-packages\\scipy\\stats\\stats.py\u001b[0m in \u001b[0;36m_contains_nan\u001b[1;34m(a, nan_policy)\u001b[0m\n\u001b[0;32m    250\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[0mnan_policy\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mpolicies\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    251\u001b[0m         raise ValueError(\"nan_policy must be one of {%s}\" %\n\u001b[1;32m--> 252\u001b[1;33m                          ', '.join(\"'%s'\" % s for s in policies))\n\u001b[0m\u001b[0;32m    253\u001b[0m     \u001b[1;32mtry\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    254\u001b[0m         \u001b[1;31m# Calling np.sum to avoid creating a huge array into memory\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mValueError\u001b[0m: nan_policy must be one of {'propagate', 'raise', 'omit'}"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = N_A + N_B\n",
    "bcr = p_A  \n",
    "d_hat = p_B - p_A\n",
    "abplot(n, bcr, d_hat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}