PythonDataBasics_BoostrapHypothesis.ipynb

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   "source": [
    "<p align=\"center\">\n",
    "    <img src=\"https://github.com/GeostatsGuy/GeostatsPy/blob/master/TCG_color_logo.png?raw=true\" width=\"220\" height=\"240\" />\n",
    "\n",
    "</p>\n",
    "\n",
    "## Data Analytics \n",
    "\n",
    "### Bootstrap Hypothesis Testing in Python \n",
    "\n",
    "#### Michael Pyrcz, Associate Professor, University of Texas at Austin \n",
    "\n",
    "##### [Twitter](https://twitter.com/geostatsguy) | [GitHub](https://github.com/GeostatsGuy) | [Website](http://michaelpyrcz.com) | [GoogleScholar](https://scholar.google.com/citations?user=QVZ20eQAAAAJ&hl=en&oi=ao) | [Book](https://www.amazon.com/Geostatistical-Reservoir-Modeling-Michael-Pyrcz/dp/0199731446) | [YouTube](https://www.youtube.com/channel/UCLqEr-xV-ceHdXXXrTId5ig)  | [LinkedIn](https://www.linkedin.com/in/michael-pyrcz-61a648a1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "##  Bootstrap Hypothesis Testing Demonstration\n",
    "\n",
    "We start with difference in means and then move to difference in variances. We answer the question:\n",
    "\n",
    "* is the observed difference in the statistic between 2 sample sets significant? \n",
    "\n",
    "* should we infer that the 2 sample sets are from 2 populations with different population parameters?\n",
    "\n",
    "* or could the observed difference be due to random effect.\n",
    "\n",
    "We will use bootstrap methods to sample realizations given the specified null hypothesis, $H_0$ is true to build the sampling distribution. Then we look at the observed effect relative to this smapling distribution to assess significance.\n",
    "\n",
    "* the tests we will demonstrated have analytical solutions and we will show that our bootstrap methods reproduce these analytically-known distributions while providing a more general workflow for any significance problem.\n",
    "\n",
    "### Boostrap and Analytical Methods for Hypothesis Testing, Difference in Means\n",
    "\n",
    "* we calculate the hypothesis test for different in means with boostrap and compare to the analytical expression\n",
    "\n",
    "* **Welch's t-test**: we assume the features are Gaussian distributed and the variance are unequal\n",
    "\n",
    "#### Michael Pyrcz, Associate Professor, University of Texas at Austin \n",
    "\n",
    "##### [Twitter](https://twitter.com/geostatsguy) | [GitHub](https://github.com/GeostatsGuy) | [Website](http://michaelpyrcz.com) | [GoogleScholar](https://scholar.google.com/citations?user=QVZ20eQAAAAJ&hl=en&oi=ao) | [Book](https://www.amazon.com/Geostatistical-Reservoir-Modeling-Michael-Pyrcz/dp/0199731446) | [YouTube](https://www.youtube.com/channel/UCLqEr-xV-ceHdXXXrTId5ig)  | [LinkedIn](https://www.linkedin.com/in/michael-pyrcz-61a648a1) | [GeostatsPy](https://github.com/GeostatsGuy/GeostatsPy)\n",
    "\n",
    "#### Hypothesis Testing\n",
    "\n",
    "Powerful methodology for spatial data analytics:\n",
    "\n",
    "1. extracted sample set 1 and 2, the means look different, but are they? \n",
    "2. should we suspect that the samples are in fact from 2 different populations?\n",
    "\n",
    "Now, let's try the t-test, hypothesis test for difference in means.  This test assumes that the variances are similar along with the data being Gaussian distributed (see the course notes for more on this).  This is our test:\n",
    "\n",
    "\\begin{equation}\n",
    "H_0: \\mu_{X1} = \\mu_{X2}\n",
    "\\end{equation}\n",
    "\n",
    "\\begin{equation}\n",
    "H_1: \\mu_{X1} \\ne \\mu_{X2}\n",
    "\\end{equation}\n",
    "\n",
    "To test this we will calculate the t statistic with the bootstrap and analytical approaches.\n",
    "\n",
    "#### The Welch's t-test for Difference in Means by Analytical Methods\n",
    "\n",
    "We work with the following test statistic, *t statistic*, from the two sample sets.\n",
    "\n",
    "\\begin{equation}\n",
    "\\hat{t} = \\frac{\\overline{x}_1 - \\overline{x}_2}{\\sqrt{\\frac{s^2_1}{n_1} + \\frac{s^2_2}{n_2}}}\n",
    "\\end{equation}\n",
    "\n",
    "where $\\overline{x}_1$ and $\\overline{x}_2$ are the sample means, $s^2_1$ and $s^2_2$ are the sample variances and $n_1$ and $n_2$ are the numer of samples from the two datasets.\n",
    "\n",
    "The critical value, $t_{critical}$ is calculated by the analytical expression by:\n",
    "\n",
    "\\begin{equation}\n",
    "t_{critical} = \\left|t(\\frac{\\alpha}{2},\\nu)\\right|\n",
    "\\end{equation}\n",
    "\n",
    "The degrees of freedom, $\\nu$, is calculated as follows:\n",
    "\n",
    "\\begin{equation}\n",
    "\\nu = \\frac{\\left(\\frac{1}{n_1} + \\frac{\\mu}{n_2}\\right)^2}{\\frac{1}{n_1^2(n_1-1)} + \\frac{\\mu^2}{n_2^2(n_2-1)}}\n",
    "\\end{equation}\n",
    "\n",
    "Alternatively, the sampling distribution of the t_{statistic} and t_{critical} may be calculated empirically with bootstrap.\n",
    "\n",
    "The workflow proceeds as:\n",
    "\n",
    "* shift both sample sets to have the mean of the combined data, $x_1$ → $x^*_1$, $x_2$ → $x^*_2$ \n",
    "\n",
    "* for each bootstrap realization, $\\ell=1\\ldots,L$\n",
    "\n",
    "    * perform $n_1$ Monte Carlo simulations, draws with replacement, from sample set $x^*_1$\n",
    "    \n",
    "    * perform $n_2$ Monte Carlo simulations, draws with replacement, from sample set $x^*_2$\n",
    "    \n",
    "    * calculate the t_{statistic} realization, $\\hat{t}^{\\ell}$ given the resulting sample means $\\overline{x}^{*,\\ell}_1$ and $\\overline{x}^{*,\\ell}_2$ and the sample variances $s^{*,2,\\ell}_1$ and $s^{*,2,\\ell}_2$\n",
    "    \n",
    "* pool the results to assemble the $t_{statistic}$ sampling distribution\n",
    "\n",
    "* calculate the cumulative probability of the observed t_{statistic}m, $\\hat{t}$, from the boostrap distribution based on $\\hat{t}^{\\ell}$, $\\ell = 1,\\ldots,L$.\n",
    "\n",
    "Here's some prerequisite information on the boostrap.\n",
    "\n",
    "#### Bootstrap\n",
    "\n",
    "Uncertainty in the sample statistics\n",
    "* one source of uncertainty is the paucity of data.\n",
    "* do 200 or even less wells provide a precise (and accurate estimate) of the mean? standard deviation? skew? P13?\n",
    "\n",
    "Would it be useful to know the uncertainty in these statistics due to limited sampling?\n",
    "* what is the impact of uncertainty in the mean porosity e.g. 20%+/-2%?\n",
    "\n",
    "**Bootstrap** is a method to assess the uncertainty in a sample statistic by repeated random sampling with replacement.\n",
    "\n",
    "Assumptions\n",
    "* sufficient, representative sampling, identical, idependent samples\n",
    "\n",
    "Limitations\n",
    "1. assumes the samples are representative \n",
    "2. assumes stationarity\n",
    "3. only accounts for uncertainty due to too few samples, e.g. no uncertainty due to changes away from data\n",
    "4. does not account for boundary of area of interest \n",
    "5. assumes the samples are independent\n",
    "6. does not account for other local information sources\n",
    "\n",
    "The Bootstrap Approach (Efron, 1982)\n",
    "\n",
    "Statistical resampling procedure to calculate uncertainty in a calculated statistic from the data itself.\n",
    "* Does this work?  Prove it to yourself, for uncertainty in the mean solution is standard error: \n",
    "\n",
    "\\begin{equation}\n",
    "\\sigma^2_\\overline{x} = \\frac{\\sigma^2_s}{n}\n",
    "\\end{equation}\n",
    "\n",
    "Extremely powerful - could calculate uncertainty in any statistic!  e.g. P13, skew etc.\n",
    "* Would not be possible access general uncertainty in any statistic without bootstrap.\n",
    "* Advanced forms account for spatial information and sampling strategy (game theory and Journel’s spatial bootstrap (1993).\n",
    "\n",
    "Steps: \n",
    "\n",
    "1. assemble a sample set, must be representative, reasonable to assume independence between samples\n",
    "\n",
    "2. optional: build a cumulative distribution function (CDF)\n",
    "    * may account for declustering weights, tail extrapolation\n",
    "    * could use analogous data to support\n",
    "\n",
    "3. For $\\ell = 1, \\ldots, L$ realizations, do the following:\n",
    "\n",
    "    * For $i = \\alpha, \\ldots, n$ data, do the following:\n",
    "\n",
    "        * Draw a random sample with replacement from the sample set or Monte Carlo simulate from the CDF (if available). \n",
    "\n",
    "6. Calculate a realization of the sammary statistic of interest from the $n$ samples, e.g. $m^\\ell$, $\\sigma^2_{\\ell}$. Return to 3 for another realization.\n",
    "\n",
    "7. Compile and summarize the $L$ realizations of the statistic of interest.\n",
    "\n",
    "This is a very powerful method.  Let's try it out and compare the result to the analytical form of the confidence interval for the sample mean. \n",
    "\n",
    "\n",
    "#### Objective \n",
    "\n",
    "Provide an example and demonstration for:\n",
    "\n",
    "1. interactive plotting in Jupyter Notebooks with Python packages matplotlib and ipywidgets\n",
    "2. provide an intuitive hands-on example of confidence intervals and compare to statistical boostrap   \n",
    "\n",
    "#### Getting Started\n",
    "\n",
    "Here's the steps to get setup in Python with the GeostatsPy package:\n",
    "\n",
    "1. Install Anaconda 3 on your machine (https://www.anaconda.com/download/). \n",
    "2. Open Jupyter and in the top block get started by copy and pasting the code block below from this Jupyter Notebook to start using the geostatspy functionality. \n",
    "\n",
    "#### Load the Required Libraries\n",
    "\n",
    "The following code loads the required libraries."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 255,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os                                                 # set working directory, run executables\n",
    "import matplotlib                                         # plotting\n",
    "import matplotlib.pyplot as plt                           # plotting\n",
    "import seaborn as sns                                     # plotting\n",
    "import numpy as np                                        # working with arrays\n",
    "import pandas as pd                                       # working with DataFrames\n",
    "import statistics as stats                                # statistics like the mode\n",
    "import random                                             # random drawing / bootstrap realizations of the data\n",
    "from scipy.stats import t                                 # Student's t distribution for analytical solution\n",
    "from scipy.stats import ttest_ind                         \n",
    "from scipy.stats import f as F                            # Student's F distribution for analytical solution\n",
    "from scipy.stats import percentileofscore                 # forward of CDF"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Set the working directory\n",
    "\n",
    "I always like to do this so I don't lose files and to simplify subsequent read and writes (avoid including the full address each time). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "metadata": {},
   "outputs": [],
   "source": [
    "os.chdir(\"c:/PGE383\")                                     # set the working directory"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Loading Tabular Data\n",
    "\n",
    "Here's the command to load our comma delimited data file in to a Pandas' DataFrame object.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_csv('sample_data_biased.csv')                # load our data table"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's drop some samples so that we increase the variations in bootstrap samples for our demonstration below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 168,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using 58 number of samples\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(seed = 73073)\n",
    "df = df.sample(frac = 0.2)                                # extract 50 random samples to reduce the size of the dataset   \n",
    "print('Using ' + str(len(df)) + ' number of samples')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Visualizing the DataFrame would be useful and we already learned about these methods in this demo (https://git.io/fNgRW). \n",
    "\n",
    "We can preview the DataFrame by printing a slice or by utilizing the 'head' DataFrame member function (with a nice and clean format, see below). With the slice we could look at any subset of the data table and with the head command, add parameter 'n=13' to see the first 13 rows of the dataset.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "metadata": {},
   "outputs": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>X</th>\n",
       "      <th>Y</th>\n",
       "      <th>Facies</th>\n",
       "      <th>Porosity</th>\n",
       "      <th>Perm</th>\n",
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       "      <th>150</th>\n",
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       "      <td>3.003225</td>\n",
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       "      <th>214</th>\n",
       "      <td>470</td>\n",
       "      <td>899</td>\n",
       "      <td>1</td>\n",
       "      <td>0.211944</td>\n",
       "      <td>1302.937858</td>\n",
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       "       X    Y  Facies  Porosity         Perm\n",
       "150   20   69       0  0.104484     3.003225\n",
       "17   400  600       1  0.163054   317.883581\n",
       "68   640  529       1  0.120547    10.801778\n",
       "234  490  289       1  0.144525    16.251107\n",
       "214  470  899       1  0.211944  1302.937858"
      ]
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     "execution_count": 169,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()                                                 # display first 4 samples in the table as a preview"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Summary Statistics for Tabular Data\n",
    "\n",
    "The table includes X and Y coordinates (meters), Facies 1 and 0 (1 is sandstone and 0 interbedded sand and mudstone), Porosity (fraction), and permeability as Perm (mDarcy). \n",
    "\n",
    "There are a lot of efficient methods to calculate summary statistics from tabular data in DataFrames. The describe command provides count, mean, minimum, maximum, and quartiles all in a nice data table. We use transpose just to flip the table so that features are on the rows and the statistics are on the columns."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 170,
   "metadata": {},
   "outputs": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>count</th>\n",
       "      <th>mean</th>\n",
       "      <th>std</th>\n",
       "      <th>min</th>\n",
       "      <th>25%</th>\n",
       "      <th>50%</th>\n",
       "      <th>75%</th>\n",
       "      <th>max</th>\n",
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       "    <tr>\n",
       "      <th>X</th>\n",
       "      <td>58.0</td>\n",
       "      <td>418.275862</td>\n",
       "      <td>231.457153</td>\n",
       "      <td>10.000000</td>\n",
       "      <td>272.500000</td>\n",
       "      <td>400.000000</td>\n",
       "      <td>560.000000</td>\n",
       "      <td>990.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Y</th>\n",
       "      <td>58.0</td>\n",
       "      <td>493.224138</td>\n",
       "      <td>287.393614</td>\n",
       "      <td>39.000000</td>\n",
       "      <td>279.000000</td>\n",
       "      <td>499.500000</td>\n",
       "      <td>676.500000</td>\n",
       "      <td>989.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Facies</th>\n",
       "      <td>58.0</td>\n",
       "      <td>0.810345</td>\n",
       "      <td>0.395452</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Porosity</th>\n",
       "      <td>58.0</td>\n",
       "      <td>0.136501</td>\n",
       "      <td>0.040473</td>\n",
       "      <td>0.074349</td>\n",
       "      <td>0.105662</td>\n",
       "      <td>0.126192</td>\n",
       "      <td>0.147067</td>\n",
       "      <td>0.223661</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Perm</th>\n",
       "      <td>58.0</td>\n",
       "      <td>270.961923</td>\n",
       "      <td>590.805185</td>\n",
       "      <td>0.093252</td>\n",
       "      <td>4.112400</td>\n",
       "      <td>15.105651</td>\n",
       "      <td>79.314434</td>\n",
       "      <td>2372.383732</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
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       "          count        mean         std        min         25%         50%  \\\n",
       "X          58.0  418.275862  231.457153  10.000000  272.500000  400.000000   \n",
       "Y          58.0  493.224138  287.393614  39.000000  279.000000  499.500000   \n",
       "Facies     58.0    0.810345    0.395452   0.000000    1.000000    1.000000   \n",
       "Porosity   58.0    0.136501    0.040473   0.074349    0.105662    0.126192   \n",
       "Perm       58.0  270.961923  590.805185   0.093252    4.112400   15.105651   \n",
       "\n",
       "                 75%          max  \n",
       "X         560.000000   990.000000  \n",
       "Y         676.500000   989.000000  \n",
       "Facies      1.000000     1.000000  \n",
       "Porosity    0.147067     0.223661  \n",
       "Perm       79.314434  2372.383732  "
      ]
     },
     "execution_count": 170,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe().transpose()                                 # data summary statistics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Visualizing Tabular Data with Location Maps \n",
    "\n",
    "It is natural to set the x and y coordinate and feature ranges manually. e.g. do you want your color bar to go from 0.05887 to 0.24230 exactly? Also, let's pick a color map for display. I heard that plasma is known to be friendly to the color blind as the color and intensity vary together (hope I got that right, it was an interesting Twitter conversation started by Matt Hall from Agile if I recall correctly). We will assume a study area of 0 to 1,000m in x and y and omit any data outside this area."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 171,
   "metadata": {},
   "outputs": [],
   "source": [
    "xmin = 0.0; xmax = 1000.0                                 # range of x values\n",
    "ymin = 0.0; ymax = 1000.0                                 # range of y values\n",
    "pormin = 0.05; pormax = 0.25;                             # range of porosity values\n",
    "permmin = 0.01; permmax = 10000                           # range of permeability values                          \n",
    "cmap = plt.cm.plasma                                      # color map\n",
    "cumul_prob = np.linspace(0.0,1.0,100)                     # list of cumulative probabilities"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's try out location maps, histograms and scatter plots. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 9 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.subplot(231)                                          # location maps, histograms and scatter plots                                      \n",
    "plt.scatter(df['X'],df['Y'],s = 20,c = df['Porosity'],cmap = plt.cm.inferno,linewidths = 0.3,edgecolor = 'black',alpha = 0.8,vmin = pormin,vmax = pormax)\n",
    "plt.colorbar(); plt.xlabel('X (m)'); plt.ylabel('Y (m)'); plt.title('Porosity Location Map')\n",
    "\n",
    "plt.subplot(232)\n",
    "plt.scatter(df['X'],df['Y'],s = 20,c = df['Perm'],cmap = plt.cm.inferno,linewidths = 0.3,edgecolor = 'black',alpha = 0.8,vmin = permmin,vmax = permmax,norm=matplotlib.colors.LogNorm())\n",
    "plt.colorbar(); plt.xlabel('X (m)'); plt.ylabel('Y (m)'); plt.title('Permeability Location Map')\n",
    "\n",
    "plt.subplot(233)\n",
    "plt.scatter(df['X'],df['Y'],s = 20,c = df['Facies'],cmap = plt.cm.gray,linewidths = 0.3,edgecolor = 'black',alpha = 0.8,vmin = 0.0,vmax = 1.0)\n",
    "plt.scatter(x=[800,800],y=[900,830],c=[1,0],cmap = plt.cm.gray,s=20,edgecolor = 'black')\n",
    "plt.text(850, 890, r'Sand', fontsize=12); plt.text(850, 820, r'Shale', fontsize=12)\n",
    "plt.colorbar(); plt.xlabel('X (m)'); plt.ylabel('Y (m)'); plt.title('Facies Location Map')\n",
    "\n",
    "plt.subplot(234)\n",
    "plt.hist(df['Porosity'],color = 'red',alpha = 0.3,edgecolor='black',bins = np.linspace(pormin,pormax,int(len(df)/3)))\n",
    "plt.xlabel('Porosity (fraction)'); plt.ylabel('Frequency'); plt.title('Porosity Histogram')\n",
    "\n",
    "plt.subplot(235)\n",
    "plt.hist(df['Perm'],color = 'red',alpha = 0.3,edgecolor='black',bins=np.logspace(np.log10(permmin),np.log10(permmax),int(len(df)/3)))\n",
    "plt.xlabel('Permeability (mD)'); plt.ylabel('Frequency'); plt.title('Permeability Histogram'); plt.xscale('log')\n",
    "\n",
    "plt.subplot(236)\n",
    "plt.scatter(df['Porosity'],df['Perm'],s = 20,color = 'red',alpha = 0.3,edgecolor='black')\n",
    "plt.ylabel('Permeability (mD)'); plt.xlabel('Porosity (fraction)'); plt.title('Permeability-Porosity Scatter Plot')\n",
    "plt.yscale('log')\n",
    "sns.kdeplot(x=df['Porosity'],y=df['Perm'],color = 'black',alpha = 0.2,levels = 4)\n",
    "\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=3.0, top=2.2, wspace=0.2, hspace=0.2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### By-Facies Data Visualization\n",
    "\n",
    "Let's check the statistics by-facies. First, let's break up the DataFrame, df, into separate DataFrames for each facies:\n",
    "\n",
    "1. Sand (facies = 0)\n",
    "2. Shale (facies = 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_sand = df[df['Facies']==1]                             # extract sand and shale facies samples to a new DataFrame\n",
    "df_shale = df[df['Facies']==0]                           "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can plot the distributions by facies."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 432x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.subplot(131)\n",
    "plt.hist(df_shale['Porosity'],color = 'gray',alpha = 0.3,edgecolor='black',bins = np.linspace(pormin,pormax,int(len(df)/3)),label='shale')\n",
    "plt.hist(df_sand['Porosity'],color = 'yellow',alpha = 0.2,edgecolor='black',bins = np.linspace(pormin,pormax,int(len(df)/3)),label='sand')\n",
    "plt.xlabel('Porosity (fraction)'); plt.ylabel('Frequency'); plt.title('Porosity Histogram')\n",
    "plt.legend()\n",
    "\n",
    "plt.subplot(132)\n",
    "plt.hist(df_shale['Perm'],color = 'gray',alpha = 0.3,edgecolor='black',bins=np.logspace(np.log10(permmin),np.log10(permmax),int(len(df)/3)),label='shale')\n",
    "plt.hist(df_sand['Perm'],color = 'yellow',alpha = 0.2,edgecolor='black',bins=np.logspace(np.log10(permmin),np.log10(permmax),int(len(df)/3)),label='sand')\n",
    "plt.legend()\n",
    "\n",
    "plt.xlabel('Permeability (mD)'); plt.ylabel('Frequency'); plt.title('Permeability Histogram'); plt.xscale('log')\n",
    "\n",
    "plt.subplot(133)\n",
    "plt.scatter(df_shale['Porosity'],df_shale['Perm'],s = 20,color = 'gray',alpha = 0.3,edgecolor='black',label='shale')\n",
    "plt.scatter(df_sand['Porosity'],df_sand['Perm'],s = 20,color = 'yellow',alpha = 0.3,edgecolor='black',label='sand')\n",
    "plt.legend()\n",
    "\n",
    "plt.ylabel('Permeability (mD)'); plt.xlabel('Porosity (fraction)'); plt.title('Permeability-Porosity Scatter Plot')\n",
    "plt.yscale('log')\n",
    "sns.kdeplot(x=df['Porosity'],y=df['Perm'],color = 'black',alpha = 0.2,levels = 4)\n",
    "\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=3.0, top=1.2, wspace=0.2, hspace=0.2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Bootstrap Hypothesis Test\n",
    "\n",
    "#### Boostrap Student's t-test, Welch's Test Difference in Means\n",
    "\n",
    "First let's calculate the t-statistic observed in our dataset, assuming unequal variances with the Welch's t-test.\n",
    "\n",
    "* the observed effect, difference in means, $\\overline{x}_1 - \\overline{x}_2$, standardized by standard error, $\\sqrt{\\frac{s^2_1}{n_1} + \\frac{s^2_2}{n_2}}$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 176,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The observed Welch's t-statistic is -8.17\n"
     ]
    }
   ],
   "source": [
    "t_stat_obs, p_value_obs = ttest_ind(df_shale['Porosity'],df_sand['Porosity'],equal_var=False)\n",
    "print(\"The observed Welch's t-statistic is \" + str(round(t_stat_obs,2)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Given our knowledge about the theory, the sampling distribution will be standard t-distributed,we already know that this effect will be significant!\n",
    "\n",
    "To build the sampling distribution given the null hypothesis is correct, we need to modifed the data so that the null hypothesis is true.\n",
    "\n",
    "* we shift both datasets to have the same mean.\n",
    "\n",
    "The procedure to accomplish this is:\n",
    "\n",
    "1. make a deep copy of the porosity values as a 1D ndarray from each sand and shale DataFrames. We do this to ensure we don't change the original DataFrame, i.e. a slice would be a shallow copy and the mean would be shifted for our original data set! \n",
    "\n",
    "2. calculate the common mean by pooling all of the data together\n",
    "\n",
    "3. apply the affine correction to shift the mean, $X^{*} = X - \\overline{X}\n",
    "+ \\overline{X}_{pooled}$ \n",
    "\n",
    "Let's make a plot to check the result."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 177,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "por_sand = df_sand.copy(deep = True)['Porosity'].values   # make a deepcopy of porosity by-facies\n",
    "por_shale = df_shale.copy(deep = True)['Porosity'].values \n",
    "\n",
    "global_average = np.average(np.concatenate([por_sand,por_shale])) # shift the means to be equal to the globla mean\n",
    "por_sand_s = por_sand - np.average(por_sand) + global_average\n",
    "por_shale_s = por_shale - np.average(por_shale) + global_average\n",
    "\n",
    "plt.subplot(111)                                          # plot the new shifted histograms\n",
    "plt.hist(por_shale_s,color = 'gray',alpha = 0.3,edgecolor='black',bins = np.linspace(pormin,pormax,int(len(df)/3)),label='shale')\n",
    "plt.hist(por_sand_s,color = 'yellow',alpha = 0.2,edgecolor='black',bins = np.linspace(pormin,pormax,int(len(df)/3)),label='sand')\n",
    "plt.xlabel('Porosity (fraction)'); plt.ylabel('Frequency'); plt.title('Porosity Histogram')\n",
    "plt.legend()\n",
    "\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=1.0, top=1.2, wspace=0.2, hspace=0.2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now have two datasets for which the null hypothesis is true. \n",
    "\n",
    "\\begin{equation} \n",
    "H_0: \\mu_{\\phi_{sand}} = \\mu_{\\phi_{shale}}\n",
    "\\end{equation}\n",
    "\n",
    "We are saying, these two sample sets came from populations with the same means.\n",
    "\n",
    "* hypothesis tests are inferential, they are related to the population.\n",
    "\n",
    "Let's demonstrate the Welch's t-test, no assumption of equal population variances\n",
    "\n",
    "* bootstrap provides a new realization of each sample set\n",
    "\n",
    "* we calculate the realization of the t-statistic given the mean and standard deviation from the sample set realization \n",
    "\n",
    "\\begin{equation}\n",
    "\\hat{t}^{\\ell} = \\frac{\\overline{x^{\\ell}}_1 - \\overline{x^{\\ell}}_2}{\\sqrt{\\frac{{s^2}^{\\ell}_1}{n_1} + \\frac{{s^2}^{\\ell}_2}{n_2}}}\n",
    "\\end{equation}\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 269,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The p-value of the observed effect is 0.0\n"
     ]
    }
   ],
   "source": [
    "L = 10000                                                 # number of bootstrap realizations, $L$, to sample the t-statistic               \n",
    "alpha = 0.05                                              # alpha level\n",
    "\n",
    "t_stat = np.zeros(L); p_value = np.zeros(L)               # make arrays to store the t-statistic, and p-value realizations\n",
    "  \n",
    "u = stats.variance(por_sand)/stats.variance(por_shale)    # calculate the DOF for the Welch's t-test, a bit complicated\n",
    "dof = ((1/len(por_shale)) + u/len(por_sand))**2/(1/(len(por_shale)**2*(len(por_shale)-1)) + u**2/(len(por_sand)**2*(len(por_sand)-1)) )\n",
    "                                                       \n",
    "for l in range(0, L):                                     # loop over bootstrap realizations\n",
    "    por_shale_real = random.choices(por_shale_s, weights=None, cum_weights=None, k=len(por_shale_s)) # bootstrap realization of shale porosity\n",
    "    por_sand_real = random.choices(por_sand_s, weights=None, cum_weights=None, k=len(por_sand_s)) # bootstrap realization of sand porosity\n",
    "    t_stat[l], p_value[l] = ttest_ind(por_shale_real,por_sand_real,equal_var=False)\n",
    "\n",
    "lower_bound = np.percentile(t_stat,alpha*0.5*100)\n",
    "upper_bound = np.percentile(t_stat,(1-alpha*0.5)*100)\n",
    "\n",
    "plt.subplot(121)                                          # original porosity histograms\n",
    "plt.hist(df_shale['Porosity'],color = 'gray',alpha = 0.3,edgecolor='black',bins = np.linspace(pormin,pormax,int(len(df)/3)),label='shale')\n",
    "plt.hist(df_sand['Porosity'],color = 'yellow',alpha = 0.2,edgecolor='black',bins = np.linspace(pormin,pormax,int(len(df)/3)),label='sand')\n",
    "plt.xlabel('Porosity (fraction)'); plt.ylabel('Frequency'); plt.title('Porosity Histogram')\n",
    "plt.legend()\n",
    "\n",
    "plt.subplot(122)                                          # bootstrap t-statistic distribution by bootstrap, analytical and observed t-statistic\n",
    "plt.hist(t_stat,color = 'red',alpha = 0.3,edgecolor='black',bins=np.linspace(-10,10,100),density=True,label='bootstrap')\n",
    "plt.axvline(x=t_stat_obs,c='black',label='observed')\n",
    "plt.xlabel('t-statistic Bootstrap Realizations'); plt.ylabel('Frequency'); plt.title(\"Bootstrap and Analytical Welch's t-test\")\n",
    "\n",
    "analytical = t.pdf(np.linspace(-10,10,100), dof,loc=0,scale=1.0) # plot the analytically-derived sampling distribution\n",
    "\n",
    "plt.plot(np.linspace(-10,10,100),analytical,color = 'black',alpha=0.4,label=\"analytical\")\n",
    "plt.fill_between(np.linspace(-10,10,100), 0, analytical, where = np.linspace(-10,10,100) <= lower_bound, facecolor='red', interpolate=True, alpha = 0.5,label = \"Reject\")\n",
    "plt.fill_between(np.linspace(-10,10,100), 0, analytical, where = np.linspace(-10,10,100) >= upper_bound, facecolor='red', interpolate=True, alpha = 0.5)\n",
    "plt.legend()\n",
    "\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=2.0, top=1.2, wspace=0.2, hspace=0.2)\n",
    "plt.show()  \n",
    "\n",
    "print('The p-value of the observed effect is ' + str(round((percentileofscore(t_stat,t_stat_obs))/100,10)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Bootstrap Student's t-test, Equal, Pooled Variance Difference in Means\n",
    "\n",
    "Let's repeat this for the Student's t-test, equal variances, pooled variance method.\n",
    "\n",
    "The t-statistic bootstrap realizations are calculated as:\n",
    "\n",
    "\\begin{equation}\n",
    "\\hat{t}^{\\ell} = \\frac{ \\overline{x^{\\ell}}_1 - \\overline{x^{\\ell}}_2 }{ \\sqrt{\\left( \\frac{1}{n_1}+\\frac{1}{n_2} \\right) \\left( \\frac{(n_1-1){s^2}^{\\ell}_1 + (n_2-1){s^2}^{\\ell}_2}{n_1 + n_2 - 2} \\right)  }}\n",
    "\\end{equation}\n",
    "\n",
    "For the SciPy statististics module, we just need to change the 'equal_var' parameter to True.\n",
    "\n",
    "But we need to go an extra step, since the test assumes the variances are equal, we must correct the data to have equal variance and not just equal means, to honor the null hypothesis to calculate the correct t-statistic sampling distribution\n",
    "\n",
    "* if you would like to see for yourself, try changing the code below:\n",
    "\n",
    "```python\n",
    "correct_samples_equal_variance = True\n",
    "```\n",
    "\n",
    "to: \n",
    "\n",
    "```python\n",
    "correct_samples_equal_variance = False\n",
    "```\n",
    "\n",
    " and observe the mismatch between the analytical and bootstrap t-statistic distributions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 268,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The p-value of the observed effect is 0.0\n"
     ]
    }
   ],
   "source": [
    "L = 10000                                                 # number of bootstrap realizations, $L$, to sample the t-statistic               \n",
    "alpha = 0.05                                              # alpha level\n",
    "correct_samples_equal_variance = True                     # True - correct sample variances, False - only correct the means\n",
    "\n",
    "t_stat = np.zeros(L); p_value = np.zeros(L)               # make arrays to store the t-statistic, and p-value realizations\n",
    " \n",
    "global_average = np.average(np.concatenate([por_sand,por_shale])) # shift the means to be equal to the globla mean\n",
    "global_stdev = np.std(np.concatenate([por_sand,por_shale])) # shift the standard deviation to be equal to the globla standard deviation\n",
    "\n",
    "por_sand_affine = (por_sand - np.average(por_sand))*global_stdev/np.std(por_sand) + global_average\n",
    "por_shale_affine = (por_shale - np.average(por_shale))*global_stdev/np.std(por_shale) + global_average   \n",
    "   \n",
    "for l in range(0, L):                                     # loop over bootstrap realizations\n",
    "    if correct_samples_equal_variance:\n",
    "        por_shale_real = random.choices(por_shale_affine, weights=None, cum_weights=None, k=len(por_shale_s)) # bootstrap realization of shale porosity\n",
    "        por_sand_real = random.choices(por_sand_affine, weights=None, cum_weights=None, k=len(por_sand_s)) # bootstrap realization of sand porosity\n",
    "    else:\n",
    "        por_shale_real = random.choices(por_shale_s, weights=None, cum_weights=None, k=len(por_shale_s)) # bootstrap realization of shale porosity\n",
    "        por_sand_real = random.choices(por_sand_s, weights=None, cum_weights=None, k=len(por_sand_s)) # bootstrap realization of sand porosity\n",
    "    \n",
    "    t_stat[l], p_value[l] = ttest_ind(por_shale_real,por_sand_real,equal_var=True)\n",
    "\n",
    "lower_bound = np.percentile(t_stat,alpha*0.5*100)\n",
    "upper_bound = np.percentile(t_stat,(1-alpha*0.5)*100)\n",
    "\n",
    "plt.subplot(121)                                          # original porosity histograms\n",
    "plt.hist(df_shale['Porosity'],color = 'gray',alpha = 0.3,edgecolor='black',bins = np.linspace(pormin,pormax,int(len(df)/3)),label='shale')\n",
    "plt.hist(df_sand['Porosity'],color = 'yellow',alpha = 0.2,edgecolor='black',bins = np.linspace(pormin,pormax,int(len(df)/3)),label='sand')\n",
    "plt.xlabel('Porosity (fraction)'); plt.ylabel('Frequency'); plt.title('Porosity Histogram')\n",
    "plt.legend()\n",
    "\n",
    "plt.subplot(122)                                          # bootstrap t-statistic distribution by bootstrap, analytical and observed t-statistic\n",
    "plt.hist(t_stat,color = 'red',alpha = 0.3,edgecolor='black',bins=np.linspace(-10,10,100),density=True,label='bootstrap')\n",
    "plt.axvline(x=t_stat_obs,c='black',label='observed')\n",
    "plt.xlabel('t-statistic Bootstrap Realizations'); plt.ylabel('Frequency'); plt.title(\"Bootstrap and Analytical Pooled Variance t-test\")\n",
    "\n",
    "analytical = t.pdf(np.linspace(-10,10,100), len(df_sand)+len(df_shale)-2,loc=0,scale=1.0) # plot the analytically-derived sampling distribution\n",
    "plt.plot(np.linspace(-10,10,100),analytical,color = 'black',alpha=0.4,label=\"analytical\")\n",
    "plt.fill_between(np.linspace(-10,10,100), 0, analytical, where = np.linspace(-10,10,100) <= lower_bound, facecolor='red', interpolate=True, alpha = 0.5,label = \"Reject\")\n",
    "plt.fill_between(np.linspace(-10,10,100), 0, analytical, where = np.linspace(-10,10,100) >= upper_bound, facecolor='red', interpolate=True, alpha = 0.5)\n",
    "plt.legend()\n",
    "\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=2.0, top=1.2, wspace=0.2, hspace=0.2)\n",
    "plt.show()  \n",
    "\n",
    "print('The p-value of the observed effect is ' + str(round((percentileofscore(t_stat,t_stat_obs))/100,10)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Bootstrap F-test for Difference in Variances\n",
    "\n",
    "Now let's try out the diffence in Variances,\n",
    "\n",
    "\\begin{equation}\n",
    "H_0: \\frac{\\sigma^2_2}{\\sigma^2_1} = 1.0\n",
    "\\end{equation}\n",
    "\n",
    "where, $\\sigma^2_2 > \\sigma^2_1$.\n",
    "\n",
    "The F-statistic bootstrap realizations are calculated as:\n",
    "\n",
    "\\begin{equation}\n",
    "\\hat{F}^{\\ell} = \\frac{{s^2}^{\\ell}_2}{{s^2}^{\\ell}_1}\n",
    "\\end{equation}\n",
    "\n",
    "Once again we need to go an extra step, since the test assumes the variances are equal, to do this we pool all the data together and bootstrap resample for each new sample set the the approapriate number $n_{1}$ and $n_{2}$.\n",
    "\n",
    "* if you would like to see for yourself, try changing the code below:\n",
    "\n",
    "```python\n",
    "correct_samples_equal_variance = True\n",
    "```\n",
    "\n",
    "to: \n",
    "\n",
    "```python\n",
    "correct_samples_equal_variance = False\n",
    "```\n",
    "\n",
    " and observe the mismatch between the analytical and bootstrap t-statistic distributions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 266,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The p-value of the observed effect is 0.0015\n"
     ]
    }
   ],
   "source": [
    "L = 10000                                                 # number of bootstrap realizations, $L$, to sample the t-statistic               \n",
    "alpha = 0.05                                              # alpha level\n",
    "correct_samples_equal_variance = True                     # True - correct sample variances, False - only correct the means\n",
    "\n",
    "if stats.pvariance(por_shale) > stats.pvariance(por_sand):\n",
    "    F_stat_obs = stats.pvariance(por_shale)/stats.pvariance(por_sand)\n",
    "    na = len(por_shale); nb = len(por_sand)\n",
    "else:\n",
    "    F_stat_obs = stats.pvariance(por_sand)/stats.pvariance(por_shale)\n",
    "    na = len(por_sand); nb = len(por_shale)\n",
    "\n",
    "F_stat = np.zeros(L)                                      # make arrays to store the t-statistic, and p-value realizations\n",
    "    \n",
    "for l in range(0, L):                                     # loop over bootstrap realizations\n",
    "    por_shale_real = random.choices(np.concatenate([por_sand,por_shale]), weights=None, cum_weights=None, k=len(por_shale)) # bootstrap realization of shale porosity\n",
    "    por_sand_real = random.choices(np.concatenate([por_sand,por_shale]), weights=None, cum_weights=None, k=len(por_sand)) # bootstrap realization of sand porosity\n",
    "    \n",
    "    if stats.variance(por_shale) > stats.variance(por_sand): # consistent with numerator and denominator selection\n",
    "        F_stat[l] = stats.variance(por_shale_real)/stats.variance(por_sand_real) \n",
    "    else:\n",
    "        F_stat[l] = stats.variance(por_sand_real)/stats.variance(por_shale_real)\n",
    "            \n",
    "lower_bound = np.percentile(F_stat,alpha*0.5*100)\n",
    "upper_bound = np.percentile(F_stat,(1-alpha*0.5)*100)\n",
    "\n",
    "plt.subplot(121)                                          # original porosity histograms\n",
    "plt.hist(df_shale['Porosity'],color = 'gray',alpha = 0.3,edgecolor='black',bins = np.linspace(pormin,pormax,int(len(df)/3)),label='shale')\n",
    "plt.hist(df_sand['Porosity'],color = 'yellow',alpha = 0.2,edgecolor='black',bins = np.linspace(pormin,pormax,int(len(df)/3)),label='sand')\n",
    "plt.xlabel('Porosity (fraction)'); plt.ylabel('Frequency'); plt.title('Porosity Histogram')\n",
    "plt.legend()\n",
    "\n",
    "plt.subplot(122)                                          # bootstrap t-statistic distribution by bootstrap, analytical and observed t-statistic\n",
    "plt.hist(F_stat,color = 'red',alpha = 0.3,edgecolor='black',bins=np.linspace(0,15,100),density=True,label='bootstrap')\n",
    "plt.axvline(x=F_stat_obs,c='black',label='observed')\n",
    "plt.xlabel('F-statistic Bootstrap Realizations'); plt.ylabel('Frequency'); plt.title(\"Bootstrap and Analytical F-test Difference in Variances\")\n",
    "plt.xlim(0,15)\n",
    "\n",
    "analytical = F.pdf(np.linspace(0,15,100),(na-1),(nb-1)) # plot the analytically-derived sampling distribution\n",
    "plt.plot(np.linspace(0,15,100),analytical,color = 'black',alpha=0.4,label=\"analytical\")\n",
    "upper_bound = F.ppf(1-alpha, na-1, nb-1)\n",
    "\n",
    "plt.fill_between(np.linspace(0,15,100), 0, analytical, where = np.linspace(0,15,100) >= upper_bound, facecolor='red', interpolate=True, alpha = 0.5)\n",
    "plt.legend()\n",
    "\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=2.0, top=1.2, wspace=0.2, hspace=0.2)\n",
    "plt.show() \n",
    "\n",
    "print('The p-value of the observed effect is ' + str(round((100 - percentileofscore(F_stat,F_stat_obs))/100,5)))"
   ]
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    "#### Observations\n",
    "\n",
    "Some observations:\n",
    "\n",
    "* bootstrap can be applied to calculate the sampling distribution for a hypothesis test\n",
    "\n",
    "* we can then calculate the p-value of the observed effect as the percentile of this sampling distribution\n",
    "     \n",
    "* we must set the sample data to honor the null hypothesis and any associated assumptions, e.g. equal variances\n",
    "\n",
    "* we bootstrap the sampling statistic, t-statistic, as it is formulated given all hypothesis assumptions, this is the reason we don't just bootstrap the effect, the difference in means\n",
    "\n",
    "#### Comments\n",
    "\n",
    "This was a demonstration of bootstrap hypothesis testing for the significance in difference in means between 2 sample sets in Jupyter Notebook Python. \n",
    "\n",
    "I have many other demonstrations on data analytics and machine learning, e.g. on the basics of working with DataFrames, ndarrays, univariate statistics, plotting data, declustering, data transformations, trend modeling and many other workflows available at https://github.com/GeostatsGuy/PythonNumericalDemos and https://github.com/GeostatsGuy/GeostatsPy. \n",
    "  \n",
    "I hope this was helpful,\n",
    "\n",
    "*Michael*\n",
    "\n",
    "#### The Author:\n",
    "\n",
    "### Michael Pyrcz, Associate Professor, University of Texas at Austin \n",
    "*Novel Data Analytics, Geostatistics and Machine Learning Subsurface Solutions*\n",
    "\n",
    "With over 17 years of experience in subsurface consulting, research and development, Michael has returned to academia driven by his passion for teaching and enthusiasm for enhancing engineers' and geoscientists' impact in subsurface resource development. \n",
    "\n",
    "For more about Michael check out these links:\n",
    "\n",
    "#### [Twitter](https://twitter.com/geostatsguy) | [GitHub](https://github.com/GeostatsGuy) | [Website](http://michaelpyrcz.com) | [GoogleScholar](https://scholar.google.com/citations?user=QVZ20eQAAAAJ&hl=en&oi=ao) | [Book](https://www.amazon.com/Geostatistical-Reservoir-Modeling-Michael-Pyrcz/dp/0199731446) | [YouTube](https://www.youtube.com/channel/UCLqEr-xV-ceHdXXXrTId5ig)  | [LinkedIn](https://www.linkedin.com/in/michael-pyrcz-61a648a1)\n",
    "\n",
    "#### Want to Work Together?\n",
    "\n",
    "I hope this content is helpful to those that want to learn more about subsurface modeling, data analytics and machine learning. Students and working professionals are welcome to participate.\n",
    "\n",
    "* Want to invite me to visit your company for training, mentoring, project review, workflow design and / or consulting? I'd be happy to drop by and work with you! \n",
    "\n",
    "* Interested in partnering, supporting my graduate student research or my Subsurface Data Analytics and Machine Learning consortium (co-PIs including Profs. Foster, Torres-Verdin and van Oort)? My research combines data analytics, stochastic modeling and machine learning theory with practice to develop novel methods and workflows to add value. We are solving challenging subsurface problems!\n",
    "\n",
    "* I can be reached at mpyrcz@austin.utexas.edu.\n",
    "\n",
    "I'm always happy to discuss,\n",
    "\n",
    "*Michael*\n",
    "\n",
    "Michael Pyrcz, Ph.D., P.Eng. Associate Professor The Hildebrand Department of Petroleum and Geosystems Engineering, Bureau of Economic Geology, The Jackson School of Geosciences, The University of Texas at Austin\n",
    "\n",
    "#### More Resources Available at: [Twitter](https://twitter.com/geostatsguy) | [GitHub](https://github.com/GeostatsGuy) | [Website](http://michaelpyrcz.com) | [GoogleScholar](https://scholar.google.com/citations?user=QVZ20eQAAAAJ&hl=en&oi=ao) | [Book](https://www.amazon.com/Geostatistical-Reservoir-Modeling-Michael-Pyrcz/dp/0199731446) | [YouTube](https://www.youtube.com/channel/UCLqEr-xV-ceHdXXXrTId5ig)  | [LinkedIn](https://www.linkedin.com/in/michael-pyrcz-61a648a1)\n"
   ]
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