Prob Plots are Better than Histograms

Prob Plots.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Prob Plots are better than histograms\n",
    "How to make and interpret them"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "np.random.seed(1)\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.stats import norm, probplot, poisson, rayleigh"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Most people are familiar with histograms use for plotting a distribution of values. While they are easy to interpret visually, they do have some draw backs, particullary when trying to compare several different distributions.\n",
    "\n",
    "A better tool is the prob plot which conveys the same information as a histogram, but in a more compact, readable form.\n",
    "\n",
    "In this article, I provide an explanation of how prob plots are created, how they relate to histograms, how they can be read more easily and how to use them to compare multiple distributions.\n",
    "\n",
    "# Problem Statement\n",
    "\n",
    "Suppose we are testing new formulas of plant food and we want to know which formulas promote more plant growth. Before we do hypothesis testing to *prove* which formula is more effective, we will do some basic EDA to visualize and review the results.\n",
    "\n",
    "For our experiment, we are testing five formuals of plant food, (A, B, C, D, E) and have grown 200 plants with each formula and measured their height. We assume that the distribution is normal (gaussian) for each formula and that each formula has a different mean and standard deviation.\n",
    "\n",
    "I'll make some synthetic data for illustrative purposes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "formulas = {'A':{'mean':22, 'std':3},\n",
    "            'B':{'mean':16, 'std':4},\n",
    "            'C':{'mean':24, 'std':4},\n",
    "            'D':{'mean':18, 'std':6},\n",
    "            'E':{'mean':20, 'std':9}}\n",
    "N = 200"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "plants = pd.DataFrame()\n",
    "for formula, params in formulas.items():\n",
    "    for _ in range(N):\n",
    "        f = pd.DataFrame(index = [formula], data = norm(loc = params['mean'], scale = params['std']).rvs(1))\n",
    "        plants = pd.concat([plants, f])\n",
    "plants.columns = ['height']\n",
    "plants.index.name = 'formula'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>height</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>formula</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>A</th>\n",
       "      <td>26.873036</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>A</th>\n",
       "      <td>20.164731</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>A</th>\n",
       "      <td>20.415485</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>A</th>\n",
       "      <td>18.781094</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>A</th>\n",
       "      <td>24.596223</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            height\n",
       "formula           \n",
       "A        26.873036\n",
       "A        20.164731\n",
       "A        20.415485\n",
       "A        18.781094\n",
       "A        24.596223"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plants.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Histogram of All Values\n",
    "The first thing we might want to do is look at a histogram of all the values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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9OFs3XDK8YkZklD/X27ZtOzTnrMnf0e+XdfxCVR1P8g+AB5P85dyZVVVJ5v3fo6r2AHsAJicna2pqqs9SVp6ZmRlWWt/9ftHGrq1nuPPw6vuOGPtenKM3Tg2vmBFZLj/XfZ2Wqarj3fNJ4LPAVcCJJOsBuueT/RYpSVqa8w73JBcnefnzr4F/CjwK7Adu6ha7Cbiv3yIlSUvTz++JE8Bne6fVWQP8l6r6b0m+DOxLcgvwJHB9/2VKkpbivMO9qr4JvH6e8b8F3tpPUZKk/vgJVUlqkOEuSQ0y3CWpQYa7JDXIcJekBhnuktQgw12SGmS4S1KDDHdJapDhLkkNMtwlqUGGuyQ1yHCXpAatvq+GacDmPr8NSVL7PHKXpAYZ7pLUIMNdkhpkuEtSgwx3SWqQV8tIWjbGdSXY0TuuHct+h8kjd0lqkOEuSQ0y3CWpQYa7JDXIcJekBnm1jKRVb5BX6ezaeoabl7C9YV2pM7RwT7Id+A/ABcAfVdUdw9rXuPT7hljqm0CSFmso4Z7kAuA/Ar8IHAO+nGR/VT0+6H15h0RJeqFhnXO/CjhSVd+sqv8LTAM7hrQvSdJZUlWD32jyDmB7Vf3zbvpdwJuq6rY5y+wEdnaTPwN8feCFLH+XAX8z7iJGbDX2DPa9moyy55+sqlfNN2Nsf1Ctqj3AnnHtfzlIcrCqJsddxyitxp7Bvsddxygtl56HdVrmOLBpzvTGbkySNALDCvcvA1uSXJ7kJcANwP4h7UuSdJahnJapqjNJbgP+O71LIe+pqseGsa8VbjWellqNPYN9rybLoueh/EFVkjRe3n5AkhpkuEtSgwz3MUiyPcnXkxxJsnvc9QxLknuSnEzy6JyxS5M8mOQb3fMrxlnjoCXZlOShJI8neSzJe7rx1vt+WZIvJfmLru/f6cYvT/LF7r3+ye4Ci6YkuSDJV5Pc300vi54N9xGbc2uGtwFXAO9McsV4qxqajwPbzxrbDRyoqi3AgW66JWeAXVV1BXA1cGv379t6388Cb6mq1wNXAtuTXA18ELirqn4aOAXcMr4Sh+Y9wBNzppdFz4b76K2aWzNU1cPA02cN7wD2dq/3AteNsqZhq6qnquor3evv0fuh30D7fVdVzXaTF3aPAt4CfKobb67vJBuBa4E/6qbDMunZcB+9DcC350wf68ZWi4mqeqp7/dfAxDiLGaYkm4E3AF9kFfTdnZ54BDgJPAj8FXC6qs50i7T4Xv994DeBH3XTr2SZ9Gy4a2yqdx1uk9fiJlkLfBp4b1V9d+68Vvuuqueq6kp6n0i/CvjZ8VY0XEneDpysqkPjrmU+flnH6K32WzOcSLK+qp5Ksp7eUV5TklxIL9g/UVWf6Yab7/t5VXU6yUPAzwPrkqzpjmRbe6+/GfjlJNcALwP+Pr3vsFgWPXvkPnqr/dYM+4Gbutc3AfeNsZaB68653g08UVUfmjOr9b5flWRd9/oiet/l8ATwEPCObrGm+q6q91XVxqraTO/n+M+r6kaWSc9+QnUMuv/pf58f35rh9vFWNBxJ7gWm6N0C9QTwAeBPgH3APwSeBK6vqrP/6LpiJfkF4H8Ah/nxedj30zvv3nLfr6P3x8ML6B007quq303yU/QuGrgU+Crwq1X17PgqHY4kU8C/qaq3L5eeDXdJapCnZSSpQYa7JDXIcJekBhnuktQgw12SGmS4S1KDDHdJatD/B9sQ9xm5Y0mzAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plants.hist();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is fairly easy to interpret. We can readily see that the mean is about 20 and the values range from about 8 to about 32 (a range of about 24). From this we can estimate (visually) that +/- 3 standard deviations is about 24, so one standard deviation is about 6.\n",
    "\n",
    "We can calculate those values more specifically:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(20.17806316729391, 6.177618617406681)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean = np.mean(plants['height'])\n",
    "std = np.std(plants['height'])\n",
    "mean, std"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that the values we calculate mathematically are comparable to the values we can read visually from the histogram.\n",
    "\n",
    "So far, so good. But what if we want to see the distributions of the different formulas? We can plot overlaid histograms of the different formulas on the same chart."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1)\n",
    "plants.groupby(plants.index).hist(ax=ax)\n",
    "plt.legend(plants.index.unique());"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Because the plots overlay each other, it becomes more difficult (or impossible) to see the values from all the formulas.\n",
    "\n",
    "We can improve this slightly by making the plots transparent:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1)\n",
    "plants.groupby(plants.index).hist(ax=ax, alpha=.2)\n",
    "plt.legend(plants.index.unique());"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "While we can now see all the data, it's still difficult to identify the different distirbutions.\n",
    "\n",
    "Perhaps we can improve this by only plotting the outlines of the histograms:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1)\n",
    "plants.groupby(plants.index).hist(ax=ax, histtype='step')\n",
    "plt.legend(plants.index.unique());"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That's about the best we can do to present this data with a histogram. While it is possible to generate a description of the distributions of the data from this plot, it is quite messy.\n",
    "\n",
    "A better way to plot this would be to use a prob plot, which we will now introduce.\n",
    "\n",
    "A prob plot can be thought of as a plot of the cumulative histogram that has been rescaled to represent the distribution of the data.\n",
    "\n",
    "Let's build a prob plot in several stages.\n",
    "\n",
    "First, for simplicity, we will work only with the data of forumla A. Then, we will add in the data from all the formulas and show that the prob plot is better for comparing multiple distributions on a single plot.\n",
    "\n",
    "We start by grabbing just the 'A' values, sorted in order from lowest to highest:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>height</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>formula</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>A</th>\n",
       "      <td>14.695487</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>A</th>\n",
       "      <td>15.095384</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>A</th>\n",
       "      <td>15.819578</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>A</th>\n",
       "      <td>15.933396</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>A</th>\n",
       "      <td>16.310917</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>A</th>\n",
       "      <td>28.300765</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>A</th>\n",
       "      <td>28.556726</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>A</th>\n",
       "      <td>28.560939</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>A</th>\n",
       "      <td>28.572099</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>A</th>\n",
       "      <td>29.584977</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>200 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            height\n",
       "formula           \n",
       "A        14.695487\n",
       "A        15.095384\n",
       "A        15.819578\n",
       "A        15.933396\n",
       "A        16.310917\n",
       "...            ...\n",
       "A        28.300765\n",
       "A        28.556726\n",
       "A        28.560939\n",
       "A        28.572099\n",
       "A        29.584977\n",
       "\n",
       "[200 rows x 1 columns]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = plants.loc['A'].sort_values('height')\n",
    "A"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A histogram of this data looks like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "counts, bins, plot = plt.hist(A['height'], bins = 40)\n",
    "plt.legend('Formula A');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To turn this histogram into a prob plot, we count the cumulative number of points to the left of any value on the x axis.\n",
    "\n",
    "First, we turn the histogram into a bar chart by determing the centers of the bins.\n",
    "\n",
    "This should give us a plot with the familiar bell-shaped distribution. (More about this later)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "bin_centers = (bins[:-1]+bins[1:])/2\n",
    "bin_centers\n",
    "plt.bar(bin_centers, counts, width=.25)\n",
    "plt.title('Formula A (as a bar chart)');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we plot the cumulative sum of these values.\n",
    "\n",
    "This produces a plot with monotonic, (but irregular) increase."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.bar(bin_centers, counts.cumsum(), width=.25);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This plot can be simplified by just plotting the values at the tops of the bars so it doesn't take up as much space."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(bin_centers, counts.cumsum());"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The next step to turning this into a prob plot is to swap the x and y axes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(counts.cumsum(),bin_centers);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then we change the scaling of the X-axis to represent evenly spaced quantiles of data from the mean.\n",
    "\n",
    "Note that becuse the normal curve is not uniform, the spacing changes. In order to determine the quantiles, we have to make the assumption that the data fits a known distribution. In this case, we know the data is normally distributed.  Also, we must take the mean and standard deviation of the sample data to construct a normal distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "A_mean = A['height'].mean()\n",
    "A_std = np.std(A['height'])\n",
    "A_norm = norm(A_mean, A_std)\n",
    "quantiles = (A_norm.ppf(counts.cumsum()/counts.sum()) - A_mean)/A_std\n",
    "plt.scatter(quantiles, bin_centers);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This final plot is the prob plot.\n",
    "\n",
    "Visually, we can interpret several important aspects of the distribution at a glance.\n",
    "\n",
    "First, because the data falls nearly on a straight line, we can determine that it is normally distributed.\n",
    "\n",
    "Second, we can read the range of data from the y-axis. Here we see it ranges from about five to thrity five.\n",
    "\n",
    "Third, the mean of the data can be immediately identified by reading the y-axis value of the point at zero on the x-axis.  (Approximately 20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(quantiles, bin_centers)\n",
    "plt.xlabel('Theoretical Quantiles')\n",
    "plt.ylabel('Measured Value')\n",
    "plt.axvline(0, color='red')\n",
    "plt.axhline(A_mean, color='red');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we can estimate the standard deviation from the slope of the line.\n",
    "\n",
    "Here we see that an increase of 1 standard deviation yields an increase in measured value by about 4.25"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(quantiles, bin_centers)\n",
    "plt.xlabel('Theoretical Quantiles')\n",
    "plt.ylabel('Measured Value')\n",
    "plt.axvline(0, color='red', linestyle = 'dotted')\n",
    "plt.axhline(A_mean, color='red', linestyle = 'dotted')\n",
    "plt.axvline(1, color='green', linestyle = 'dotted')\n",
    "plt.axhline(A_mean+A_std, color='green', linestyle = 'dotted');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we have created a prob plot for one of our five formulas of plant food, let's see what it looks like if we "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(1,2, figsize = (14,6))\n",
    "\n",
    "for formula in 'ABCDE':\n",
    "    axs[0].scatter(*(probplot(plants.loc[formula]['height'])[0]), label = formula)\n",
    "axs[0].legend()\n",
    "plants.groupby(plants.index).hist(ax=axs[1], histtype='step');\n",
    "axs[0].set_xlabel('Theoretical Quantiles')\n",
    "axs[0].set_ylabel('Measured Values');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Presenting the data this way is much cleaner than the histograms presented earlier.\n",
    "\n",
    "Note that these two charts present exactly the same information, but the one on the left is much easier to read and identify key statistics.\n",
    "\n",
    "We can now tell several things at a glance:\n",
    "* All distributions fit well to a straight line, therefore they are normally distirbuted\n",
    "* Green has the highest mean value, followed by blue, purple, red and then orage\n",
    "* Purple has the highest standard deviation (highest slope)\n",
    "* Blue has the lowest standard deviation\n",
    "* Green and orange have roughly the same standard deviation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Non-normal data\n",
    "Another advantage of the prob plot is that it can be used for non-normal data.\n",
    "\n",
    "For example, if we have some data that is rayleigh distributed:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "r = rayleigh().rvs(300)\n",
    "plt.hist(r);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we do a prob plot assuming it is normal:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(*(probplot(r)[0]))\n",
    "plt.title('Curved line indicates the data is not normally distributed');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can tell from the curvature of this line that the data is not normally distributed.\n",
    "\n",
    "However, if we do a prob plot as a rayleigh distribution, we get this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(*(probplot(r, dist=rayleigh)[0]))\n",
    "plt.title('Straight line indicates the data is rayleigh distributed');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Thereby providing visual evidence that this data is, in fact, rayleigh distributed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}