{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# IntroStat Week 5: Hypothesis Testing\n", "\n", "Welcome to the 5th lecture in IntroStat\n", "\n", "During the lectures we will present both slides and notebooks. \n", "\n", "This is the notebook used in the lecture in week 5.\n" ] }, { "cell_type": "code", "execution_count": 90, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import scipy.stats as stats" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Simulation: Sample from normal distribution" ] }, { "cell_type": "code", "execution_count": 91, "metadata": {}, "outputs": [], "source": [ "np.random.seed(24) # Seed for reproducibility" ] }, { "cell_type": "code", "execution_count": 92, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# (repeat this cell many times to see the randomness)\n", "mu = 100\n", "sigma = 12\n", "n = 10\n", "data = stats.norm.rvs(mu, sigma, size=n) # generate the random normal data\n", "x = np.arange(70,130,0.1)\n", "plt.xlim(70,130)\n", "# plot the normal distribution\n", "plt.plot(x, .2*np.sqrt(2*np.pi*sigma**2)*stats.norm.pdf(x, loc=mu, scale=sigma), color=\"red\",alpha=0.3) \n", "plt.plot(x, .2*np.sqrt(2*np.pi*sigma**2/n)*stats.norm.pdf(x, loc=mu, scale=sigma/np.sqrt(n)), color=\"black\", linestyle='--',alpha=0.3)\n", "# Histogram\n", "plt.hist(data, density=True, color='deepskyblue', bins=6)\n", "plt.axvline(data.mean(), linestyle='-', color=\"blue\", ymin=0, ymax=1) # Mean\n", "plt.plot([data.mean()-data.std(ddof=1)/np.sqrt(n), data.mean()+data.std(ddof=1)/np.sqrt(n)], [0.25/2,0.25/2], linestyle='-', color=\"blue\")\n", "# Confidence interval\n", "plt.axvline(stats.t.ppf(0.025, df=n-1)*data.std(ddof=1)/np.sqrt(n)+data.mean(), linestyle='--', color=\"blue\", ymin=0, ymax=1)\n", "plt.axvline(stats.t.ppf(0.975, df=n-1)*data.std(ddof=1)/np.sqrt(n)+data.mean(), linestyle='--', color=\"blue\", ymin=0, ymax=1)\n", "plt.tick_params(left = False, right = False , labelleft = False) \n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Simulation: ECDF and Q-Q plot" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Creating a Quantile-Quantile (Q-Q) plot step-by-step" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's walk through the process of creating a Quantile-Quantile (Q-Q) plot step-by-step using the given student height data:\n", "\n", "**Student Height Data**:\n", "`x = [168, 161, 167, 179, 184, 166, 198, 187, 191, 179]`\n", "\n", "**Goal**:\n", "To manually create a Q-Q plot to understand if the data is normally distributed. Q-Q plots compare the quantiles of the given data (`x`) with the quantiles of a standard normal distribution.\n", "\n", "## Step-by-Step Guide for Creating a Q-Q Plot\n", "\n", "### Step 1: Organize the Data\n", "First, you need to organize and sort your dataset.\n" ] }, { "cell_type": "code", "execution_count": 94, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[161, 166, 167, 168, 179, 179, 184, 187, 191, 198]\n" ] } ], "source": [ "#### Given data\n", "x = [168, 161, 167, 179, 184, 166, 198, 187, 191, 179]\n", "\n", "#### Sort the data in ascending order\n", "x_sorted = sorted(x)\n", "\n", "#### Print sorted data\n", "print(x_sorted)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Step 2: Rank the Data and Calculate Probabilities\n", "Calculate the empirical cumulative distribution function (ECDF) quantiles. Since there are 10 values, we'll calculate each value's rank and the corresponding probabilities:\n", "\n", "- $i $ is the rank (starting from 1 to $n $), where $n = 10 $ is the number of observations.\n", "- The empirical probability for each value is calculated as:\n", "\n", " $\n", " p_i = \\frac{i - 0.5}{n}\n", " $\n", "\n", " So the probabilities for our sorted data are:\n", "\n", " - $p_1 = \\frac{1 - 0.5}{10} = 0.05 $\n", " - $p_2 = \\frac{2 - 0.5}{10} = 0.15 $\n", " - $p_3 = \\frac{3 - 0.5}{10} = 0.25 $\n", " - $p_4 = \\frac{4 - 0.5}{10} = 0.35 $\n", " - $p_5 = \\frac{5 - 0.5}{10} = 0.45 $\n", " - $p_6 = \\frac{6 - 0.5}{10} = 0.55 $\n", " - $p_7 = \\frac{7 - 0.5}{10} = 0.65 $\n", " - $p_8 = \\frac{8 - 0.5}{10} = 0.75 $\n", " - $p_9 = \\frac{9 - 0.5}{10} = 0.85 $\n", " - $p_{10} = \\frac{10 - 0.5}{10} = 0.95 $\n", "\n", "#### Step 3: Find Theoretical Quantiles\n", "Next, find the theoretical quantiles for a standard normal distribution corresponding to the calculated probabilities. These quantiles are called the \"theoretical quantiles\".\n", "\n", "You can use the inverse of the cumulative distribution function (CDF), also known as the quantile function, to find these values. In the context of the standard normal distribution, this is often done using the Z-table or a Python function like `scipy.stats.norm.ppf()`:\n", "\n", "- Theoretical Quantiles ($q_i $) = $\\Phi^{-1}(p_i) $\n", "\n", "For example:\n", "\n", "- $q_1 = \\Phi^{-1}(0.05) \\approx -1.645 $\n", "- $q_2 = \\Phi^{-1}(0.15) \\approx -1.036 $\n", "- $q_3 = \\Phi^{-1}(0.25) \\approx -0.674 $\n", "- $q_4 = \\Phi^{-1}(0.35) \\approx -0.385 $\n", "- $q_5 = \\Phi^{-1}(0.45) \\approx -0.126 $\n", "- $q_6 = \\Phi^{-1}(0.55) \\approx 0.126 $\n", "- $q_7 = \\Phi^{-1}(0.65) \\approx 0.385 $\n", "- $q_8 = \\Phi^{-1}(0.75) \\approx 0.674 $\n", "- $q_9 = \\Phi^{-1}(0.85) \\approx 1.036 $\n", "- $q_{10} = \\Phi^{-1}(0.95) \\approx 1.645 $\n", "\n", "#### Step 4: Plot the Data\n", "Now that you have the sorted data values (`x_sorted`) and the corresponding theoretical quantiles (`q_i`), you can create the Q-Q plot:\n", "\n", "- **X-axis**: Theoretical quantiles ($q_i $) of the normal distribution.\n", "- **Y-axis**: Sorted sample quantiles (`x_sorted`).\n", "\n", "#### Step 5: Draw the Q-Q Line\n", "Draw a line that represents the theoretical relationship between the data and the normal distribution. This line should pass through the mean of the data and have a slope equal to the ratio of the standard deviation of the data and the standard deviation of the theoretical quantiles (which is 1 for a standard normal distribution).\n", "\n", "In Python, you can use scipy.stats.probplot() to create the Q-Q plot and plot the Q-Q line:" ] }, { "cell_type": "code", "execution_count": 106, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Height data: [161, 166, 167, 168, 179, 179, 184, 187, 191, 198]\n", "Z-score of each of the height data: [-1.4674816 -1.03586936 -0.94954692 -0.86322447 0.08632245 0.08632245\n", " 0.51793468 0.77690202 1.12219181 1.72644894]\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# In Python, you can use scipy.stats.probplot() to create the Q-Q plot and plot the Q-Q line:\n", "\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import scipy.stats as stats\n", "\n", "# Data\n", "x = np.array([168, 161, 167, 179, 184, 166, 198, 187, 191, 179])\n", "x_sorted = sorted(x)\n", "\n", "# Standardize the data (optional step)\n", "x_standardized = (x_sorted - np.mean(x)) / np.std(x)\n", "\n", "print(\"Height data: \", x_sorted)\n", "print (\"Z-score of each of the height data:\", x_standardized)\n", "\n", "# Plotting the Q-Q plot\n", "fig, ax = plt.subplots(figsize=(6, 6))\n", "stats.probplot(x, dist=\"norm\", plot=ax)\n", "\n", "#probplot() returns osm and osr: Ordered sample and theoretical quantiles.When plot=ax is provided, it generates a Q-Q plot using matplotlib\n", "\n", "plt.xlabel(\"Theoretical Quantiles\")\n", "plt.ylabel(\"Sample Quantiles\")\n", "plt.title(\"Q-Q Plot of Student Heights\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The simplest observations in a Q-Q plot before conducting a hypothesis test using a small dataset are:\n", "\n", "1. **Linearity of Points**: Check if the points fall approximately along a straight line. This indicates that the data is consistent with the theoretical distribution (e.g., normal).\n", "\n", "2. **Systematic Deviations**: Look for any systematic patterns, such as curves or S-shapes, which suggest the presence of skewness in the data.\n", "\n", "3. **Ends of the Plot**: Observe if the points at the ends deviate significantly from the line, indicating heavy tails or kurtosis (extreme values more frequent than expected).\n", "\n", "4. **Outliers**: Identify any points that fall far away from the reference line, which could be potential outliers in the dataset.\n", "\n", "These basic observations help determine if the data distribution is approximately normal or has deviations that should be considered before performing hypothesis testing.\n", "\n", "### Summary\n", "1. **Sort the data**.\n", "2. **Calculate the empirical probabilities**.\n", "3. **Find theoretical quantiles** using the normal distribution's quantile function.\n", "4. **Plot the data quantiles vs. the theoretical quantiles**.\n", "5. **Check the Q-Q line** to see if the data is approximately normally distributed.\n", "\n", "This manual process helps in understanding each step involved in constructing a Q-Q plot, giving you insights into the distribution of your data." ] }, { "cell_type": "code", "execution_count": 80, "metadata": {}, "outputs": [], "source": [ "np.random.seed(24)" ] }, { "cell_type": "code", "execution_count": 81, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# (repeat this cell many times)\n", "data = stats.norm.rvs(mu, sigma, size=n) # Again, generate the random normal data\n", "plt.ecdf(data)\n", "plt.plot(np.arange(70,130,1), stats.norm.cdf(np.arange(70,130,1), loc=mu, scale=sigma))\n", "plt.show()\n", "# It should roughly follow the \"perfect\" normal distribution" ] }, { "cell_type": "code", "execution_count": 82, "metadata": {}, "outputs": [], "source": [ "np.random.seed(24)" ] }, { "cell_type": "code", "execution_count": 83, "metadata": {}, "outputs": [], "source": [ "# import statsmodels.api to do automated q-q-plot\n", "import statsmodels.api as sm" ] }, { "cell_type": "code", "execution_count": 84, "metadata": {}, "outputs": [ { "data": { "image/png": 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0LnUJsuY8VRVk9WFal7q67NyFaM6OiIgImCsf9+lj3vIBoG5dmDkTatXK9yXRkcG0DA9iY+JxUtLPUcnfPHWljo5rUdgREZGSzTDgk0/M+1idPAmlS8OIETB4sNnZuQJPD4suL3dxCjsiIlJy/fEHPPkk/PCDOb7jDvMmnhERzq1LHEpzdkREpOQxDJg+3Qw1P/wA3t7w2muwbp2CjhtSZ0dEREqWw4ehd29YtswcN2oEH38Mt97q3Lqk0KizIyIiJYNhwPvvQ2SkGXR8fOCNN2DNGgUdN6fOjoiIuL+DB+GJJ2DFCnPctKnZzalRw6llSdFwamdn9erVxMTEEBISgsViYeHChTmeNwyDkSNHEhISgq+vL82bN2fXrl059mnevDkWiyXH47HHHivCn0JERFxWdjZMnWp2c1asAF9fePNNWLVKQacEcWrYOX36NLVr12bKlCl5Pj9hwgQmTZrElClT2LRpE0FBQbRs2ZL09PQc+/Xu3ZukpCTb4/333y+K8kVExJX9/jvcc495X6vTp6FZM9ixA2JjwdPT2dVJEXLqaaw2bdrQpk2bPJ8zDIPJkyczfPhwOnToAMAnn3xCYGAgn3/+OX369LHt6+fnR1BQUJHULCIiLi47G959F4YOhTNnwM/PvNKqb1/w0FTVkshl/9YTExNJTk6mVatWtm3e3t5ERUWxbt26HPvOnj2bChUqEBERwfPPP5+r8/NvGRkZpKWl5XiIiIgb2LcPmjeH/v3NoNO8OezcCf36KeiUYC47QTk5ORmAwMDAHNsDAwM5dOiQbdy5c2fCwsIICgoiPj6eYcOGsX37dpYvX57vsceNG8eoUaMKp3ARESl6WVnw9tswfDicPQvXXQcTJpi3f1DIKfFcNuxcZLHkvL+IYRg5tvXu3dv258jISKpXr079+vXZunUrdevWzfOYw4YNY+DAgbZxWloaoaGhDq5cRESKxJ490LOnuSAgwL33wocfwo03OrUscR0uG3cvzsG52OG5KCUlJVe351J169bFy8uLffv25buPt7c3ZcuWzfEQEZFiJivLXCfn9tvNoOPvDx98YK6ho6Ajl3DZsHPx1NSlp6MyMzNZtWoVTZo0yfd1u3bt4vz58wQHBxdFmSIi4gy7d5tr5QweDOfOQevWEB9vroxs0R3HJSennsY6deoU+/fvt40TExOJi4sjICCAKlWqEBsby9ixY6levTrVq1dn7Nix+Pn50alTJwB+//13Zs+eTdu2balQoQIJCQkMGjSIOnXq0LRpU2f9WCIiUlguXICJE827kmdkQNmy5ro5PXoo5Ei+nBp2Nm/eTIsWLWzji/NounXrxsyZMxkyZAhnz56lb9++nDhxgoYNG7Js2TL8/f0BKF26NCtWrOCtt97i1KlThIaGct999zFixAg8tYaCiIh7iY835+Zs2mSO27Y1b/9www3OrUtcnsUwDMPZRThbWloaVquV1NRUzd8REXE158+bV1aNGmX++frr4a23oGtXdXNKuIL+/nb5q7FERMR9ZGUbbEw8Tkr6OSr5+9AgLABPj8sElh07oHt32LbNHMfEwHvvQUhIkdQr7kFhR0REisSS+CRGLUogKfWcbVuw1YcRMeFER/7ropLMTBg3DsaMMbs5AQHmOjqdOqmbI3Zz2auxRETEfSyJT+LpWVtzBB2A5NRzPD1rK0vik/63MS4OGjSAkSPNoPPAA7BrF3TurKAjV0VhR0REClVWtsGoRQnkNUH04rZRixLIOpcBr7wCd9wB27dD+fIwZw7Mnw+6/6FcA53GEhGRQrUx8Xiujs6lDKD8nnjO3d6fMnsSzI0PPwxTpkClSkVTpLg1hR0RESlUKen5B53SF87Tf90cnvr1a0oZ2VCxonnH8ocfLsIKxd0p7IiISKGq5O+T5/bbkvbyxuLJ1PjnMADH2v2HCh+/bwYeEQeye87O1q1b2blzp238zTff8MADD/Diiy+SmZnp0OJERKT4axAWQLDVh4tTi70vZPLCypks+Ox5avxzmL/LXM/QziMp9808BR0pFHaHnT59+rB3714ADhw4wGOPPYafnx9fffUVQ4YMcXiBIiJyeVnZBut//4dv4v5k/e//kJXtWmvFenpYGBETDkDdP3ezeEZ/nt7wNZ5GNgvDm9Oq11SaD33y8uvtiFwDu09j7d27l9tvvx2Ar776irvuuovPP/+ctWvX8thjjzF58mQHlygiIvmxa+0aJ4qudj0/JS+i6uwP8DAMUsqU48XW/dhVP4pxLlaruB+7w45hGGRnZwPw448/0q5dOwBCQ0M5duyYY6sTEZF8XVy75t99nItr10zrUtc1QsTatdCzJ2H/f1YgpcNjbB7wEr0qB115BWURB7D7NFb9+vV59dVX+eyzz1i1ahX33XcfYN6xPDAw0OEFiohIbgVeu8aZp7TOnIHnnoNmzWDvXqhcGb77jkrz5tD2rggaVyuvoCNFwu6wM3nyZLZu3Uq/fv0YPnw4N998MwBff/01TZo0cXiBIiKSW0HWrklKPcfGxONFV9SlVq+G226DyZPBMMy7lcfHw///A1mkKNl9Guu2227LcTXWRa+//jqenp4OKUpERC7vcmvXXM1+DnPqFAwbZi4ICHDDDfDhhxAdXbR1iFziqm4XcfLkST766COGDRvG8ePmvxoSEhJISUlxaHEiIpK3/Nauudr9HOLnn81uzsWg8+ST5j2tFHTEyezu7OzYsYN77rmH66+/noMHD9K7d28CAgJYsGABhw4d4tNPPy2MOkVE5BIX165JTj2X57wdCxBk9aFBWEDhF5OeDi+8ANOmmeMqVeCjj6Bly8J/b5ECsLuzM3DgQHr06MG+ffvw8fnfvxjatGnD6tWrHVqciIjk7dK1a/49xffieERMeOFPAP7xR6hV639B5+mnzbk5CjriQuwOO5s2baJPnz65tleuXJnk5GSHFCUiIlcWHRnMtC51CbLmPFUVZPUp/MvO09LM01QtW8KhQxAWBj/9BFOngr9/4b2vyFWw+zSWj48PaWlpubbv2bOHilrmW0SkSEVHBtMyPIiNicdJST9HJX+fwl+7ZulS6N0bjhwxx/36wbhxcN11hfeeItfA7rDTvn17/vvf//Lll18CYLFYOHz4MEOHDuXBBx90eIEiInJ5nh4WGlcrX/hvdPIkDBoEH39sjqtVg+nTISqq8N9b5BrYfRrrjTfe4O+//6ZSpUqcPXuWqKgobr75Zvz9/RkzZkxh1CgiIs62eDFERppBx2KB2FjYvl1BR4oFuzs7ZcuWZc2aNfz0009s3bqV7Oxs6taty7333lsY9YmIiDOdOGGugvzJJ+a4enWYMQOaNnVuXSJ2sBiG4Vq3x3WCtLQ0rFYrqamplC1b1tnliIi4hm+/haeegqQks5szcCD897/g5+fsykSAgv/+LlBn5+233y7wG/fv37/A+4qIiAv65x8YMABmzzbHNWua3ZzGjZ1bl8hVKlBnJywsrGAHs1g4cODANRdV1NTZERH5fwsWmGvl/PUXeHjA88/DyJHg6+vsykRycWhnJzEx0WGFiYiIC/r7b3j2WZg71xyHh5vdnAYNnFuXiANc1b2xRETEjXz9NUREmEHH0xNefBG2blXQEbdRoM7OwIEDGT16NGXKlGHgwIGX3XfSpEkOKUxERApZSgo884wZdsC8tHzmTKhXz6lliThagcLOtm3bOH/+vO3PIiJSjBkGfPmlGXT++QdKlYJhw+Cll6B0aWdXJ+JwuvQcTVAWkRIkORn69jUnIgPUrm3OzalTx7l1iVyFgv7+tnvOTs+ePUlPT8+1/fTp0/Ts2dPew4mISFEwDPNS8ogIM+iUKgWjRsHGjQo64vbs7ux4enqSlJREpUqVcmw/duwYQUFBXLhwwaEFFgV1dkTErSUlmYsDfvutOa5Tx+zm1K7t3LpErpHDOztpaWmkpqZiGAbp6emkpaXZHidOnOD777/PFYCuZPXq1cTExBASEoLFYmHhwoU5njcMg5EjRxISEoKvry/Nmzdn165dOfbJyMjg2WefpUKFCpQpU4b777+fP/74w646RETckmGYt3kIDzeDjpcXvPoqbNigoCMlSoHDzvXXX09AQAAWi4UaNWpQrlw526NChQr07NmTZ555xq43P336NLVr12bKlCl5Pj9hwgQmTZrElClT2LRpE0FBQbRs2TLHabTY2FgWLFjAF198wZo1azh16hTt2rUjKyvLrlpERNzKn39Cu3bQvbt5t/L69c3LyYcPN0OPSAlS4NNYq1atwjAM7r77bubNm0dAQIDtudKlS1O1alVCQkKuvhCLhQULFvDAAw8AZlcnJCSE2NhYXnjhBcDs4gQGBvLaa6/Rp08fUlNTqVixIp999hmPPvooAEePHiU0NJTvv/+e1q1bF+i9dRpLRNyGYZinqAYOhNRU8+qqUaPMlZBL2X3vZxGX5tAVlAGioqIAczXl0NBQPDwKdz3CxMREkpOTadWqlW2bt7c3UVFRrFu3jj59+rBlyxbOnz+fY5+QkBAiIyNZt25dvmEnIyODjIwM2zgtLa3wfhARkaJy5Aj07g1Ll5rjhg3h44/N01giJZjdMb9q1aqcPHmSjRs3kpKSQnZ2do7nH3/8cYcUlpycDEBgYGCO7YGBgRw6dMi2T+nSpSlXrlyufS6+Pi/jxo1j1KhRDqlTRMTpDAM++ggGDYL0dPD2NufmPPecuSKySAlnd9hZtGgRnTt35vTp0/j7+2OxWGzPWSwWh4WdS495KcMwcm37tyvtM2zYsBwrQaelpREaGnpthYqIOMPBg2Y358cfzXGTJmY3p2ZNp5Yl4krsPhc1aNAg21o7J0+e5MSJE7bH8ePHHVZYUFAQQK4OTUpKiq3bExQURGZmJidOnMh3n7x4e3tTtmzZHA8RkWIlOxumTYNatcyg4+sLEyfC6tUKOiL/YnfY+fPPP+nfvz9+fn6FUY9NWFgYQUFBLF++3LYtMzOTVatW0aRJEwDq1auHl5dXjn2SkpKIj4+37SMi4nYOHIB77zVXQj51Cu68E7ZvNycl67SVSC52n8Zq3bo1mzdv5qabbrrmNz916hT79++3jRMTE4mLiyMgIIAqVaoQGxvL2LFjqV69OtWrV2fs2LH4+fnRqVMnAKxWK7169WLQoEGUL1+egIAAnn/+eWrVqsW99957zfWJiLiU7GyYOhVeeAHOnAE/Pxg3Dvr1g0K+aESkOLM77Nx3330MHjyYhIQEatWqhde/1mu4//77C3yszZs306JFC9v44jyabt26MXPmTIYMGcLZs2fp27cvJ06coGHDhixbtgx/f3/ba958801KlSrFI488wtmzZ7nnnnuYOXMmnvrXjYi4k/37oVcv8zQVQFQUTJ8O1ao5ty6RYsDu20Vc7pJzi8VSLBfz0zo7IuKysrPhnXfMu5KfPQtlysCECebtH9TNkRLO4evsXPTvS81FRKSQ7N0LPXvC2rXm+O67zUvMw8KcW5dIMaN/FoiIuJqsLPPKqtq1zaBz3XXw3nvmVVcKOiJ2u6q1w0+fPs2qVas4fPgwmZmZOZ7r37+/QwoTESmRfvsNevSAX381xy1bwocfQtWqzq1LpBizO+xs27aNtm3bcubMGU6fPk1AQADHjh3Dz8+PSpUqKeyIiFyNCxfMbs6IEZCRAWXLwqRJ5mmsKyykKiKXZ/dprOeee46YmBiOHz+Or68vv/76K4cOHaJevXq88cYbhVGjiIh727XLXPl46FAz6LRpA/Hx5tVXCjoi18zusBMXF8egQYPw9PTE09OTjIwMQkNDmTBhAi+++GJh1Cgi4p4uXICxY6FuXdi0CaxW847lixeDbmEj4jB2hx0vLy/bfacCAwM5fPgwYC7wd/HPIiJyBTt3QqNGMHw4ZGZCu3Zmh6d7d3VzRBzM7jk7derUYfPmzdSoUYMWLVrwyiuvcOzYMT777DNq1apVGDWKiLiP8+dh/HgYPdr8c7ly8Pbb0LmzQo5IIbG7szN27FiCg4MBGD16NOXLl+fpp58mJSWFDz74wOEFioi4jbg4aNAAXnnFDDrt25vdnC5dFHRECpHdKyi7I62gLCKFKjPTnJszZow5TycgAKZMgcceU8gRuQaFtoKyiIjYYetWc92cHTvMcYcO5s08AwOdW5dICWJ32AkLC7NNUM7LgQMHrqkgERG3kJFhzssZP95cEblCBXj3XXj4YXVzRIqY3WEnNjY2x/j8+fNs27aNJUuWMHjwYEfVJSJSfG3aZHZzdu0yx488Yp62qljRuXWJlFB2h50BAwbkuf3dd99l8+bN11yQiEixde4cjBpl3pU8OxsqVTJPWT34oLMrEynRHHYj0DZt2jBv3jxHHU5EpHj59VdzccDx482g06mT2dlR0BFxOoeFna+//pqAgABHHU5EpHg4exYGD4amTWH3bnPi8YIFMHu2OU9HRJzuqhYVvHSCsmEYJCcn8/fffzN16lSHFici4tLWrTPn5uzda467doXJk81Ly0XEZdgddh544IEcYw8PDypWrEjz5s255ZZbHFWXiIjrOnMGXnrJDDaGASEh8P775i0fRMTlaFFBtKigiNjhl1+gZ0/Yv98cd+8OkyaZt30QkSJVaIsK/vnnn8ybN4+9e/dSunRpatasySOPPEI5/R9dRNzZ6dPw4ovwzjtmN6dyZfjwQ2jTxtmVicgV2BV2pk6dysCBA8nMzMRqtWIYBmlpaQwcOJCPPvqIjh07YhgGcXFx1KlTp7BqFhEpWitXQq9ecHHR1CeegDfeAKvVqWWJSMEU+GqsxYsX079/f/r168eff/7JiRMnOHnyJH/++Sd9+vShW7durFmzhs6dO7No0aLCrFlEpGicOgXPPAMtWsCBA2QEV2bd1NmsHzqeLH+d8hYpLgo8ZycqKopmzZrx6quv5vn8Sy+9xMSJEwkKCmLlypVUrVrVoYUWJs3ZEZFcVqwwOzgHDwKwoEE7Xm7yOKe8/QAItvowIiac6MhgJxYpUrIV9Pd3gcNO2bJl2bRpEzVr1szz+T179nDrrbdy8OBBqlSpcnVVO4nCjojYpKXBkCHm1VXA2ZAbeKLZU6y98fYcu11cgGNal7oKPCJO4vAJytnZ2Xh5eeX7vJeXF76+vsUu6IiI2CxbZnZzjhwBIPvpp2lXqQ2/n8t9xt/ADDyjFiXQMjwITw/d3FPEVRV4zk5ERATffPNNvs8vXLiQiIgIhxQlIlKkUlPNkNO6tRl0wsLg55/ZMGh0nkHnIgNISj3HxsTjRVeriNitwGGnb9++DB8+nKlTp3LhwgXb9gsXLvDuu+/y0ksv0bdv30IpUkSk0PzwA0RGwvTp5rh/f9i5E5o3JyX9XIEOUdD9RMQ5Cnwaq1u3buzcuZN+/foxbNgwqlWrBsDvv//OqVOn6N+/P927dy+sOkVEHOvECRg4EGbONMc33wwffwzNmtl2qeTvU6BDFXQ/EXEOu9bZeeONN3jooYeYM2cO+/btA6BZs2Z07NiRRo0aFUqBIiIO99130KcPHD0KFgvExsKrr4KfX47dGoQFEGz1ITn1HHldyWEBgqw+NAjTvbBEXJndKyg3atRIwUZEiqfjx81g89ln5rhGDZgxA5o0yXN3Tw8LI2LCeXrWViyQI/BcnI48IiZck5NFXFyB5+yIiBRrCxdCRIQZdDw84PnnIS4u36BzUXRkMNO61CXImvNUVZDVR5edixQTdnd2RESKlWPHzEnHc+aY41tvNbs5DRsW+BDRkcG0DA9iY+JxUtLPUcnfPHWljo5I8eDynZ309HRiY2OpWrUqvr6+NGnShE2bNtme7969OxaLJcdDp9lEBIB588xuzpw5Zjdn6FDYutWuoHORp4eFxtXK0/72yjSuVl5BR6QYcfnOzhNPPEF8fDyfffYZISEhzJo1i3vvvZeEhAQqV64MQHR0NDNmzLC9pnTp0s4qV0Rcwd9/Q79+8OWX5jgiwuzm3HGHc+sSEae4qs7OhQsX+PHHH3n//fdJT08H4OjRo5w6dcqhxZ09e5Z58+YxYcIE7rrrLm6++WZGjhxJWFgY06ZNs+3n7e1NUFCQ7REQoCsjREokwzADTni4+b+enjB8OGzZoqAjUoLZ3dk5dOgQ0dHRHD58mIyMDFq2bIm/vz8TJkzg3LlzvPfeew4r7sKFC2RlZeHjk3NioK+vL2vWrLGNV65cSaVKlbj++uuJiopizJgxVKpUKd/jZmRkkJGRYRunpaU5rGYRcZK//jLvUD5vnjmuVcvs5tSr59y6RMTp7O7sDBgwgPr163PixAl8fX1t2//zn/+wYsUKhxbn7+9P48aNGT16NEePHiUrK4tZs2axYcMGkpKSAGjTpg2zZ8/mp59+YuLEiWzatIm77747R5j5t3HjxmG1Wm2P0NBQh9YtIkXIMMw5ORERZtApVQpGjIDNmxV0RASw467nF1WoUIG1a9dSs2ZN/P392b59OzfddBMHDx4kPDycM2fOOLTA33//nZ49e7J69Wo8PT2pW7cuNWrUYOvWrSQkJOTaPykpiapVq/LFF1/QoUOHPI+ZV2cnNDRUdz0XKW6SkuDpp+Hifftuv93s5tx+uzOrEpEiUtC7ntvd2cnOziYrKyvX9j/++AN/f397D3dF1apVY9WqVZw6dYojR46wceNGzp8/T1hYWJ77BwcHU7VqVdsKz3nx9vambNmyOR4iUowYhrleTkSEGXS8vOC//4WNGxV0RCQXu8NOy5YtmTx5sm1ssVg4deoUI0aMoG3bto6sLYcyZcoQHBzMiRMnWLp0Ke3bt89zv3/++YcjR44QHKyFvkTc0p9/wv33w+OPm/e3qlvXnID88stm6BER+Re7T2MdPXqUFi1a4Onpyb59+6hfvz779u2jQoUKrF69+rITg6/G0qVLMQyDmjVrsn//fgYPHoy3tzdr1qwhIyODkSNH8uCDDxIcHMzBgwd58cUXOXz4MLt37y5wp6mgbTARcSLDgE8+MW/3kJoKpUubc3MGD1bIESmhCvr72+6rsUJCQoiLi2POnDls3bqV7OxsevXqRefOnXNMWHaU1NRUhg0bxh9//EFAQAAPPvggY8aMwcvLiwsXLrBz504+/fRTTp48SXBwMC1atGDu3LmFckpNRJzkyBHzxp0//GCO77jDnJsTEeHcukSkWLC7s+OO1NkRcVGGAR9/DAMHQloaeHubc3MGDjSvuhKREs2hnZ1vv/22wG98//33F3hfEZF8HT4MvXvDsmXmuFEjM/jceqtz6xKRYqdAYeeBBx4o0MEsFkueV2qJiBSYYcAHH5hzcdLTwccHXn3VnKvj6ens6kSkGCpQ2MnOzi7sOkRE4OBBeOIJuLhAadOmZjenRg2nliUixZvL3/VcREqA7Gx4912IjDSDjq8vvPkmrFqloCMi1+yqws6KFSto164d1apV4+abb6Zdu3b8+OOPjq5NREqC33+Hu+8271J++jQ0awY7dui0lYg4jN1hZ8qUKURHR+Pv78+AAQPo378/ZcuWpW3btkyZMqUwahQRd5SdDW+/DbfdZnZw/PzgnXdg5Uq4+WZnVycibsTuS88rV67MsGHD6NevX47t7777LmPGjOHo0aMOLbAo6NJzkSK2bx/06gW//GKOmzeH6dPhppucWpaIFC+Fdm+stLQ0oqOjc21v1aoVaWlp9h5OREqSrCxzLk7t2mbQue46mDrVnKejoCMihcTusHP//fezYMGCXNu/+eYbYmJiHFKUiLihPXvM+TgDB8LZs3DPPbBzp3nXcg9dKyEihcfuJUhvvfVWxowZw8qVK2ncuDEAv/76K2vXrmXQoEG8/fbbtn379+/vuEpFpHjKyoJJk8wbdWZkgL8/vPGGuWCgxeLs6kSkBLB7zk5YWFjBDmyxcODAgasqqqhpzo5IIUlIgJ49YcMGc9yqFXz4IVSp4ty6RMQtFNqNQBMTE6+pMBEpAS5cMLs3I0ZAZiaULWvO1enRQ90cESlyupOeiDhWfLwZajZvNsdt28L778MNNzi3LhEpsewOO4Zh8PXXX/Pzzz+TkpKS61YS8+fPd1hxIlKMnD8Pr71m3pX8/Hm4/np46y3o2lXdHBFxKrvDzoABA/jggw9o0aIFgYGBWPQfMRHZsQO6d4dt28xxTAy89x6EhDi1LBERuIqwM2vWLObPn0/btm0Lox4RKU4yM2HcOPOu5BcuQLly5irInTqpmyMiLsPusGO1WrlJi3+JyLZt5tyc7dvN8QMPwLRpEBTk1LJERP7N7pW8Ro4cyahRozh79mxh1CMiri4zE155BRo0MINO+fIwZw7Mn6+gIyIuye7OzsMPP8ycOXOoVKkSN954I15eXjme37p1q8OKExEXs3mz2c2JjzfHDz0EU6ZAYKBz6xIRuQy7w0737t3ZsmULXbp00QRlkZIiIwNGjYIJE8wVkStWhHffhYcfdnZlIiJXZHfYWbx4MUuXLuXOO+8sjHpExNVs3Gh2cxISzPGjj5qTkCtWdG5dIiIFZPecndDQUN1SQaQkOHcOXngBGjc2g06lSjBvHnzxhYKOiBQrdoediRMnMmTIEA4ePFgI5YiIS1i/Hm6/3TxtlZ0NnTubgadDB2dXJiJiN7tPY3Xp0oUzZ85QrVo1/Pz8ck1QPn78uMOKE5EiduaMeXfyN98EwzCvrnr/fbj/fmdXJiJy1ewOO5MnTy6EMkTE6dasMe9Qvm+fOX78cTP0BAQ4ty4RkWtkd9jp1q1bYdQhIs5y+jQMHw5vv212c0JC4IMP4L77nFJOVrbBxsTjpKSfo5K/Dw3CAvD00FWfInL1rumu52fPnuX8+fM5tmnyskgxsmqV2c05cMAc9+wJEyeaN/F0giXxSYxalEBS6jnbtmCrDyNiwomODHZKTSJS/Nk9Qfn06dP069ePSpUqcd1111GuXLkcDxEpBk6dgn79oHlzM+jccAP88ANMn+7UoPP0rK05gg5Acuo5np61lSXxSU6pS0SKP7vDzpAhQ/jpp5+YOnUq3t7efPTRR4waNYqQkBA+/fTTwqhRRBzpp5+gVi1zUUCA3r3NFZGjo51WUla2wahFCRh5PHdx26hFCWRl57WHiMjl2R12Fi1axNSpU3nooYcoVaoUzZo146WXXmLs2LHMnj27MGoUEUdIT4enn4Z77oGDB6FKFVi2zJyfY7U6tbSNicdzdXQuZQBJqefYmKirPUXEfnaHnePHjxMWFgaY83MuXmp+5513snr1asdWJyKOsXw5REbCe++Z46eeMrs5LVs6t67/l5Kef9C5mv1ERC5ld9i56aabbAsKhoeH8+WXXwJmx+d6J53rF5F8pKbCk09Cq1Zw+DDceCOsWAHTpoG/v7Ors6nk7+PQ/URELmV32OnRowfbt28HYNiwYba5O8899xyDBw92eIEicpWWLDG7OR9+aI779YOdO+Huu51bVx4ahAUQbPUhvwvMLZhXZTUI05o/ImI/u8POc889R//+/QFo0aIFu3fvZs6cOWzdupUBAwY4vMD09HRiY2OpWrUqvr6+NGnShE2bNtmeNwyDkSNHEhISgq+vL82bN2fXrl0Or0Ok2Dh50ryEvE0b+OMPuOkmWLnSvHnnddc5u7o8eXpYGBETDpAr8Fwcj4gJ13o7InJV7A47/1a1alU6dOhA7dq1HVFPLk888QTLly/ns88+Y+fOnbRq1Yp7772XP//8E4AJEyYwadIkpkyZwqZNmwgKCqJly5akp6cXSj0iLm3xYoiIgBkzwGKBAQNgxw6IinJ2ZVcUHRnMtC51CbLmPFUVZPVhWpe6WmdHRK6axTCMAl3LuWHDBo4fP06bNm1s2z799FNGjBjB6dOneeCBB3jnnXfw9vZ2WHFnz57F39+fb775hvsuWc319ttvp127dowePZqQkBBiY2N54YUXAMjIyCAwMJDXXnuNPn365HncjIwMMjIybOO0tDRCQ0NJTU3VoohSPJ04AbGxcHH5h+rV4eOP4c47nVrW1dAKyiJSUGlpaVit1iv+/i5wZ2fkyJHs2LHDNt65cye9evXi3nvvZejQoSxatIhx48ZdW9X/cuHCBbKysvDxyfkvPV9fX9asWUNiYiLJycm0atXK9py3tzdRUVGsW7cu3+OOGzcOq9Vqe4SGhjq0bpEi9e23EB5uBh2LBQYOhLi4Yhl0wDyl1bhaedrfXpnG1cor6IjINStw2ImLi+Oee+6xjb/44gsaNmzIhx9+yMCBA3n77bdtV2Y5ir+/P40bN2b06NEcPXqUrKwsZs2axYYNG0hKSiI5ORmAwMDAHK8LDAy0PZeXYcOGkZqaanscOXLEoXWLFIl//oEuXaB9e0hOhpo1zZt5TpwIfn7Ork5ExGUUOOycOHEiR6hYtWoV0ZesuHrHHXcUSmj47LPPMAyDypUr4+3tzdtvv02nTp3w9PS07WOx5PyXn2EYubZdytvbm7Jly+Z4iBQr8+ebc3NmzwYPDxgyBLZtgyZNnF2ZiIjLKXDYCQwMJDExEYDMzEy2bt1K48aNbc+np6fj5eXl8AKrVavGqlWrOHXqFEeOHGHjxo2cP3+esLAwgoKCAHJ1cVJSUnJ1e0Tcwt9/w2OPwYMPwl9/maev1q2D114DX19nVyci4pIKHHaio6MZOnQov/zyC8OGDcPPz49mzZrZnt+xYwfVqlUrlCIBypQpQ3BwMCdOnGDp0qW0b9/eFniWL19u2y8zM5NVq1bRRP/CFXfz1VdmN2fuXPD0hGHDYMsWaNjQ2ZWJiLi0UgXd8dVXX6VDhw5ERUVx3XXX8cknn1C6dGnb8x9//HGOicKOsnTpUgzDoGbNmuzfv5/BgwdTs2ZNevTogcViITY2lrFjx1K9enWqV6/O2LFj8fPzo1OnTg6vRcQpUlLgmWfg66/NcWSkeWl5/frOrUtEpJgocNipWLEiv/zyC6mpqVx33XU55swAfPXVV1xXCAuWpaamMmzYMP744w8CAgJ48MEHGTNmjO2U2ZAhQzh79ix9+/blxIkTNGzYkGXLluHvQkvhi1wVwzC7OP36mZORPT3hxRdh+HBw4BIPIiLursDr7Lizgl6nL1JkkpPNO5QvXGiOa9c2uzl16ji1LBERV+LwdXZEpAgYhnmFVXi4GXRKlYKRI2HjRgUdEZGrVODTWCJSyI4ehaeegkWLzHGdOmY3p5BuxSIiUlKosyPibIYBn3xiXmm1aBF4ecHo0bBhg4KOiIgDqLMj4kx//AF9+sD335vjevXMbk6tWs6tS0TEjSjsiDiDYZih5rnnIC0NSpeGUaPg+efNeTqFTDfbFJGSRGFHpKgdPgxPPglLl5rjBg3M4BMeXiRvvyQ+iVGLEkhKPWfbFmz1YURMONGRwUVSg4hIUdKcHZGiYhjwwQfmooBLl5pr5UyYAGvXFmnQeXrW1hxBByA59RxPz9rKkvikIqlDRKQoKeyIFIWDB6FVK3N+Tno6NG4McXEweHCRnLYC89TVqEUJ5LWw1sVtoxYlkJVd4pfeEhE3o7AjUpiys2HaNHPC8Y8/go8PTJwIv/wCt9xSpKVsTDyeq6NzKQNISj3HxsTjRVeUiEgR0JwdkcJy4AD06gUrV5rjO++Ejz+G6tWdUk5Kev5B52r2ExEpLtTZEXG07Gx45x2zm7NyJfj6wltvwapVTgs6AJX8fRy6n4hIcaHOjogj7d9vdnNWrzbHUVEwfTpUq+bcuoAGYQEEW31ITj2X57wdCxBkNS9DFxFxJ+rsiDhCVhbZb75JVq3bYPVqsvzKkP3OO/DTTy4RdAA8PSyMiDGv+vr3ijoXxyNiwrXejoi4HYUdkWu1dy8n7miMx8CBeJ47y7oqtxHV9S2apt/KkoS/nF1dDtGRwUzrUpcga85TVUFWH6Z1qat1dkTELVkMwyjx15kW9BbxIjlkZcHkyWQNfwnPjHOcKu3L2BY9+bx2NFgstm6JK4YIraAsIu6goL+/NWdH5Grs3g09e8Kvv+IJrL6xDsOin+VPayXbLgbm6aFRixJoGR7kUmHC08NC42rlnV2GiEiRUNgRsceFC+Y6OSNGQEYGF8pcx/BmPZh7Wyuw5A4zl65do3AhIuIcCjsiBbVrF/ToAZs2mePoaFYM+C9zV6Zc8aVau0ZExHk0QVnkSi5cgLFjoW5dM+hYreaNO7//nrLVbyrQIbR2jYiI86izI3I5O3aY3ZytW83xfffB++9D5cqA1q4RESkO1NkRycv58zB6NNSvbwad66+HTz+FRYtsQQe0do2ISHGgsCPyb3Fx0KABvPKKGXruvx8SEqBr1zwnIWvtGhER16bTWCIXZWbCmDHm/JwLFyAgwLzHVceOeYacS0VHBtMyPEhr14iIuCCFHREwT1X16GHO0QHo0AGmToXAwAIfQmvXiIi4Jp3GkpItIwNeesk8bbVjB1SoAHPnwtdf2xV0RETEdamzIyXXpk1mN2fXLnP8yCMwZQpUrOjcukRExKHU2ZGS59w5GDoUGjUyg07FivDVV2ZHR0FHRMTtqLMjJcuvv5rdnN9+M8cdO8Lbb5unr0RExC2psyMlw9mzMHgwNG1qBp3AQFiwAD7/XEFHRMTNqbMj7m/dOrObs3evOe7SBd56y7y0XERE3J46O+K+zpyBgQPhzjvNoBMcDN9+C599pqAjIlKCqLMj7umXX6BnT9i/3xx37w6TJkG5ck4tS0REip5Ld3YuXLjASy+9RFhYGL6+vtx0003897//JTs727ZP9+7dsVgsOR6NGjVyYtXiVKdPQ//+EBVlBp3KleH77827lCvoiIiUSC7d2Xnttdd47733+OSTT4iIiGDz5s306NEDq9XKgAEDbPtFR0czY8YM27h06dLOKFecbeVK6NULDhwwx716wcSJYLU6tSwREXEulw4769evp3379tx3330A3HjjjcyZM4fNmzfn2M/b25ugoCBnlCiu4NQpeOEF8/YOAKGh8OGH0Lq1c+sSERGX4NKnse68805WrFjB3v+/imb79u2sWbOGtm3b5thv5cqVVKpUiRo1atC7d29SUlIue9yMjAzS0tJyPKSYWrECIiP/F3SefBLi4xV0RETExqU7Oy+88AKpqanccssteHp6kpWVxZgxY+jYsaNtnzZt2vDwww9TtWpVEhMTefnll7n77rvZsmUL3t7eeR533LhxjBo1qqh+DCkMaWkwZAi8/745rloVPvoI7r3XuXWJiIjLsRiGYTi7iPx88cUXDB48mNdff52IiAji4uKIjY1l0qRJdOvWLc/XJCUlUbVqVb744gs6dOiQ5z4ZGRlkZGTYxmlpaYSGhpKamkrZsmUL5WcRB1q2DJ54Ao4cMcd9+8L48eDv79y6RESkSKWlpWG1Wq/4+9ulOzuDBw9m6NChPPbYYwDUqlWLQ4cOMW7cuHzDTnBwMFWrVmXfvn35Htfb2zvfro+4sNRUGDQIpk83x2Fh5p9btHBuXSIi4tJces7OmTNn8PDIWaKnp2eOS8//7Z9//uHIkSMEBwcXdnlSlH74wZybczHoPPss7NihoCMiIlfk0p2dmJgYxowZQ5UqVYiIiGDbtm1MmjSJnj17AnDq1ClGjhzJgw8+SHBwMAcPHuTFF1+kQoUK/Oc//3Fy9eIQJ06YqyDPnGmOq1WDjz+Gu+5yalkiIlJ8uHTYeeedd3j55Zfp27cvKSkphISE0KdPH1555RXA7PLs3LmTTz/9lJMnTxIcHEyLFi2YO3cu/pq/UfwtWgR9+kBSElgsMGAAjBkDfn7OrkxERIoRl56gXFQKOsFJisjx42awmTXLHNeoYXZzmjZ1bl0iIuJSCvr726Xn7EgJtHAhhIebQcfDA55/HuLiFHREROSqufRpLClBjh0z72k1Z445vuUW835Wus+ZiIhcI3V2xPnmzYOICDPoeHiYt37Ytk1BR0REHEKdHXGelBTo1w+++soch4eb3ZwGDZxbl4iIuBV1dqToGQZ8+aXZzfnqK/D0hOHDYetWBR0REXE4dXakaP31l3l7h/nzzXGtWmY3p14959YlIiJuS50dKRqGYc7JCQ83g06pUvDKK7B5s4KOiIgUKnV2pPAlJcHTT8M335jj2rXJ+ngGG61VSEn4m0r+PjQIC8DTw+LcOkVExC0p7EjhMQxzvZwBA8zbPnh5wUsvsTSmOyOX7CMp9aht12CrDyNiwomO1D3NRETEsXQaSwrHn39CTAw8/rgZdOrWhc2bWdKhN0/N3UlS6rkcuyennuPpWVtZEp/kpIJFRMRdKeyIYxmGOeE4IgIWL4bSpc37Wf36K1mRtRi1KIG87k9ycduoRQlkZZf4O5iIiIgDKeyI4xw5Am3bQs+ekJoKd9xhXk7+4ovg5cXGxOO5OjqXMoCk1HNsTDxedDWLiIjbU9iRa2cY8NFHEBkJS5aAtzeMHw/r1pkdnv+Xkp5/0LlUQfcTEREpCE1Qlmtz+DA88QQsX26OGzY0T2PdemuuXSv5+xTokAXdT0REpCDU2ZGrYxjw/vtm52b5cvDxgddfh7Vr8ww6AA3CAgi2+pDfBeYWzKuyGoQFFFrZIiJS8ijsiP0SE+Hee+Gpp+DUKWjaFLZvh+efN2/9kA9PDwsjYsIBcgWei+MRMeFab0dERBxKYUcKLjsb3n3XvMXDTz+Bry+8+SasWgU1ahToENGRwUzrUpcga85TVUFWH6Z1qat1dkRExOE0Z0cK5vffoVcvM9gANGsGH38MN99s96GiI4NpGR7ExsTjpKSf0wrKIiJSqBR25PKys2HKFBg2DM6cAT8/eO0182aeHlffGPT0sNC4WnkHFioiIpI3hR3J37595po5a9aY4+bNYfp0uOkmp5YlIiJiD83Zkdyyssy5OLfdZgadMmVg6lRYsUJBR0REih11diSnPXugRw9Yv94c33OPuWDgjTc6tSwREZGrpc6OmLKyzHVyatc2g46/v7mOzvLlCjoiIlKsqbMjkJBgzs3ZsMEct2oFH34IVao4ty4REREHUGenJLtwAcaNgzp1zKBTtqw5AXnJEgUdERFxG+rslFTx8ebcnM2bzXHbtuZpqxtucG5dIiIiDqbOTklz/jy8+irUrWsGneuvh5kz4bvvFHRERMQtqbNTAFnZhnus9rtjB3TvDtu2meN27cxuTkiIU8sSEREpTAo7V7AkPolRixJISj1n2xZs9WFETHjxuY9TZqY5N+fVV815OuXKwdtvQ+fOYCmGoU1ERMQOOo11GUvik3h61tYcQQcgOfUcT8/aypL4JCdVZodt26BBAxg50gw6DzxgXn3VpYuCjoiIlAgKO/nIyjYYtSgBI4/nLm4btSiBrOy89nABmZnwyitm0Nm+HcqXhzlzYP58CApydnUiIiJFRmEnHxsTj+fq6FzKAJJSz7Ex8XjRFVVQmzdDvXowerTZzXnoIdi1Cx57TN0cEREpcVw67Fy4cIGXXnqJsLAwfH19uemmm/jvf/9Ldna2bR/DMBg5ciQhISH4+vrSvHlzdu3adc3vnZKef9C5mv2KREYGvPgiNGpkXlpesSJ8+SV89RUEBjq7OhEREadw6bDz2muv8d577zFlyhR2797NhAkTeP3113nnnXds+0yYMIFJkyYxZcoUNm3aRFBQEC1btiQ9Pf2a3ruSv49D9yt0Gzeal5OPG2fe+uHRR81uzsMPO7syERERp3LpsLN+/Xrat2/Pfffdx4033shDDz1Eq1at2Pz/C+EZhsHkyZMZPnw4HTp0IDIykk8++YQzZ87w+eefX9N7NwgLINjqQ34nfSyYV2U1CAu4pve5ZufOwQsvQOPG5sTjSpVg3jz44guzsyMiIlLCuXTYufPOO1mxYgV79+4FYPv27axZs4a2bdsCkJiYSHJyMq1atbK9xtvbm6ioKNatW5fvcTMyMkhLS8vx+DdPDwsjYsIBcgWei+MRMeHOXW9n/Xq4/XaYMAGys6FTJzPwdOjgvJpERERcjEuHnRdeeIGOHTtyyy234OXlRZ06dYiNjaVjx44AJCcnAxD4r/kogYGBtufyMm7cOKxWq+0RGhqa537RkcFM61KXIGvOU1VBVh+mdanrvHV2zpyBQYOgaVPYs8e8umrhQpg927zqSkRERGxcelHBuXPnMmvWLD7//HMiIiKIi4sjNjaWkJAQunXrZtvP8q8rjAzDyLXtUsOGDWPgwIG2cVpa2mUDT8vwINdZQXnNGvMO5fv2mePHH4c334QAJ59OExERcVEuHXYGDx7M0KFDeeyxxwCoVasWhw4dYty4cXTr1o2g/18vJjk5meDg/3VZUlJScnV7LuXt7Y23t3eB6/D0sNC4mpM7JqdPw/Dh5srHhmHe4uGDD+C++5xbl4iIiItz6dNYZ86cwcMjZ4menp62S8/DwsIICgpi+fLltuczMzNZtWoVTZo0KdJaC9WqVXDbbfDWW2bQ6dnTvNJKQUdEROSKXLqzExMTw5gxY6hSpQoRERFs27aNSZMm0bNnT8A8fRUbG8vYsWOpXr061atXZ+zYsfj5+dGpUycnV+8Ap07B0KHw7rvm+IYb4MMPITrauXWJiIgUIy4ddt555x1efvll+vbtS0pKCiEhIfTp04dXXnnFts+QIUM4e/Ysffv25cSJEzRs2JBly5bh7+/vxMod4KefoFcvOHjQHPfuDa+/DlarU8sSEREpbiyGYbjozZ2KTlpaGlarldTUVMqWLevcYtLTYcgQeO89c1ylCnz0EbRs6dy6REREXExBf3+7dGenxPnxR7Obc/iwOX7qKXMNneLepRIREXEihR1XkJoKgweb83EAbrwRpk+Hu+92alkiIiLuwKWvxioRliyByMj/BZ1+/WDnTgUdERERB1Fnx1lOnoSBA2HGDHN8003w8ccQFeXUskRERNyNOjvOsHgxRESYQcdigQEDYMcOBR0REZFCoM5OUTpxAmJj4dNPzXH16mY35847nVqWiIiIO1Nnp6h8+y2Eh5tBx2IxT2HFxSnoiIiIFDJ1dgrbP/+Yp6lmzzbHNWua3Rx3up2FiIiIC1NnpzDNn2/OzZk9Gzw8zMUCt21T0BERESlC6uwUhr//hmefhblzzfGtt5qTkRs2dG5dIiIiJZA6O4721VdmN2fuXPD0hGHDYOtWBR0REREnUWfHUVJS4Jln4OuvzXFkpNnNqV/fuXWJiIiUcOrsXCvDgC++MK+0+vprs5vz8suwebOCjoiIiAtQZ+daJCfD00/DwoXmuHZts5tTp45TyxIREZH/UWfnahiGeYVVeLgZdEqVgpEjYeNGBR0REREXo86OvY4ehaeegkWLzHGdOmY3p3Zt59YlIiIieVJnp6AMAz75xLzSatEi8PKC0aNhwwYFHRERERemzk5BGAY8+qh5WTlAvXpmN6dWLefWJSIiIlekzk5BWCzmPaxKl4Zx4+DXXxV0REREigl1dgqqXz9o2xZuvtnZlYiIiIgd1NkpKA8PBR0REZFiSGFHRERE3JrCjoiIiLg1hR0RERFxawo7IiIi4tYUdkRERMStKeyIiIiIW1PYEREREbemsCMiIiJuTWFHRERE3JrCjoiIiLg1hR0RERFxawo7IiIi4tYUdkRERMStlXJ2Aa7AMAwA0tLSnFyJiIiIFNTF39sXf4/nR2EHSE9PByA0NNTJlYiIiIi90tPTsVqt+T5vMa4Uh0qA7Oxsjh49ir+/PxaL5aqOkZaWRmhoKEeOHKFs2bIOrtA96TOznz4z++kzs58+M/vpM7OfIz4zwzBIT08nJCQED4/8Z+aoswN4eHhwww03OORYZcuW1RfdTvrM7KfPzH76zOynz8x++szsd62f2eU6OhdpgrKIiIi4NYUdERERcWsKOw7i7e3NiBEj8Pb2dnYpxYY+M/vpM7OfPjP76TOznz4z+xXlZ6YJyiIiIuLW1NkRERERt6awIyIiIm5NYUdERETcmsKOiIiIuDWFnas0ZswYmjRpgp+fH9dff32BXtO9e3csFkuOR6NGjQq3UBdyNZ+ZYRiMHDmSkJAQfH19ad68Obt27SrcQl3IiRMn6Nq1K1arFavVSteuXTl58uRlX1MSv2dTp04lLCwMHx8f6tWrxy+//HLZ/VetWkW9evXw8fHhpptu4r333iuiSl2HPZ/ZypUrc32nLBYLv/32WxFW7FyrV68mJiaGkJAQLBYLCxcuvOJrSvr3zN7PrDC/Zwo7VykzM5OHH36Yp59+2q7XRUdHk5SUZHt8//33hVSh67maz2zChAlMmjSJKVOmsGnTJoKCgmjZsqXtfmburlOnTsTFxbFkyRKWLFlCXFwcXbt2veLrStL3bO7cucTGxjJ8+HC2bdtGs2bNaNOmDYcPH85z/8TERNq2bUuzZs3Ytm0bL774Iv3792fevHlFXLnz2PuZXbRnz54c36vq1asXUcXOd/r0aWrXrs2UKVMKtL++Z/Z/ZhcVyvfMkGsyY8YMw2q1Fmjfbt26Ge3bty/UeoqDgn5m2dnZRlBQkDF+/HjbtnPnzhlWq9V47733CrFC15CQkGAAxq+//mrbtn79egMwfvvtt3xfV9K+Zw0aNDCeeuqpHNtuueUWY+jQoXnuP2TIEOOWW27Jsa1Pnz5Go0aNCq1GV2PvZ/bzzz8bgHHixIkiqM71AcaCBQsuu4++ZzkV5DMrzO+ZOjtFbOXKlVSqVIkaNWrQu3dvUlJSnF2Sy0pMTCQ5OZlWrVrZtnl7exMVFcW6deucWFnRWL9+PVarlYYNG9q2NWrUCKvVesWfv6R8zzIzM9myZUuO7whAq1at8v2M1q9fn2v/1q1bs3nzZs6fP19otbqKq/nMLqpTpw7BwcHcc889/Pzzz4VZZrFX0r9n16IwvmcKO0WoTZs2zJ49m59++omJEyeyadMm7r77bjIyMpxdmktKTk4GIDAwMMf2wMBA23PuLDk5mUqVKuXaXqlSpcv+/CXpe3bs2DGysrLs+o4kJyfnuf+FCxc4duxYodXqKq7mMwsODuaDDz5g3rx5zJ8/n5o1a3LPPfewevXqoii5WCrp37OrUZjfM931/BIjR45k1KhRl91n06ZN1K9f/6qO/+ijj9r+HBkZSf369alatSqLFy+mQ4cOV3VMZyvszwzAYrHkGBuGkWtbcVLQzwxy/+xw5Z/fHb9nV2LvdySv/fPa7s7s+cxq1qxJzZo1bePGjRtz5MgR3njjDe66665CrbM40/fMPoX5PVPYuUS/fv147LHHLrvPjTfe6LD3Cw4OpmrVquzbt89hxyxqhfmZBQUFAea/kIKDg23bU1JScv2LqTgp6Ge2Y8cO/vrrr1zP/f3333b9/O7wPctPhQoV8PT0zNWRuNx3JCgoKM/9S5UqRfny5QutVldxNZ9ZXho1asSsWbMcXZ7bKOnfM0dx1PdMYecSFSpUoEKFCkX2fv/88w9HjhzJ8Yu8uCnMzywsLIygoCCWL19OnTp1AHO+wapVq3jttdcK5T2LQkE/s8aNG5OamsrGjRtp0KABABs2bCA1NZUmTZoU+P3c4XuWn9KlS1OvXj2WL1/Of/7zH9v25cuX0759+zxf07hxYxYtWpRj27Jly6hfvz5eXl6FWq8ruJrPLC/btm1zy++Uo5T075mjOOx75vApzyXEoUOHjG3bthmjRo0yrrvuOmPbtm3Gtm3bjPT0dNs+NWvWNObPn28YhmGkp6cbgwYNMtatW2ckJiYaP//8s9G4cWOjcuXKRlpamrN+jCJl72dmGIYxfvx4w2q1GvPnzzd27txpdOzY0QgODi4xn1l0dLRx2223GevXrzfWr19v1KpVy2jXrl2OfUr69+yLL74wvLy8jOnTpxsJCQlGbGysUaZMGePgwYOGYRjG0KFDja5du9r2P3DggOHn52c899xzRkJCgjF9+nTDy8vL+Prrr531IxQ5ez+zN99801iwYIGxd+9eIz4+3hg6dKgBGPPmzXPWj1Dk0tPTbf/NAoxJkyYZ27ZtMw4dOmQYhr5nebH3MyvM75nCzlXq1q2bAeR6/Pzzz7Z9AGPGjBmGYRjGmTNnjFatWhkVK1Y0vLy8jCpVqhjdunUzDh8+7JwfwAns/cwMw7z8fMSIEUZQUJDh7e1t3HXXXcbOnTuLvngn+eeff4zOnTsb/v7+hr+/v9G5c+dcl2Xqe2YY7777rlG1alWjdOnSRt26dY1Vq1bZnuvWrZsRFRWVY/+VK1caderUMUqXLm3ceOONxrRp04q4Yuez5zN77bXXjGrVqhk+Pj5GuXLljDvvvNNYvHixE6p2nouXRf/70a1bN8Mw9D3Li72fWWF+zyyG8f8zpkRERETckC49FxEREbemsCMiIiJuTWFHRERE3JrCjoiIiLg1hR0RERFxawo7IiIi4tYUdkRERMStKeyIiIiIW1PYEXFzBw8exGKxEBcX5+xS7HLjjTcyefJkhx2vefPmxMbGOux4zmSxWFi4cCFQfP9+RYqSwo5IMWaxWC776N69u7NLvKKZM2dy/fXX59q+adMmnnzyySKt5ezZs4wYMYKaNWvi7e1NhQoVeOihh9i1a1eR1nHRyJEjuf3223NtT0pKok2bNkVfkEgxpbueixRjSUlJtj/PnTuXV155hT179ti2+fr6cuLECWeURlZWFhaLBQ+Pq/s3VcWKFR1c0eVlZGRw7733cvjwYSZOnEjDhg3566+/GDduHA0bNuTHH3+kUaNGRVpTfoKCgpxdgkixos6OSDEWFBRke1itViwWS65tFx04cIAWLVrg5+dH7dq1Wb9+fY5jrVu3jrvuugtfX19CQ0Pp378/p0+ftj1/4sQJHn/8ccqVK4efnx9t2rRh3759tucvdmi+++47wsPD8fb25tChQ2RmZjJkyBAqV65MmTJlaNiwIStXrgRg5cqV9OjRg9TUVFs3auTIkUDu01gnT57kySefJDAwEB8fHyIjI/nuu+8A+Oeff+jYsSM33HADfn5+1KpVizlz5tj1WU6ePJn169fz3Xff8cgjj1C1alUaNGjAvHnzuPXWW+nVqxcXbyWY1ymxBx54IEcnbdasWdSvXx9/f3+CgoLo1KkTKSkptudXrlyJxWJhxYoV1K9fHz8/P5o0aWILqzNnzmTUqFFs377d9tnMnDkTyHkaKy8JCQm0bduW6667jsDAQLp27cqxY8dsz3/99dfUqlULX19fypcvz7333pvj71rE3SjsiJQQw4cP5/nnnycuLo4aNWrQsWNHLly4AMDOnTtp3bo1HTp0YMeOHcydO5c1a9bQr18/2+u7d+/O5s2b+fbbb1m/fj2GYdC2bVvOnz9v2+fMmTOMGzeOjz76iF27dlGpUiV69OjB2rVr+eKLL9ixYwcPP/ww0dHR7Nu3jyZNmjB58mTKli1LUlISSUlJPP/887lqz87Opk2bNqxbt45Zs2aRkJDA+PHj8fT0BODcuXPUq1eP7777jvj4eJ588km6du3Khg0bCvz5fP7557Rs2ZLatWvn2O7h4cFzzz1HQkIC27dvL/DxMjMzGT16NNu3b2fhwoUkJibmeVpx+PDhTJw4kc2bN1OqVCl69uwJwKOPPsqgQYOIiIiwfTaPPvroFd83KSmJqKgobr/9djZv3sySJUv466+/eOSRR2zPd+zYkZ49e7J7925WrlxJhw4d0D2hxa055N7pIuJ0M2bMMKxWa67tiYmJBmB89NFHtm27du0yAGP37t2GYRhG165djSeffDLH63755RfDw8PDOHv2rLF3714DMNauXWt7/tixY4avr6/x5Zdf2t4fMOLi4mz77N+/37BYLMaff/6Z49j33HOPMWzYsMvWXbVqVePNN980DMMwli5danh4eBh79uwp8OfRtm1bY9CgQbZxVFSUMWDAgHz39/Hxyff5rVu3GoAxd+7cfI/Vvn17o1u3bvkef+PGjQZgpKenG4ZhGD///LMBGD/++KNtn8WLFxuAcfbsWcMwDGPEiBFG7dq1cx0LMBYsWGAYxv/+frdt22YYhmG8/PLLRqtWrXLsf+TIEQMw9uzZY2zZssUAjIMHD+Zbq4i70ZwdkRLitttus/05ODgYgJSUFG655Ra2bNnC/v37mT17tm0fwzDIzs4mMTGRffv2UapUKRo2bGh7vnz58tSsWZPdu3fbtpUuXTrH+2zduhXDMKhRo0aOWjIyMihfvnyBa4+Li+OGG27IdZyLsrKyGD9+PHPnzuXPP/8kIyODjIwMypQpU+D3uBzj/7sepUuXLvBrtm3bxsiRI4mLi+P48eNkZ2cDcPjwYcLDw2375ff3UqVKlauqdcuWLfz8889cd911uZ77/fffadWqFffccw+1atWidevWtGrVioceeohy5cpd1fuJFAcKOyIlhJeXl+3PFosFwPYLODs7mz59+tC/f/9cr6tSpQp79+7N85iGYdiOBeaE6EvH2dnZeHp6smXLFtspp4vy+mWcH19f38s+P3HiRN58800mT55MrVq1KFOmDLGxsWRmZhb4PapXr05CQkKez/32228AtrDl4eGR67TPpafzTp8+TatWrWjVqhWzZs2iYsWKHD58mNatW+eq6XJ/L1cjOzubmJgYXnvttVzPBQcH4+npyfLly1m3bh3Lli3jnXfeYfjw4WzYsIGwsLCrfl8RV6awIyLUrVuXXbt2cfPNN+f5fHh4OBcuXGDDhg00adIEMCcF7927l1tvvTXf49apU4esrCxSUlJo1qxZnvuULl2arKysy9Z322238ccff7B37948uzu//PIL7du3p0uXLoD5C3/fvn2Xre3fOnbsyPDhw9m+fXuOeTvZ2dm8+eab1K9f39aRqVixYo4r4bKysoiPj6dFixaAGY6OHTvG+PHjCQ0NBWDz5s0FruWignw2/1a3bl3mzZvHjTfeSKlSef8n3mKx0LRpU5o2bcorr7xC1apVWbBgAQMHDrS7RpHiQBOURYQXXniB9evX88wzzxAXF8e+ffv49ttvefbZZwGz69G+fXt69+7NmjVr2L59O126dKFy5cq0b98+3+PWqFGDzp078/jjjzN//nwSExPZtGkTr732Gt9//z1gXnV16tQpVqxYwbFjxzhz5kyu40RFRXHXXXfx4IMPsnz5chITE/nhhx9YsmQJADfffLOtW7F792769OlDcnKyXZ/Bc889R4MGDYiJieGrr77i8OHDbNq0iQcffJB9+/bZroQCuPvuu1m8eDGLFy/mt99+o2/fvpw8edL2fJUqVShdujTvvPMOBw4c4Ntvv2X06NF21XPxs0lMTCQuLo5jx46RkZFxxdc888wzHD9+nI4dO7Jx40YOHDjAsmXL6NmzJ1lZWWzYsIGxY8eyefNmDh8+zPz58/n777/tCoYixY3Cjohw2223sWrVKvbt20ezZs2oU6cOL7/8sm0OCcCMGTOoV68e7dq1o3HjxhiGwffff5/jNExeZsyYweOPP86gQYOoWbMm999/Pxs2bLB1PJo0acJTTz3Fo48+SsWKFZkwYUKex5k3bx533HEHHTt2JDw8nCFDhti6Hi+//DJ169aldevWNG/enKCgIB544AG7PgMfHx9WrFjB448/zrBhw6hWrRoNGjQgPj6e+Ph4IiIibPv27NmTbt268fjjjxMVFUVYWJitqwNm52fmzJl89dVXhIeHM378eN544w276gF48MEHiY6OpkWLFlSsWLFAl9OHhISwdu1asrKyaN26NZGRkQwYMACr1YqHhwdly5Zl9erVtG3blho1avDSSy8xceJELVIobs1i/PvEs4iIAPDDDz/wn//8hzfeeCPHZfgiUryosyMiko82bdrwww8/cPz48RyL8olI8aLOjoiIiLg1dXZERETErSnsiIiIiFtT2BERERG3prAjIiIibk1hR0RERNyawo6IiIi4NYUdERERcWsKOyIiIuLWFHZERETErf0flg1UZFa0ajMAAAAASUVORK5CYII=", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# (repeat this cell many times). Sometimes it does not look great, because of the small sample size combined with randomness!\n", "data = stats.norm.rvs(mu, sigma, size=n)\n", "sm.qqplot(data,line=\"q\",a=3/8) \n", "# OBS: \"a = 3/8\" is preferred for n <= 10 \n", "# (\"a = 1/2\" is preferred for n > 10) \n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now try larger samples:" ] }, { "cell_type": "code", "execution_count": 85, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# (repeat this cell many times - then increase n and repeat again)\n", "n=10 # also try n = 100\n", "data = stats.norm.rvs(mu, sigma, size=n)\n", "fig, axs = plt.subplots(1, 3, figsize=(10,4))\n", "axs[0].hist(data, density=True) # plot 1) - histogram\n", "axs[1].ecdf(data) # plot 2) - Empirical CDF\n", "axs[1].plot(np.arange(70,130,1), stats.norm.cdf(np.arange(70,130,1), loc=mu, scale=sigma))\n", "sm.qqplot(data,line=\"q\",a=1/2,ax=axs[2]) # plot 3) - Q-Q plot\n", "\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 86, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# examples with exponentially distributed data:\n", "\n", "n=10 # also try n = 100\n", "data = stats.expon.rvs(mu, sigma, size=n) # Not normal random data anymore\n", "fig, axs = plt.subplots(1, 3, figsize=(10,4))\n", "axs[0].hist(data, density=True)\n", "axs[1].ecdf(data)\n", "axs[1].plot(np.arange(70,150,1), stats.norm.cdf(np.arange(70,150,1), loc=stats.expon.mean(loc=mu, scale=sigma), scale=stats.expon.std(loc=mu, scale=sigma)))\n", "axs[1].set_xlim(70,150)\n", "sm.qqplot(data,line=\"q\",a=1/2,ax=axs[2])\n", "\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 87, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# examples with uniformly distributed data:\n", "\n", "n=10 # also try n = 100\n", "data = stats.uniform.rvs(mu, sigma, size=n)\n", "fig, axs = plt.subplots(1, 3, figsize=(10,4))\n", "axs[0].hist(data, density=True)\n", "axs[1].ecdf(data)\n", "axs[1].plot(np.arange(90,120,1), stats.norm.cdf(np.arange(90,120,1), loc=stats.uniform.mean(loc=mu, scale=sigma), scale=stats.uniform.std(loc=mu, scale=sigma)))\n", "axs[1].set_xlim(90,120)\n", "sm.qqplot(data,line=\"q\",a=1/2,ax=axs[2])\n", "\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example: Voltage drop" ] }, { "cell_type": "code", "execution_count": 107, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 0.75 -0.85 4.23 2.12 3.04 0.53 -0.35 1.69 1.52 -0.42]\n", "10\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Enter data\n", "x = np.array([0.75,-0.85,4.23,2.12,3.04,0.53,-0.35,1.69,1.52,-0.42])\n", "n = len(x)\n", "print(x)\n", "print(n)\n", "# Histogram\n", "plt.hist(x)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 108, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1.226, 1.6203374134214559, 0.5123956804397685]\n" ] } ], "source": [ "# Compute best estimate for the mean (and the standard error)\n", "mean_hat = x.mean()\n", "se_mean = x.std(ddof=1)/np.sqrt(n)\n", "print([mean_hat, x.std(ddof=1), se_mean])" ] }, { "cell_type": "code", "execution_count": 110, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[0.06688044127767756, 2.385119558722322]\n" ] } ], "source": [ "# confidence interval for the mean: (manually)\n", "mu_lower = mean_hat - stats.t.ppf(0.975, df=9)*se_mean\n", "mu_upper = mean_hat + stats.t.ppf(0.975, df=9)*se_mean\n", "print([mu_lower, mu_upper])" ] }, { "cell_type": "code", "execution_count": 111, "metadata": {}, "outputs": [], "source": [ "# Define the null hypothesis\n", "mean_null_hyp = 0" ] }, { "cell_type": "code", "execution_count": 112, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2.3926821532682983\n" ] } ], "source": [ "# Compute the \"test statistic\" from the oberserved data\n", "tobs = (mean_hat - mean_null_hyp) / se_mean\n", "print(tobs)" ] }, { "cell_type": "code", "execution_count": 113, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2.2621571628540993\n" ] } ], "source": [ "# compare with t_0.975 from t-distribution with df = 9\n", "t_criticial = stats.t.ppf(0.975, df=n-1)\n", "print(t_criticial)" ] }, { "cell_type": "code", "execution_count": 114, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.04037944695746913\n" ] } ], "source": [ "p_value= 2*stats.t.cdf(-tobs, df=n-1)\n", "print(p_value)" ] }, { "cell_type": "code", "execution_count": 115, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "TtestResult(statistic=2.3926821532682974, pvalue=0.04037944695746921, df=9)\n" ] } ], "source": [ "# You can also use the ttest_1samp funtion from scipy.stats:\n", "print(stats.ttest_1samp(x, popmean=0))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example: Difference in calorie-intake" ] }, { "cell_type": "code", "execution_count": 64, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Plot histogram of data\n", "x = np.array([1350, 1250, 1755, 1020, 745, 1835, 1540, 1540, 725, 1330, 1435])\n", "plt.hist(x, density=True)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "How well does the data actually follow a normal distribution?
\n", "\n", "How well can we expect 11 obervations to \"look\" like a normal distribution?" ] }, { "cell_type": "code", "execution_count": 65, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1320.4545454545455 110.57793332687574\n" ] } ], "source": [ "# calculate mean and SEM (Standard Error of the Mean)\n", "xbar = x.mean()\n", "n = 11\n", "SEM = x.std(ddof=1)/np.sqrt(n)\n", "print(xbar, SEM)" ] }, { "cell_type": "code", "execution_count": 66, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "11.941392877647603\n" ] } ], "source": [ "# calculate t_obs\n", "t_obs = (xbar-0)/SEM\n", "print(t_obs)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can already now see that t_obs is very large" ] }, { "cell_type": "code", "execution_count": 68, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "3.059020942934875e-07\n" ] } ], "source": [ "# calculate p-value\n", "pval = 2*stats.t.cdf(-t_obs,df=n-1)\n", "print(pval)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "p-value is smaller than 0.05 (and also smaller than 0.001).\n", "So we reject the nulhypothesis " ] }, { "cell_type": "code", "execution_count": 69, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1074.0715560389451, 1566.8375348701459]\n" ] } ], "source": [ "# we could also calculate the 95% conficence interval for the mean\n", "mu_lower = xbar - stats.t.ppf(0.975,df=n-1)*SEM\n", "mu_upper = xbar + stats.t.ppf(0.975,df=n-1)*SEM\n", "print([mu_lower, mu_upper])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice the confidence interval does not include the value 0" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# You can also use the ttest_1samp funtion from scipy.stats:\n", "print(stats.ttest_1samp(x, popmean=0))" ] } ], "metadata": { "kernelspec": { "display_name": "pernille", "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": "3.11.9" } }, "nbformat": 4, "nbformat_minor": 2 }