1. Descriptive Statistics.ipynb

{
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div style=\"width: 100%; overflow: hidden;\">\n",
    "    <div style=\"width: 150px; float: left;\"> <img src=\"https://raw.githubusercontent.com/DataForScience/Networks/master/data/D4Sci_logo_ball.png\" alt=\"Data For Science, Inc\" align=\"left\" border=\"0\" width=150px> </div>\n",
    "    <div style=\"float: left; margin-left: 10px;\"> \n",
    "        <h1>Probability And Statistics For Everyone</h1>\n",
    "        <h1>Descriptive Statistics</h1>\n",
    "        <p>Bruno Gonçalves<br/>\n",
    "        <a href=\"http://www.data4sci.com/\">www.data4sci.com</a><br/>\n",
    "        @bgoncalves, @data4sci</p></div>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from collections import Counter\n",
    "import numpy as np\n",
    "\n",
    "import seaborn as sns\n",
    "\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "import sklearn\n",
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "import scipy\n",
    "from scipy.stats import pearsonr\n",
    "\n",
    "import watermark\n",
    "\n",
    "%load_ext watermark\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Python implementation: CPython\n",
      "Python version       : 3.8.5\n",
      "IPython version      : 7.19.0\n",
      "\n",
      "Compiler    : Clang 10.0.0 \n",
      "OS          : Darwin\n",
      "Release     : 22.4.0\n",
      "Machine     : x86_64\n",
      "Processor   : i386\n",
      "CPU cores   : 16\n",
      "Architecture: 64bit\n",
      "\n",
      "Git hash: 593e30c0dfcafd50401dbb083769424707ebe00c\n",
      "\n",
      "scipy     : 1.6.1\n",
      "pandas    : 1.5.3\n",
      "seaborn   : 0.11.0\n",
      "watermark : 2.1.0\n",
      "json      : 2.0.9\n",
      "sklearn   : 0.0\n",
      "numpy     : 1.24.2\n",
      "matplotlib: 3.3.2\n",
      "\n"
     ]
    }
   ],
   "source": [
    "%watermark -n -v -m -g -iv"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Set the default style"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.style.use('./d4sci.mplstyle')\n",
    "colors = plt.rcParams['axes.prop_cycle'].by_key()['color']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Descriptive Statistics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us start by generating 1,000 randomly chosen integers around 100. This will be our \"dataset\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 1000\n",
    "values = np.random.normal(100, 15, N).astype('int')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "we can take a quick look at a few of the values generated"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([108,  92, 101,  97, 128,  97, 112,  95,  71, 107])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "values[:10]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Mean"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The mean is defined as $$\\mu=\\frac{1}{N}\\sum_{i=1}^Nx_i$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "mean = 0\n",
    "\n",
    "for i in range(N):\n",
    "    mean += values[i]\n",
    "    \n",
    "mean /= N"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "99.727"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "or, more conveniently:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "99.727"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(values)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Standard deviation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Similarly, for the standard deviation, we have $$\\sigma=\\sqrt{\\frac{1}{N}\\sum_{i=1}^N\\left(x_i-\\mu\\right)^2} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "std = 0\n",
    "\n",
    "for i in range(N):\n",
    "    std += (values[i]-mean)**2\n",
    "    \n",
    "std /= N\n",
    "std = np.sqrt(std)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "14.948928757606682"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "std"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "or"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "14.948928757606682"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.std(values)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Extreme values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The maximum and minimum are"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "142"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Max = np.max(values)\n",
    "Max"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "48"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Min = np.min(values)\n",
    "Min"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Histogram"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can generate a histogram by counting how many times we see each value. Here we use the Max and Min values to generate an empty array of zeros within that range."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "hist = np.zeros(Max-Min+1)\n",
    "x = np.arange(Min, Max+1)\n",
    "\n",
    "for value in values:\n",
    "    hist[value-Min] += 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And to visualize it, we must only generate a bar plot with the counts for each value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Count')"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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      "text/plain": [
       "<Figure size 3840x2640 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1)\n",
    "ax.bar(x, hist)\n",
    "ax.set_xlabel('Value')\n",
    "ax.set_ylabel('Count')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A more pythonic way would be to use numpy's histogram function where we must specify the number of bins of we want to include in our histogram. The count associated with each bin will be the number of values that fall within that range.\n",
    "\n",
    "This function returns the counts for each bin, as well as the bin edges (the min and max value for each edge). Since the bins are continuous, the minimum value of bin $i$ is the maximum value of bin $i-1$ and the maximum value of bin $i$ is the minimum value of bin $i+i$, so the bin_edges array contains $bins+1$ values, the minimum value for each bin, plus the maximum value for the last one."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "counts, bin_edges = np.histogram(values, bins=50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Count')"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 3840x2640 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1)\n",
    "# We exclude the last bin edge so that we have as many x as y values\n",
    "ax.bar(bin_edges[:-1], counts)\n",
    "ax.set_xlabel('Value')\n",
    "ax.set_ylabel('Count')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Unfortunately, not all datasets are as easily visualizable as this one so we often have to rely purely on descriptive statistics to compare multiple datasets"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Anscombe quartet"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Anscombe quartet is a set of 4 different dataset with multiple summary statistics having the same value. Even a straight line fit produces the same set of parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'x')"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 3840x2640 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax_lst = plt.subplots(2, 2, sharex=True, sharey=True)\n",
    "ax_lst = np.array(ax_lst).flatten()\n",
    "\n",
    "for i in range(1, 5):\n",
    "    data = pd.read_csv('data/Anscombe%u.dat' % i, header=None, sep=' ')\n",
    "    data.plot(x=0, y=1, kind='scatter', s=300, ax=ax_lst[i-1], label=None)\n",
    "    \n",
    "    lm = LinearRegression()\n",
    "    lm.fit(data[0].values.reshape(-1, 1), data[1])\n",
    "    x = np.linspace(4, 19, 10).reshape(-1, 1)\n",
    "    y = lm.predict(x)\n",
    "    \n",
    "    ax_lst[i-1].plot(x, y, color=colors[1], label='y=%1.2fx+%1.2f' % (lm.coef_[0], lm.intercept_))\n",
    "    ax_lst[i-1].legend(loc='lower right')\n",
    "\n",
    "ax_lst[0].set_ylabel('y')\n",
    "ax_lst[2].set_ylabel('y')\n",
    "ax_lst[2].set_xlabel('x')\n",
    "ax_lst[3].set_xlabel('x')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This example highlights the necessity of using slightly more sophisticated statistics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Boxplots"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A boxplot provides a quick overview of the full distribution of our data. For our example above, we have"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 3840x2640 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.boxplot(x=values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'whiskers': [<matplotlib.lines.Line2D at 0x7f91b93cb580>,\n",
       "  <matplotlib.lines.Line2D at 0x7f91b93cb8e0>],\n",
       " 'caps': [<matplotlib.lines.Line2D at 0x7f91b93cbc40>,\n",
       "  <matplotlib.lines.Line2D at 0x7f91b93cbfa0>],\n",
       " 'boxes': [<matplotlib.lines.Line2D at 0x7f91b93cb220>],\n",
       " 'medians': [<matplotlib.lines.Line2D at 0x7f9190558340>],\n",
       " 'fliers': [<matplotlib.lines.Line2D at 0x7f91905586a0>],\n",
       " 'means': []}"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 3840x2640 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.boxplot(values)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "which provides us with a lot of information on our distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Median"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The median is the 50% quantile of the distribution. The value in the center when we sort all the values. If the number of points is even, then the median is defined as the average of the two center points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "sorted_values = sorted(values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "N = len(sorted_values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "99.0"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "median = (sorted_values[N//2-1] + sorted_values[N//2+1])/2\n",
    "median"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The box is defined by the 25% and 75% quantiles:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "89"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sorted_values[N//4]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "110"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sorted_values[(3*N)//4]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 89., 110.])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.quantile(values, [.25, .75])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The whiskers are give by 1.5x the interquantile range: 1.5x the difference between the 75th and 25th quantiles calculated above"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "IQR = np.quantile(values, .75) - np.quantile(values, .25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "21.0"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "IQR"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "so the left whisker extends all the way to"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "57.5"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.quantile(values, .25) - 1.5*IQR"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "while the right whisker extends to"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "141.5"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.quantile(values, .75) + 1.5*IQR"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Any points further left or right of these limits are known as outliers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 95% Reference Range"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The 95% Reference Range is defined as the central 95% range of the values. In other words, the range between the 2.75% and 97.25% quantiles"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "129.0"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.quantile(values, .975)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "71.0"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.quantile(values, .025)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this example, 95% of the values are in the range between these two values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Correlation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Pearson correlation coefficient is defined as $$ \\rho\\left(x, y\\right)=\\frac{1}{N-1}\\sum_{i=1}^N\\frac{\\left(x_i-\\mu_x\\right)\\left(y_i-\\mu_y\\right)}{\\sigma_x\\sigma_y} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "which we can easily implement as:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "def pearson(x, y):\n",
    "    N = len(x)\n",
    "    meanx = x.mean()\n",
    "    meany = y.mean()\n",
    "    stdx = x.std()\n",
    "    stdy = y.std()\n",
    "    \n",
    "    return np.sum((x - meanx) * (y - meany)) / (stdx * stdy * (N - 1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the first dataset of the Anscombe quartet"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
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       "      <th>0</th>\n",
       "      <td>10.0</td>\n",
       "      <td>8.04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>8.0</td>\n",
       "      <td>6.95</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>13.0</td>\n",
       "      <td>7.58</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>9.0</td>\n",
       "      <td>8.81</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>11.0</td>\n",
       "      <td>8.33</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>14.0</td>\n",
       "      <td>9.96</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>6.0</td>\n",
       "      <td>7.24</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>4.0</td>\n",
       "      <td>4.26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>12.0</td>\n",
       "      <td>10.84</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>7.0</td>\n",
       "      <td>4.82</td>\n",
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       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>5.0</td>\n",
       "      <td>5.68</td>\n",
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      "text/plain": [
       "       0      1\n",
       "0   10.0   8.04\n",
       "1    8.0   6.95\n",
       "2   13.0   7.58\n",
       "3    9.0   8.81\n",
       "4   11.0   8.33\n",
       "5   14.0   9.96\n",
       "6    6.0   7.24\n",
       "7    4.0   4.26\n",
       "8   12.0  10.84\n",
       "9    7.0   4.82\n",
       "10   5.0   5.68"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "data = pd.read_csv('data/Anscombe1.dat', header=None, sep=' ')\n",
    "data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
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      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
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   "source": [
    "pearson(data[0], data[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also use a standard implementation from scipy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.81642051634484, 0.0021696288730787875)"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pearsonr(data[0], data[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "which in addition to the value of the pearson correlation it also provides us with the p-value"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div style=\"width: 100%; overflow: hidden;\">\n",
    "     <img src=\"data/D4Sci_logo_full.png\" alt=\"Data For Science, Inc\" align=\"center\" border=\"0\" width=300px> \n",
    "</div>"
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