{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercise 4.2: Hacker stats with bee sperm data\n",
    "\n",
    "<hr>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Neonicotinoid pesticides are thought to have inadvertent effects on service-providing insects such as bees. A study of this was [featured in the New York Times](http://www.nytimes.com/2016/07/29/science/neonicotinoid-insecticide-bee-sperm.html) in 2016. The original paper is [Straub, et al.,  Proc. Royal Soc. B 283(1835): 20160506](http://dx.doi.org/10.1098/rspb.2016.0506). Straub and coworkers put their [data in the Dryad repository](http://dx.doi.org/10.5061/dryad.bs515), which means we can work with it!\n",
    "\n",
    "(Do you see a trend here? If you want people to think deeply about your results, explore them, learn from them, further science with them, *make your data publicly available.* Strongly encourage the members of your lab to do the same.)\n",
    "\n",
    "We will look at the weight of drones (male bees) using the data set stored in `~/git/bootcamp/data/bee_weight.csv` and the sperm quality of drone bees using the data set stored in `~/git/bootcamp/data/bee_sperm.csv`.\n",
    "\n",
    "**a)** Load the drone weight data in as a Pandas `DataFrame`.  Note that the unit of the weight is milligrams (mg).\n",
    "\n",
    "**b)** Plot ECDFs of the drone weight for control and also for those exposed to pesticide. Do you think there is a clear difference?\n",
    "\n",
    "**c)** Compute the mean drone weight for control and those exposed to pesticide. Compute 95% bootstrap confidence intervals on the mean.\n",
    "\n",
    "**d)** Repeat parts (a)-(c) for drone sperm. Use the `'Quality'` column as your measure. This is defined as the percent of sperm that are alive in a 500 µL sample.\n",
    "\n",
    "**e)** As you have seen in your analysis in part (d), both the control and pesticide treatments have some outliers with very low sperm quality. This can tug heavily on the mean. So, get 95% bootstrap confidence intervals for the *median* sperm quality of the two treatments."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br />"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solution\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "    <div class=\"bk-root\">\n",
       "        <a href=\"https://bokeh.org\" target=\"_blank\" class=\"bk-logo bk-logo-small bk-logo-notebook\"></a>\n",
       "        <span id=\"1002\">Loading BokehJS ...</span>\n",
       "    </div>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "\n",
       "(function(root) {\n",
       "  function now() {\n",
       "    return new Date();\n",
       "  }\n",
       "\n",
       "  const force = true;\n",
       "\n",
       "  if (typeof root._bokeh_onload_callbacks === \"undefined\" || force === true) {\n",
       "    root._bokeh_onload_callbacks = [];\n",
       "    root._bokeh_is_loading = undefined;\n",
       "  }\n",
       "\n",
       "  const JS_MIME_TYPE = 'application/javascript';\n",
       "  const HTML_MIME_TYPE = 'text/html';\n",
       "  const EXEC_MIME_TYPE = 'application/vnd.bokehjs_exec.v0+json';\n",
       "  const CLASS_NAME = 'output_bokeh rendered_html';\n",
       "\n",
       "  /**\n",
       "   * Render data to the DOM node\n",
       "   */\n",
       "  function render(props, node) {\n",
       "    const script = document.createElement(\"script\");\n",
       "    node.appendChild(script);\n",
       "  }\n",
       "\n",
       "  /**\n",
       "   * Handle when an output is cleared or removed\n",
       "   */\n",
       "  function handleClearOutput(event, handle) {\n",
       "    const cell = handle.cell;\n",
       "\n",
       "    const id = cell.output_area._bokeh_element_id;\n",
       "    const server_id = cell.output_area._bokeh_server_id;\n",
       "    // Clean up Bokeh references\n",
       "    if (id != null && id in Bokeh.index) {\n",
       "      Bokeh.index[id].model.document.clear();\n",
       "      delete Bokeh.index[id];\n",
       "    }\n",
       "\n",
       "    if (server_id !== undefined) {\n",
       "      // Clean up Bokeh references\n",
       "      const cmd_clean = \"from bokeh.io.state import curstate; print(curstate().uuid_to_server['\" + server_id + \"'].get_sessions()[0].document.roots[0]._id)\";\n",
       "      cell.notebook.kernel.execute(cmd_clean, {\n",
       "        iopub: {\n",
       "          output: function(msg) {\n",
       "            const id = msg.content.text.trim();\n",
       "            if (id in Bokeh.index) {\n",
       "              Bokeh.index[id].model.document.clear();\n",
       "              delete Bokeh.index[id];\n",
       "            }\n",
       "          }\n",
       "        }\n",
       "      });\n",
       "      // Destroy server and session\n",
       "      const cmd_destroy = \"import bokeh.io.notebook as ion; ion.destroy_server('\" + server_id + \"')\";\n",
       "      cell.notebook.kernel.execute(cmd_destroy);\n",
       "    }\n",
       "  }\n",
       "\n",
       "  /**\n",
       "   * Handle when a new output is added\n",
       "   */\n",
       "  function handleAddOutput(event, handle) {\n",
       "    const output_area = handle.output_area;\n",
       "    const output = handle.output;\n",
       "\n",
       "    // limit handleAddOutput to display_data with EXEC_MIME_TYPE content only\n",
       "    if ((output.output_type != \"display_data\") || (!Object.prototype.hasOwnProperty.call(output.data, EXEC_MIME_TYPE))) {\n",
       "      return\n",
       "    }\n",
       "\n",
       "    const toinsert = output_area.element.find(\".\" + CLASS_NAME.split(' ')[0]);\n",
       "\n",
       "    if (output.metadata[EXEC_MIME_TYPE][\"id\"] !== undefined) {\n",
       "      toinsert[toinsert.length - 1].firstChild.textContent = output.data[JS_MIME_TYPE];\n",
       "      // store reference to embed id on output_area\n",
       "      output_area._bokeh_element_id = output.metadata[EXEC_MIME_TYPE][\"id\"];\n",
       "    }\n",
       "    if (output.metadata[EXEC_MIME_TYPE][\"server_id\"] !== undefined) {\n",
       "      const bk_div = document.createElement(\"div\");\n",
       "      bk_div.innerHTML = output.data[HTML_MIME_TYPE];\n",
       "      const script_attrs = bk_div.children[0].attributes;\n",
       "      for (let i = 0; i < script_attrs.length; i++) {\n",
       "        toinsert[toinsert.length - 1].firstChild.setAttribute(script_attrs[i].name, script_attrs[i].value);\n",
       "        toinsert[toinsert.length - 1].firstChild.textContent = bk_div.children[0].textContent\n",
       "      }\n",
       "      // store reference to server id on output_area\n",
       "      output_area._bokeh_server_id = output.metadata[EXEC_MIME_TYPE][\"server_id\"];\n",
       "    }\n",
       "  }\n",
       "\n",
       "  function register_renderer(events, OutputArea) {\n",
       "\n",
       "    function append_mime(data, metadata, element) {\n",
       "      // create a DOM node to render to\n",
       "      const toinsert = this.create_output_subarea(\n",
       "        metadata,\n",
       "        CLASS_NAME,\n",
       "        EXEC_MIME_TYPE\n",
       "      );\n",
       "      this.keyboard_manager.register_events(toinsert);\n",
       "      // Render to node\n",
       "      const props = {data: data, metadata: metadata[EXEC_MIME_TYPE]};\n",
       "      render(props, toinsert[toinsert.length - 1]);\n",
       "      element.append(toinsert);\n",
       "      return toinsert\n",
       "    }\n",
       "\n",
       "    /* Handle when an output is cleared or removed */\n",
       "    events.on('clear_output.CodeCell', handleClearOutput);\n",
       "    events.on('delete.Cell', handleClearOutput);\n",
       "\n",
       "    /* Handle when a new output is added */\n",
       "    events.on('output_added.OutputArea', handleAddOutput);\n",
       "\n",
       "    /**\n",
       "     * Register the mime type and append_mime function with output_area\n",
       "     */\n",
       "    OutputArea.prototype.register_mime_type(EXEC_MIME_TYPE, append_mime, {\n",
       "      /* Is output safe? */\n",
       "      safe: true,\n",
       "      /* Index of renderer in `output_area.display_order` */\n",
       "      index: 0\n",
       "    });\n",
       "  }\n",
       "\n",
       "  // register the mime type if in Jupyter Notebook environment and previously unregistered\n",
       "  if (root.Jupyter !== undefined) {\n",
       "    const events = require('base/js/events');\n",
       "    const OutputArea = require('notebook/js/outputarea').OutputArea;\n",
       "\n",
       "    if (OutputArea.prototype.mime_types().indexOf(EXEC_MIME_TYPE) == -1) {\n",
       "      register_renderer(events, OutputArea);\n",
       "    }\n",
       "  }\n",
       "\n",
       "  \n",
       "  if (typeof (root._bokeh_timeout) === \"undefined\" || force === true) {\n",
       "    root._bokeh_timeout = Date.now() + 5000;\n",
       "    root._bokeh_failed_load = false;\n",
       "  }\n",
       "\n",
       "  const NB_LOAD_WARNING = {'data': {'text/html':\n",
       "     \"<div style='background-color: #fdd'>\\n\"+\n",
       "     \"<p>\\n\"+\n",
       "     \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n",
       "     \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n",
       "     \"</p>\\n\"+\n",
       "     \"<ul>\\n\"+\n",
       "     \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n",
       "     \"<li>use INLINE resources instead, as so:</li>\\n\"+\n",
       "     \"</ul>\\n\"+\n",
       "     \"<code>\\n\"+\n",
       "     \"from bokeh.resources import INLINE\\n\"+\n",
       "     \"output_notebook(resources=INLINE)\\n\"+\n",
       "     \"</code>\\n\"+\n",
       "     \"</div>\"}};\n",
       "\n",
       "  function display_loaded() {\n",
       "    const el = document.getElementById(\"1002\");\n",
       "    if (el != null) {\n",
       "      el.textContent = \"BokehJS is loading...\";\n",
       "    }\n",
       "    if (root.Bokeh !== undefined) {\n",
       "      if (el != null) {\n",
       "        el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n",
       "      }\n",
       "    } else if (Date.now() < root._bokeh_timeout) {\n",
       "      setTimeout(display_loaded, 100)\n",
       "    }\n",
       "  }\n",
       "\n",
       "\n",
       "  function run_callbacks() {\n",
       "    try {\n",
       "      root._bokeh_onload_callbacks.forEach(function(callback) {\n",
       "        if (callback != null)\n",
       "          callback();\n",
       "      });\n",
       "    } finally {\n",
       "      delete root._bokeh_onload_callbacks\n",
       "    }\n",
       "    console.debug(\"Bokeh: all callbacks have finished\");\n",
       "  }\n",
       "\n",
       "  function load_libs(css_urls, js_urls, callback) {\n",
       "    if (css_urls == null) css_urls = [];\n",
       "    if (js_urls == null) js_urls = [];\n",
       "\n",
       "    root._bokeh_onload_callbacks.push(callback);\n",
       "    if (root._bokeh_is_loading > 0) {\n",
       "      console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n",
       "      return null;\n",
       "    }\n",
       "    if (js_urls == null || js_urls.length === 0) {\n",
       "      run_callbacks();\n",
       "      return null;\n",
       "    }\n",
       "    console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n",
       "    root._bokeh_is_loading = css_urls.length + js_urls.length;\n",
       "\n",
       "    function on_load() {\n",
       "      root._bokeh_is_loading--;\n",
       "      if (root._bokeh_is_loading === 0) {\n",
       "        console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n",
       "        run_callbacks()\n",
       "      }\n",
       "    }\n",
       "\n",
       "    function on_error(url) {\n",
       "      console.error(\"failed to load \" + url);\n",
       "    }\n",
       "\n",
       "    for (let i = 0; i < css_urls.length; i++) {\n",
       "      const url = css_urls[i];\n",
       "      const element = document.createElement(\"link\");\n",
       "      element.onload = on_load;\n",
       "      element.onerror = on_error.bind(null, url);\n",
       "      element.rel = \"stylesheet\";\n",
       "      element.type = \"text/css\";\n",
       "      element.href = url;\n",
       "      console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n",
       "      document.body.appendChild(element);\n",
       "    }\n",
       "\n",
       "    for (let i = 0; i < js_urls.length; i++) {\n",
       "      const url = js_urls[i];\n",
       "      const element = document.createElement('script');\n",
       "      element.onload = on_load;\n",
       "      element.onerror = on_error.bind(null, url);\n",
       "      element.async = false;\n",
       "      element.src = url;\n",
       "      console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n",
       "      document.head.appendChild(element);\n",
       "    }\n",
       "  };\n",
       "\n",
       "  function inject_raw_css(css) {\n",
       "    const element = document.createElement(\"style\");\n",
       "    element.appendChild(document.createTextNode(css));\n",
       "    document.body.appendChild(element);\n",
       "  }\n",
       "\n",
       "  \n",
       "  const js_urls = [\"https://cdn.bokeh.org/bokeh/release/bokeh-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-gl-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-widgets-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-tables-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-mathjax-2.4.2.min.js\"];\n",
       "  const css_urls = [];\n",
       "  \n",
       "\n",
       "  const inline_js = [\n",
       "    function(Bokeh) {\n",
       "      Bokeh.set_log_level(\"info\");\n",
       "    },\n",
       "    function(Bokeh) {\n",
       "    \n",
       "    \n",
       "    }\n",
       "  ];\n",
       "\n",
       "  function run_inline_js() {\n",
       "    \n",
       "    if (root.Bokeh !== undefined || force === true) {\n",
       "      \n",
       "    for (let i = 0; i < inline_js.length; i++) {\n",
       "      inline_js[i].call(root, root.Bokeh);\n",
       "    }\n",
       "    if (force === true) {\n",
       "        display_loaded();\n",
       "      }} else if (Date.now() < root._bokeh_timeout) {\n",
       "      setTimeout(run_inline_js, 100);\n",
       "    } else if (!root._bokeh_failed_load) {\n",
       "      console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n",
       "      root._bokeh_failed_load = true;\n",
       "    } else if (force !== true) {\n",
       "      const cell = $(document.getElementById(\"1002\")).parents('.cell').data().cell;\n",
       "      cell.output_area.append_execute_result(NB_LOAD_WARNING)\n",
       "    }\n",
       "\n",
       "  }\n",
       "\n",
       "  if (root._bokeh_is_loading === 0) {\n",
       "    console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n",
       "    run_inline_js();\n",
       "  } else {\n",
       "    load_libs(css_urls, js_urls, function() {\n",
       "      console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n",
       "      run_inline_js();\n",
       "    });\n",
       "  }\n",
       "}(window));"
      ],
      "application/vnd.bokehjs_load.v0+json": "\n(function(root) {\n  function now() {\n    return new Date();\n  }\n\n  const force = true;\n\n  if (typeof root._bokeh_onload_callbacks === \"undefined\" || force === true) {\n    root._bokeh_onload_callbacks = [];\n    root._bokeh_is_loading = undefined;\n  }\n\n  \n\n  \n  if (typeof (root._bokeh_timeout) === \"undefined\" || force === true) {\n    root._bokeh_timeout = Date.now() + 5000;\n    root._bokeh_failed_load = false;\n  }\n\n  const NB_LOAD_WARNING = {'data': {'text/html':\n     \"<div style='background-color: #fdd'>\\n\"+\n     \"<p>\\n\"+\n     \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n     \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n     \"</p>\\n\"+\n     \"<ul>\\n\"+\n     \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n     \"<li>use INLINE resources instead, as so:</li>\\n\"+\n     \"</ul>\\n\"+\n     \"<code>\\n\"+\n     \"from bokeh.resources import INLINE\\n\"+\n     \"output_notebook(resources=INLINE)\\n\"+\n     \"</code>\\n\"+\n     \"</div>\"}};\n\n  function display_loaded() {\n    const el = document.getElementById(\"1002\");\n    if (el != null) {\n      el.textContent = \"BokehJS is loading...\";\n    }\n    if (root.Bokeh !== undefined) {\n      if (el != null) {\n        el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n      }\n    } else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(display_loaded, 100)\n    }\n  }\n\n\n  function run_callbacks() {\n    try {\n      root._bokeh_onload_callbacks.forEach(function(callback) {\n        if (callback != null)\n          callback();\n      });\n    } finally {\n      delete root._bokeh_onload_callbacks\n    }\n    console.debug(\"Bokeh: all callbacks have finished\");\n  }\n\n  function load_libs(css_urls, js_urls, callback) {\n    if (css_urls == null) css_urls = [];\n    if (js_urls == null) js_urls = [];\n\n    root._bokeh_onload_callbacks.push(callback);\n    if (root._bokeh_is_loading > 0) {\n      console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n      return null;\n    }\n    if (js_urls == null || js_urls.length === 0) {\n      run_callbacks();\n      return null;\n    }\n    console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n    root._bokeh_is_loading = css_urls.length + js_urls.length;\n\n    function on_load() {\n      root._bokeh_is_loading--;\n      if (root._bokeh_is_loading === 0) {\n        console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n        run_callbacks()\n      }\n    }\n\n    function on_error(url) {\n      console.error(\"failed to load \" + url);\n    }\n\n    for (let i = 0; i < css_urls.length; i++) {\n      const url = css_urls[i];\n      const element = document.createElement(\"link\");\n      element.onload = on_load;\n      element.onerror = on_error.bind(null, url);\n      element.rel = \"stylesheet\";\n      element.type = \"text/css\";\n      element.href = url;\n      console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n      document.body.appendChild(element);\n    }\n\n    for (let i = 0; i < js_urls.length; i++) {\n      const url = js_urls[i];\n      const element = document.createElement('script');\n      element.onload = on_load;\n      element.onerror = on_error.bind(null, url);\n      element.async = false;\n      element.src = url;\n      console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n      document.head.appendChild(element);\n    }\n  };\n\n  function inject_raw_css(css) {\n    const element = document.createElement(\"style\");\n    element.appendChild(document.createTextNode(css));\n    document.body.appendChild(element);\n  }\n\n  \n  const js_urls = [\"https://cdn.bokeh.org/bokeh/release/bokeh-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-gl-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-widgets-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-tables-2.4.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-mathjax-2.4.2.min.js\"];\n  const css_urls = [];\n  \n\n  const inline_js = [\n    function(Bokeh) {\n      Bokeh.set_log_level(\"info\");\n    },\n    function(Bokeh) {\n    \n    \n    }\n  ];\n\n  function run_inline_js() {\n    \n    if (root.Bokeh !== undefined || force === true) {\n      \n    for (let i = 0; i < inline_js.length; i++) {\n      inline_js[i].call(root, root.Bokeh);\n    }\n    if (force === true) {\n        display_loaded();\n      }} else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(run_inline_js, 100);\n    } else if (!root._bokeh_failed_load) {\n      console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n      root._bokeh_failed_load = true;\n    } else if (force !== true) {\n      const cell = $(document.getElementById(\"1002\")).parents('.cell').data().cell;\n      cell.output_area.append_execute_result(NB_LOAD_WARNING)\n    }\n\n  }\n\n  if (root._bokeh_is_loading === 0) {\n    console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n    run_inline_js();\n  } else {\n    load_libs(css_urls, js_urls, function() {\n      console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n      run_inline_js();\n    });\n  }\n}(window));"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "import iqplot\n",
    "\n",
    "import bokeh.io\n",
    "import bokeh.plotting\n",
    "\n",
    "bokeh.io.output_notebook()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**a)** After inspecting the data set, we see that the comments are given by `#`, and this is a standard CSV file."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_weight = pd.read_csv('data/bee_weight.csv', comment='#')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**b)** We will plot the ECDFs with confidence intervals to help visualize the difference between them."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "\n",
       "\n",
       "\n",
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Application\",\"version\":\"2.4.2\"}};\n",
       "  const render_items = [{\"docid\":\"c9ea4c0f-a02a-4ef8-9432-bc9067bb299d\",\"root_ids\":[\"1003\"],\"roots\":{\"1003\":\"65d8e0a9-28ed-4c36-bcc0-74584146780f\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    let attempts = 0;\n",
       "    const timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        clearInterval(timer);\n",
       "        embed_document(root);\n",
       "      } else {\n",
       "        attempts++;\n",
       "        if (attempts > 100) {\n",
       "          clearInterval(timer);\n",
       "          console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        }\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "1003"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "p = iqplot.ecdf(\n",
    "    data=df_weight,\n",
    "    q='Weight',\n",
    "    cats='Treatment',\n",
    "    conf_int=True,\n",
    "    x_axis_label='weight (mg)',\n",
    ")\n",
    "\n",
    "bokeh.io.show(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There is strong overlap of the ECDFs, which suggests there is no difference between pesticide and control. Now, let's compute confidence intervals on the mean weight of the drones."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**c)** First, we'll get point estimates for the mean weight under control and pesticide conditions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean control:   277.0563 mg\n",
      "Mean pesticide: 278.27333333333326 mg\n"
     ]
    }
   ],
   "source": [
    "mean_control = np.mean(df_weight.loc[df_weight['Treatment']=='Control', 'Weight'])\n",
    "mean_pest = np.mean(df_weight.loc[df_weight['Treatment']=='Pesticide', 'Weight'])\n",
    "\n",
    "print('Mean control:  ', mean_control, 'mg')\n",
    "print('Mean pesticide:', mean_pest, 'mg')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The means are really close. Let's now compute the confidence intervals. We'll use the bootstrap replicate generating function we wrote in [Exercise 4.1](exercise_4.1.ipynb)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def draw_bs_reps(data, func, rg, size=1, args=()):\n",
    "    return np.array(\n",
    "        [\n",
    "            func(rg.choice(data, replace=True, size=len(data)), *args)\n",
    "            for _ in range(size)\n",
    "        ]\n",
    "    )\n",
    "\n",
    "\n",
    "rg = np.random.default_rng()\n",
    "\n",
    "# Draw 10,000 bootstrap reps for both.\n",
    "bs_reps_control = draw_bs_reps(\n",
    "    df_weight.loc[df_weight[\"Treatment\"] == \"Control\", \"Weight\"].values,\n",
    "    np.mean,\n",
    "    rg,\n",
    "    size=10000,\n",
    ")\n",
    "bs_reps_pest = draw_bs_reps(\n",
    "    df_weight.loc[df_weight[\"Treatment\"] == \"Pesticide\", \"Weight\"].values,\n",
    "    np.mean,\n",
    "    rg,\n",
    "    size=10000,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we can use `np.percentile()` to compute the 95% confidence interval."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Confidence interval for control: [274.69325875 279.37617   ]\n",
      "Confidence interval for pesticide: [275.06833333 281.51764583]\n"
     ]
    }
   ],
   "source": [
    "conf_int_control = np.percentile(bs_reps_control, [2.5, 97.5])\n",
    "conf_int_pest = np.percentile(bs_reps_pest, [2.5, 97.5])\n",
    "\n",
    "print('Confidence interval for control:', conf_int_control)\n",
    "print('Confidence interval for pesticide:', conf_int_pest)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "They have nearly the same confidence interval, as we would expect from the ECDFs."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**d)** We just go through the same steps as before. First, the ECDF."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
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       "  const render_items = [{\"docid\":\"f69b2314-e53a-4acf-9206-673345468f53\",\"root_ids\":[\"1165\"],\"roots\":{\"1165\":\"04f5ba15-0e4e-4562-b6d1-2382d2121918\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    let attempts = 0;\n",
       "    const timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        clearInterval(timer);\n",
       "        embed_document(root);\n",
       "      } else {\n",
       "        attempts++;\n",
       "        if (attempts > 100) {\n",
       "          clearInterval(timer);\n",
       "          console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        }\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "1165"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Load data set\n",
    "df_sperm = pd.read_csv('data/bee_sperm.csv', comment='#')\n",
    "\n",
    "# Make ECDF\n",
    "p = iqplot.ecdf(\n",
    "    data=df_sperm,\n",
    "    q='Quality',\n",
    "    cats='Treatment',\n",
    "    conf_int=True,\n",
    "    x_axis_label='quality',\n",
    ")\n",
    "\n",
    "p.legend.location = 'top_left'\n",
    "\n",
    "bokeh.io.show(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have some very low quality samples from both, but it is pretty clear that on a whole the pesticide samples have much lower sperm quality. Let's compute the confidence interval on the mean. We have to be careful, though, because there are some `NaN`s in the data set, so we have to use `dropna()`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Confidence interval for control: [84.26541319 89.46672476]\n",
      "Confidence interval for pesticide: [73.98761529 82.00900716]\n"
     ]
    }
   ],
   "source": [
    "# Draw 10,000 bootstrap reps for both.\n",
    "bs_reps_control = draw_bs_reps(\n",
    "    df_sperm.loc[df_sperm[\"Treatment\"] == \"Control\", \"Quality\"].dropna().values,\n",
    "    np.mean,\n",
    "    rg,\n",
    "    size=10000,\n",
    ")\n",
    "bs_reps_pest = draw_bs_reps(\n",
    "    df_sperm.loc[df_sperm[\"Treatment\"] == \"Pesticide\", \"Quality\"].dropna().values,\n",
    "    np.mean,\n",
    "    rg,\n",
    "    size=10000,\n",
    ")\n",
    "\n",
    "# Compute and print confidence interval\n",
    "conf_int_control = np.percentile(bs_reps_control, [2.5, 97.5])\n",
    "conf_int_pest = np.percentile(bs_reps_pest, [2.5, 97.5])\n",
    "\n",
    "print(\"Confidence interval for control:\", conf_int_control)\n",
    "print(\"Confidence interval for pesticide:\", conf_int_pest)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The confidence intervals of the mean do not overlap, further confirming that the pesticide-tested drones have lower sperm quality.\n",
    "\n",
    "**e)** Now, let's try bootstrapping the median. This is the same procedure as before, except we just put `np.median` for our function where we have `np.median`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Confidence interval for control: [89.70654852 94.2353021 ]\n",
      "Confidence interval for pesticide: [80.0560062  85.84421182]\n"
     ]
    }
   ],
   "source": [
    "# Draw 10,000 bootstrap reps for both.\n",
    "bs_reps_control = draw_bs_reps(\n",
    "    df_sperm.loc[df_sperm[\"Treatment\"] == \"Control\", \"Quality\"].dropna().values,\n",
    "    np.median,\n",
    "    rg,\n",
    "    size=10000,\n",
    ")\n",
    "bs_reps_pest = draw_bs_reps(\n",
    "    df_sperm.loc[df_sperm[\"Treatment\"] == \"Pesticide\", \"Quality\"].dropna().values,\n",
    "    np.median,\n",
    "    rg,\n",
    "    size=10000,\n",
    ")\n",
    "\n",
    "# Compute and print confidence interval\n",
    "conf_int_control = np.percentile(bs_reps_control, [2.5, 97.5])\n",
    "conf_int_pest = np.percentile(bs_reps_pest, [2.5, 97.5])\n",
    "\n",
    "print(\"Confidence interval for control:\", conf_int_control)\n",
    "print(\"Confidence interval for pesticide:\", conf_int_pest)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, we see that the confidence intervals do not overlap. The median is of course higher than the mean, since the low-quality outliers have little effect on the median."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Computing environment"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Python implementation: CPython\n",
      "Python version       : 3.9.12\n",
      "IPython version      : 8.3.0\n",
      "\n",
      "numpy     : 1.21.5\n",
      "pandas    : 1.4.2\n",
      "bokeh     : 2.4.2\n",
      "iqplot    : 0.2.4\n",
      "jupyterlab: 3.3.2\n",
      "\n"
     ]
    }
   ],
   "source": [
    "%load_ext watermark\n",
    "%watermark -v -p numpy,pandas,bokeh,iqplot,jupyterlab"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.9.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}