Module3-Statistics/M3C_HypothesisTesting_Significance_Pvalues.ipynb

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    "Introduction to Basic Probability and Statistics - Hypothesis Testing, Significance, P-Values\n",
    "<html>\n",
    "    <summary></summary>\n",
    "         <div> <p></p> </div>\n",
    "         <div style=\"font-size: 20px; width: 800px;\"> \n",
    "              <h1>\n",
    "               <left>Intro to Basic Probability and Statistics: Hypothesis Testing, Significance, P-Values.</left>\n",
    "              </h1>\n",
    "              <p><left>============================================================================</left> </p>\n",
    "<pre>Course: BIOM 421, Spring 2024\n",
    "Instructor: Brian Munsky\n",
    "Authors: Huy Vo, Ania Baetica, Brian Munsky\n",
    "Contact Info: munsky@colostate.edu\n",
    "</pre>\n",
    "         </div>\n",
    "    </p>\n",
    "\n",
    "</html>\n",
    "\n",
    "<details>\n",
    "  <summary>Copyright info</summary>\n",
    "\n",
    "```\n",
    "Copyright 2024 Brian Munsky\n",
    "\n",
    "Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:\n",
    "\n",
    "1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.\n",
    "\n",
    "2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.\n",
    "\n",
    "3. Neither the name of the copyright holder nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.\n",
    "\n",
    "THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS \"AS IS\" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.\n",
    "```\n",
    "<details>\n",
    "\n"
   ]
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    "![alt text](figuresC/image.png)"
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      "Note: you may need to restart the kernel to use updated packages.\n",
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      "Note: you may need to restart the kernel to use updated packages.\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy.random as rng\n",
    "import scipy.stats as stats\n",
    "%pip install statsmodels   \n",
    "%pip install seaborn\n",
    "\n",
    "# if you don't have it, uncomment the line above to install it\n",
    "import statsmodels"
   ]
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    "![alt text](figuresC/image-1.png)"
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      "C:\\Users\\Brian Munsky\\AppData\\Local\\Temp\\ipykernel_18808\\249685750.py:34: RuntimeWarning: invalid value encountered in log\n",
      "  LogNPairBefore = rng.lognormal(np.log(parametersPatients), 1)\n",
      "C:\\Users\\Brian Munsky\\AppData\\Local\\Temp\\ipykernel_18808\\249685750.py:35: RuntimeWarning: invalid value encountered in log\n",
      "  LogNPairAfter = rng.lognormal(np.log(parametersPatients+effect), 1)\n"
     ]
    }
   ],
   "source": [
    "# Example Data Sets\n",
    "# In this notebook, we are going to use several different pairs of data sets to illustrate\n",
    "# different hypothesis tests.\n",
    "\n",
    "# The first two data sets are unpaired sets of random numbers drawn from a NORMAL distribution\n",
    "# with different means but the same standard deviations.\n",
    "Nnormal = [100,120]\n",
    "normal0 = rng.normal(0, 1, Nnormal[0])\n",
    "normal1 = rng.normal(0.5, 1, Nnormal[1])\n",
    "\n",
    "# The next pair are paired data sets, where each pair of numbers is drawn from a NORMAL distribution,\n",
    "# but the second number in each pair is drawn from a normal distribution with a mean that is\n",
    "# different than the mean of the first number in the pair. The standard deviation of the two\n",
    "# distributions is the same.\n",
    "Npaired = 100\n",
    "parametersPatients = rng.normal(10, 0.5, Npaired) # \n",
    "effect = 0.2\n",
    "NormalPairBefore = rng.normal(parametersPatients, 1) \n",
    "NormalPairAfter = rng.normal(parametersPatients+effect, 1) \n",
    "\n",
    "# The next pair of data sets are unpaired data sets drawn from a LOGNORMAL distribution with the\n",
    "# same standard deviation and the same means.\n",
    "Nlognormal = [100,120]\n",
    "lognormal0 = rng.lognormal(0, 1, Nlognormal[0])\n",
    "lognormal1 = rng.lognormal(0, 1, Nlognormal[1])\n",
    "\n",
    "# The next pair are paired data sets, where each pair of numbers is drawn from a LOGNORMAL distribution,\n",
    "# but the second number in each pair is drawn from a lognormal distribution with a mean that is\n",
    "# different than the mean of the first number in the pair. The standard deviation of the two\n",
    "# distributions is the same.\n",
    "Npaired = 100\n",
    "parametersPatients = rng.normal(0, 0.5, Npaired) \n",
    "effect = 0.2\n",
    "LogNPairBefore = rng.lognormal(np.log(parametersPatients), 1)\n",
    "LogNPairAfter = rng.lognormal(np.log(parametersPatients+effect), 1)\n"
   ]
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   "source": [
    "# Hypothesis testing\n",
    "\n",
    "![alt text](figuresC/image-2.png)\n",
    "\n",
    "## The Testing Process\n",
    "\n",
    "![alt text](figuresC/image-3.png)\n",
    "\n",
    "## Interpreting Results\n",
    "\n",
    "The outcome of a hypothesis test provides insights into the plausibility of the null hypothesis. A rejection of the null hypothesis suggests evidence in favor of the alternative hypothesis, while a failure to reject implies insufficient evidence to warrant rejection."
   ]
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   "metadata": {},
   "source": [
    "# Significance and P-Values\n",
    "\n",
    "Hypothesis testing involves two critical concepts that serve as guiding beacons in our statistical journey: **significance** and **p-values**. These concepts provide us with quantitative measures to evaluate the strength of evidence in support of our hypotheses and to make informed decisions based on our analyses.\n",
    "\n",
    "## Significance: Separating Signal from Noise\n",
    "\n",
    "![alt text](figuresC/image-4.png)\n",
    "\n",
    "## Test Statistics: Quantifying Differences\n",
    "\n",
    "![alt text](figuresC/image-5.png)\n",
    "\n",
    "## P-Values: Assessing Evidence\n",
    "\n",
    "![alt text](figuresC/image-6.png)\n",
    "\n",
    "## Interpreting P-Values in the Context of Significance\n",
    "\n",
    "![alt text](figuresC/image-7.png)\n",
    "\n",
    "## Significance, P-Values, and Decision Making\n",
    "\n",
    "Significance, p-values, and test statistics play pivotal roles in the decision-making process during hypothesis testing. By setting a significance level ($\\alpha$) beforehand, we establish a threshold for rejecting the null hypothesis. If the calculated p-value falls below this threshold, and the test statistic exceeds critical values, we deem the results statistically significant and infer that the observed effect is unlikely to occur due to chance alone."
   ]
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   "source": [
    "# Parametric and Non-Parametric Tests \n",
    "\n",
    "**Parametric tests** make assumptions about the distribution of the data, typically assuming that the data follow a specific probability distribution, such as the normal distribution (see t-test below.)\n",
    "\n",
    "**Non-parametric tests**, on the other hand, do not make assumptions about the distribution of the data or make fewer assumptions compared to parametric tests (see Wilcox signed rank test below). They are used when the data do not meet the assumptions of parametric tests or when the data are ordinal or non-normally distributed.\n",
    "\n",
    "Here are some key differences between parametric and non-parametric tests:\n",
    "\n",
    "**Assumptions**: Parametric tests make specific assumptions about the population distribution, such as normality and homogeneity of variances, while non-parametric tests make fewer or no assumptions about the distribution of the data.\n",
    "\n",
    "**Type of Data**: Parametric tests are often used for interval or ratio scale data that are normally distributed, while non-parametric tests are more flexible and can be used with ordinal, interval, or ratio scale data, as well as non-normally distributed data.\n",
    "\n",
    "**Test Statistics**: Parametric tests use test statistics that are based on the parameters of the population distribution (e.g., mean, standard deviation), while non-parametric tests use test statistics that are based on the ranks or order of the data.\n",
    "\n",
    "**Power**: Parametric tests tend to have higher statistical power (ability to detect true differences or effects) when the assumptions are met, while non-parametric tests may have lower power but are more robust to violations of assumptions.\n",
    "\n",
    "In summary, the choice between parametric and non-parametric tests depends on the nature of the data, the assumptions that can be made about the data, and the specific research question being addressed. If the assumptions of parametric tests are met, they are generally preferred because they can provide more powerful statistical tests. However, if the assumptions are violated, non-parametric tests may be more appropriate."
   ]
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   "metadata": {},
   "source": [
    "# Parametric Test Example -- Student's T-Test\n",
    "![alt text](FiguresC/image8A.png)"
   ]
  },
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    "\n",
    "The **Student's t-test** is a **parametric statistical test** used to determine **is there is a significant difference between the means of two groups**. The t-test is commonly used in scientific research, especially in fields such as psychology, medicine, and biology, where it is used to compare means from experiments. For example, it often used to assess the effectiveness of interventions or treatments.\n",
    "\n",
    "It was developed by **William Sealy Gosset**, who published it **under the pseudonym \"Student\" in 1908** while working at the Guinness Brewery in Dublin, Ireland. \n",
    "\n",
    "The t-test is particularly useful when working with **small sample sizes** or **when the population standard deviation is unknown**.\n",
    "\n",
    "The formula for the t-test depends on whether the samples being compared are independent or dependent (paired). \n",
    "\n",
    "### Independent Samples t-test\n",
    "For independent samples, the t-statistic is computed by:\n",
    "$$\n",
    "t = \\frac{{\\bar{X}_1 - \\bar{X}_2}}{{s_p \\sqrt{\\frac{1}{n_1} + \\frac{1}{n_2}}}}\n",
    "$$\n",
    "\n",
    "Where:\n",
    "\n",
    "\\begin{align*}\n",
    "    & \\bar{X}_1 \\text{ and } \\bar{X}_2 \\text{ are the sample means of the two groups}, \\\\\n",
    "    & n_1 \\text{ and } n_2 \\text{ are the sample sizes of the two groups}, \\\\\n",
    "    & s_p \\text{ is the pooled standard deviation, given by:} \\\\\n",
    "    & s_p = \\sqrt{\\frac{{(n_1 - 1)s_1^2 + (n_2 - 1)s_2^2}}{{n_1 + n_2 - 2}}}, \\\\\n",
    "    & \\text{where } s_1 \\text{ and } s_2 \\text{ are the standard deviations of the two groups}.\n",
    "\\end{align*}\n",
    "\n",
    "Under the **Null Hypothesis** that the means of the two groups are equal, the t-statistic would follow a **t-distribution** with $n_1+n_2−2$ degrees of freedom.\n"
   ]
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",
      "text/plain": [
       "<Figure size 300x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plotting the Student's t Distribution\n",
    "\n",
    "# Make a figure plotting the Student's t distribution. Shade the area under the curve\n",
    "# that corresponds to the significance level alpha. Also, plot a vertical line at the\n",
    "# observed t-statistic value. The title of the plot should be the title parameter.\n",
    "def plot_t_distribution(ax, alpha, observed_value, title=' ', sided='two-sided'):\n",
    "    # Create a range of x values from -4 to 4\n",
    "    x = np.linspace(-4, 4, 1000)\n",
    "    # Create a t-distribution with df degrees of freedom\n",
    "    t = stats.t.pdf(x, 5)\n",
    "    # Plot the t-distribution\n",
    "    ax.plot(x, t, 'b', label='t-distribution')\n",
    "    # Shade the area under the curve that corresponds to the significance level alpha\n",
    "    if sided == 'two-sided':\n",
    "        ax.fill_between(x, 0, t, where=(x > stats.t.ppf(1-alpha/2, 5)) | (x < stats.t.ppf(alpha/2, 5)), color='b', alpha=0.3, label='reject H0 region')\n",
    "    elif sided == 'less':\n",
    "        ax.fill_between(x, 0, t, where=(x < stats.t.ppf(alpha, 5)), color='b', alpha=0.3, label='reject H0 region')\n",
    "    elif sided == 'greater':\n",
    "        ax.fill_between(x, 0, t, where=(x > stats.t.ppf(1-alpha, 5)), color='b', alpha=0.3, label='reject H0 region')\n",
    "\n",
    "    # Plot a vertical line at the observed t-statistic value\n",
    "    ax.axvline(observed_value, color='r', linestyle='--', label='observed t-statistic')\n",
    "    # Add a legend\n",
    "    ax.legend()\n",
    "    # Set the title of the plot\n",
    "    ax.set_xlabel('t-statistic')\n",
    "    ax.set_ylabel('P(t)')\n",
    "    ax.set_title(title)\n",
    "   \n",
    "t_statistic = -3.1\n",
    "significance_level = 0.05\n",
    "sided = 'less'\n",
    "fig, ax = plt.subplots(1, 1, figsize=(3, 3))\n",
    "plot_t_distribution(ax, significance_level, t_statistic, sided=sided, \\\n",
    "                    title=f't-distribution')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "#### P-values\n",
    "Under the null hypothesis that the two distributions have the same mean, the t-statistic would be close to zero. The P-value using the t-test is found by calculating the probability that the a random sample drawn from from a t-distributon would be at least as large/small as the calculated t-statistic.  \n",
    "\n",
    "The probability that a larger $t$ would be sampled by chance is found by calculating **survival function** for the absolute value of $t$ (i.e., $\\text{surv}(|t|) = 1-CDF(|t|)$). \n",
    "\n",
    "*Two-Sided Test*: In a two-sided test, the null hypothesis typically states that there is no difference between the means of the two related groups, while the alternative hypothesis states that there is a difference, without specifying the direction of the difference. The two-sided test is used when you want to determine if there is a significant difference between the means in either direction. In this case, the critical region is split between the two tails of the distribution, and the p-value that at last as large a difference would be observed in the mean of the two populations is determined as $PV(t) = 2*\\text{surv}(|t|)$.\n",
    "\n",
    "*One-Sided Test*: In a one-sided test, the null hypothesis states that there is no difference or that group 2 is greater than or equal to group 1, while the alternative hypothesis specifies that group 1 is greater than group 2. The one-sided test is used when you are specifically interested in whether one group is greater than the other, but not if it's smaller. The critical region is located entirely in one tail of the distribution, and the p-value for testing if is determined as $PV(t) = \\text{surv}(t)$.\n",
    "\n",
    "#### Important limitations of the t-test:\n",
    "\n",
    "Like any test, the t-test has important limitations that one should consider before applying the test:\n",
    "\n",
    "1) **Assumption of Normality**: The t-test assumes that the data in each group are normally distributed. If this assumption is violated, the results of the test may be invalid.\n",
    "\n",
    "2) **Sensitive to Outliers**: The t-test can be sensitive to outliers, particularly when sample sizes are small.\n",
    "\n",
    "3) **Equal Variances Assumption**: The traditional independent samples t-test assumes that the variances of the two groups are equal. If this assumption is violated, alternative versions of the t-test, such as Welch's t-test, should be used.\n",
    "\n",
    "4) **Sample Size**: The t-test may not perform well with very small sample sizes, as the t-distribution approaches the normal distribution only as sample size increases.\n",
    "\n",
    "### Examples of One- and Two-Sided t-tests."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "t-test using our code: t = -4.002976394333476 p-value = 8.575171337299273e-05\n",
      "t-test using built in code: t = -4.002976394333476 p-value = 8.575171337299273e-05\n"
     ]
    }
   ],
   "source": [
    "# Illustration of the Independent Student's t-test\n",
    "\n",
    "# Define a function for the t-test\n",
    "def ttest(data0, data1, alternative='two-sided' ):\n",
    "    # Compute the number of samples in each group\n",
    "    N = [len(data0), len(data1)]\n",
    "    Ndof = N[0] + N[1] - 2 # number of degrees of freedom\n",
    "    \n",
    "    # Compute the t-statistic\n",
    "    sp = np.sqrt(((N[0]-1)*np.var(data0) + (N[1]-1)*np.var(data1)) / (N[0]+N[1]-2))\n",
    "    t = (np.mean(data0) - np.mean(data1)) / (sp * np.sqrt(1/N[0] + 1/N[1]))\n",
    "    \n",
    "    # Compute the p-value for 1- and 2-sided t-test.\n",
    "    if alternative=='two-sided':\n",
    "        pv = 2*stats.t.sf(np.abs(t), Ndof)\n",
    "    elif alternative=='greater':\n",
    "        pv = stats.t.sf(t, Ndof)\n",
    "    elif alternative=='less':\n",
    "        pv = stats.t.sf(-t, Ndof)\n",
    "   \n",
    "    return t, pv\n",
    "\n",
    "# Compute the t-test\n",
    "alternative = 'two-sided'  # 'two-sided', 'greater', or 'less'\n",
    "t, pv = ttest(normal0, normal1, alternative=alternative)\n",
    "\n",
    "# Print the results of the t-test\n",
    "print('t-test using our code: t =', t, 'p-value =', pv)\n",
    "\n",
    "# Compare to built in t-test function:\n",
    "t_statistic, p_value = stats.ttest_ind(normal0, normal1, alternative=alternative)\n",
    "print('t-test using built in code: t =', t, 'p-value =', pv)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plotting Test Results to Visualize Significance\n",
    "\n",
    "Below are examples of various pots to visualize samples and their significance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 300x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the t-distribution and the observed t-statistic\n",
    "\n",
    "# Here, we plot the t-distribution with the observed t-statistic and the significance level\n",
    "# shaded. The title of the plot is the title parameter.  This give some insight into the\n",
    "# interpretation of the p-value, but is not typically included in a publication or report.\n",
    "\n",
    "degrees_of_freedom = len(normal0) + len(normal1) - 2\n",
    "significance_level = 0.05\n",
    "\n",
    "fig, ax = plt.subplots(1, 1, figsize=(3, 3))\n",
    "plot_t_distribution(ax, significance_level, t_statistic, sided=alternative, \\\n",
    "                    title=f't-distribution')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Significance Levels:\n",
      "* = 0.05\n",
      "** = 0.01\n",
      "*** = 0.001\n",
      "Significance Levels:\n",
      "* = 0.05\n",
      "** = 0.01\n",
      "*** = 0.001\n",
      "Significance Levels:\n",
      "* = 0.05\n",
      "** = 0.01\n",
      "*** = 0.001\n",
      "Significance Levels:\n",
      "* = 0.005\n",
      "** = 0.001\n",
      "*** = 0.0001\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 2000x500 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Making Box Plots and showing Significance using Seaborn\n",
    "import pandas as pd\n",
    "#!pip install seaborn\n",
    "import seaborn as sns\n",
    "\n",
    "# Put normal0 and normal1 into a pandas DataFrame\n",
    "df1 = pd.DataFrame({'Normal 0': normal0})  # Create a DataFrame with normal0\n",
    "df2 = pd.DataFrame({'Normal 1': normal1})  # Create a DataFrame with normal1\n",
    "df = pd.concat([df1, df2], axis=1) # Concatenate the two DataFrames (note, axis=1 means concatenate along the columns)\n",
    "\n",
    "def add_signif_bar(ax, x0, x1, p_value, bar_col='k', linewidth=1.2, fontsize=12, significance_levels=[0.05, 0.01, 0.001]):\n",
    "    # Add significance annotations to the plot\n",
    "    # Get the y-axis limits\n",
    "    ylim = ax.get_ylim()\n",
    "    edge = (ylim[1] - ylim[0]) * 0.02\n",
    "    bary = ylim[1] + (ylim[1] - ylim[0]) * 0.1\n",
    "    ax.plot([x0,x0,x1,x1], [bary-edge, bary, bary, bary-edge], lw=linewidth, c=bar_col)\n",
    "    ax.set_ylim([ylim[0], ylim[1] + (ylim[1] - ylim[0]) * 0.2])\n",
    "    # Add significance annotations to the plot\n",
    "    if p_value > significance_levels[0]: \n",
    "        significance_level = 'n.s.'\n",
    "    else:\n",
    "        significance_level = ''\n",
    "        for i, alpha in enumerate(significance_levels):\n",
    "            if p_value < alpha:\n",
    "                significance_level += '*' \n",
    "            else:\n",
    "                break\n",
    "    \n",
    "    ax.text((x0+x1)/2, bary, significance_level, ha='center', va='bottom', c='k')\n",
    "\n",
    "    print('Significance Levels:')\n",
    "    for i, significance_level in  enumerate(significance_levels):\n",
    "        stars = '*'*(i+1)\n",
    "        print(f'{stars} = {significance_level}')\n",
    "\n",
    "\n",
    "# Create figures with three subplots\n",
    "fig, ax = plt.subplots(1, 4, figsize=(20, 5))\n",
    "\n",
    "# Create a boxplot of the data using seaborn \n",
    "ax[0] = sns.boxplot(data=df, ax=ax[0])\n",
    "ax[0].set_title('Boxplot of Normal 0 and Normal 1')  # Set the title of the plot \n",
    "ax[0].set_ylabel('Value')  # Set the y-axis label of the plot\n",
    "add_signif_bar(ax[0], 0, 1, p_value)\n",
    "\n",
    "# Create a boxenplot of the data using seaborn \n",
    "ax[1] = sns.boxenplot(data=df, ax=ax[1])\n",
    "ax[1].set_title('Boxenplot of Normal 0 and Normal 1')  # Set the title of the plot \n",
    "ax[1].set_ylabel('Value')  # Set the y-axis label of the plot\n",
    "add_signif_bar(ax[1], 0, 1, p_value)\n",
    "\n",
    "# Create a violin of the data using seaborn \n",
    "ax[2] = sns.violinplot(data=df, ax=ax[2])\n",
    "ax[2].set_title('Violin of Normal 0 and Normal 1')  # Set the title of the plot \n",
    "ax[2].set_ylabel('Value')  # Set the y-axis label of the plot\n",
    "add_signif_bar(ax[2], 0, 1, p_value)\n",
    "\n",
    "# Create a pointplot of the data using seaborn\n",
    "ax[3] = sns.swarmplot(data=df, ax=ax[3])\n",
    "ax[3].set_title('Swarm plot of Normal 0 and Normal 1')  # Set the title of the plot \n",
    "ax[3].set_ylabel('Value')  # Set the y-axis label of the plot\n",
    "add_signif_bar(ax[3], 0, 1, p_value, significance_levels=[0.005, 0.001, 0.0001])\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### An aside on the one sided and two sided tests. \n",
    "\n",
    "Consider the situation for two data sets, where the t-statistic is 2.2. The positive t-statistic arises when the mean of the first group (Group0) is larger than that of the second group (Group1).  We can plot the t-distribution as we did above with as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x300 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Make 2 panel figures, one with two-sided and one with one-sided test:\n",
    "fig, ax = plt.subplots(1, 2, figsize=(6, 3))\n",
    "plot_t_distribution(ax[0], significance_level, 2.2, sided='two-sided', \\\n",
    "                    title=f't-distribution (two-sided)')\n",
    "plot_t_distribution(ax[1], significance_level, 2.2, sided='greater', \\\n",
    "                    title=f't-distribution (one-sided)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice on the left, that we do **not** have sufficient evidence to reject the hypothesis that the *two means are different*.\n",
    "\n",
    "But on the right, we **do** have sufficient evidence to reject the hypothesis that the mean of Group 1 is greater than or equal than that for Group 0.\n",
    "\n",
    "This seems like a paradox and can lead to a lot of confusion.  Read more about it here:\n",
    "\n",
    "https://www.onesided.org/articles/the-paradox-of-one-sided-v-two-sided-tests-of-significance.php"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Paired Values t-test\n",
    "\n",
    "The **paired t-test** is a statistical test used to determine whether there is a significant difference between the means of two related groups. It's typically used when the samples being compared are not independent but instead have some sort of natural pairing or matching. For example, the paired t-test might be used to compare the effectiveness of a medication before and after treatment in the same group of patients.\n",
    "\n",
    "Here's how the paired t-test works:\n",
    "\n",
    "**Data Collection**: You collect data from two related groups, where each observation in one group is paired with a corresponding observation in the other group. For example, if you're comparing measurements before and after giving a hypothetical medication, each patient's measurement before treatment is paired with their measurement after treatment.\n",
    "\n",
    "**Calculate Differences**: For each pair of observations, calculate the difference between the two measurements. You'll end up with a new set of differences.\n",
    "\n",
    "**Calculate Sample Mean and Standard Deviation of Differences**: Calculate the mean ($d$) and standard deviation ($\\sigma_d$) of these differences.\n",
    "\n",
    "**Compute the t-statistic**: Use the formula for the one-sample t-test to calculate the t-statistic:\n",
    "\n",
    "$$ t=\\frac{d}{\\sigma_d/\\sqrt{n}} $$\n",
    "\n",
    "Where:\n",
    "* $d$ is the mean of the differences.\n",
    "* $\\sigma_d$​ is the standard deviation of the differences.\n",
    "* $n$ is the number of pairs.\n",
    "\n",
    "**Determine the p-value**: Use the t-distribution with $n-1$ degrees of freedom to determine the p-value associated with the calculated t-statistic.\n",
    "\n",
    "**Limitations**\n",
    "* The differences between pairs should be normally distributed.\n",
    "* The paired differences should be independent of each other.\n",
    "\n",
    "## "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "t-test using our code: t = -0.662023069321699 p-value = 0.5087262037853344\n",
      "t-test using built in code: t = -0.662023069321699 p-value = 0.5087262037853344\n",
      "Significance Levels:\n",
      "* = 0.05\n",
      "** = 0.01\n",
      "*** = 0.001\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x300 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Let's Illustrate of the Paired t-test\n",
    "# Generate some paired data\n",
    "def pairedTTest(data0,data1,alternative='two-sided'):\n",
    "    # Compute the number of samples in each group\n",
    "    N = len(data0)\n",
    "    Ndof = N - 1 # number of degrees of freedom\n",
    "    \n",
    "    # Compute the t-statistic\n",
    "    mu = np.mean(data0-data1)\n",
    "    sig = np.std(data0-data1)\n",
    "    t = mu / (sig / np.sqrt(N))\n",
    "    \n",
    "    # Compute the p-value for the 1- and 2-sided test:\n",
    "    if alternative=='two-sided':\n",
    "        pv = 2*stats.t.sf(np.abs(t), Ndof)\n",
    "    elif alternative=='greater':\n",
    "        pv = stats.t.sf(t, Ndof)\n",
    "    elif alternative=='less':\n",
    "        pv = stats.t.sf(-t, Ndof)\n",
    "    return t, pv    \n",
    "\n",
    "N = len(NormalPairBefore) # number of patients\n",
    "\n",
    "# Compute the t-test\n",
    "alternative = 'two-sided'  # 'two-sided', 'greater', or 'less'\n",
    "t, pv = ttest(NormalPairBefore, NormalPairAfter, alternative=alternative)\n",
    "\n",
    "# Print the results of the t-test\n",
    "print('t-test using our code: t =', t, 'p-value =', pv)\n",
    "\n",
    "# Compare to built in t-test function:\n",
    "t_statistic, p_value = stats.ttest_rel(NormalPairBefore, NormalPairAfter, alternative=alternative)\n",
    "print('t-test using built in code: t =', t, 'p-value =', pv)\n",
    "\n",
    "# Plot the t-distribution and the observed t-statistic using our previous function\n",
    "degrees_of_freedom = N - 1\n",
    "significance_level = 0.05\n",
    "fig, ax = plt.subplots(1, 2, figsize=(6, 3))\n",
    "plot_t_distribution(ax[0], significance_level, t_statistic, sided=alternative, \\\n",
    "                    title=f't-distribution')\n",
    "\n",
    "# Plot the data and the significance using seaborn\n",
    "df1 = pd.DataFrame({'Before': NormalPairBefore})  # Create a DataFrame with NormalPairBefore\n",
    "df2 = pd.DataFrame({'After': NormalPairAfter})  # Create a DataFrame with NormalPairAfter\n",
    "df = pd.concat([df1, df2], axis=1) # Concatenate the two DataFrames (note, axis=1 means concatenate along the columns)\n",
    "\n",
    "# Create a boxenplot \n",
    "ax[1] = sns.boxenplot(data=df)\n",
    "ax[1].set_title('Boxplot of Pair 0 and Pair 1')  # Set the title of the plot \n",
    "ax[1].set_ylabel('Value')  # Set the y-axis label of the plot\n",
    "add_signif_bar(ax[1], 0, 1, pv)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Non-Parametric Test Example 1 - Wilcox Ranked Sum Test (a.k.a, the Mann-Whitney U Test)\n",
    "\n",
    "This **Wilcox Ranked Sum** test is used to compare the **medians** of two independent groups. This **non-parametric test** is typically used when the assumptions of the independent samples (needed for the t-test above) are not met, such as when the data are not normally distributed or when the variances are not equal.\n",
    "\n",
    "Here's a brief overview of the Wilcoxon rank-sum test (Mann-Whitney U test):\n",
    "\n",
    "**Purpose**: The Wilcoxon rank-sum test is used to determine whether the distributions of two independent groups differ significantly in terms of their medians.\n",
    "\n",
    "**Assumptions**: The main assumption of the Wilcoxon rank-sum test is that the two groups are independent and that the data within each group are at least ordinal (that is there is some natural ranking for the data, i.g., $a<b<c<c<d,\\ldots $).\n",
    "\n",
    "**Null Hypotheses**.  Like the t-test, the Wilcox Ranked Sum can be evaluated as a **two-sided** or **one-sided** test.  The corresponding Null-Hypotheses are:     \n",
    "* **Two-Sided Test Null Hypothesis**:  The medians of the two independent groups are equal.\n",
    "* **Left Tailed Test Null Hypothesis**: The median of group 1 is greater than or equal to the median of group 2.\n",
    "* **Right Tailed Test Null Hypothesis**: The median of group 1 is less than or equal to the median of group 2.\n",
    "\n",
    "**Procedure**:\n",
    "1) Combine the data from the two groups into a single dataset.\n",
    "2) Rank all the observations in the combined dataset from smallest to largest, ignoring the group labels.\n",
    "3) Calculate the sum of ranks for each group.\n",
    "4) Use the smaller of the two sums of ranks as the test statistic (often denoted as U).\n",
    "5) Compare the test statistic to critical values from the Wilcoxon rank-sum distribution or calculate a p-value.\n",
    "\n",
    "**Interpretation**: If the test statistic is significantly different from what would be expected by chance, it suggests that the distributions of the two groups differ significantly in terms of their medians.\n",
    "\n",
    "**Limitations**\n",
    "The Wilcoxon rank-sum test is a non-parametric alternative to the independent samples t-test and is particularly useful when the assumptions of the t-test are not met. It does not assume normality or equal variances and is based on the ranks of the observations rather than their actual values.  However, like all tests, it has limitations:\n",
    "\n",
    "* **Assumption of Independence**: The Wilcoxon rank-sum test assumes that the observations within each group are independent of each other and that the two groups are independent of each other. Violations of this assumption can lead to inaccurate results.\n",
    "\n",
    "* **Ordinal Data Requirement**: While the Wilcoxon rank-sum test does not require the data to be normally distributed, it does require that the data be at least ordinal. If the data are purely nominal (e.g., categories without a natural order), the test may not be appropriate.\n",
    "\n",
    "* **Sensitivity to Ties**: The Wilcoxon rank-sum test can be sensitive to ties (i.e., identical values) in the data, especially if there are many ties or if the ties are not evenly distributed between the groups. This can affect the accuracy of the test results.\n",
    "\n",
    "* **Less Power Than the t-test**: In general, parametric tests such as the independent samples t-test tend to have more statistical power (i.e., are better at detecting true differences) than non-parametric tests like the Wilcoxon rank-sum test, especially when the assumptions of the parametric tests are met.\n",
    "\n",
    "* **Difficulty in Interpreting Effect Size**: While the Wilcoxon rank-sum test can determine whether there is a statistically significant difference between the groups, it does not provide a direct measure of effect size. Interpreting the practical significance of the results can therefore be more challenging compared to parametric tests.\n",
    "\n",
    "## Example for Performing the Wilcox Ranked Sum test for unpaired data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Wilcoxon ranked sum test: t = -3.8650826968376326 p-value = 0.00011105156694776047\n"
     ]
    }
   ],
   "source": [
    "# Now, let's apply the Wilcoxon Ranked Sum Test to our original data sets\n",
    "# Compute the Wilcoxon ranked sum test\n",
    "t, pv = stats.ranksums(normal0, normal1)\n",
    "print('Wilcoxon ranked sum test: t =', t, 'p-value =', pv)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example for Performing the Wilcox Ranked Sum test for Paired data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Wilcoxon ranked sum test: t = 2327.0 p-value = 0.49600544229157995\n",
      "t-test: t = -0.7525486295274858 p-value = 0.45350687005184187\n"
     ]
    }
   ],
   "source": [
    "# Now, let's apply the Wilcoxon Ranked Sum Test to our paired data sets\n",
    "# Compute the Wilcoxon ranked sum test\n",
    "t, pv = stats.wilcoxon(NormalPairBefore, NormalPairAfter)\n",
    "print('Wilcoxon ranked sum test: t =', t, 'p-value =', pv)\n",
    "\n",
    "# Let's see how that compares to the t-test\n",
    "t, pv = pairedTTest(NormalPairBefore, NormalPairAfter)\n",
    "print('t-test: t =', t, 'p-value =', pv)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Non-Parametric Test Example 2 - Komogorov Smirnov (KS) Test\n",
    "\n",
    "The **Kolmogorov-Smirnov test**, often abbreviated as the **KS test**, is another non-parametric test after mathematicians Andrey Kolmogorov and Nikolai Smirnov. It was first introduced by Kolmogorov in 1933 and later refined by Smirnov in 1948. Originally developed to test goodness-of-fit for continuous probability distributions (we will use it for this a lot later int he course), the KS test has since found widespread application in various fields, including statistics, physics, biology, and finance.\n",
    "\n",
    "As a **non-parametric** test, meaning it makes no assumptions about the underlying probability distribution of the data. Unlike parametric tests, which rely on specific distributional assumptions, the KS test is more flexible and can be applied to data with unknown distributions or distributions that deviate from normality.\n",
    "\n",
    "**Specific Null Hypotheses:**\n",
    "The KS test is designed to test whether a sample comes from a specific continuous distribution, or to compare two samples to determine if they are drawn from the same distribution. The specific null hypotheses tested by the KS test depend on the context:\n",
    "\n",
    "* **Goodness-of-Fit Test**: The null hypothesis for a goodness-of-fit test is that the sample data are drawn from a specified theoretical distribution.\n",
    "\n",
    "* **Two-Sample Test**: The null hypothesis for a two-sample KS test is that the two samples are drawn from the same continuous distribution.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "**The KS Statistic** \n",
    "\n",
    "The test statistic, denoted as $D$, is computed as the maximum absolute difference between the empirical cumulative distribution functions (ECDFs) of the two samples (for a two-sample test) or between the ECDF of the sample and CDF of the theoretical distribution (for a one-sample test). Mathematically, it is calculated as follows:\n",
    "\n",
    "$$D_{\\text{2-sample}}= {\\rm max}_i \\left| F_1(x_i)−F_2(x_i) \\right|$$\n",
    "$$D_{\\text{1-sample}}= {\\rm max}_j \\left| F_1(x_j)−F(x_j) \\right|$$\n",
    "where $F_1(x_i)$ and $F_2(x_i)$ are the empirical CDFs of the two samples at the $i^{\\rm th}$ observation, $F(x_i)$ is the CDF of the theoretical distribution at the $i^{\\rm th}$  observation, $x_i$ and $y_j$ are the ordered values of the samples and the theoretical distribution, respectively.\n",
    "\n",
    "**Calculating P-Values for the KS Test**:\n",
    "Once the test statistic $D$ is computed, the p-value is obtained by comparing it to critical values from the Kolmogorov distribution (for one-sample tests) or the limiting distribution (for large sample sizes in two-sample tests) or by simulation or tabulation (for small sample sizes in two-sample tests). The specific distribution of the test statistic under the null hypothesis depends on the sample size, denoted by $n$, and whether it's a one-sample or two-sample test.\n",
    "\n",
    "* **P-Values for One-Sample Test**:\n",
    "    \n",
    "    For a one-sample KS test (where we compare a sample to a specified theoretical distribution), the distribution of the test statistic $D$ is approximated by the **Kolmogorov distribution**, which is derived from the properties of the Kolmogorov-Smirnov statistic. The Kolmogorov distribution's cumulative distribution function (CDF) is complex and cannot be represented by a simple mathematical formula. Instead, critical values or p-values are typically obtained from tables or computational algorithms.\n",
    "\n",
    "* **P-Values for Two-Sample Test**:\n",
    "    \n",
    "    For a two-sample KS test, when comparing two samples to determine if they are drawn from the same distribution, the distribution of the test statistic $D$ depends on the sample sizes $n_1$​ and $n_2$​. When both sample sizes are large (usually $n_1,n_2>35$), the distribution of $D$ can be approximated by the limiting distribution derived by Smirnov. However, for smaller sample sizes, the distribution of $D$ can be complex and is typically determined empirically through simulation or tabulation.\n",
    "\n",
    "For **two-sided** tests, where the alternative hypothesis is that the samples are not drawn from the same distribution, the p-value is computed as the probability of observing a test statistic greater than or equal to the observed value, plus the probability of observing a test statistic smaller than or equal to the negative of the observed value. \n",
    "\n",
    "For **one-sided** tests, the p-value is calculated using only one of these probabilities, depending on the direction of the alternative hypothesis.\n",
    "\n",
    "In summary, the Kolmogorov-Smirnov test is a powerful tool in statistical analysis, particularly useful when distributional assumptions are unknown or not met. Its versatility and simplicity make it a valuable asset in hypothesis testing and model validation across a wide range of disciplines."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Python Example of KS Test."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Significance Levels:\n",
      "* = 0.05\n",
      "** = 0.01\n",
      "*** = 0.001\n",
      "KS test using built in code: KS = 0.26666666666666666 p-value = 0.000667268621404735\n"
     ]
    },
    {
     "data": {
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mJydHUZOSnp6O6Oho7N27Fzt37oS3tzd27typdRwtW7bEu+++i0aNGqFChQq4efMmtmzZAj8/P9jY2Kg97t1338Xs2bMxffp0BAQE4Pbt25g1axa8vLxU/m4UxcTEBLNnz8bw4cPRvXt3jBgxAi9fvsSMGTNU3rrRRIUKFXDw4EG8/fbb6NevH3788Uf07t0bhw8fxrhx4zBw4ED4+/ujYsWKiI2NxbZt27Bv3z4MGjSo0Nt2W7ZswZo1azBgwAA0b94cjo6OePToEdatW4fr16/jyy+/VNx6fOONNwAAS5cuRWhoKMzNzVGvXj34+/ujQoUKGDlyJKZPnw5zc3Ns3boVly9fLnA9+TnmzZuHkJAQmJqaolGjRkrdleW6dOmiGAfI1dUVDx48wJIlS+Dh4aG47aYuJlW1Mv3798fGjRsxcuRI3L59G+3atUNOTg5Onz4Nb29v9OvXT8ufChkEKVvPEhXWmwb5WtwDEEaPHq10vLxnxYIFC5T2y3ug/PTTT4p9AQEBQoMGDYSIiAjB19dXsLS0FCpXrixMnTpVyMzMVDoeanrTnD17Vu1ryN+TIDw8XAgICBBsbW0FGxsbwcfHR5g3b57i+UePHgk9e/YUKlSoINjb2wvvvPOOcO3atQK9GTTtTSP377//CqNGjRJq164tWFpaCtbW1oKPj48QFhamFGNoaKjSe21tbS3UqFFD6NKli7BhwwYhPT29wLnl72FhJk+eLPj6+goVKlQQLC0thZo1awoTJkwQ4uPjCz0uPT1dmDhxolC1alXByspKaNq0qfDrr78KoaGhSj1f1P3MBaHgz00QBGHdunVCnTp1BAsLC6Fu3brChg0bCpxTHXWv9+XLl0KLFi0EMzMzYceOHcLDhw+FL774QmjdurVQqVIlwczMTLC3txdatmwpLF++XKnXjyo3btwQPvnkE8HX11dwdXUVzMzMhAoVKggBAQHCli1bCpSfMmWKUKVKFcHExETpd+PkyZOCn5+fYGNjI7i6ugrDhw8XLly4IAAQNm7cqDg+PT1dGD58uODq6irIZDKl39/8v3+LFi0S/P39BRcXF8HCwkKoUaOGMGzYMCEqKkqjmPL3phEEQUhNTRW+/PJLxc+lYsWKQvv27YWTJ08W+j6R4ZIJgpp6ZCIDExgYiPj4eL2aQ4WIyBiwzQgRERFJiskIERERSYq3aYiIiEhSrBkhIiIiSTEZISIiIkkxGSEiIiJJ6cWgZzk5OXjy5Ans7e01Go6biIiIpCcIAl69elXkfER6kYw8efIE1atXlzoMIiIiKoaHDx8WOgqxXiQj8iGFHz58CAcHB4mjISIiIk0kJiaievXqRU7YqBfJiPzWjIODA5MRIiIiPVNUEws2YCUiIiJJMRkhIiIiSTEZISIiIknpRZsRTQiCgKysLGRnZ0sdClG5MDc3h6mpqdRhEBGVmEEkIxkZGYiJiUFKSorUoRCVG5lMhmrVqsHOzk7qUIiISkTvk5GcnBxERkbC1NQUVapUgYWFBQdGI4MnCALi4uLw6NEj1KlThzUkRKTX9D4ZycjIQE5ODqpXrw4bGxupwyEqN66uroiKikJmZiaTESLSawbTgLWwYWaJDBFrAInIUPAbnIiIiCTFZISIiIgkpXUycvToUXTp0gVVqlSBTCbDr7/+WuQxR44cQbNmzWBlZYWaNWvi22+/LU6sREREZIC0TkaSk5PRuHFjrFixQqPykZGR6NSpE9q0aYOLFy9i6tSpGDt2LH755RetgzU0gwcPhkwmK/B45513FGUuXryI3r17w93dHVZWVqhbty5GjBiBO3fuAACioqKUjrW3t0eDBg0wevRo3L17V+l6mzZtUnm9devWFRrnL7/8Ah8fH1haWsLHxwe7d+8u/TeDiIiMlta9aUJCQhASEqJx+W+//RY1atTAkiVLAADe3t44d+4cFi5ciJ49e6o8Jj09Henp6YrtxMREbcPUG++88w42btyotM/S0hIAsGfPHvTs2RPBwcHYunUratWqhdjYWPz000+YNm0aduzYoTjm4MGDaNCgAVJSUnD16lUsXboUjRs3xh9//IEOHTooyjk4OOD27dtK13N0dFQb36lTp9C3b1/Mnj0b3bt3x+7du9GnTx8cP34cLVu2LI23gIiICrFlC3D+fNmd/63LK1AxIRKVw/qj/v/5lt2FClHmXXtPnTqFoKAgpX3BwcFYv349MjMzYW5uXuCYuXPnYubMmcW6niAAUo19ZmMDaNvBwdLSEpUqVSqwPyUlBUOGDEGnTp2UaiK8vLzQsmVLvHz5Uql8xYoVFeepWbMmunTpgg4dOmDYsGH4999/FV0/ZTKZyuups2TJErz99tuYMmUKAGDKlCk4cuQIlixZgm3btmn3YomISCsPHwKDBpXtNXpiB9rgOE6dbgYYajLy9OlTuLu7K+1zd3dHVlYW4uPjUbly5QLHTJkyBWFhYYrtxMREVK9eXaPrpaQAUg1ImZQE2NqWzrn++usvxMfH49NPP1X5vJOTU6HHm5iYYNy4cejevTvOnz+PFi1aFCuOU6dOYcKECUr7goODFTVdRERUdl7fkYebGzB8eNlco+k3N4FUoOJb3mVzAQ2Uy6Bn+cdDEARB5X45S0tLxa0KQ7dnz54Cw3l/9tlnitdfv379Yp9bfmxUVJQiGUlISFC6np2dHZ4+far2HOqSycKOISLSJcnJwM2bUkdRPEeOiMsx1X/DtOOLgdKefy0nB0h9BshkqNulXumeWwtlnoxUqlSpwBdXbGwszMzMULFixVK/no2NWEMhheIMANuuXTusXr1aaZ+zszO+++67EsejKumzt7fHhQsXFNvyweKio6Ph4+Oj2D916lRMnTq1wPHy83LALSLSF61aAdeuSR1FyQx+MAOIv1R2F2jcuHhfYqWkzJMRPz8//PHHH0r79u/fD19fX5XtRUpKJiu9WyXlwdbWFrVr1y6wv27dugCAW7duwc/Pr1jnvvn6XwEvLy/FPhMTE5XXq1KlCi5duqTYdnZ2BqA+mcxfW0JEpItevsxNRGrUkDSUYnO0y0bVf2+JG2vWAC4upXsBmQzw9y/dc2pJ62QkKSkJ9+7dU2xHRkbi0qVLcHZ2Ro0aNTBlyhQ8fvwYmzdvBgCMHDkSK1asQFhYGEaMGIFTp05h/fr1bPxYhKCgILi4uGD+/Pkqu9K+fPmy0HYjOTk5WLZsGby8vPDmm28WeT0zMzOVSYqfnx8OHDig1G5k//798Jf4F5eISBORkeLSzQ148EDaWDQWGwu89ZbYehUA/hOA9HTA0hIYNgwwwLmotE5Gzp07h3bt2im25Q1NQ0NDsWnTJsTExCA6OlrxvJeXF8LDwzFhwgSsXLkSVapUwbJly9R26zU26enpBWoezMzM4OLignXr1qF379547733MHbsWNSuXRvx8fHYuXMnoqOjsX37dsUxz549w9OnT5GSkoJr165hyZIlOHPmDP78888STaI2btw4tG3bFvPmzUPXrl3x22+/4eDBgzh+/Hixz0lE+mniRGDPHqmj0E5ysrisWVPaOLRy4ACQb5woAMA77xhkIgIUIxkJDAxUtEVQZdOmTQX2BQQEKLVToFz79u0r0KOoXr16uHXrFrp27YqTJ09i7ty5GDBggKJXUfv27TFnzhylYzp27AgAsLGxgYeHB9q1a4e1a9eqrO3Qhr+/P7Zv344vvvgC06ZNQ61atbBjxw6OMUJkZF69AhYtkjqK4ivm3e6yFxkJpKYq7ztxQlz+3/8B8s96mQyoVq18YytHMqGwzEJHJCYmwtHREQkJCXBwcFB6Li0tDZGRkfDy8oKVlZVEERKVP/7uU3m6fBlo0gSoUAH47Tepo9GOhQXQrBlgVi79R7WwZAmQb+iEAs+PG1de0ZSJwr6/89K1Hw0REZWx48eBiAjtjpGPd1GnDtCmTamHZJz27xeX9vZie5C8XF2Brl3LPyaJMBkhIjIiWVlAp07ibZfiqCfdUBT6JSkJ2LsXSEtTX0beg3HPHqBt23IJS1cxGSEiMiIPH4qJiLk5MGSIdsdaWgIff1w2cRmcL78EvvlGs7Le0o18qiuYjBARGZi0NEDdIMn//CMua9YUh6ygMnL6tLhs2lS85aJOu3aFP28kmIwQERmQlBSgbl3g8ePCy9WqVT7x6LzsbGDx4qLfMG1duSIuN2wQRzelQjEZISIyIDdu5H6vWlurLmNpCQwcWH4x6bT9+wE1E5KWmJWVmBlSkZiMEBEZkPv3xWXr1mKvGSqCvAajcWOgc+fSPXdAgPqMkJQwGSEi0kOPHgEffQS8eKG8/8kTcalXI45qIydHbEV7+XLpnE+evfXsCUybVjrnJK0xGSEi0kM//FD40Oy+vuUXS7m6dAlYtar0z6uzQ7QaByYjRER6SD5f6YAB4j/1ednbA4GB5R5S+bhxQ1w2agRMn14653RzE+9rkXQEPZCQkCAAEBISEgo8l5qaKty4cUNITU2VILKSCQ0NFQAUeAQHByvKXLhwQejVq5fg5uYmWFpaCnXq1BGGDx8u3L59WxAEQYiMjFQ61s7OTvDx8RFGjRol3LlzR+l6GzduVHm97777Tm2M165dE3r06CF4eHgIAIRvvvmmTN4L0p4+/+5TyeTkCAIgPrZskTqacnTkSO4L//BDqaMhDRT2/Z2XSfmnP5TXO++8g5iYGKXHtm3bAAB79uxBq1atkJ6ejq1bt+LmzZvYsmULHB0dMS3fvc2DBw8iJiYGly9fxtdff42bN2+icePGOHTokFI5BweHAtcbWEiz+pSUFNSsWRP/+9//UKlSpdJ/A4hIa/JRxAGghHNh6pcdO3LXQ0Kki4NKneHdphEEsaO9FGxsxJkVtWBpaanySz4lJQVDhgxBp06dsHv3bsV+Ly8vtGzZEi9fvlQqX7FiRcV5atasiS5duqBDhw4YNmwY/v33X5i+nnZaJpNplVQ0b94czZs3BwBMnjxZq9dGRGUjb9vNFi2ki0NrOTnA3bvi2B7FIZ/9ffFio5q3xRgYXjKSkgLY2Ulz7aQkwNa2VE71119/IT4+Hp+q6f/u5ORU6PEmJiYYN24cunfvjvPnz6OFXn1iEVFh/1fJJ62bNg0w0af67VGjSmfY17feKvk5SKcYXjKiZ/bs2QO7fMnTZ599BsvXMzjWr1+/2OeWHxsVFaVIRhISEpSuZ2dnh6fqxo0mIkkIgtgA9ejRwsvp3SiqBw6ISycnwKyYXz9NmogPMiiGl4zY2Ig1FFJdW0vt2rXD6tWrlfY5Ozvju+++K3E4giAAEG/NyNnb2+OCvKoTYg0KAERHR8PHx0exf+rUqZg6dWqJYyAi7cXGFp2IVKyoZz1mTp/OHdPj9m2xBwvRa4aXjMhkpXarpDzY2tqitooWaHVfDyF869Yt+BWz//vNmzcBiO1M5ExMTFRer0qVKrgkn84aYkJERNKQf2dXqyZ+b6tiYVH8yoVyl5AAtGolrlesyInhqAB9+VU2OkFBQXBxccH8+fOVGrDKvXz5stB2Izk5OVi2bBm8vLzw5ptvFnk9MzMzlUkKEZWvvXuBTp3E9dq1i1Xhqnuio3PXlyzRuqE/GT4mIxJLT08v0GbDzMwMLi4uWLduHXr37o333nsPY8eORe3atREfH4+dO3ciOjoa27dvVxzz7NkzPH36FCkpKbh27RqWLFmCM2fO4M8//1T0pCmOjIwM3Hg9yFBGRgYeP36MS5cuwc7OjskLURn45JPcdYOZ7DU+XlzWrw/83/9JGwvpJCYjEtu3bx8qV66stK9evXq4desWunbtipMnT2Lu3LkYMGAAEhMTUb16dbRv3x5z5sxROqZjx44AABsbG3h4eKBdu3ZYu3ZtiROGJ0+eKNWsLFy4EAsXLkRAQAAiIiJKdG4iUpaTA/z7r7g+cyYwbpy08ZSauDhxydszpIZMkLdy1GGJiYlwdHREQkICHBwclJ5LS0tDZGQkvLy8YGVlJVGEROWPv/u6TRDEWXNjYzU/5uVLYPhwsS1IaqoetQkpysqVwJgxQI8ewC+/SB0NlaPCvr/zMpRfdSIinXLwIBAUVLxjvbwMKBEBgC+/FJcuLtLGQTrLkH7diYh0xrlz4rJyZe2GbDcxAT76qGxikkRCAvD8ubher560sZDOYjJCRFQG5N1zP/yw9CaX1UuvhxgAAHz8sXRxkE5jMkJEVAIJCeLs8/KGp3Lp6eKyZs3yj0knxMeLb0xkpLjdoQNgbi5tTKSzmIwQEZXAiRPA9euqn7O2NuJpVA4ezJ1EBwA6d5YuFtJ5TEaIiEpAXiMSEgLkm9kBzs6AvX35xySJ58+BvGMmHT8uLvv3F2fZ1WK2cDI+TEaIiLR09Cjwww9i992zZ8V9DRoAHh7SxiWZR4+AunXF/sj5+foyEaEiMRkhItLSyJHK7TIBIM88k8bn+HExETE3Bxwdc/e7ugLdukkWFukPJiNERFrIzgbu3hXXJ08G7OzEud8GDJA2rnKRlgaEhwPJycr7f/9dXA4aBKxbV/5xkd5jMkLFFhgYiCZNmmDJkiXFOj4iIgLt2rXDixcvCp30j0iXPHoEZGWJlQBz5gAlmPpJ/yxaBHzxhfrnjbp6iErCROoAjNXgwYPRLV/15c8//wwrKyvMnz8fAJCcnIzPPvsMNWvWhJWVFVxdXREYGIg9e/YU65qbNm0q1pd+REQEZDIZXr58qbR/165dmD17tkbnCAwMxPjx45X2+fv7IyYmBo55q3WJdJy8waqXl5ElIgBw+rS4fOMNIDhY+TFgAPD++9LGR3qLNSM6Yt26dRg9ejRWrlyJ4cOHAwBGjhyJM2fOYMWKFfDx8cGzZ89w8uRJPHv2TOJoRc7OziU63sLCApXYsI30jHwwM6MaPyQ9XawV+eMPcXvJEqB9e0lDIgMj6IGEhAQBgJCQkFDgudTUVOHGjRtCamqq0v6k9CS1j9RMzcumZKRoVFZboaGhQteuXQVBEIR58+YJlpaWws8//6xUxtHRUdi0aZNW57106ZIQGBgo2NnZCfb29kLTpk2Fs2fPCocPHxYAKD2mT58uCIIgbNmyRWjWrJlgZ2cnuLu7C/379xf+++8/QRAEITIyssBxoaGhgiAIQkBAgDBu3DjFtVeuXCnUrl1bsLS0FNzc3ISePXsqXmv+c0RGRipievHiheIcx48fF9q2bStYW1sLTk5OQlBQkPD8+XOt3gNjoe53n8rWlCmCAAjC6NFSR1KOtm4VXzQgCCYmgvD684GoKIV9f+dlsDUjdnPt1D7XqU4n/DngT8W220I3pGSmqCwb4BGAiMERim3PpZ6IT4kvUE6YXrzJjydPnoyVK1diz5496Nixo9JzlSpVQnh4OHr06AF7DQcrGDhwIN58802sXr0apqamuHTpEszNzeHv748lS5bgyy+/xO3btwEAdnbie5SRkYHZs2ejXr16iI2NxYQJEzB48GCEh4ejevXq+OWXX9CzZ0/cvn0bDg4OsLa2LnDdc+fOYezYsdiyZQv8/f3x/PlzHDt2DACwdOlS3LlzBw0bNsSsWbMAAK6uroiKilI6x6VLl9ChQwcMHToUy5Ytg5mZGQ4fPozs7Gyt3lOi4khJAd59F7h3r/By8mlWjKpm5MqV3PVffgHc3KSLhQySwSYj+mDv3r347bffcOjQIbRXUeW5du1aDBw4EBUrVkTjxo3x1ltvoVevXmjdurXac0ZHR2PSpEmoX78+AKBOnTqK5xwdHSGTyQrcGhk6dKhivWbNmli2bBlatGiBpKQk2NnZKW7HuLm5qW1zEh0dDVtbW7z77ruwt7eHh4cH3nzzTcV1LSwsYGNjU+htmfnz58PX1xerVq1S7GvQoIHa8kSl6cQJ4PBhzcsX8meov44cAWbOBDIylPfLR1JdvpxddalMGGwykjQlSe1zpibKrc5iJ8aqLWsiU27jGzUuqkRx5dWoUSPEx8fjyy+/RPPmzQvUfrRt2xb379/HP//8gxMnTuDvv//G0qVLMXPmTEybNk3lOcPCwjB8+HBs2bIFHTt2RO/evVGrVq1C47h48SJmzJiBS5cu4fnz58jJyQEgJhg+GraOf/vtt+Hh4YGaNWvinXfewTvvvIPu3bvDxsZGo+MBsWakd+/eGpcnKk3yhqkBAWLziMK4ugI1apR9TOXum28Kz8j8/MovFjIqBtubxtbCVu3DysxK47LW5tYalS2OqlWr4siRI4iJicE777yDV69eFShjbm6ONm3aYPLkydi/fz9mzZqF2bNnIyP/fy6vzZgxA9evX0fnzp3x999/w8fHB7t371YbQ3JyMoKCgmBnZ4cffvgBZ8+eVZRXdw1V7O3tceHCBWzbtg2VK1fGl19+icaNGxfogVMYVbd/iMpaYiIwb544oioANGkCNGtW+MMgExEAiH39j9lnn4m3Y/I+Tp8WXzxRGTDYZERf1KhRA0eOHEFsbCyCgoKQmJhYaHkfHx9kZWUhLS1NbZm6detiwoQJ2L9/P3r06IGNGzcCEHuv5G9/cevWLcTHx+N///sf2rRpg/r16yM2VrmmyMLCAgCKbLthZmaGjh07Yv78+bhy5QqioqLw999/q712fo0aNcKhQ4cKLUNU2r77Thy87MQJcfv1HU7jFBcnLjt3Bnr0UH60aCFtbGTQmIzogGrVqiEiIgLPnj1DUFAQEhISAIhjc6xZswbnz59HVFQUwsPDMXXqVLRr1w4ODg4FzpOamooxY8YgIiICDx48wIkTJ3D27Fl4e3sDADw9PZGUlIRDhw4hPj4eKSkpqFGjBiwsLLB8+XLcv38fv//+e4GxQzw8PCCTybBnzx7ExcUhKangLbA9e/Zg2bJluHTpEh48eIDNmzcjJycH9erVU1z79OnTiIqKQnx8vOJWUF5TpkzB2bNnMWrUKFy5cgW3bt3C6tWrER9fsMEwUWm5cUNctmkDzJoF/N//SRuPpOR/a66u0sZBxqeceveUSHG69uq6vF175Z48eSLUq1dPaN68ufDixQvh66+/Fvz8/ARnZ2fByspKqFmzpjB27FghPj5e5TnT09OFfv36CdWrVxcsLCyEKlWqCGPGjFF6b0aOHClUrFhRqWvvjz/+KHh6egqWlpaCn5+f8PvvvwsAhIsXLyqOmzVrllCpUiVBJpOp7Np77NgxISAgQKhQoYJgbW0tNGrUSNixY4fi+Nu3bwutWrUSrK2tC+3aGxERIfj7+wuWlpaCk5OTEBwcrPQ85dLX331dEhcnCG5uYo/VrVuljqYMRUcLwvXrhT+uXMntvhsXJ3XEZCA07dorEwSheH1Sy1FiYiIcHR2RkJBQoEYgLS0NkZGR8PLygpWVlZozEBke/u6XzN274ky7mZni9qlTQKtW0sZUJrZt027iHBMTsTeN0Q0vS2WhsO/vvAy2Nw0RUWFOnsxNRAIDgdc90Q3P/v3i0tYW0KSReO/eTESo3DEZISKjJO/K+8EHwJo10sZS6hISgH37xBqOU6fEfRs3iokGkQ5iMkJEBi88XBzLS14TAgDR0eLSIEdS/fRTYO1a5X2cUZd0GJMRIjJ4ixYBZ86ofs4ge6zKZ9dt3hxwdhbvQTEZIR3GZISIDJ78lsw33yiPI+LmZmBtRQ4dEmfWvXVL3P7xR6B2bWljItIAkxEiMljJycD33wMPHojbffsClStLG1OZEQSgX7/csULs7QEvL2ljItIQkxEiMlirVwOTJonr9vZAIfM06r+YGDERMTERh5Tt2JG9YkhvMBkhIoN15Uru+oYNgEwmXSxl7uZNcVmrFvDVV9LGQqQlJiNEZFCysoAXL8R1+cz3O3YAvXpJF1O5kCcjr6d/INInnJtGR8lkMvz6668lOsfgwYPRrVu3QstERERAJpNpNbtuWdMk7uLYtGkTnJycFNszZsxAkyZNSv06qq5F5SMtDahXT2yY6uaW26nEILvv5iefZIfJCOkhJiMSKeoLNyYmBiEhISW6xtKlS7Fp0ybFdmBgIMaPH69Uxt/fHzExMXB0dCzRtYoiT3pkMhlMTEzg6OiIN998E59++iliYmIKjbsw2iQuffv2xR35v8qlyNPTE0uWLCmXa1HhbtwA7t9X3tekCfDGG5KEUzoWLQLs7MTRUwt7yEduYzJCeoi3aXRUpVJoaadJgmFhYVEq19LU7du34eDggMTERFy4cAHz58/H+vXrERERgTdef2OURWKUmZkJa2trWGsyHHYpKM9rUS55ItKqVe7Ao3pv/XqxW5AmbGzEse2J9IzB1owkJyerfaSlpWlcNjU1VaOypS3vbZqoqCjIZDLs3LkTbdq0gbW1NZo3b447d+7g7Nmz8PX1hZ2dHd555x3ExcUpzpG31mDw4ME4cuQIli5dqqihiIqKKnCbRn574a+//oK3t7fivHlrL7KysjB27Fg4OTmhYsWK+OyzzxAaGqpRDYWbmxsqVaqEunXrol+/fjhx4gRcXV3x0UcfqYwbAH7++We88cYbsLa2RsWKFdGxY0ckJydjxowZ+P777/Hbb78pXlNERITS+xUYGAgrKyv88MMPam+drFmzBtWrV4eNjQ169+6tdMtKVW1St27dMHjwYMXzDx48wIQJExQx5H0f81q9ejVq1aoFCwsL1KtXD1u2bFF6XiaTYd26dejevTtsbGxQp04d/P7770W+p5RLPp5IrVrSxlFqMjPFGf0AMbuKiir88d9/gIeHNLESlUCxkpFVq1YpZgpt1qwZjh07Vmj5rVu3onHjxrCxsUHlypUxZMgQPHv2rFgBa8rOzk7to2fPnkpl3dzc1JbNf6vE09NTZbnyMH36dHzxxRe4cOECzMzM0L9/f3z66adYunQpjh07hn///RdffvmlymOXLl0KPz8/jBgxAjExMYiJiUH16tVVlk1JScHChQuxZcsWHD16FNHR0Zg4caLi+Xnz5mHr1q3YuHEjTpw4gcTExGK3b7G2tsbIkSNx4sQJxMbGFng+JiYG/fv3x9ChQ3Hz5k1ERESgR48eEAQBEydORJ8+fRTJUkxMDPz9/RXHfvbZZxg7dixu3ryJ4OBglde/d+8edu7ciT/++AP79u3DpUuXMHr0aI3j37VrF6pVq4ZZs2YpYlBl9+7dGDduHD755BNcu3YNH374IYYMGYLDhw8rlZs5cyb69OmDK1euoFOnThg4cCCeP3+ucTzGTl4zYjBtRO7dE1vk2toCLVuKiUZhj3L6LCIqbVonIzt27MD48ePx+eef4+LFi2jTpg1CQkIQLZ/oIZ/jx49j0KBBGDZsGK5fv46ffvoJZ8+exfDhw0scvLGZOHEigoOD4e3tjXHjxuHChQuYNm0aWrdujTfffBPDhg0r8OUm5+joCAsLC9jY2KBSpUqoVKkSTNWMQZCZmYlvv/0Wvr6+aNq0KcaMGYNDhw4pnl++fDmmTJmC7t27o379+lixYkWJGmvWfz0kZlRUVIHnYmJikJWVhR49esDT0xNvvPEGRo0apUgCra2tYWlpqXhNFhYWimPHjx+PHj16wMvLC1WqVFF57bS0NHz//fdo0qQJ2rZti+XLl2P79u14+vSpRrE7OzvD1NQU9vb2ihhUWbhwIQYPHoxRo0ahbt26CAsLQ48ePbBw4UKlcoMHD0b//v1Ru3ZtfP3110hOTsYZdeOYUwEGVzMi7yFTv76B90smY6d1m5HFixdj2LBhimRiyZIl+Ouvv7B69WrMnTu3QPl//vkHnp6eGDt2LADAy8sLH374IebPn1/C0AuXlJSk9rn8X8Kq/iOXMzFRztdUfWGWl0aNGinW3d3dAUDRzkK+r7DXoikbGxvUyvNpXrlyZcV5ExIS8N9//6FFngk9TE1N0axZM+Tk5BTreoIgAIDiFkdejRs3RocOHfDGG28gODgYQUFB6NWrFypUqFDkeX19fYssU6NGDVSrVk2x7efnh5ycHNy+fbtU29LcvHkTH3zwgdK+1q1bY+nSpUr78v6MbW1tYW9vXyo/U0OUni5OgJf3T/36dXGp9zUjmZnA3r3ATz+J25xXhgycVslIRkYGzp8/j8mTJyvtDwoKwsmTJ1Ue4+/vj88//xzh4eEICQlBbGwsfv75Z3Tu3FntddLT05Genq7YTkxM1CZMAOIHudRlS5u5ubliXf7FnX9fcRMCddeRn1eeMOS/vlz+57Vx8/V/f56engWeMzU1xYEDB3Dy5Ens378fy5cvx+eff47Tp0/Dq4ihrovzs5K/LvnSxMSkwGvLzDv1azHOLScIQoF9qt770viZGqLly3NHV81P72tGNm0C8iavTEbIwGl1myY+Ph7Z2dmK/8rl3N3d1VZr+/v7Y+vWrejbt6+i54aTkxOWL1+u9jpz586Fo6Oj4qGubQNpx8LCAtnZ2SU6h6OjI9zd3ZVuHWRnZ+PixYvFOl9qairWrl2Ltm3bwtXVVWUZmUyG1q1bY+bMmbh48SIsLCywe/duACV/TdHR0Xjy5Ili+9SpUzAxMUHdunUBAK6urkrtQLKzs3Ht2jWlc2gSg7e3N44fP6607+TJk/BmN8xiu3BBXHp7A8HBuY/ZswE1d+X0h3yAlLp1xflmXjeYJjJUxeraq8l/eHI3btzA2LFj8eWXXyI4OBgxMTGYNGkSRo4cifXr16s8ZsqUKQgLC1NsJyYmGmRCkpCQgEuXLintc3Z2Ro0aNcrkep6enjh9+jSioqJgZ2cHZ2fnYp3n448/xty5c1G7dm3Ur18fy5cvx4sXL9T+DuQVGxuLtLQ0vHr1CufPn8f8+fMRHx+PXbt2qSx/+vRpHDp0CEFBQXBzc8Pp06cRFxen+BL39PTEX3/9hdu3b6NixYpadwu2srJCaGgoFi5ciMTERIwdOxZ9+vRR3KJp3749wsLC8Oeff6JWrVr45ptvCgwQ5+npiaNHj6Jfv36wtLSEi4tLgetMmjQJffr0QdOmTdGhQwf88ccf2LVrFw4ePKhVvCQShNz2IXPmAD16SBuPVg4cAP78s+gyADBzppiMEBk4rZIRFxcXmJqaFqgFiY2NLVBbIjd37ly0bt0ak17XpzZq1Ai2trZo06YN5syZg8oqptC0tLSEpaWlNqHppYiICLyZb/7y0NBQjQf80tbEiRMRGhoKHx8fpKamIjIysljn+eyzz/D06VMMGjQIpqam+OCDDxAcHKy2QWxe9erVg0wmg52dHWrWrImgoCCEhYWpbZ/h4OCAo0ePYsmSJUhMTISHhwcWLVqk6OU0YsQIREREwNfXF0lJSTh8+LDK2z3q1K5dGz169ECnTp3w/PlzdOrUCatWrVI8P3ToUFy+fBmDBg2CmZkZJkyYgHbt2imdY9asWfjwww9Rq1YtpKenq7xl1a1bNyxduhQLFizA2LFj4eXlhY0bNyKQY0JoLSpKHEfkv//Ebb1qH5KTA/TpA2g64nHjxmUaDpGukAla3uxv2bIlmjVrpvSB7ePjg65du6pswNqzZ0+YmZlhx44din2nTp2Cv78/Hj9+rLaXQ16JiYlwdHREQkICHBwclJ5LS0tDZGSkoqsxlb+cnBx4e3ujT58+mD17ttThGA1j/d3fvBkIDRXXa9cGrl4F9OblP3gAeHoCZmbAp58WXtbHBxg4sFzCIiorhX1/56X1bZqwsDC8//778PX1hZ+fH9auXYvo6GiMHDkSgHiL5fHjx9i8eTMAoEuXLhgxYgRWr16tuE0zfvx4tGjRQqNEhHTPgwcPsH//fgQEBCA9PR0rVqxAZGQkBgwYIHVoZATkk+B16ADs2yd+r+sNebJety5n1iXKQ+s/4759++LZs2eKQZ4aNmyI8PBweLwe9S8mJkZpzJHBgwfj1atXWLFiBT755BM4OTmhffv2mDdvXum9CipXJiYm2LRpEyZOnAhBENCwYUMcPHiQjTGpXMiTkTp19CwRAQD5OEAG2AaOqCS0vk0jBd6mISrIWH/3x44Vu/VOmQJ8/bXU0WjJwQF49UrsCpSvvRiRIdL0No3Bzk1DRIZJXjOiwbh3uiU9XUxEALHdCBEp6Fslp1p6UMFDVKqM7Xf+0SOxsap83ji9S0bi48WlqSlQgukTiAyR3icj8hErU1JSOGU7GZWMjAwABac3MEQZGeJdDfn3OQBUrChdPMUin1HbxYXzzBDlo/fJiKmpKZycnBTzd9jY2Gg0+BaRPsvJyUFcXBxsbGxgpnetOLUXGSkmImZmQKNGQNWqQMeOUkelJXkyomakYSJjZhCfYvIBszihGBkTExMT1KhRwyiS7/v3xaW3N3D+vLSxFNu9e+KyjEZYJtJnBpGMyGQyVK5cGW5ubsWexIxI31hYWBSYVdrQrF4NzJgBJCeL23o9Ad7rCSE56R1RQQaRjMiZmpoaxf1zImOxdi2Qt8Iz30j8+kWejHA8HqICDCoZISLDkXcyvPBw8Ttcr3vEsmaESC0mI0SkE3JygCVLAPkAzpmZucNytGunJ/PPxMUBS5cCSUnK+3NygMePxXXWjBAVwGSEiHTC0aPAJ58U3F+zpp4kIoCYiBQ254yHB+DoWH7xEOkJJiNEpBPyNqno3l1cl8mA996TLiatXbkiLjt3Bho3Vn5OJgO6dCn/mIj0AJMRItIJ8u67wcF6OKHt7t3iPSZ5v+OwMKB9e0lDItInTEaISCfIk5GaNaWNo1imTxfHqgfEe0r5a0WIqFCGPUgBEekNec8ZvRtLJCsLuH1bXF+7VpyRV+/GqieSFpMRIpKcIOhhzYggiA1a7OzEyXOsrYFhw9hbhqgYmIwQkWTu3wf8/YH69cVuvDKZHo0l8ugR8McfQHq6uB0SAhj4iLhEZYVtRohIMjt2AKdO5W6/+aYedON9+RJ48gT45x9xu04d4OBBoHp1ScMi0mdMRohIMvJ2IsOHA4MGAU2aSBpO0WJjxUYteQc1e+MNTn5HVEJMRoio3Jw5A+zfn7t99Ki4DAgA2rSRJiatnD4tJiJmZoCTk1iNM2SI1FER6T0mI0RULgQB6NoVePq04HN165Z/PFq7fRuYMkVc790b+PFHaeMhMiBMRoioXDx/npuIjBghNlYFgNq1gebNpYtLI9nZwFtvAfHx4jYnuyMqVUxGiKhMxcYCKSm5Y4JVriwOx6FX7t/PTUR69waGDpU2HiIDw2SEiMrMli1iw9S89GpQs3XrgGvXgIcPxe0mTYCdOyUNicgQMRkhojIjb6xqZgaYm4uP/MmJzrp9W7yflBeHeScqE0xGiKjMyEdV/fFH8e6GXpHPwOvhAQwcCFha8vYMURlhMkJEpW7nTmDFitxJbHV+iHdBAMaPzw0YEAc2A4B27fRwGmEi/cJkhIhK3fTpwK1b4rqdnR503b15E1i2TPVzfn7lGwuREWIyQkSlKicn9/bM2rXigGb29tLGVKQbN8SltzcwZ07ufkdHIDBQkpCIjAmTESIqkYMHc4d1B8QJ7zIyxEarQ4aIS50UGyuOHfLwIZCVJe5r2RLo0UPauIiMkK5+TBCRHrhxA3j7bdXP1aypw4kIIHb1uXs3d1smE2feJaJyp8sfFUSk4+QdTtzcgNatc/ebmOjQlC0pKUBUVMH9J06Iy/ffB2bPBmxtAReXcg2NiERMRoio2OQVCyEhwKZNkoaiWmamOHT7gwfqy/j6it13iUgyTEaIqFjS0oAvvxTXdXZU1bt3xUREJgMqViz4vJubOHsfEUmKyQgRFcv167nr77wjXRwFXLwoDuEOAJcuiUtfX+DMGclCIqLCMRkhomKR96Bp3lyHZt199kwcFyQ9XXl/gwbSxENEGmEyQkQamT8fOHUqd1uejNSrJ008Kl2+LCYi9vaAv7+4z9oaCAuTNi4iKhSTESIq0qNHwGefqX5Op+aOW7BAXAYGAr//LmkoRKQ5JiNEVKR798Rl5crAjBm5++3tgW7dpIhIhZQUYN8+cf2NN6SNhYi0wmSEiNR68QI4cgT4+29xu1Ej4IMPpI1JLflkOADwySfSxUFEWmMyQkRqDRoE7NmTu62zXXi3bQMGDBDX27QBnJ2ljYeItMJkhIjUun1bXDZuLN6i+egjaeNR6/PPc9c5yy6R3mEyQkRqPX8uLn/4AWjYUNpY1Mo73PumTUDfvlJGQ0TFYCJ1AESkmwQBePlSXK9QQdJQCpowAbCxEbvtVqggBluxIhAaClhZSR0dEWmJNSNEpNKrV0B2triuU8lITg6wZg2Qmqq8v3NnaeIhohJjMkJEKr14IS4tLcUKCJ0RHS0mIubmYg8aU1NxmuBq1aSOjIiKickIkRHKzga++gp4+FB9GXkyUqGCOM+czrhxQ1zWrQvUrCltLERUKpiMEBmhQ4eA6dM1K1u9etnGorWbN8Wlt7e0cRBRqWEyQmSE5F12GzUC+vRRX87EBOjatXxi0sjLl8Ds2eK6j4+koRBR6TH6ZCQ5I1ntc6YmprAys9KorInMBNbm1sUqm5KZAkEQVJaVyWSwMbcpVtnUzFTkCDlq47C1sC1W2bSsNGTnZJdKWRtzG8he3wNIz0pHVk5WqZS1NreGiUzsLJaRnYHM7MxSKWtlZgVTE1Oty2ZmZyIjO0NtWUszS5iZmGldNisnC+lZ6WrLWphawNzUHGlpwOmzWUh7XfbISQDmQGAQMH6SclkAyM7JRlpWmuI8yfnCMTc1h4Wphcqy+eUtmyPkIDUztfhlw8YAKQmAOWBWvw4sX+8WBAEpmSlqz2tmYgZLM0uNymrzd8/PCNVl+Rmhf58RUpMJ6n5rdUhiYiIcHR2RkJAABweHUj23bKb6m+Gd6nTCnwP+VGzbfm2r9kMswCMAEYMjFNuuC1wRnxKvsqxvFV+cHXFWse25xBMPEh6oLOvj6oPro64rthusaoAbcTdUlvVw9EDU+CjFdvPvmuPck3Mqy7rYuCBuUpxiO3BTII48OKKyrI25DZKn5n5wdv6xM8LvhqssCwDC9Nxfqd4/9cbPN35WWzZpSpLig2nwr4Px/eXv1ZaNnRgLV1tXAMDoP0dj1blVastGjouEp5MnAGDS/klYeGqh2rLXPrqGBm7iFPMzImZg5pGZasueGX4Gzas2BwAsOLEAnx78VG3Zw6GHEegZCABYeWYlxuwdo7bsnv570Lmu2Btk06VNGPLbELVld/baid4NegMAfrr+E/r8rL5qY2PXjRjcZDB69wZ+vvwnMPBdtWVXhKzA6BajAQARURFo9307tWXnd5yPSa3FLObs47Nosa6F2rLTA6ZjRuAMAMD12OtouFr9gCUT/SZiQZA42V3Uyyh4LfVSW3bUmx9g5XtrAABxyXFwW+imtmxo41Bs6rYJgJgE2M21U1u2l08v/NT7J8U2PyNE/Iww7M+IsqLp9zfHGSEyAqdOSR1BGTA1+opdIoNh9DUjrILVviyrYPWrCjYrwxw2NgBMshD1KB3W9slwX+QOAPjvk/8UP6/CbtPkV663aXJyxG67iYliIScnIDoaZmYWGt964W0a1WX5GcHPiLK+TaPp97fRJyNEhu7rr8WpWxwcxPafKZm5tynyVoHrrKgowMtLHFdk0iQgOBho21bqqIhIA5p+f7Oek8jAHTggLp2cdGy8EHWiooAxY3LHopfXiNStKw6OQkQGh8kIkYG7f19cbt4sbRwa27gR+PPPgvs5Gy+RwWIyQmTAoqPFBwDUry9tLBqTj7A6fDgQEiKum5sD7dT37iEi/Vas3jSrVq2Cl5cXrKys0KxZMxw7dqzQ8unp6fj888/h4eEBS0tL1KpVCxs2bChWwESkOfn4YCYmgJv6nq/lLzERaNhQnPQm/+OXX8QyPXsCPXqIjy5dADv13XGJSL9pXTOyY8cOjB8/HqtWrULr1q2xZs0ahISE4MaNG6hRo4bKY/r06YP//vsP69evR+3atREbG4usLPWtnImodERGisuBA3Pbi5iamKJTnU6KdUmcOQNcv67++YoVgRbqxy4hIsOidW+ali1bomnTpli9erVin7e3N7p164a5c+cWKL9v3z7069cP9+/fh7Ozc7GCZG8aIu1kZwN37ogdTx4+BI4dA956S+qo8ti2DRgwQGwHsm1bweddXSH2RyYifVYmg55lZGTg/PnzCAoKUtofFBSEkydPqjzm999/h6+vL+bPn4+qVauibt26mDhxIlJT1Y81kJ6ejsTERKUHEWmud29x6hb5rLw6N7lt3OuRPatVAzw8Cj6YiBAZFa1u08THxyM7Oxvu7u5K+93d3fH06VOVx9y/fx/Hjx+HlZUVdu/ejfj4eIwaNQrPnz9X225k7ty5mDlT/XC7RFS406fFpZOTWDtSubKk4RQU/3oYdBcXaeMgIp1QrAassnyDFQiCUGCfXE5ODmQyGbZu3YoWLVqgU6dOWLx4MTZt2qS2dmTKlClISEhQPB7K/70jIo28eCEuL1wAtm9XHl8kOSMZtl/bwvZr20JHAS0TkZHAli2549O7upbv9YlIJ2lVM+Li4gJTU9MCtSCxsbEFakvkKleujKpVq8LR0VGxz9vbG4Ig4NGjR6hTp06BYywtLWFpaVlgPxEVLS0NkOf5FSqoLlPYcOhlRhCA9u3FQc3k1HxuEJFx0apmxMLCAs2aNcMB+ZCOrx04cAD+/v4qj2ndujWePHmCpKQkxb47d+7AxMQE1apVK0bIRFQYea2IiYk4BLzOiIvLTUSCg8UuPr17SxoSEekGrW/ThIWFYd26ddiwYQNu3ryJCRMmIDo6GiNHjgQg3mIZNGiQovyAAQNQsWJFDBkyBDdu3MDRo0cxadIkDB06FNbW1uouQ0TFJE9GnJzEhERnfP966ncvL2DfPuCHH3ibhogAFGOckb59++LZs2eYNWsWYmJi0LBhQ4SHh8PDwwMAEBMTg2j5kI8A7OzscODAAXz88cfw9fVFxYoV0adPH8yZM6f0XgURARArH+R/Wupu0Uhm7VpxWbWqtHEQkc7hrL1EBmT4cGD9enHd3x84caJgmeQMiWbtrVoVePIE+PlncXRVIjJ4ZTLOCBHptqtXxaWjIzBvnrSxFCAfL6hJE0nDICLdw4nyiPTcixeAfHaFf/8Vl0eOAI0bqy5vIjNBgEeAYr1cZGcD8kbs9vblc00i0htMRoj02IwZgKrxAQsbcdXa3BoRgyPKKiTV8vSm060uPkSkC3ibhkiP/fFHwX3du+tg5cOrV+LS3BzgGEJElA9rRoj02P374vLqVaBhQ2ljKZS8vYiDg/JwsEREYM0Ikd56/hx4+VJc12YivOSMZLgucIXrAtfyGQ4+KQm4ckVc5y0aIlKBNSNEekpeK1KpkvaT3ManxJd+QKqkpgJ16gDyKSR07v4REekCJiNEekrec6ZWLWnjKNS1a2IiYmIijrY6dKjUERGRDmIyQqQnLlwArl/P3d67V1xqc4umXGVl5Q52EhAA/P23tPEQkc5iMkKkB549A1q1AjIzCz6nszUjmzcDv/wirvv4SBsLEek0JiNEeiA6WkxErKzESgY5Jydg2DDJwirc6dO56x9/LF0cRKTzmIwQ6QH5TLy1aokT3uqc48fFWpC8U1399Ze4/OEHoF49aeIiIr3AZIRIDzx/Li5LYyZeE5kJfKv4KtZLRWhobvee/NSNS09ECAwMREREhMb7i3pOXzEZIdID8pqR0khGrM2tcXbE2ZKfSO7Vq9xE5NNPAbM8Hyv16+v4aGxE5e/EiRNITU1Fx44dFfsOHjwIa2trtfsBqH2udevW5Rd8GWEyQqQHSjMZKXULF4pLd3cdnCqYSPfUqFEDYWFh2LVrF169eoVRo0bh+fPnmDdvHiZOnFhg/6JFi5CTk6PymEWLFkn9ckoFR2Al0kHXrolDcgwcKD62bBH362QysmuXuKxRQ9o4iPRE9erV8dNPP8HR0REXLlyAk5MTtm/fDg8PD5X7q1atqvaYqlWrSv1ySgWTESIdNHs2sHEj8OOP4uPaNXG/p2fJz52SmQLPJZ7wXOKJlMyUkp0sOxu4e1dcX7Om5MERGYHHjx+jX79+ePnyJZo2bYoXL16gX79+he4v7DlDIBOEvM3fdVNiYiIcHR2RkJAAB85tQUagaVPg4kVg5MjcjigODkC/ftoP/Z5fckYy7ObaAQCSpiTB1sK2eCf64w/gvffEdSsrcQ4aU9OSBUdkBPK2GZE3Rs3fZiT/fgBqn9PlNiOafn+zzQiRjkhMBE6dAnJycod6//hjHR4vbOvW3PWQECYiRBpSlTzkbZiqyf6intM3TEaIdET//kB4uPI+Ly9pYtGIfHj3lSvFKhwi0pq6LrqFdd01tG69AJMRIp1x5oy4bNAAsLQU74C8rp3VPb/8AsTFievvvCNOhEdEVExMRoh0QGIiEB8vrp88KbYP0WkHD+aul0arWiIyavx3hkgHyMcMc3HRg0QEAG7cEJdbtrBWhIhKjDUjRDpAnozUrFn215LJZPBx9VGsF8vNm+LS27uUoiIiY8ZkhEgHyJORWrXK/lo25ja4Pup68U/w7Flue5H69UsnKCIyaqxfJZJYdDQwaZK4Xh41IyWSnQ0MGyaue3gAtsUco4SIKA8mI0QS+9//ctd1/q7HgQPAb7+J65yNl4hKCZMRIok9eSIu69cHevUq++ulZKagwaoGaLCqgfbDwV+5kru+eHHpBkZERottRogkJp+Rd8YMcXyRsiYIAm7E3VCsa+zECeCzz8T1mTPLp4ELERkF1owQSUyejDg7SxtHkRYuzF3385MuDiIyOExGiCQmT0YqVJA2jiLJxxaZMQMwoDkxiEh6TEaIJPb8ubjU6WSkZ0/gzh1xffhwoLjjkxARqcBkhEgCz54B7dqJjVZTXrch1dlk5NkzYNcucb1BA6BKFWnjISKDwwasRBLYswfIO/FmtWqAk5NU0RTh6lVxaWoKXLrEWhEiKnWsGSGSwL//istu3YCjR4HLl8tviheZTAYPRw94OHpoNhy8vL/x228DZvz/hYhKHz9ZiMrZH38As2eL635+QJs25Xt9G3MbRI2P0qxwejrw8qW4/t57ZRUSERk51owQlaPHj4GuXXO369aVLhaN3L0rDgFvbw+MHCl1NERkoJiMEJWjW7cA+Thj06cDnTtLG0+R8s7Oy7YiRFRGmIwQlQNBECfEO3dO3O7USRyuw9y8/GNJzUxF8++ao/l3zZGamVp4YXky4uNT9oERkdFimxGicjBwILBtW+62lLPz5gg5OPfknGK9UHlrRoiIygiTEaJysH+/uLS0BBwdy2dCvFIhH3WVyQgRlSEmI0RlLCFBHDcMAOLixLageiE7G7h9W1xnMkJEZYhtRojK0IkTuZPburrqUSICAFFRYtdeS0vAy0vqaIjIgDEZISpDixfn1or4+kobi9bkt2jq1RNHXyUiKiNMRojKkHyk1REjgK1bpY1Fa2y8SkTlhG1GiErZo0fA3r1ATg5w7564LyxMtybCc7Fxyd3IzATat8/td5x3P8BuvURU5piMEJWyQYOAw4dzt01NAU9PycIpwNbCFnGT4nJ3XLgAHD+uurCZmTgnDRFRGTL6ZCQ5I1ntc6YmprAys9KorInMBNbm1sUqm5KZAkE+LGc+MpkMNuY2xSqbmpla6DgStha2xSqblpWG7JzsUilrY26jmKwtPSsdWTlZpVLW2twaJjLxLmRGdgYyszNLpayVmRVMTUwLLXvpOgBz4O12VrCzNUVICGBqnonkjAy157U0s4SZifjnmJmdiYxszcpm5WQhPStdbVkLUwuYm5orl334EEhOyi10aD9gDlj4toD5tp0AgOycbKRlpwOODoCjE5Dv99nc1BwWpha5ZbPS1MaQt2yOkFPoQGvalDUzMYOlmSUAQBAEpGSmlEpZbf7u+Rmhuiw/Iwr/jFBVVpu/+7L6jJCS0ScjdnPt1D7XqU4n/DngT8W220I3tR9iAR4BiBgcodj2XOqJ+JR4lWV9q/ji7Iizim2flT54kPBAZVkfVx9cH3Vdsd38u+a4EXdDZVkPRw+lCdDabmqrGNwqPxcbF6X/jkO2huDIgyMqy9qY2yB5au4HZ8+dPRF+N1xlWQAQpud+EL6/+338fONntWWTpiQpPpg+3PMhvr/8vdqysRNj4WrrCgAI+ysMq86tUls2clwkPJ08AQCfH/ocC08tVFv22kfX0MCtAQDg62NfY+aRmWrLnhl+Bs2rNgcALP1nKT49+GnBQqPExYQ+hxHiHQgAWHlmLcbsHaP2vHv670HnuuLY8FuvbsWQ34aoLbuz1070btAbALD75m70+bmP2rIbu27E4CaDAQB/3fsL7257V3XBz4EVCeYY7eEBADgWFYF2W9upPe/8jvMxqfUkAMCFmAtosa6F2rLTA6ZjRuAMAMDNuJtouLqh2rIT/SZiQdACAEB0QjS8lqrvxTPKdxRWdl4JAIhPiYfbQje1ZUMbh2JTt00AxC/rwv7ue/n0wk+9f1Js8zNCxM+IUvyMeO1w6GEEegYCANael/4zQkpswEpURqytiy6jU5qrTyiIiMqSTFBXn6dDEhMT4ejoiISEBDg4OJTquVkFq31ZVsGqroLtPwD443dx/YMPgFXLdKsKNisjDel2r3/vduwoMEtf3rLa3HrhbRp+RuQvy88I3qaR0/T72+iTEaLS0rgxcOUK8MsvQI8eUkejwubNQGiouH73LlC7trTxEJHB0/T7m7dpiEro11/F5OPWLXG7QQNJw1Hv9GlxaWvLRISIdIrRN2AlKqmxY8UOKgDg4KBb3XiVyAcxW7lS2jiIiPJhzQhRCaSl5SYiS5YAR46IU7noJHkywkHMiEjHsGaEqBjS04G//wbu3xe37e3FGpLXbed0z4sXwNOn4nr9+tLGQkSUT7FqRlatWgUvLy9YWVmhWbNmOHbsmEbHnThxAmZmZmjSpElxLkukMxYsADp1Asa8Hhagdm0dTkQA4H//E5fVqunZ1MFEZAy0TkZ27NiB8ePH4/PPP8fFixfRpk0bhISEIDo6utDjEhISMGjQIHTo0KHYwRLpCvk0LnXrAoGBwPTpkoZTtN9+E5evBzUjItIlWnftbdmyJZo2bYrVq1cr9nl7e6Nbt26YO3eu2uP69euHOnXqwNTUFL/++isuXbqk8TXZtZd0TaNGwNWrQHg4EBIidTRFyMwEbGyArCwx6IbqR0AlIipNZdK1NyMjA+fPn0dQUJDS/qCgIJw8eVLtcRs3bsS///6L6Rr++5ieno7ExESlB5Gu+PBD8TsdAGrWlDYWjdy7JyYidnY63O+YiIyZVslIfHw8srOz4e7urrTf3d0dT+WN4/K5e/cuJk+ejK1bt8LMTLP2snPnzoWjo6PiUb16dW3CJCozWVnAhg3iesWKepKM3Hg9T0n9+jresIWIjFWxGrDK8n2gCYJQYB8AZGdnY8CAAZg5cybq1q2r8fmnTJmChIQExeOhvO8kkcQePRITEvm6ufSTXRbtzBlx6e0tbRxERGpo1bXXxcUFpqamBWpBYmNjC9SWAMCrV69w7tw5XLx4EWNedzvIycmBIAgwMzPD/v370b59+wLHWVpawlJnB2sgY/b96wlD69UDrKwKL6sTEhKA+fPFdY4vQkQ6SquaEQsLCzRr1gwHDhxQ2n/gwAH4+/sXKO/g4ICrV6/i0qVLisfIkSNRr149XLp0CS1btixZ9ETlbNMmcVmliqRhaO7Chdx1nZwwh4ioGIOehYWF4f3334evry/8/Pywdu1aREdHY+TIkQDEWyyPHz/G5s2bYWJigob5Wu67ubnBysqqwH4iXZedDTx5Iq7PmCFpKJr75Rdx2aWL2A+ZiEgHaZ2M9O3bF8+ePcOsWbMQExODhg0bIjw8HB6vxy+IiYkpcswRIn105gyQkQGYmQGtW0sdjQbS03PnoeGoq0Skw7QeZ0QKHGeEpBYbC8ibRdWuDdy9K208GomOzh3k7P59wMtL2niIyOiUyTgjRMYqb/Lx6afSxaGV+HhxWbkyExEi0mlMRog08OKFuPT1BUaMkDYWjcXFiUtXV2njICIqApMRIg08fy4unZ2ljUMrTEaISE9o3YCVyBjJa0YqVJA2Do388QewcKE4KhsAuLhIGw8RURGYjBBpQK+SkRkzlMcX4WBnRKTjmIwQaWDzZnGp88lITg5w86a4vno14OkJtGsnaUhEREVhMkJUhPh4IDJSXNfpkVfDw4HOncV1Cwtg+HBxUBQiIh3HBqxERbhzJ3f9/feli6NIP/6Yux4czESEiPQGkxGiQsTGAidOiOuBgYCjo6ThFE5+e2bpUuDXXyUNhYhIG/zXiUiNS5fEcUWys8XtWrUkDadweduKBAcDJvw/g4j0B5MRIjXOnxcTEXNzsa3IwIFSR1SI6GggNVUMVqezJiKigpiMEKkh787bty+wZYu0sRRJXitSty7bihCR3mFdLpEaejW2iDwZ8faWNg4iomJgMkKkhl4lIzduiEsOcEZEeojJCJEa8vlo9CIZYc0IEekx3lwmyufFC2D7duDyZXFb55MRQWAyQkR6jckIUT5z5gCLF+duu7tLF4tGYmPFDMrERGzASkSkZ5iMEOVz9aq4fOstoHVroEMHaeMpkry9iJcXYG0tbSxERMXAZIQoH3ky8tVXQNu20saiEd6iISI9xwasRHn8+Sfw9Km4rjdjhzEZISI9x2SEKI/jx3PXdXqG3rzkyQi79RKRnmIyQpRHcrK4nDoVkMmkjUVj8jYjrBkhIj3FZIQoD3kyYmcnbRwai44GYmLE9fr1pY2FiKiYmIwQ5ZGUJC5tbaWNQyPPngEeHuJ61aqAo6O08RARFROTEaI89Kpm5OzZ3PUxY6SLg4iohJiMEOWhNzUjd+8CU6aI6716AZMnSxsPEVEJcJwRojz0omYkJ0ccAEXeB5m9aIhIz7FmhCgPvagZiY7OTUR69ACGD5c2HiKiEmLNCBHEueYAPagZuXgRGDhQXG/QAPjlF2njISIqBawZIaOXkADUqSPOM/fwobhPZ5ORUaNyBzlr3FjaWIiISgmTETJ6p04B//6bu+3lBXh6ShaOejk5wJUr4vqAAcDcudLGQ0RUSnibhoze/fviMiQE2LwZcHICzHThLyM5GRg6FHj8WNzOygJSUgBzc+D773UkSCKikuOnGRmlpCTgiy+AuLjcyob69QEXF2njUrJnD7BzZ8H9zZszESEig8JPNDJKP/0ELF2qvO+NN6SJRS35nDPBwcAHH4jrMhnw1lvSxUREVAaYjJBRunNHXAYGAl27As7OQL9+koYkOnsWeO894OVLICND3BcUJHbhJSIyUExGyOikpABr14rr770HjB8vaTjKfv45dwwRQGwf0rGjdPEQEZUD9qYhozN6NPD8ubhes6a0sRQQESEuv/oKiIoSG7U0aiRlREREZY41I2R0zpwRlxUqAG+/LW0sSs6cyQ3Ozy93Rl4iIgPHmhEyKoKQ25X37FnAxkbaeJQcOpS73qqVdHEQEZUz1oyQUVm/HkhLA0xNgRo1JA7m0SPxtox8LPq//hKXc+YA1taShUVEVN6YjJBRkVc+ZGeLbUMl9d574lwz+XEWXiIyMkxGyKjIG66uWydtHEhLAy5fFtc7dhSragCgWjVxKFgiIiPCZISMyosX4tLNTcIgNm0CjhwR55pxcgL27xcHMyMiMlJMRsioyJORChUkCiAyEhgyJHe7cWMmIkRk9JiMkFGR36aRLBm5elVcVq0qToI3YIBEgRAR6Q4mI2TwsrLEHCArSxxlHZAgGfnhB3HYV/kMvG3bArNmlXMQRES6ickIGbxBg4Bt25T3lXsyMnUq8PBh7rafXzkHQESku5iMkME7flxcVqoEWFgA775bzsN4vHqVm4hs3Qq4ugLt2pVjAEREuo3JCBm09HRxbDFA7EkrSS+aW7fEpbs724gQEanAZIQMwunTwKhRQHKy8v6sLHGAU1tbsUJCEtHR4lLnZuUjItINTEbIIKxbB1y4oP55Pz8Je9DGxYlLSQc3ISLSXUxGyCDIJ7+bNq3gTLwyGdC0afnHpBAfLy4lq5ohItJtTEZIL8XGAps3i6OqA8CVK+IyOBho3Vq6uFSS14y4uEgbBxGRjmIyQnpp5kxg1SrlfTIZULu2NPEUas8eccmaESIilZiMkF66dk1cvv024OUlrrdqJXZY0Sn37+feQ9K54IiIdAOTEdJZiYm5w7fnd++euJw1S0xCdNa5c7nrXbpIFwcRkQ4zKc5Bq1atgpeXF6ysrNCsWTMcO3ZMbdldu3bh7bffhqurKxwcHODn54e//vqr2AGTcbh3T6xI8PJS/XjyRCxXq5a0cRbq6VOgf39xfcgQwMFB2niIiHSU1snIjh07MH78eHz++ee4ePEi2rRpg5CQEETLx1LI5+jRo3j77bcRHh6O8+fPo127dujSpQsuXrxY4uDJcB07JjZONTERR0tV9ejeXcfbhC5aBOTkiOuNG0sbCxGRDpMJgiBoc0DLli3RtGlTrF69WrHP29sb3bp1w9y5czU6R4MGDdC3b198+eWXGpVPTEyEo6MjEhIS4MD/Lo3CtGnAnDnAyJFAnl81/RIcDOzfD9SvL96usbWVOiIionKl6fe3VjUjGRkZOH/+PIKCgpT2BwUF4eTJkxqdIycnB69evYKzs7PaMunp6UhMTFR6kPE4cUJMRAA9HLT0wAFx3pm33hKrdwBxRDYmIkREammVjMTHxyM7Oxvu+XoFuLu74+nTpxqdY9GiRUhOTkafPn3Ulpk7dy4cHR0Vj+rVq2sTJum5RYty15s1ky6OYvnqKyAiQsyoUlPFJKRhQ6mjIiLSacVqwCrLN662IAgF9qmybds2zJgxAzt27IBbIUNjT5kyBQkJCYrHw7xTr5PB+/dfcfn553o4ue2NG+Jy8WLgl1+A8+cBR0dpYyIi0nFade11cXGBqalpgVqQ2NjYArUl+e3YsQPDhg3DTz/9hI4dOxZa1tLSEpaWltqERhI7f165F2tJyLvtvv++hPPJaCsnB2jTJne01Q8+4K0ZIiINaZWMWFhYoFmzZjhw4AC6d++u2H/gwAF07dpV7XHbtm3D0KFDsW3bNnTu3Ln40ZJOSkkBAgIKzphbEqamgKdn6Z2vzEVGAvJ2U4GBTESIiLSg9aBnYWFheP/99+Hr6ws/Pz+sXbsW0dHRGDlyJADxFsvjx4+xefNmAGIiMmjQICxduhStWrVS1KpYW1vDkdXXBuHff8VExMoKCAkpnXN26gToReXYixdATAxw9Ki47ewMHDwobUxERHpG62Skb9++ePbsGWbNmoWYmBg0bNgQ4eHh8PDwAADExMQojTmyZs0aZGVlYfTo0Rg9erRif2hoKDZt2lTyV0CSSE8HsrLEdXkziYYNgV27pIup3D15AtSpI1YNyQUFidU6RESkMa3HGZECxxnRLTt3Av/3f0BmpvL+vn2B7duliUkSP/8M9O4NmJuLjVRtbIC1a8XxRYiISOPvb85NQ1r7/feCiYi5OVBIsyHDk5KSOxjKwIHAxo3SxkNEpMeYjJDW5F1vt24FunUT183MAAsLyUIqf/PmAZcvi+s+PtLGQkSk54o1zggZp/BwoGdP4MoVcdvbW7wzYWNjZIkIAJw+nbs+aJB0cRARGQDWjJDGwsKA27fFdWtroHZtaeMpF4mJ4gBmL18q7z97VlweOyZOL0xERMXGZIQ0kp0N3L8vrs+fL46Mam8vbUzlYsMGYOZM1c+ZmfEWDRFRKWAyQhp59EhstGpuLtaQGE3vVfk9qfbtgVatlJ9r1UocV4SIiEqEyQhpRN5o1cvLiBIRALh5U1yOHCl24yUiolLHBqykEfktmpo1pY2jXAlCbjLi7S1tLEREBozJCGnEKJORmBggIQEwMRFHWiUiojLB2zRGLjkZaN06t5eMOhkZ4rJWrbKPSSesXQt8+KG4XquWnkyUQ0Skn5iMGLmLF3PH7iqKubk4Ia1RyDuiKmeaJiIqU0xGjNzz5+KycWPgt98KL+vkJE7BYvAePgT++Udc37uXc80QEZUxJiNG7sULcVmpEvB64mXjtn070L+/uG5iIg6oIpNJGxMRkYFjA1YjJ09GKlSQNg6dceBA7vqoUWwrQkRUDlgzYuSYjOSRnS2OuAoAO3YAffpIGw8RkZFgzYgRy8nJrQhgMgLgl19y1znMOxFRuWEyYsSWLQNOnRLXOao5cmfilcmABg2kjYWIyIjwNo0RkyciANC9u3RxSComBli+HEhJAf78U9y3ejUbrRIRlSMmI0ZMPqrqr78a2ciqec2bByxdqryvcWNpYiEiMlJMRozI3r3AuHFAWpq4/fixuDSaUVVVkc/K2727OP9MzZpAy5bSxkREZGSYjBiRdeuAu3eV97m7A7VrSxOPTpBPhDd5MtCihbSxEBEZKSYjRkR+W2bZMsDfX1yvVQuwspIuJkm9eAE8fSqu168vbSxEREaMyYgBEwRg/frcJOTOHXHZsaN4R8LoyWtFqlYFHBykjYWIyIgxGTFgZ88CI0Yo77OwALy8pIlHUhMmAGvWiBmaXHa2uOSYIkREkmIyYsDk//h7eQFdu4rr7doZ4W2ZnBwxEUlNVf18p07lGw8RESlhMmLADh0Sl0FBwDffSBtLqXryBHj5UvPyT5+KiYi5OXDrFmBqmvuclZXYipeIiCTDZMRALV8ObNkirhvUGCIHDojZVXHUq2dgbwYRkWFgMmKgDh/OXZffojEIBw+KS2trwNZW8+NMTYGPPiqbmIiIqESYjBgoeQ+aPXvECgG9cukScPWq6ufkWdbChcCoUeUWEhERlR0mIwZIEIB//xXX9W501RcvAD+/3GFi1WEPGCIig8FkxADFxwNJSeK6p6ekoWjv6lUxEbGzA1q3Vl2mdm2gTZvyjYuIiMoMkxEDJL9FU7WqjnTjTU0FFi8G4uKKLnvrlrhs0wYIDy/buIiISCcwGdEDBw/mzuemCXlZnblFs2sX8MUX2h3DmXOJiIwGkxEd9/QpEBwsjtulrTp1Sj+eYnn0SFw2bgx07lx0eTs74IMPyjYmIiLSGUxGdNyNG2IiUqGCdgOFWlsDn35adnFpRX57pmNH4KuvpI2FiIh0DpMRHZOVJXYokZPfcmnVCvjhB2liKjF5MuLqKm0cRESkk5iM6JCMDKBhQ+Du3YLP6fXAofHx4pLJCBERqWAidQCU684d1YmInR3QrVu5h1M6li3L7RXj4iJtLEREpJNYM6JD5AOVNWsGnDsnbSylZv363PVmzaSLg4iIdBaTER3y+efiUme65ALaz5CblyAAt2+L65cviwOfEBER5cNkREekpgLXr4vrDRpIG4vCvn1ASEjJz2NlpUMvioiIdA2TER0RFZW7rjNdcos7Q25+Q4aIs+YSERGpwGRER0REiMsmTSQawv3xY3FGXEEoGNQ33wAffihBUEREZAyYjOiIiRPFpWQT2/XoAZw5o/o5zpBLRERliMmIDkhPF9uMAMDw4RIEkJkJXLggrrdvD5ib5z5Xpw7g7y9BUEREZCyYjOiAyEjx7oitrXZDvis8fQosXw4kJxcvgFevxKFf7ezEdiIyWfHOQ0REVAxMRiS2bBkwbpy4XqtWMfOABQuAxYtLHkyjRkxEiIio3DEZkdj27bnrXboU8yTyCWy6di1+F1pTU6Bv32IGQEREVHxMRiR2/764PHRIbK6B7Gyx58qtW5qfRN7e47PPAD+/Uo+RiIioLDEZKUeLFwPnz+duCwLw33/ietOmr3eeOqU8hLqm7Ow4sBgREeklJiPlJDIS+OQT1c9Vrw44Ob3euHFDXDZvDkyerPkFGjYEHBxKEiIREZEkmIyUkzt3xGW1asDuOpPQ+PhKyCAOMGYSC8D6dcHMTHHZpo049gcREZGBYzJSTLduibUdmtq3T1w2fVOAb8QaIDNVfWETEyA4uGQBEhER6QkmI8Xw6HgUegekIDtHu+O8AXS0jBfH9TA1FWe0NVPxI7C3B5ydSyVWIiIiXcdkRFvffotqH32Eq8U9/ufXy9q1xYFFiIiIjByTEW0dOAAAeAU7CJZWcLAvxjlMTYFRo0o3LiIiIj1l3MnIsWNAVJRWhwjnzkEGoBd+hu8nwfjqqzKJjIiIyGgUKxlZtWoVFixYgJiYGDRo0ABLlixBmzZt1JY/cuQIwsLCcP36dVSpUgWffvopRo4cWeygS83q1cC2bVodIh8s/QZ88ElA6YdERERkbLRORnbs2IHx48dj1apVaN26NdasWYOQkBDcuHEDNWrUKFA+MjISnTp1wogRI/DDDz/gxIkTGDVqFFxdXdGzZ89SeRHF1qgRkmNj1T5tKpPBytRUsZ2clYXYOODbK37IruyM1q2TFXPTmZiYwNraOrdsIZPW5S+bkpICQRBUlpXJZLCxsSlW2dTUVOTkqG9la2trW6yyaWlpyM7OLpWyNjY2kL2eDyc9PR1ZWVmlUtba2homJiYAgIyMDGTKu0yXsKyVlRVMX/9OaFM2MzMTGRkZastaWlrC7HVjZm3KZmVlIT09XW1ZCwsLmL+ehVmbstnZ2UhLS1Nb1tzcHBYWFlqXzcnJQWqq+p5k2pQ1MzODpaUlAEAQBKSkpJRKWVNTU1hZWSm2C/tb1qYsPyOKV5afEaLy+IyQlKClFi1aCCNHjlTaV79+fWHy5Mkqy3/66adC/fr1lfZ9+OGHQqtWrdReIy0tTUhISFA8Hj58KAAQEhIStA23UN9/LwgA1D48PTsJ48YJioeZmY3asgEBAUrndnFxUVvW19dXqayHh4fasj4+PkplfXx81Jb18PBQKuvr66u2rIuLi1LZgIAAtWVtbGyUynbq1KnQ9y2vXr16FVo2KSlJUTY0NLTQsrGxsYqyo0aNKrRsZGSkouzEiRMLLXvt2jVF2enTpxda9syZM4qy8+fPL7Ts4cOHFWVXrFhRaNk9e/Yoym7cuLHQsjt37lSU3blzZ6FlN27cqCi7Z8+eQsuuWLFCUfbw4cOFlp0/f76i7JkzZwotO336dEXZa9euFVp24sSJirKRkZGFlh01apSibGxsbKFlQ0NDFWWTkpIKLdurVy+l3+HCynbq1EmprI0NPyMEgZ8Rcvr2GVEWEhISBKDo728x1dNQRkYGzp8/j6CgIKX9QUFBOHnypMpjTp06VaB8cHAwzp07pzZjnDt3LhwdHRWP6tWraxOmxuRjf6gTFQUsXZr7KCTJJiIiomKSCYKa+jwVnjx5gqpVq+LEiRPw9/dX7P/666/x/fff4/bt2wWOqVu3LgYPHoypU6cq9p08eRKtW7fGkydPULly5QLHpKenK1UrJSYmonr16khISIBDKQ55vmMHcO5cYVWlpjAzy62CzcgQy9rZAUOHKg8FwirY4pVlFayIt2m0L8vbNCJ+RhSvLD8jRGV9myYxMRGOjo5Ffn8XqwGr/IctJwhCgX1FlVe1X87S0lLxwVGW+vYF+va1LbqgguZl8/6xFSXvh0Npls37YVaaZfN++JZmWW1+7tqUtbCwUHzBSVXW3Nxc4z94bcqamZkpPnRKs6ypqanGv8PalDUxMSmTsjKZrEzKAtr9LZdVWX5GiPgZoX1Zbf7upaTVbRoXFxeYmpri6dOnSvtjY2Ph7u6u8phKlSqpLG9mZoaKFStqGS4REREZGq2SEQsLCzRr1gwHXg/8JXfgwAGl2zZ5+fn5FSi/f/9++Pr66kYLXiIiIpKUVskIAISFhWHdunXYsGEDbt68iQkTJiA6OloxbsiUKVMwaNAgRfmRI0fiwYMHCAsLw82bN7FhwwasX78eEydOLL1XQURERHpL6xtJffv2xbNnzzBr1izExMSgYcOGCA8Ph4eHBwAgJiYG0dHRivJeXl4IDw/HhAkTsHLlSlSpUgXLli2TfowRIiIi0gla9aaRiqatcYmIiEh3aPr9rfVtGiIiIqLSxGSEiIiIJMVkhIiIiCTFZISIiIgkxWSEiIiIJMVkhIiIiCTFZISIiIgkxWSEiIiIJKX7U/khd5bfxMREiSMhIiIiTcm/t4saX1UvkpFXr14BAKpXry5xJERERKStV69ewdHRUe3zejEcfE5ODp48eQJ7e3vIZLJinycxMRHVq1fHw4cPOax8KeL7Wjb4vpYNvq9lh+9t2dDn91UQBLx69QpVqlSBiYn6liF6UTNiYmKCatWqldr5HBwc9O4Hqg/4vpYNvq9lg+9r2eF7Wzb09X0trEZEjg1YiYiISFJMRoiIiEhSRpWMWFpaYvr06bC0tJQ6FIPC97Vs8H0tG3xfyw7f27JhDO+rXjRgJSIiIsNlVDUjREREpHuYjBAREZGkmIwQERGRpJiMEBERkaSYjBAREZGkjDIZiYqKwrBhw+Dl5QVra2vUqlUL06dPR0ZGhtShGYSvvvoK/v7+sLGxgZOTk9Th6K1Vq1bBy8sLVlZWaNasGY4dOyZ1SHrv6NGj6NKlC6pUqQKZTIZff/1V6pD03ty5c9G8eXPY29vDzc0N3bp1w+3bt6UOS++tXr0ajRo1Uoy66ufnh71790odVpkxymTk1q1byMnJwZo1a3D9+nV88803+PbbbzF16lSpQzMIGRkZ6N27Nz766COpQ9FbO3bswPjx4/H555/j4sWLaNOmDUJCQhAdHS11aHotOTkZjRs3xooVK6QOxWAcOXIEo0ePxj///IMDBw4gKysLQUFBSE5Oljo0vVatWjX873//w7lz53Du3Dm0b98eXbt2xfXr16UOrUxwnJHXFixYgNWrV+P+/ftSh2IwNm3ahPHjx+Ply5dSh6J3WrZsiaZNm2L16tWKfd7e3ujWrRvmzp0rYWSGQyaTYffu3ejWrZvUoRiUuLg4uLm54ciRI2jbtq3U4RgUZ2dnLFiwAMOGDZM6lFJnlDUjqiQkJMDZ2VnqMIiQkZGB8+fPIygoSGl/UFAQTp48KVFURJpJSEgAAH6elqLs7Gxs374dycnJ8PPzkzqcMqEXs/aWtX///RfLly/HokWLpA6FCPHx8cjOzoa7u7vSfnd3dzx9+lSiqIiKJggCwsLC8NZbb6Fhw4ZSh6P3rl69Cj8/P6SlpcHOzg67d++Gj4+P1GGVCYOqGZkxYwZkMlmhj3Pnzikd8+TJE7zzzjvo3bs3hg8fLlHkuq847y2VjEwmU9oWBKHAPiJdMmbMGFy5cgXbtm2TOhSDUK9ePVy6dAn//PMPPvroI4SGhuLGjRtSh1UmDKpmZMyYMejXr1+hZTw9PRXrT548Qbt27eDn54e1a9eWcXT6Tdv3lorPxcUFpqamBWpBYmNjC9SWEOmKjz/+GL///juOHj2KatWqSR2OQbCwsEDt2rUBAL6+vjh79iyWLl2KNWvWSBxZ6TOoZMTFxQUuLi4alX38+DHatWuHZs2aYePGjTAxMahKolKnzXtLJWNhYYFmzZrhwIED6N69u2L/gQMH0LVrVwkjIypIEAR8/PHH2L17NyIiIuDl5SV1SAZLEASkp6dLHUaZMKhkRFNPnjxBYGAgatSogYULFyIuLk7xXKVKlSSMzDBER0fj+fPniI6ORnZ2Ni5dugQAqF27Nuzs7KQNTk+EhYXh/fffh6+vr6LmLjo6GiNHjpQ6NL2WlJSEe/fuKbYjIyNx6dIlODs7o0aNGhJGpr9Gjx6NH3/8Eb/99hvs7e0VNXqOjo6wtraWODr9NXXqVISEhKB69ep49eoVtm/fjoiICOzbt0/q0MqGYIQ2btwoAFD5oJILDQ1V+d4ePnxY6tD0ysqVKwUPDw/BwsJCaNq0qXDkyBGpQ9J7hw8fVvm7GRoaKnVoekvdZ+nGjRulDk2vDR06VPH37+rqKnTo0EHYv3+/1GGVGY4zQkRERJJiQwkiIiKSFJMRIiIikhSTESIiIpIUkxEiIiKSFJMRIiIikhSTESIiIpIUkxEiIiKSFJMRIiIikhSTESIiIpIUkxEiIiKSFJMRIiIiktT/A9u/y9HXTeSXAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Example for the KS Test.\n",
    "\n",
    "# Make a function called \"KS_illustrate\" to compute and plot the cumnulative distributions for two empirical data sets.\n",
    "# The function should also compute the KS statistic, and draw a vertical line at the location\n",
    "# of the KS statistic on the plot between the two CDFs. The title of the plot should be the\n",
    "# title parameter. The function should return the KS statistic and the p-value for the KS test.\n",
    "from statsmodels.distributions.empirical_distribution import ECDF\n",
    "\n",
    "def KS_illustrate(data0, data1, title=' ', significance_levels=[0.05, 0.01, 0.001]):\n",
    "    # Compute the empirical CDFs\n",
    "    ecdf0 = ECDF(data0)\n",
    "    ecdf1 = ECDF(data1)\n",
    "    \n",
    "    # Create a range of x values from -4 to 4\n",
    "    x = np.linspace(min(data0.min(),data1.min()), max(data0.max(),data1.max()), 1000)\n",
    "    # Compute the CDFs for the two data sets\n",
    "    y0 = ecdf0(x)\n",
    "    y1 = ecdf1(x)\n",
    "    # Compute the KS statistic\n",
    "    ks = np.max(np.abs(y0 - y1))\n",
    "    # Compute the p-value for the KS test\n",
    "    pv = stats.ks_2samp(data0, data1)\n",
    "    # Create a figure and axis\n",
    "    ax = plt\n",
    "    # Plot the CDFs for the two data sets\n",
    "    ax.plot(x, y0, 'b', label='ECDF-0')\n",
    "    ax.plot(x, y1, 'r', label='ECDF-1')\n",
    "    # Draw a vertical line at the location of the KS statistic\n",
    "    ax.plot([ks,ks],[ECDF(data0)(ks),ECDF(data1)(ks)],'g--',label='KS statistic' )\n",
    "    # Draw a horizontal line at the height of the KS statistic\n",
    "    ax.plot([min(data0.min(),data1.min()),max(data0.max(),data1.max())],[ECDF(data0)(ks),ECDF(data0)(ks)],'g--')\n",
    "    ax.plot([min(data0.min(),data1.min()),max(data0.max(),data1.max())],[ECDF(data1)(ks),ECDF(data1)(ks)],'g--')\n",
    "\n",
    "    # make a plot of the limiting distribution of the KS statistic in a new plot\n",
    "    ax.plot(x, stats.kstwobign.cdf(x, len(data0), len(data1)), 'k--', label='Limiting Distribution')\n",
    "\n",
    "    # Add a legend\n",
    "    ax.legend()\n",
    "    # Set the title of the plot\n",
    "    ax.title(title)\n",
    "\n",
    "    # Add significance annotations to the plot\n",
    "    if pv.pvalue > significance_levels[0]: \n",
    "        significance_level = 'n.s.'\n",
    "    else:\n",
    "        significance_level = ''\n",
    "        for i, alpha in enumerate(significance_levels):\n",
    "            if pv.pvalue < alpha:\n",
    "                significance_level += '*' \n",
    "            else:\n",
    "                break\n",
    "    \n",
    "    xlim = ax.xlim()\n",
    "    ysign = (ECDF(data0)(ks)+ECDF(data1)(ks))*0.475\n",
    "    ax.text(xlim[1]-0.1*(xlim[1]-xlim[0]), ysign, significance_level, ha='center', va='bottom', c='k')\n",
    "\n",
    "    print('Significance Levels:')\n",
    "    for i, significance_level in  enumerate(significance_levels):\n",
    "        stars = '*'*(i+1)\n",
    "        print(f'{stars} = {significance_level}')\n",
    "\n",
    "    return ks, pv\n",
    "\n",
    "# Compute the KS statistic and p-value for the KS test\n",
    "ks, pv = KS_illustrate(normal0, normal1, title='Empirical CDFs and KS Statistic')\n",
    "\n",
    "# Or if we just want to compute using builtin function:\n",
    "ks_statistic, p_value = stats.ks_2samp(normal0, normal1)\n",
    "print('KS test using built in code: KS =', ks_statistic, 'p-value =', p_value)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Plot the K"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# ANOVA (ANalysis Of VAriance)\n",
    "\n",
    "![alt text](figuresC/image-8.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Steps for Performing the ANOVA\n",
    "![alt text](figuresC/image-9.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example of the ANOVA test in Python"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Using our own (Unoptimized) Codes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ANOVA (Custom): F = 30.089327833389003 p-value = 1.2613243782766403e-12\n"
     ]
    }
   ],
   "source": [
    "# example of a data set on which to perform ANOVA\n",
    "N = 100\n",
    "Ngroups = 3\n",
    "group0 = rng.normal(0, 1, N)\n",
    "group1 = rng.normal(0.01, 1, N)\n",
    "group2 = rng.normal(1, 1, N)\n",
    "\n",
    "# Running the ANOVA test without the use of the built-in function\n",
    "# compute the f statistic\n",
    "N = [len(group0), len(group1), len(group2)]\n",
    "Ngroups = len(N)\n",
    "Ndata = N[0] + N[1] + N[2]\n",
    "data = np.concatenate((group0, group1, group2))\n",
    "\n",
    "# Compute the group means and overall means.\n",
    "grandMean = np.mean(data)\n",
    "groupMean = [np.mean(group0), np.mean(group1), np.mean(group2)]\n",
    "\n",
    "# Compute the group variances\n",
    "groupVar = [np.var(group0), np.var(group1), np.var(group2)]\n",
    "\n",
    "# Compute the within group mean square differences\n",
    "dfwithin = Ndata - Ngroups\n",
    "SSW = np.dot(N, groupVar)\n",
    "MSwithin = SSW / dfwithin\n",
    "\n",
    "# Compute the between group mean square differences\n",
    "dfbetween = Ngroups - 1\n",
    "SSB = np.dot(N, (groupMean - grandMean)**2)\n",
    "MSbetween = SSB / dfbetween\n",
    "\n",
    "# Comptue teh F-statistic\n",
    "F = MSbetween / MSwithin\n",
    "\n",
    "# Compute the p-value using the F-distribution\n",
    "pv = 1 - stats.f.cdf(F, dfbetween, dfwithin)\n",
    "print('ANOVA (Custom): F =', F, 'p-value =', pv)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Using the Builtin Stats routines."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ANOVA (Built in): F = 30.089327833389028 p-value = 1.2613517588652497e-12\n"
     ]
    }
   ],
   "source": [
    "# Now, lets compare our result to the built-in ANOVA function\n",
    "F, pv = stats.f_oneway(group0, group1, group2)\n",
    "print('ANOVA (Built in): F =', F, 'p-value =', pv)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Tukey HSD Test\n",
    "\n",
    "Upon rejecting the null hypothesis in the ANOVA test, we have evidence that the groups do not all have the same mean, but we do not yet know which groups are significantly different from which other groups. And, when there are lots of groups (e.g., lots of different drugs being tested), this may not be a trivial concern.\n",
    "\n",
    "The Tukey HSD test is a pairwise comparison test, and it is used to determine which groups are different from which other groups. The test is based on the studentized range distribution, and it is used to determine the minimum difference between group means that is statistically significant.  The more groups that there are the more likely it is that some pairs will be different by mere chance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Multiple Comparison of Means - Tukey HSD, FWER=0.05\n",
      "==================================================\n",
      "group1 group2 meandiff p-adj  lower  upper  reject\n",
      "--------------------------------------------------\n",
      "     0      1   0.6036   0.0  0.2826 0.9245   True\n",
      "     0      2   0.7765   0.0  0.4555 1.0974   True\n",
      "     1      2   0.1729 0.414 -0.1481 0.4938  False\n",
      "--------------------------------------------------\n",
      "[3.94287810e-05 8.72068027e-08 4.14004253e-01]\n"
     ]
    }
   ],
   "source": [
    "# Illustration of the Tukey Honestly Significant Difference (HSD) Test\n",
    "\n",
    "#mLet's generate some data to use for the Tukey HSD test\n",
    "N = 100\n",
    "Ngroups = 3\n",
    "means = np.zeros(Ngroups)\n",
    "stds = np.ones(Ngroups)\n",
    "\n",
    "# Change the means for the last two groups\n",
    "means[-2:] = [0.5,0.75]\n",
    "\n",
    "groups = [rng.normal(means[i], stds[i], N) for i in range(Ngroups)]\n",
    "\n",
    "from statsmodels.stats.multicomp import MultiComparison \n",
    "from statsmodels.stats.libqsturng import qsturng\n",
    "\n",
    "# Create the data\n",
    "data = np.concatenate(groups)\n",
    "groupLabels = np.concatenate([[i]*N for i in range(Ngroups)])\n",
    "\n",
    "# Create a MultiComparison object\n",
    "mc = MultiComparison(data, groupLabels)\n",
    "\n",
    "# Compute the Tukey HSD test\n",
    "result = mc.tukeyhsd()\n",
    "print(result)\n",
    "# Print the p-values\n",
    "print(result.pvalues)\n",
    "\n",
    "# Now go back and change the number of groups and see how the p-values change.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Significance Levels:\n",
      "* = 0.05\n",
      "** = 0.01\n",
      "*** = 0.001\n",
      "Significance Levels:\n",
      "* = 0.05\n",
      "** = 0.01\n",
      "*** = 0.001\n",
      "Significance Levels:\n",
      "* = 0.05\n",
      "** = 0.01\n",
      "*** = 0.001\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Make Violin Plots to Visualize the Data and Significance\n",
    "# Create a pandas DataFrame with each group in a separate column\n",
    "dflist = [] # Create an empty list to store the DataFrames\n",
    "for i in range(Ngroups):\n",
    "    dflist.append(pd.DataFrame({f'Group {i}': groups[i]}))  # Create a DataFrame for each group and append it to the list\n",
    "df = pd.concat(dflist, axis=1)  # Concatenate the list of DataFrames into a single DataFrame\n",
    "\n",
    "# Create a violin plot of the data using seaborn\n",
    "ax = sns.violinplot(data=df)\n",
    "ax.set_title('Violin plot of Group 0, Group 1, and Group 2')  # Set the title of the plot\n",
    "ax.set_ylabel('Value')  # Set the y-axis label of the plot\n",
    "\n",
    "# Add significance annotations to the plot\n",
    "add_signif_bar(ax, 0, 1, result.pvalues[0])\n",
    "add_signif_bar(ax, 0, 2, result.pvalues[1])\n",
    "add_signif_bar(ax, 1, 2, result.pvalues[2])"
   ]
  }
 ],
 "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": "3.11.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}