{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Sebastian Raschka](http://www.sebastianraschka.com)\n",
    "\n",
    "[back](https://github.com/rasbt/matplotlib-gallery) to the `matplotlib-gallery` at [https://github.com/rasbt/matplotlib-gallery](https://github.com/rasbt/matplotlib-gallery)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%load_ext watermark"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Last updated: 30/07/2014 \n",
      "\n",
      "CPython 3.4.1\n",
      "IPython 2.1.0\n",
      "\n",
      "matplotlib 1.3.1\n",
      "numpy 1.8.1\n",
      "scipy 0.14.0\n"
     ]
    }
   ],
   "source": [
    "%watermark -u -v -d -p matplotlib,numpy,scipy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Errorbar Plots in matplotlib"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sections"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- [Standard Deviation, Standard Error, and Confidence Intervals](#Standard-Deviation,-Standard-Error,-and-Confidence-Intervals)\n",
    "- [Adding error bars to a barplot](#Adding-error-bars-to-a-barplot)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Standard Deviation, Standard Error, and Confidence Intervals"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[[back to top](#Sections)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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EXV6sFixYQIsWLejYsSNt2rShffv27N69O/Tat28fOTk5AKSkpNCnTx/mzZvH3LlzGTJk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\nEN90La91AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10635a2e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "from scipy.stats import t\n",
    "\n",
    "# Generating 15 random data points in the range 5-15 (inclusive)\n",
    "X = np.random.randint(5, 15, 15)\n",
    "\n",
    "# sample size\n",
    "n = X.size\n",
    "\n",
    "# mean\n",
    "X_mean = np.mean(X)\n",
    "\n",
    "# standard deviation\n",
    "X_std = np.std(X)\n",
    "\n",
    "# standard error\n",
    "X_se = X_std / np.sqrt(n)\n",
    "# alternatively:\n",
    "#    from scipy import stats\n",
    "#    stats.sem(X)\n",
    "\n",
    "# 95% Confidence Interval\n",
    "\n",
    "dof = n - 1         # degrees of freedom\n",
    "alpha = 1.0 - 0.95\n",
    "conf_interval = t.ppf(1-alpha/2., dof) * X_std*np.sqrt(1.+1./n)\n",
    "\n",
    "fig = plt.gca()\n",
    "plt.errorbar(1, X_mean, yerr=X_std, fmt='-o')\n",
    "plt.errorbar(2, X_mean, yerr=X_se, fmt='-o')\n",
    "plt.errorbar(3, X_mean, yerr=conf_interval, fmt='-o')\n",
    "\n",
    "plt.xlim([0,4])\n",
    "plt.ylim(X_mean-conf_interval-2, X_mean+conf_interval+2)\n",
    "\n",
    "# axis formatting\n",
    "fig.axes.get_xaxis().set_visible(False)\n",
    "fig.spines[\"top\"].set_visible(False)  \n",
    "fig.spines[\"right\"].set_visible(False)  \n",
    "plt.tick_params(axis=\"both\", which=\"both\", bottom=\"off\", top=\"off\",  \n",
    "                labelbottom=\"on\", left=\"on\", right=\"off\", labelleft=\"on\")  \n",
    "\n",
    "plt.legend(['Standard Deviation', 'Standard Error', 'Confidence Interval'], \n",
    "           loc='upper left',\n",
    "           numpoints=1,\n",
    "           fancybox=True)\n",
    "\n",
    "plt.ylabel('random variable')\n",
    "plt.title('15 random values in the range 5-15')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Adding error bars to a barplot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[[back to top](#Sections)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1066ce0f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# input data\n",
    "mean_values = [1, 2, 3]\n",
    "variance = [0.2, 0.4, 0.5]\n",
    "bar_labels = ['bar 1', 'bar 2', 'bar 3']\n",
    "\n",
    "fig = plt.gca()\n",
    "\n",
    "# plot bars\n",
    "x_pos = list(range(len(bar_labels)))\n",
    "plt.bar(x_pos, mean_values, yerr=variance, align='center', alpha=0.5)\n",
    "\n",
    "# set height of the y-axis\n",
    "max_y = max(zip(mean_values, variance)) # returns a tuple, here: (3, 5)\n",
    "plt.ylim([0, (max_y[0] + max_y[1]) * 1.1])\n",
    "\n",
    "# set axes labels and title\n",
    "plt.ylabel('variable y')\n",
    "plt.xticks(x_pos, bar_labels)\n",
    "plt.title('Bar plot with error bars')\n",
    "\n",
    "# axis formatting\n",
    "fig.axes.get_xaxis().set_visible(False)\n",
    "fig.spines[\"top\"].set_visible(False)  \n",
    "fig.spines[\"right\"].set_visible(False)  \n",
    "plt.tick_params(axis=\"both\", which=\"both\", bottom=\"off\", top=\"off\",  \n",
    "                labelbottom=\"on\", left=\"on\", right=\"off\", labelleft=\"on\")  \n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "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": "3.4.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}