Interactive Python notebook for proportion test simulation study

proportion_test_simulation_study.ipynb

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    "# Proportion test simulation study\n",
    "\n",
    "**Instructions to get started:**\n",
    "\n",
    "1. In the menu, select ``Kernel > Restart & Clear Output``.\n",
    "2. In the menu, select ``Cell > Run All``.\n",
    "3. Scroll down to \"Step 1: Individual Sample\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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   "source": [
    "%matplotlib inline\n",
    "import random\n",
    "import matplotlib.pyplot as plt\n",
    "import ipywidgets as ipw\n",
    "import IPython.display\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "history = []\n",
    "\n",
    "\n",
    "trials_so_far = ipw.widgets.BoundedIntText(\n",
    "    value=0,\n",
    "    min=0,\n",
    "    max=1000000000,\n",
    "    step=1,\n",
    "    description='Sims so far:',\n",
    "    disabled=True\n",
    ")\n",
    "\n",
    "addl_trials_input = ipw.widgets.BoundedIntText(\n",
    "    value=10000,\n",
    "    min=0,\n",
    "    max=1000000,\n",
    "    step=1,\n",
    "    description=\"Add'l sims:\",\n",
    "    disabled=False\n",
    ")\n",
    "\n",
    "def single_sample():\n",
    "    global probability\n",
    "    global sample_size\n",
    "    probability = prob_input.value\n",
    "    sample_size = sample_size_input.value\n",
    "    return sum([int(random.random() + probability) for j in range(0, sample_size)])\n",
    "\n",
    "def sample_widget_output():\n",
    "    global probability\n",
    "    global sample_size\n",
    "    probability = prob_input.value\n",
    "    sample_size = sample_size_input.value\n",
    "    global history\n",
    "    history.append(single_sample())\n",
    "    return 'In the sample of size n = {:d}, with a probability of {:f} of \"success\" each trial, we had {} \"successes\".'.format(\n",
    "        sample_size, probability, history[-1])\n",
    "\n",
    "sample_size_input = ipw.widgets.BoundedIntText(\n",
    "    value=20,\n",
    "    min=0,\n",
    "    max=1000,\n",
    "    step=1,\n",
    "    description='Sample size:',\n",
    "    disabled=False\n",
    ")\n",
    "\n",
    "prob_input = ipw.widgets.FloatSlider(\n",
    "    value=0.5,\n",
    "    min=0,\n",
    "    max=1,\n",
    "    step=0.0001,\n",
    "    description='Prob of \"Success\":',\n",
    "    disabled=False,\n",
    "    continuous_update=False,\n",
    "    orientation='horizontal',\n",
    "    readout=True,\n",
    "    readout_format='.1f',\n",
    ")\n",
    "\n",
    "sample_button = ipw.widgets.Button(description=\"Take a sample\")\n",
    "clear_history_button = ipw.widgets.Button(description=\"Clear history\")\n",
    "run_simulation_button = ipw.widgets.Button(description=\"Run simulations\")\n",
    "\n",
    "def sample_button_action(b):\n",
    "    global probability\n",
    "    global sample_size\n",
    "    probability = prob_input.value\n",
    "    sample_size = sample_size_input.value\n",
    "    trials_so_far.value += 1\n",
    "    addl_trials_input.value -= 1\n",
    "    print(sample_widget_output())\n",
    "    \n",
    "def clear_history_action(b):\n",
    "    global history\n",
    "    history = []\n",
    "    IPython.display.clear_output()\n",
    "    trials_so_far.value = 0\n",
    "    addl_trials_input.value = 1000\n",
    "    print(\"History cleared.\")\n",
    "\n",
    "\n",
    "def run_simulation_button_action(b):\n",
    "    global probability\n",
    "    global sample_size\n",
    "    global history\n",
    "    num_trials = addl_trials_input.value\n",
    "    for j in range(0, num_trials):\n",
    "        history.append(single_sample())\n",
    "        trials_so_far.value += 1\n",
    "        addl_trials_input.value -= 1\n",
    "    history_min = min(history)\n",
    "    history_max = max(history)\n",
    "    plt.hist(history, bins=np.arange(history_min, history_max + 2,1))\n",
    "    history_counts = [history.count(k) for k in range(0, sample_size + 1)]\n",
    "    scale = max(history_counts)\n",
    "    for j in range(history_min, history_max + 1):\n",
    "        plt.text(j + 0.5, -scale*0.05, str(j))\n",
    "        plt.text(j + 0.25, history_counts[j]+scale*0.05, str(history_counts[j]))\n",
    "    plt.grid(True)\n",
    "    fig = plt.gcf()\n",
    "    ax = plt.gca()\n",
    "    ax.get_xaxis().set_ticks([])\n",
    "    fig.set_size_inches(15, 5)\n",
    "    plt.show()\n",
    "    hc_df = pd.DataFrame(history_counts, columns=[\"Number of simulations\"])\n",
    "    with pd.option_context('display.max_rows', 1000, 'display.max_columns', 5):\n",
    "        IPython.display.display(hc_df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Step 1: Individual sample\n",
    "\n",
    "1. Specify the sample size and probability of \"success\" each trial.\n",
    "2. Click \"Take a sample\" a few times to simulate a few samples. The computer will report the results.\n",
    "3. When you are ready to take a massive number of samples and plot a histogram of all the simulated samples, scroll down to \"Step 2: Run a simulation study\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "IPython.display.display(sample_size_input)\n",
    "IPython.display.display(prob_input)\n",
    "IPython.display.display(sample_button)\n",
    "IPython.display.display(clear_history_button)\n",
    "\n",
    "sample_button.on_click(sample_button_action)\n",
    "clear_history_button.on_click(clear_history_action)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Step 2: Run a simulation study\n",
    "\n",
    "1. Specify how many additional samples you want. The default is to end up with 10,000 simulations overall.\n",
    "2. Click on \"Run simulations\" and wait a few minutes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "IPython.display.display(trials_so_far)\n",
    "IPython.display.display(addl_trials_input)\n",
    "IPython.display.display(run_simulation_button)\n",
    "\n",
    "run_simulation_button.on_click(run_simulation_button_action)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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