12_2_Two_Way_anova_interaction_post_hoc.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "f3d2d55c",
   "metadata": {},
   "outputs": [],
   "source": [
    "import statsmodels.api as sm\n",
    "from scipy.stats import norm\n",
    "from scipy.stats import t\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "from matplotlib import figure\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "33574046",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "128b3f44",
   "metadata": {},
   "source": [
    "## PlantFood Research : \n",
    "\n",
    "- your are a researcher interested in the effectiveness of three different cotton plant food : \n",
    "1. Awesome Advantage  (AA)\n",
    "2. Big Buds (BB)\n",
    "3. Copious Cotton (CC)\n",
    "\n",
    "- Therefor you design an experiment in which you test each plantfood AA,BB,CC with one feeding per day for 75 days after planting. \n",
    "- Eight plants will be tested for each combination. \n",
    "- The variable of interest is the plant height in cm . \n",
    "\n",
    "- The same type of cotton seed will be used for the entire experiment.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "413b3cb4",
   "metadata": {},
   "outputs": [],
   "source": [
    "import statsmodels.api as sm\n",
    "from statsmodels.formula.api import ols\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "bbe8fb5d",
   "metadata": {},
   "outputs": [],
   "source": [
    "data = pd.read_csv(\"plantgrowth.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "14803896",
   "metadata": {},
   "outputs": [],
   "source": [
    "onefeeding = data.loc[data[\"Feedings\"]==\"ONE FEEDING\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "750b7cbc",
   "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>Feedings</th>\n",
       "      <th>FoodType</th>\n",
       "      <th>PlantGrowth</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>ONE FEEDING</td>\n",
       "      <td>AA</td>\n",
       "      <td>65</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>ONE FEEDING</td>\n",
       "      <td>AA</td>\n",
       "      <td>70</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>ONE FEEDING</td>\n",
       "      <td>AA</td>\n",
       "      <td>60</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>ONE FEEDING</td>\n",
       "      <td>AA</td>\n",
       "      <td>60</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>ONE FEEDING</td>\n",
       "      <td>AA</td>\n",
       "      <td>60</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>ONE FEEDING</td>\n",
       "      <td>AA</td>\n",
       "      <td>55</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>ONE FEEDING</td>\n",
       "      <td>AA</td>\n",
       "      <td>60</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>ONE FEEDING</td>\n",
       "      <td>AA</td>\n",
       "      <td>50</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>ONE FEEDING</td>\n",
       "      <td>BB</td>\n",
       "      <td>70</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>ONE FEEDING</td>\n",
       "      <td>BB</td>\n",
       "      <td>65</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>ONE FEEDING</td>\n",
       "      <td>BB</td>\n",
       "      <td>60</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>ONE FEEDING</td>\n",
       "      <td>BB</td>\n",
       "      <td>70</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>ONE FEEDING</td>\n",
       "      <td>BB</td>\n",
       "      <td>65</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>ONE FEEDING</td>\n",
       "      <td>BB</td>\n",
       "      <td>60</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>ONE FEEDING</td>\n",
       "      <td>BB</td>\n",
       "      <td>60</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>ONE FEEDING</td>\n",
       "      <td>BB</td>\n",
       "      <td>50</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>ONE FEEDING</td>\n",
       "      <td>CC</td>\n",
       "      <td>55</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>ONE FEEDING</td>\n",
       "      <td>CC</td>\n",
       "      <td>65</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>ONE FEEDING</td>\n",
       "      <td>CC</td>\n",
       "      <td>70</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>ONE FEEDING</td>\n",
       "      <td>CC</td>\n",
       "      <td>55</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>ONE FEEDING</td>\n",
       "      <td>CC</td>\n",
       "      <td>55</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>ONE FEEDING</td>\n",
       "      <td>CC</td>\n",
       "      <td>60</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>ONE FEEDING</td>\n",
       "      <td>CC</td>\n",
       "      <td>50</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>ONE FEEDING</td>\n",
       "      <td>CC</td>\n",
       "      <td>50</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Feedings FoodType  PlantGrowth\n",
       "0   ONE FEEDING       AA           65\n",
       "1   ONE FEEDING       AA           70\n",
       "2   ONE FEEDING       AA           60\n",
       "3   ONE FEEDING       AA           60\n",
       "4   ONE FEEDING       AA           60\n",
       "5   ONE FEEDING       AA           55\n",
       "6   ONE FEEDING       AA           60\n",
       "7   ONE FEEDING       AA           50\n",
       "8   ONE FEEDING       BB           70\n",
       "9   ONE FEEDING       BB           65\n",
       "10  ONE FEEDING       BB           60\n",
       "11  ONE FEEDING       BB           70\n",
       "12  ONE FEEDING       BB           65\n",
       "13  ONE FEEDING       BB           60\n",
       "14  ONE FEEDING       BB           60\n",
       "15  ONE FEEDING       BB           50\n",
       "16  ONE FEEDING       CC           55\n",
       "17  ONE FEEDING       CC           65\n",
       "18  ONE FEEDING       CC           70\n",
       "19  ONE FEEDING       CC           55\n",
       "20  ONE FEEDING       CC           55\n",
       "21  ONE FEEDING       CC           60\n",
       "22  ONE FEEDING       CC           50\n",
       "23  ONE FEEDING       CC           50"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "onefeeding"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "e523e92a",
   "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>FoodType</th>\n",
       "      <th>AA</th>\n",
       "      <th>BB</th>\n",
       "      <th>CC</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>PlantGrowth</th>\n",
       "      <td>60.0</td>\n",
       "      <td>62.5</td>\n",
       "      <td>57.5</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "FoodType       AA    BB    CC\n",
       "PlantGrowth  60.0  62.5  57.5"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "onefeeding.pivot_table(values=\"PlantGrowth\",columns=\"FoodType\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "9a1323d3",
   "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": [
    "onefeeding.pivot_table(values=\"PlantGrowth\",index=\"FoodType\").plot()\n",
    "plt.yticks(np.arange(40,75,5))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "d2282918",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "\n",
       "        if (window._pyforest_update_imports_cell) { window._pyforest_update_imports_cell('from scipy import stats'); }\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "F_onewayResult(statistic=1.1666666666666667, pvalue=0.33078541251317667)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.f_oneway(onefeeding[onefeeding[\"FoodType\"]==\"AA\"][\"PlantGrowth\"],\n",
    "              onefeeding[onefeeding[\"FoodType\"]==\"BB\"][\"PlantGrowth\"],\n",
    "              onefeeding[onefeeding[\"FoodType\"]==\"CC\"][\"PlantGrowth\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "91890991",
   "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>sum_sq</th>\n",
       "      <th>df</th>\n",
       "      <th>F</th>\n",
       "      <th>PR(&gt;F)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>C(FoodType)</th>\n",
       "      <td>100.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.166667</td>\n",
       "      <td>0.330785</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Residual</th>\n",
       "      <td>900.0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             sum_sq    df         F    PR(>F)\n",
       "C(FoodType)   100.0   2.0  1.166667  0.330785\n",
       "Residual      900.0  21.0       NaN       NaN"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "model = ols('PlantGrowth ~ C(FoodType)' , data=onefeeding).fit()\n",
    "aov_table = sm.stats.anova_lm(model, typ=2)\n",
    "aov_table"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a9628e13",
   "metadata": {},
   "source": [
    "   **if there a difference in heights amonth three foods ?** \n",
    "\n",
    "\n",
    "   **based on one way anova test , we reject null hypothesis .** \n",
    "   **there's no difference among the plant food means based on one feedings per day .** \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "22518b40",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "3622d468",
   "metadata": {},
   "source": [
    "- ### Is there any difference in plant growth when comparing 1 feeding to 2 feedings per day ? \n",
    "\n",
    "- ### DO some plant foods work better once per day and others better at twice per day . ? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "9133bd4c",
   "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>Feedings</th>\n",
       "      <th>FoodType</th>\n",
       "      <th>PlantGrowth</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>ONE FEEDING</td>\n",
       "      <td>BB</td>\n",
       "      <td>60</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46</th>\n",
       "      <td>TWO FEEDINGS</td>\n",
       "      <td>CC</td>\n",
       "      <td>45</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>ONE FEEDING</td>\n",
       "      <td>AA</td>\n",
       "      <td>60</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>ONE FEEDING</td>\n",
       "      <td>BB</td>\n",
       "      <td>60</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>ONE FEEDING</td>\n",
       "      <td>AA</td>\n",
       "      <td>60</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        Feedings FoodType  PlantGrowth\n",
       "10   ONE FEEDING       BB           60\n",
       "46  TWO FEEDINGS       CC           45\n",
       "3    ONE FEEDING       AA           60\n",
       "13   ONE FEEDING       BB           60\n",
       "6    ONE FEEDING       AA           60"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.sample(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "0f494986",
   "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>FoodType</th>\n",
       "      <th>AA</th>\n",
       "      <th>BB</th>\n",
       "      <th>CC</th>\n",
       "      <th>All</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feedings</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>ONE FEEDING</th>\n",
       "      <td>60.0000</td>\n",
       "      <td>62.5000</td>\n",
       "      <td>57.5000</td>\n",
       "      <td>60.0000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TWO FEEDINGS</th>\n",
       "      <td>66.8750</td>\n",
       "      <td>66.8750</td>\n",
       "      <td>40.6250</td>\n",
       "      <td>58.1250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>All</th>\n",
       "      <td>63.4375</td>\n",
       "      <td>64.6875</td>\n",
       "      <td>49.0625</td>\n",
       "      <td>59.0625</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "FoodType           AA       BB       CC      All\n",
       "Feedings                                        \n",
       "ONE FEEDING   60.0000  62.5000  57.5000  60.0000\n",
       "TWO FEEDINGS  66.8750  66.8750  40.6250  58.1250\n",
       "All           63.4375  64.6875  49.0625  59.0625"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.pivot_table(values=\"PlantGrowth\",columns=\"FoodType\",index =\"Feedings\",margins=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "64016662",
   "metadata": {},
   "source": [
    "    We make table of means , the values are not individual data points .\n",
    "    they are all means with their own distribution .\n",
    "\n",
    "    in two way anova, \n",
    "    the way the distributions fit together  is the very heart of the technique."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "1e3b9dfd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='FoodType'>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "data.pivot_table(values=\"PlantGrowth\",index=\"FoodType\",columns =\"Feedings\").plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "29341753",
   "metadata": {},
   "source": [
    "### Questions : \n",
    "- For AA, howmany feedings produce more growht ? \n",
    "- For BB, Howmany feedings produce more growth and for CC ?\n",
    "\n",
    "- DO two feedings produce more growth across all plant foods consistantly? \n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6337ea3b",
   "metadata": {},
   "source": [
    "No, it appears that two feedings are better for AA and BB , Not for CC/\n",
    "\n",
    "This type of situatation is called an **Interaction.**\n",
    "\n",
    "An interaction occurs when the effect of one factor changes , for different level of other factor.\n",
    "\n",
    "\n",
    "In this case the most effective feeding frequency changes across plant food types.\n",
    "\n",
    "On a marginal chart as a general rule , we look to see if the lines cross or would cross ! "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7c936528",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "cefbdfc5",
   "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>sum_sq</th>\n",
       "      <th>df</th>\n",
       "      <th>F</th>\n",
       "      <th>PR(&gt;F)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>C(Feedings)</th>\n",
       "      <td>42.1875</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.577982</td>\n",
       "      <td>0.451351</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C(FoodType)</th>\n",
       "      <td>2412.5000</td>\n",
       "      <td>2.0</td>\n",
       "      <td>16.525994</td>\n",
       "      <td>0.000005</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C(Feedings):C(FoodType)</th>\n",
       "      <td>1362.5000</td>\n",
       "      <td>2.0</td>\n",
       "      <td>9.333333</td>\n",
       "      <td>0.000443</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Residual</th>\n",
       "      <td>3065.6250</td>\n",
       "      <td>42.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                            sum_sq    df          F    PR(>F)\n",
       "C(Feedings)                42.1875   1.0   0.577982  0.451351\n",
       "C(FoodType)              2412.5000   2.0  16.525994  0.000005\n",
       "C(Feedings):C(FoodType)  1362.5000   2.0   9.333333  0.000443\n",
       "Residual                 3065.6250  42.0        NaN       NaN"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "model = ols('PlantGrowth ~ C(Feedings) + C(FoodType) + C(Feedings):C(FoodType)', data=data).fit()\n",
    "aov_table = sm.stats.anova_lm(model, typ=2)\n",
    "aov_table"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "20ae3730",
   "metadata": {},
   "outputs": [],
   "source": [
    "# From above anova two way test , we have the significant interaction . \n",
    "# That leads us to see the factors individually. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0caa37f3",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "83a55c64",
   "metadata": {},
   "source": [
    "on the marginal means graph : \n",
    "\n",
    "the factor of interest or the factor with the most levels is on the horizontal axis. \n",
    "\n",
    "the dependent variable the vertical axis . (what is being measured. )\n",
    "\n",
    "the second factor makes up the series lines by graphing the dependent variable value for each level/category of the first factor.\n",
    "\n",
    "look for crossing or non parallel line on the graph. \n",
    "\n",
    "**if the interaction is significant  ,then the main factors significance cannot be analysed , the factors are too intertwined.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4f71830a",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "7ad15e82",
   "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>FoodType</th>\n",
       "      <th>AA</th>\n",
       "      <th>BB</th>\n",
       "      <th>CC</th>\n",
       "      <th>All</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feedings</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>ONE FEEDING</th>\n",
       "      <td>60.0000</td>\n",
       "      <td>62.5000</td>\n",
       "      <td>57.5000</td>\n",
       "      <td>60.0000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TWO FEEDINGS</th>\n",
       "      <td>66.8750</td>\n",
       "      <td>66.8750</td>\n",
       "      <td>40.6250</td>\n",
       "      <td>58.1250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>All</th>\n",
       "      <td>63.4375</td>\n",
       "      <td>64.6875</td>\n",
       "      <td>49.0625</td>\n",
       "      <td>59.0625</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "FoodType           AA       BB       CC      All\n",
       "Feedings                                        \n",
       "ONE FEEDING   60.0000  62.5000  57.5000  60.0000\n",
       "TWO FEEDINGS  66.8750  66.8750  40.6250  58.1250\n",
       "All           63.4375  64.6875  49.0625  59.0625"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.pivot_table(values=\"PlantGrowth\",columns=\"FoodType\",index =\"Feedings\",margins=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5423e0fa",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "1418507c",
   "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": [
    "data.pivot_table(values=\"PlantGrowth\",index=\"FoodType\",columns =\"Feedings\").plot()\n",
    "\n",
    "plt.axhline(60,linestyle=\"--\")\n",
    "plt.axhline(58.1250,linestyle=\"--\",color=\"orange\")\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6a22e293",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "5e71fdb4",
   "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>sum_sq</th>\n",
       "      <th>df</th>\n",
       "      <th>mean_sq</th>\n",
       "      <th>F</th>\n",
       "      <th>PR(&gt;F)</th>\n",
       "      <th>eta_sq</th>\n",
       "      <th>omega_sq</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>C(Feedings)</th>\n",
       "      <td>42.1875</td>\n",
       "      <td>1.0</td>\n",
       "      <td>42.187500</td>\n",
       "      <td>0.577982</td>\n",
       "      <td>0.451351</td>\n",
       "      <td>0.006129</td>\n",
       "      <td>-0.004428</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C(FoodType)</th>\n",
       "      <td>2412.5000</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1206.250000</td>\n",
       "      <td>16.525994</td>\n",
       "      <td>0.000005</td>\n",
       "      <td>0.350511</td>\n",
       "      <td>0.325846</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C(Feedings):C(FoodType)</th>\n",
       "      <td>1362.5000</td>\n",
       "      <td>2.0</td>\n",
       "      <td>681.250000</td>\n",
       "      <td>9.333333</td>\n",
       "      <td>0.000443</td>\n",
       "      <td>0.197957</td>\n",
       "      <td>0.174892</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Residual</th>\n",
       "      <td>3065.6250</td>\n",
       "      <td>42.0</td>\n",
       "      <td>72.991071</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                            sum_sq    df      mean_sq          F    PR(>F)  \\\n",
       "C(Feedings)                42.1875   1.0    42.187500   0.577982  0.451351   \n",
       "C(FoodType)              2412.5000   2.0  1206.250000  16.525994  0.000005   \n",
       "C(Feedings):C(FoodType)  1362.5000   2.0   681.250000   9.333333  0.000443   \n",
       "Residual                 3065.6250  42.0    72.991071        NaN       NaN   \n",
       "\n",
       "                           eta_sq  omega_sq  \n",
       "C(Feedings)              0.006129 -0.004428  \n",
       "C(FoodType)              0.350511  0.325846  \n",
       "C(Feedings):C(FoodType)  0.197957  0.174892  \n",
       "Residual                      NaN       NaN  "
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def anova_table(aov):\n",
    "    aov['mean_sq'] = aov[:]['sum_sq']/aov[:]['df']\n",
    "\n",
    "    aov['eta_sq'] = aov[:-1]['sum_sq']/sum(aov['sum_sq'])\n",
    "\n",
    "    aov['omega_sq'] = (aov[:-1]['sum_sq']-(aov[:-1]['df']*aov['mean_sq'][-1]))/(sum(aov['sum_sq'])+aov['mean_sq'][-1])\n",
    "\n",
    "    cols = ['sum_sq', 'df', 'mean_sq', 'F', 'PR(>F)', 'eta_sq', 'omega_sq']\n",
    "    aov = aov[cols]\n",
    "    return aov\n",
    "\n",
    "anova_table(aov_table)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2ca1b201",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "7fabdea0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>Multiple Comparison of Means - Tukey HSD, FWER=0.05</caption>\n",
       "<tr>\n",
       "  <th>group1</th> <th>group2</th> <th>meandiff</th> <th>p-adj</th>   <th>lower</th>   <th>upper</th>  <th>reject</th>\n",
       "</tr>\n",
       "<tr>\n",
       "    <td>AA</td>     <td>BB</td>     <td>1.25</td>    <td>0.9</td>   <td>-7.2903</td> <td>9.7903</td>   <td>False</td>\n",
       "</tr>\n",
       "<tr>\n",
       "    <td>AA</td>     <td>CC</td>    <td>-14.375</td> <td>0.001</td> <td>-22.9153</td> <td>-5.8347</td>  <td>True</td> \n",
       "</tr>\n",
       "<tr>\n",
       "    <td>BB</td>     <td>CC</td>    <td>-15.625</td> <td>0.001</td> <td>-24.1653</td> <td>-7.0847</td>  <td>True</td> \n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.table.SimpleTable'>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import statsmodels.stats.multicomp as mc\n",
    "\n",
    "comp = mc.MultiComparison(data['PlantGrowth'], data['FoodType'])\n",
    "post_hoc_res = comp.tukeyhsd()\n",
    "post_hoc_res.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c8a70e10",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ec29abab",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "510a47d4",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f98ab5d9",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6c17802f",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "016fba9f",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "91563bc3",
   "metadata": {},
   "source": [
    "## Roller Coaster Wait Times : "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "170119be",
   "metadata": {},
   "source": [
    "- Tou are an analyst for kings island amusement park . YOu have been asked to determine `if there's a difference in wait time between three big roller coasters` in the park . **The Beast , Banshee and Diamondback.**\n",
    "\n",
    "\n",
    "- To conduct your analysis , you track the wait time for 25 random riders on each ride. While one way anova procedure will test the hypothesis that all three mean weait times are equal . The test will not tell you **Where those differences occure** amongs the coasters. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6898e921",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "0c6dab75",
   "metadata": {},
   "outputs": [],
   "source": [
    "data = pd.read_csv(\"RollerCoster_waitTime.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "1523a1fa",
   "metadata": {},
   "outputs": [],
   "source": [
    "RollerCosters = data.melt(value_name=\"wait_time\",var_name=\"Rides\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "d9058d56",
   "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>Rides</th>\n",
       "      <th>wait_time</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>BEAST</td>\n",
       "      <td>23.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>BEAST</td>\n",
       "      <td>19.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>BEAST</td>\n",
       "      <td>14.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>BEAST</td>\n",
       "      <td>24.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>BEAST</td>\n",
       "      <td>40.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>70</th>\n",
       "      <td>DIAMONDBACK</td>\n",
       "      <td>56.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>71</th>\n",
       "      <td>DIAMONDBACK</td>\n",
       "      <td>56.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>72</th>\n",
       "      <td>DIAMONDBACK</td>\n",
       "      <td>75.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>73</th>\n",
       "      <td>DIAMONDBACK</td>\n",
       "      <td>70.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>74</th>\n",
       "      <td>DIAMONDBACK</td>\n",
       "      <td>51.4</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>75 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "          Rides  wait_time\n",
       "0         BEAST       23.5\n",
       "1         BEAST       19.7\n",
       "2         BEAST       14.8\n",
       "3         BEAST       24.2\n",
       "4         BEAST       40.2\n",
       "..          ...        ...\n",
       "70  DIAMONDBACK       56.4\n",
       "71  DIAMONDBACK       56.0\n",
       "72  DIAMONDBACK       75.6\n",
       "73  DIAMONDBACK       70.1\n",
       "74  DIAMONDBACK       51.4\n",
       "\n",
       "[75 rows x 2 columns]"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "RollerCosters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "9d57ad49",
   "metadata": {
    "scrolled": true
   },
   "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>sum_sq</th>\n",
       "      <th>df</th>\n",
       "      <th>F</th>\n",
       "      <th>PR(&gt;F)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>C(Rides)</th>\n",
       "      <td>8788.2912</td>\n",
       "      <td>2.0</td>\n",
       "      <td>21.353955</td>\n",
       "      <td>5.231290e-08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Residual</th>\n",
       "      <td>14815.9200</td>\n",
       "      <td>72.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              sum_sq    df          F        PR(>F)\n",
       "C(Rides)   8788.2912   2.0  21.353955  5.231290e-08\n",
       "Residual  14815.9200  72.0        NaN           NaN"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "model = ols('wait_time ~ C(Rides)' , data=RollerCosters).fit()\n",
    "aov_table = sm.stats.anova_lm(model, typ=2)\n",
    "aov_table"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "97a0715f",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "1c492fcd",
   "metadata": {},
   "source": [
    "- **If the f-test is significant, we do not know where the differences are located** "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8e3d8354",
   "metadata": {},
   "source": [
    "- There are several multiple comparision procedures : Fisher's LSD . Tukey HSD , Scheffe's Method, Bonferroni . "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "b8b3b8e0",
   "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>sum_sq</th>\n",
       "      <th>df</th>\n",
       "      <th>mean_sq</th>\n",
       "      <th>F</th>\n",
       "      <th>PR(&gt;F)</th>\n",
       "      <th>eta_sq</th>\n",
       "      <th>omega_sq</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>C(Rides)</th>\n",
       "      <td>8788.2912</td>\n",
       "      <td>2.0</td>\n",
       "      <td>4394.145600</td>\n",
       "      <td>21.353955</td>\n",
       "      <td>5.231290e-08</td>\n",
       "      <td>0.372319</td>\n",
       "      <td>0.351816</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Residual</th>\n",
       "      <td>14815.9200</td>\n",
       "      <td>72.0</td>\n",
       "      <td>205.776667</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              sum_sq    df      mean_sq          F        PR(>F)    eta_sq  \\\n",
       "C(Rides)   8788.2912   2.0  4394.145600  21.353955  5.231290e-08  0.372319   \n",
       "Residual  14815.9200  72.0   205.776667        NaN           NaN       NaN   \n",
       "\n",
       "          omega_sq  \n",
       "C(Rides)  0.351816  \n",
       "Residual       NaN  "
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def anova_table(aov):\n",
    "    aov['mean_sq'] = aov[:]['sum_sq']/aov[:]['df']\n",
    "\n",
    "    aov['eta_sq'] = aov[:-1]['sum_sq']/sum(aov['sum_sq'])\n",
    "\n",
    "    aov['omega_sq'] = (aov[:-1]['sum_sq']-(aov[:-1]['df']*aov['mean_sq'][-1]))/(sum(aov['sum_sq'])+aov['mean_sq'][-1])\n",
    "\n",
    "    cols = ['sum_sq', 'df', 'mean_sq', 'F', 'PR(>F)', 'eta_sq', 'omega_sq']\n",
    "    aov = aov[cols]\n",
    "    return aov\n",
    "\n",
    "anova_table(aov_table)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4da2b5f6",
   "metadata": {},
   "source": [
    "#### Difference Matrix : \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "8c9347de",
   "metadata": {},
   "outputs": [],
   "source": [
    "diffs = data.mean().sort_values(ascending=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "dfbdcb1a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DIAMONDBACK    58.904\n",
       "BANSHEE        42.440\n",
       "BEAST          32.672\n",
       "dtype: float64"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diffs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "1dc4cab4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([58.904, 42.44 , 32.672])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.array(diffs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "ff9891b9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([ 0.   , 16.464, 26.232]),\n",
       " array([-16.464,   0.   ,   9.768]),\n",
       " array([-26.232,  -9.768,   0.   ])]"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diffmat = []\n",
    "for i in np.array(diffs):\n",
    "    diffmat.append(i-np.array(diffs))\n",
    "diffmat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "98a68c70",
   "metadata": {},
   "outputs": [],
   "source": [
    "diffmat = pd.DataFrame(diffmat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "dae77fcf",
   "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>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.000</td>\n",
       "      <td>16.464</td>\n",
       "      <td>26.232</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-16.464</td>\n",
       "      <td>0.000</td>\n",
       "      <td>9.768</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-26.232</td>\n",
       "      <td>-9.768</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        0       1       2\n",
       "0   0.000  16.464  26.232\n",
       "1 -16.464   0.000   9.768\n",
       "2 -26.232  -9.768   0.000"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diffmat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "713092df",
   "metadata": {},
   "outputs": [],
   "source": [
    "diffmat.columns = ['DIAMONDBACK', 'BANSHEE', 'BEAST']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "9b111ca5",
   "metadata": {},
   "outputs": [],
   "source": [
    "diffmat.index = ['DIAMONDBACK', 'BANSHEE', 'BEAST']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "2f2fdb45",
   "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>DIAMONDBACK</th>\n",
       "      <th>BANSHEE</th>\n",
       "      <th>BEAST</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>DIAMONDBACK</th>\n",
       "      <td>0.000</td>\n",
       "      <td>16.464</td>\n",
       "      <td>26.232</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BANSHEE</th>\n",
       "      <td>-16.464</td>\n",
       "      <td>0.000</td>\n",
       "      <td>9.768</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BEAST</th>\n",
       "      <td>-26.232</td>\n",
       "      <td>-9.768</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             DIAMONDBACK  BANSHEE   BEAST\n",
       "DIAMONDBACK        0.000   16.464  26.232\n",
       "BANSHEE          -16.464    0.000   9.768\n",
       "BEAST            -26.232   -9.768   0.000"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diffmat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "528b5388",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='Rides', ylabel='wait_time'>"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "sns.boxplot(x = RollerCosters[\"Rides\"],\n",
    "           y=  RollerCosters[\"wait_time\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "02a1bab3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>Multiple Comparison of Means - Tukey HSD, FWER=0.05</caption>\n",
       "<tr>\n",
       "  <th>group1</th>    <th>group2</th>    <th>meandiff</th>  <th>p-adj</th>   <th>lower</th>   <th>upper</th>  <th>reject</th>\n",
       "</tr>\n",
       "<tr>\n",
       "  <td>BANSHEE</td>    <td>BEAST</td>     <td>-9.768</td>  <td>0.0483</td> <td>-19.4778</td> <td>-0.0582</td>  <td>True</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <td>BANSHEE</td> <td>DIAMONDBACK</td>  <td>16.464</td>   <td>0.001</td>  <td>6.7542</td>  <td>26.1738</td>  <td>True</td> \n",
       "</tr>\n",
       "<tr>\n",
       "   <td>BEAST</td>  <td>DIAMONDBACK</td>  <td>26.232</td>   <td>0.001</td>  <td>16.5222</td> <td>35.9418</td>  <td>True</td> \n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.table.SimpleTable'>"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import statsmodels.stats.multicomp as mc\n",
    "\n",
    "comp = mc.MultiComparison(RollerCosters['wait_time'], RollerCosters['Rides'])\n",
    "post_hoc_res = comp.tukeyhsd()\n",
    "post_hoc_res.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1173c58f",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "8374b7d2",
   "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>BEAST</th>\n",
       "      <th>BANSHEE</th>\n",
       "      <th>DIAMONDBACK</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>BEAST</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.862747e-02</td>\n",
       "      <td>1.242146e-04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BANSHEE</th>\n",
       "      <td>0.018627</td>\n",
       "      <td>1.000000e+00</td>\n",
       "      <td>1.053171e-08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>DIAMONDBACK</th>\n",
       "      <td>0.000124</td>\n",
       "      <td>1.053171e-08</td>\n",
       "      <td>1.000000e+00</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                BEAST       BANSHEE   DIAMONDBACK\n",
       "BEAST        1.000000  1.862747e-02  1.242146e-04\n",
       "BANSHEE      0.018627  1.000000e+00  1.053171e-08\n",
       "DIAMONDBACK  0.000124  1.053171e-08  1.000000e+00"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import scikit_posthocs as sp\n",
    "sp.posthoc_ttest(RollerCosters, val_col='wait_time', group_col='Rides', p_adjust=None, pool_sd=True )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "24c7a678",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ea63b14b",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9c76dfc1",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b6715a89",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "61144db3",
   "metadata": {},
   "source": [
    "https://www.statsmodels.org/devel/generated/statsmodels.sandbox.stats.multicomp.MultiComparison.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "96a8cb0d",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "188e741e",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "840ebf5c",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "dc476ebc",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "22e4e9ce",
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_csv(\"https://raw.githubusercontent.com/researchpy/Data-sets/master/difficile.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "f1b4ebf4",
   "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>dose</th>\n",
       "      <th>libido</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>placebo</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>placebo</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>placebo</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>placebo</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>placebo</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>low</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>low</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>low</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>low</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>low</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>high</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>high</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>high</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>high</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>high</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       dose  libido\n",
       "0   placebo       3\n",
       "1   placebo       2\n",
       "2   placebo       1\n",
       "3   placebo       1\n",
       "4   placebo       4\n",
       "5       low       5\n",
       "6       low       2\n",
       "7       low       4\n",
       "8       low       2\n",
       "9       low       3\n",
       "10     high       7\n",
       "11     high       4\n",
       "12     high       5\n",
       "13     high       3\n",
       "14     high       6"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.drop('person', axis= 1, inplace= True)\n",
    "\n",
    "# Recoding value from numeric to string\n",
    "df['dose'].replace({1: 'placebo', 2: 'low', 3: 'high'}, inplace= True)\n",
    "\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "4c5ce4e1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "\n",
       "        if (window._pyforest_update_imports_cell) { window._pyforest_update_imports_cell('from scipy import stats'); }\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "F_onewayResult(statistic=5.11864406779661, pvalue=0.024694289538222603)"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "stats.f_oneway(df['libido'][df['dose'] == 'high'],\n",
    "               df['libido'][df['dose'] == 'low'],\n",
    "               df['libido'][df['dose'] == 'placebo'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "2650529c",
   "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>sum_sq</th>\n",
       "      <th>df</th>\n",
       "      <th>F</th>\n",
       "      <th>PR(&gt;F)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>C(dose)</th>\n",
       "      <td>20.133333</td>\n",
       "      <td>2.0</td>\n",
       "      <td>5.118644</td>\n",
       "      <td>0.024694</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Residual</th>\n",
       "      <td>23.600000</td>\n",
       "      <td>12.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             sum_sq    df         F    PR(>F)\n",
       "C(dose)   20.133333   2.0  5.118644  0.024694\n",
       "Residual  23.600000  12.0       NaN       NaN"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = ols('libido ~ C(dose)', data=df).fit()\n",
    "aov_table = sm.stats.anova_lm(model, typ=2)\n",
    "aov_table"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "d4abc8f6",
   "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>sum_sq</th>\n",
       "      <th>df</th>\n",
       "      <th>mean_sq</th>\n",
       "      <th>F</th>\n",
       "      <th>PR(&gt;F)</th>\n",
       "      <th>eta_sq</th>\n",
       "      <th>omega_sq</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>C(dose)</th>\n",
       "      <td>20.133333</td>\n",
       "      <td>2.0</td>\n",
       "      <td>10.066667</td>\n",
       "      <td>5.118644</td>\n",
       "      <td>0.024694</td>\n",
       "      <td>0.460366</td>\n",
       "      <td>0.354486</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Residual</th>\n",
       "      <td>23.600000</td>\n",
       "      <td>12.0</td>\n",
       "      <td>1.966667</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             sum_sq    df    mean_sq         F    PR(>F)    eta_sq  omega_sq\n",
       "C(dose)   20.133333   2.0  10.066667  5.118644  0.024694  0.460366  0.354486\n",
       "Residual  23.600000  12.0   1.966667       NaN       NaN       NaN       NaN"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "def anova_table(aov):\n",
    "    aov['mean_sq'] = aov[:]['sum_sq']/aov[:]['df']\n",
    "\n",
    "    aov['eta_sq'] = aov[:-1]['sum_sq']/sum(aov['sum_sq'])\n",
    "\n",
    "    aov['omega_sq'] = (aov[:-1]['sum_sq']-(aov[:-1]['df']*aov['mean_sq'][-1]))/(sum(aov['sum_sq'])+aov['mean_sq'][-1])\n",
    "\n",
    "    cols = ['sum_sq', 'df', 'mean_sq', 'F', 'PR(>F)', 'eta_sq', 'omega_sq']\n",
    "    aov = aov[cols]\n",
    "    return aov\n",
    "\n",
    "anova_table(aov_table)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ee1dfeea",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d966dae3",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "001abc97",
   "metadata": {},
   "source": [
    "#### HOMOGENEITY OF VARIANCE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "0401eb99",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "\n",
       "        if (window._pyforest_update_imports_cell) { window._pyforest_update_imports_cell('from scipy import stats'); }\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "LeveneResult(statistic=0.11764705882352934, pvalue=0.8900225182757423)"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.levene(df['libido'][df['dose'] == 'high'],\n",
    "             df['libido'][df['dose'] == 'low'],\n",
    "             df['libido'][df['dose'] == 'placebo'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "1e92d635",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize= (7, 7))\n",
    "ax = fig.add_subplot(111)\n",
    "\n",
    "ax.set_title(\"Box Plot of Libido by Dosage\", fontsize= 20)\n",
    "ax.set\n",
    "\n",
    "data = [df['libido'][df['dose'] == 'placebo'],\n",
    "        df['libido'][df['dose'] == 'low'],\n",
    "        df['libido'][df['dose'] == 'high']]\n",
    "\n",
    "ax.boxplot(data,\n",
    "           labels= ['Placebo', 'Low', 'High'],\n",
    "           showmeans= True)\n",
    "\n",
    "plt.xlabel(\"Drug Dosage\")\n",
    "plt.ylabel(\"Libido Score\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6cac8b4f",
   "metadata": {},
   "source": [
    "#### TUKEY HONESTLY SIGNIFICANT DIFFERENCE (HSD)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "d8d7e66d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>Multiple Comparison of Means - Tukey HSD, FWER=0.05</caption>\n",
       "<tr>\n",
       "  <th>group1</th> <th>group2</th>  <th>meandiff</th>  <th>p-adj</th>  <th>lower</th>   <th>upper</th>  <th>reject</th>\n",
       "</tr>\n",
       "<tr>\n",
       "   <td>high</td>    <td>low</td>     <td>-1.8</td>   <td>0.1472</td> <td>-4.1651</td> <td>0.5651</td>   <td>False</td>\n",
       "</tr>\n",
       "<tr>\n",
       "   <td>high</td>  <td>placebo</td>   <td>-2.8</td>   <td>0.0209</td> <td>-5.1651</td> <td>-0.4349</td>  <td>True</td> \n",
       "</tr>\n",
       "<tr>\n",
       "    <td>low</td>  <td>placebo</td>   <td>-1.0</td>   <td>0.5171</td> <td>-3.3651</td> <td>1.3651</td>   <td>False</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.table.SimpleTable'>"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import statsmodels.stats.multicomp as mc\n",
    "\n",
    "comp = mc.MultiComparison(df['libido'], df['dose'])\n",
    "post_hoc_res = comp.tukeyhsd()\n",
    "post_hoc_res.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b073da63",
   "metadata": {},
   "source": [
    "- At the top the table testing information is provided\n",
    "\n",
    "\n",
    "- FWER is the familywise error rate, i.e. what  is being set to and controlled at\n",
    "- group1 and group2 columns are the groups being compared\n",
    "- meandiff is the difference between the group means\n",
    "- p-adj is the corrected p-value which takes into account the multiple comparisons being conducted\n",
    "- lower is the lower band of the confidence interval. In the current example the confidence interval at the 95% level since = 0.05.\n",
    "\n",
    "- upper is the upper band of the confidence interval. In the current example the confidence interval at the 95% level since = 0.05.\n",
    "- reject is the decision rule based on the corrected p-value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c3300918",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "e547301c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "post_hoc_res.plot_simultaneous(ylabel= \"Drug Dose\", xlabel= \"Score Difference\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b65f957a",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "2eef2a7f",
   "metadata": {},
   "source": [
    "#### BONFERRONI CORRECTION"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "dbe0b0c6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "\n",
       "        if (window._pyforest_update_imports_cell) { window._pyforest_update_imports_cell('from scipy import stats'); }\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>Test Multiple Comparison ttest_ind \n",
       "FWER=0.05 method=bonf\n",
       "alphacSidak=0.02, alphacBonf=0.017</caption>\n",
       "<tr>\n",
       "  <th>group1</th> <th>group2</th>   <th>stat</th>   <th>pval</th>  <th>pval_corr</th> <th>reject</th>\n",
       "</tr>\n",
       "<tr>\n",
       "   <td>high</td>    <td>low</td>    <td>1.964</td> <td>0.0851</td>  <td>0.2554</td>    <td>False</td>\n",
       "</tr>\n",
       "<tr>\n",
       "   <td>high</td>  <td>placebo</td> <td>3.0551</td> <td>0.0157</td>  <td>0.0471</td>    <td>True</td> \n",
       "</tr>\n",
       "<tr>\n",
       "    <td>low</td>  <td>placebo</td> <td>1.2127</td> <td>0.2598</td>  <td>0.7795</td>    <td>False</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.table.SimpleTable'>"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "comp = mc.MultiComparison(df['libido'], df['dose'])\n",
    "tbl, a1, a2 = comp.allpairtest(stats.ttest_ind, method= \"bonf\")\n",
    "\n",
    "tbl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e9524e33",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "9091c83c",
   "metadata": {},
   "source": [
    "https://www.pythonfordatascience.org/anova-python/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f6c2bdaf",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2ad50e6f",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6f0ffe99",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ca5e147e",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1774c99e",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "beb2a8b2",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a6c970db",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3ee6b73d",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9c8b71b9",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d0a4c004",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6004f8cd",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "70eb652a",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "26e98766",
   "metadata": {},
   "source": [
    "\n",
    "# One way anova for not equal sample size across different groups and post Hoc analysis : "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "88a6aa40",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "581ca8ba",
   "metadata": {},
   "outputs": [],
   "source": [
    "drug1 = pd.Series(np.random.normal(4.0,0.2,52))\n",
    "drug2 = pd.Series(np.random.normal(4.0,0.2,45))\n",
    "drug3 = pd.Series(np.random.normal(3.0,0.2,38))\n",
    "drug4 = pd.Series(np.random.normal(4.0,0.2,53))\n",
    "drug5 = pd.Series(np.random.normal(4.0,0.2,40))\n",
    "data = pd.DataFrame([drug1,drug2,drug3,drug4,drug5]).T\n",
    "data.columns = [\"drug1\",\"drug2\",\"drug3\",\"drug4\",\"drug5\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "0a256649",
   "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>drug1</th>\n",
       "      <th>drug2</th>\n",
       "      <th>drug3</th>\n",
       "      <th>drug4</th>\n",
       "      <th>drug5</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>3.764755</td>\n",
       "      <td>4.025635</td>\n",
       "      <td>3.095830</td>\n",
       "      <td>3.911340</td>\n",
       "      <td>3.974582</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3.840444</td>\n",
       "      <td>3.969777</td>\n",
       "      <td>2.748366</td>\n",
       "      <td>4.211119</td>\n",
       "      <td>4.236597</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3.745722</td>\n",
       "      <td>4.080607</td>\n",
       "      <td>3.233194</td>\n",
       "      <td>4.298885</td>\n",
       "      <td>3.966080</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3.916050</td>\n",
       "      <td>4.036066</td>\n",
       "      <td>3.373375</td>\n",
       "      <td>3.719750</td>\n",
       "      <td>3.991745</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3.804726</td>\n",
       "      <td>3.621389</td>\n",
       "      <td>3.056826</td>\n",
       "      <td>3.757733</td>\n",
       "      <td>3.884321</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>3.720713</td>\n",
       "      <td>4.309853</td>\n",
       "      <td>3.211481</td>\n",
       "      <td>3.683453</td>\n",
       "      <td>4.036868</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>3.998014</td>\n",
       "      <td>3.957164</td>\n",
       "      <td>2.906787</td>\n",
       "      <td>3.994782</td>\n",
       "      <td>3.829746</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>3.878856</td>\n",
       "      <td>3.860672</td>\n",
       "      <td>2.451703</td>\n",
       "      <td>4.111374</td>\n",
       "      <td>3.990854</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>4.077380</td>\n",
       "      <td>3.999300</td>\n",
       "      <td>3.119305</td>\n",
       "      <td>4.158393</td>\n",
       "      <td>3.931297</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>3.719556</td>\n",
       "      <td>3.800585</td>\n",
       "      <td>3.530357</td>\n",
       "      <td>3.868288</td>\n",
       "      <td>3.734504</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>3.643375</td>\n",
       "      <td>4.536348</td>\n",
       "      <td>2.993798</td>\n",
       "      <td>4.351854</td>\n",
       "      <td>3.929099</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>3.676748</td>\n",
       "      <td>4.081347</td>\n",
       "      <td>2.862971</td>\n",
       "      <td>4.106758</td>\n",
       "      <td>3.621145</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>4.173535</td>\n",
       "      <td>4.115569</td>\n",
       "      <td>2.892877</td>\n",
       "      <td>4.319461</td>\n",
       "      <td>4.009870</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>4.164681</td>\n",
       "      <td>4.196060</td>\n",
       "      <td>3.104167</td>\n",
       "      <td>4.091183</td>\n",
       "      <td>3.772543</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>3.636512</td>\n",
       "      <td>3.838964</td>\n",
       "      <td>2.434653</td>\n",
       "      <td>3.936931</td>\n",
       "      <td>4.209167</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>4.049453</td>\n",
       "      <td>3.953411</td>\n",
       "      <td>3.170294</td>\n",
       "      <td>3.910191</td>\n",
       "      <td>4.111941</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>3.785972</td>\n",
       "      <td>4.354315</td>\n",
       "      <td>2.835520</td>\n",
       "      <td>3.649864</td>\n",
       "      <td>4.146112</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>3.789231</td>\n",
       "      <td>4.181382</td>\n",
       "      <td>2.833041</td>\n",
       "      <td>3.990717</td>\n",
       "      <td>3.968302</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>3.899103</td>\n",
       "      <td>3.423049</td>\n",
       "      <td>3.055090</td>\n",
       "      <td>4.032473</td>\n",
       "      <td>3.641582</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>3.854270</td>\n",
       "      <td>3.634185</td>\n",
       "      <td>2.668984</td>\n",
       "      <td>3.963291</td>\n",
       "      <td>4.134753</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>3.879670</td>\n",
       "      <td>3.861512</td>\n",
       "      <td>3.007343</td>\n",
       "      <td>3.975133</td>\n",
       "      <td>4.093516</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>4.072622</td>\n",
       "      <td>3.860427</td>\n",
       "      <td>3.004374</td>\n",
       "      <td>3.898092</td>\n",
       "      <td>3.965435</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>3.728799</td>\n",
       "      <td>4.221912</td>\n",
       "      <td>3.262057</td>\n",
       "      <td>4.112487</td>\n",
       "      <td>3.816717</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>3.865515</td>\n",
       "      <td>3.846827</td>\n",
       "      <td>2.904603</td>\n",
       "      <td>3.806556</td>\n",
       "      <td>3.499550</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>4.023430</td>\n",
       "      <td>3.836706</td>\n",
       "      <td>2.984230</td>\n",
       "      <td>4.090756</td>\n",
       "      <td>4.254226</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>4.050785</td>\n",
       "      <td>3.805871</td>\n",
       "      <td>3.468154</td>\n",
       "      <td>4.155479</td>\n",
       "      <td>4.121908</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>4.034149</td>\n",
       "      <td>3.721571</td>\n",
       "      <td>2.879509</td>\n",
       "      <td>3.971957</td>\n",
       "      <td>4.515472</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>3.945679</td>\n",
       "      <td>3.891187</td>\n",
       "      <td>3.294752</td>\n",
       "      <td>3.607573</td>\n",
       "      <td>4.091709</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>3.843137</td>\n",
       "      <td>4.323316</td>\n",
       "      <td>2.822802</td>\n",
       "      <td>3.873433</td>\n",
       "      <td>3.964222</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>3.974785</td>\n",
       "      <td>4.354445</td>\n",
       "      <td>3.150123</td>\n",
       "      <td>3.843556</td>\n",
       "      <td>3.850498</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>3.956831</td>\n",
       "      <td>4.024758</td>\n",
       "      <td>2.866446</td>\n",
       "      <td>4.061016</td>\n",
       "      <td>3.997268</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>3.965645</td>\n",
       "      <td>3.797112</td>\n",
       "      <td>2.953049</td>\n",
       "      <td>4.175121</td>\n",
       "      <td>3.554824</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>3.990686</td>\n",
       "      <td>3.883894</td>\n",
       "      <td>2.845360</td>\n",
       "      <td>4.202219</td>\n",
       "      <td>3.844661</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>4.083613</td>\n",
       "      <td>3.800829</td>\n",
       "      <td>3.018783</td>\n",
       "      <td>3.949249</td>\n",
       "      <td>4.286405</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>4.143809</td>\n",
       "      <td>4.146388</td>\n",
       "      <td>2.917106</td>\n",
       "      <td>4.047088</td>\n",
       "      <td>3.938825</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>4.285757</td>\n",
       "      <td>4.179206</td>\n",
       "      <td>3.118451</td>\n",
       "      <td>3.606439</td>\n",
       "      <td>4.461538</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>4.020027</td>\n",
       "      <td>4.115059</td>\n",
       "      <td>3.016304</td>\n",
       "      <td>4.022006</td>\n",
       "      <td>4.065747</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>4.172698</td>\n",
       "      <td>4.214938</td>\n",
       "      <td>3.122524</td>\n",
       "      <td>3.874536</td>\n",
       "      <td>3.763537</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>4.010807</td>\n",
       "      <td>3.524695</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3.936923</td>\n",
       "      <td>4.258112</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>4.011506</td>\n",
       "      <td>4.092256</td>\n",
       "      <td>NaN</td>\n",
       "      <td>4.047106</td>\n",
       "      <td>3.754918</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>3.899154</td>\n",
       "      <td>3.709658</td>\n",
       "      <td>NaN</td>\n",
       "      <td>4.256149</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td>4.186152</td>\n",
       "      <td>3.906460</td>\n",
       "      <td>NaN</td>\n",
       "      <td>4.035269</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>4.236288</td>\n",
       "      <td>4.095081</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3.685961</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>43</th>\n",
       "      <td>4.184363</td>\n",
       "      <td>3.971617</td>\n",
       "      <td>NaN</td>\n",
       "      <td>4.217493</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>44</th>\n",
       "      <td>4.108431</td>\n",
       "      <td>3.828467</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3.976292</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45</th>\n",
       "      <td>4.399487</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>4.112256</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46</th>\n",
       "      <td>3.886083</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>4.117316</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td>3.534260</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>4.178580</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>48</th>\n",
       "      <td>4.286656</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>4.429376</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>49</th>\n",
       "      <td>4.011833</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>4.431810</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50</th>\n",
       "      <td>3.744583</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>4.111228</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>51</th>\n",
       "      <td>3.606908</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3.823645</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>52</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>4.048533</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       drug1     drug2     drug3     drug4     drug5\n",
       "0   3.764755  4.025635  3.095830  3.911340  3.974582\n",
       "1   3.840444  3.969777  2.748366  4.211119  4.236597\n",
       "2   3.745722  4.080607  3.233194  4.298885  3.966080\n",
       "3   3.916050  4.036066  3.373375  3.719750  3.991745\n",
       "4   3.804726  3.621389  3.056826  3.757733  3.884321\n",
       "5   3.720713  4.309853  3.211481  3.683453  4.036868\n",
       "6   3.998014  3.957164  2.906787  3.994782  3.829746\n",
       "7   3.878856  3.860672  2.451703  4.111374  3.990854\n",
       "8   4.077380  3.999300  3.119305  4.158393  3.931297\n",
       "9   3.719556  3.800585  3.530357  3.868288  3.734504\n",
       "10  3.643375  4.536348  2.993798  4.351854  3.929099\n",
       "11  3.676748  4.081347  2.862971  4.106758  3.621145\n",
       "12  4.173535  4.115569  2.892877  4.319461  4.009870\n",
       "13  4.164681  4.196060  3.104167  4.091183  3.772543\n",
       "14  3.636512  3.838964  2.434653  3.936931  4.209167\n",
       "15  4.049453  3.953411  3.170294  3.910191  4.111941\n",
       "16  3.785972  4.354315  2.835520  3.649864  4.146112\n",
       "17  3.789231  4.181382  2.833041  3.990717  3.968302\n",
       "18  3.899103  3.423049  3.055090  4.032473  3.641582\n",
       "19  3.854270  3.634185  2.668984  3.963291  4.134753\n",
       "20  3.879670  3.861512  3.007343  3.975133  4.093516\n",
       "21  4.072622  3.860427  3.004374  3.898092  3.965435\n",
       "22  3.728799  4.221912  3.262057  4.112487  3.816717\n",
       "23  3.865515  3.846827  2.904603  3.806556  3.499550\n",
       "24  4.023430  3.836706  2.984230  4.090756  4.254226\n",
       "25  4.050785  3.805871  3.468154  4.155479  4.121908\n",
       "26  4.034149  3.721571  2.879509  3.971957  4.515472\n",
       "27  3.945679  3.891187  3.294752  3.607573  4.091709\n",
       "28  3.843137  4.323316  2.822802  3.873433  3.964222\n",
       "29  3.974785  4.354445  3.150123  3.843556  3.850498\n",
       "30  3.956831  4.024758  2.866446  4.061016  3.997268\n",
       "31  3.965645  3.797112  2.953049  4.175121  3.554824\n",
       "32  3.990686  3.883894  2.845360  4.202219  3.844661\n",
       "33  4.083613  3.800829  3.018783  3.949249  4.286405\n",
       "34  4.143809  4.146388  2.917106  4.047088  3.938825\n",
       "35  4.285757  4.179206  3.118451  3.606439  4.461538\n",
       "36  4.020027  4.115059  3.016304  4.022006  4.065747\n",
       "37  4.172698  4.214938  3.122524  3.874536  3.763537\n",
       "38  4.010807  3.524695       NaN  3.936923  4.258112\n",
       "39  4.011506  4.092256       NaN  4.047106  3.754918\n",
       "40  3.899154  3.709658       NaN  4.256149       NaN\n",
       "41  4.186152  3.906460       NaN  4.035269       NaN\n",
       "42  4.236288  4.095081       NaN  3.685961       NaN\n",
       "43  4.184363  3.971617       NaN  4.217493       NaN\n",
       "44  4.108431  3.828467       NaN  3.976292       NaN\n",
       "45  4.399487       NaN       NaN  4.112256       NaN\n",
       "46  3.886083       NaN       NaN  4.117316       NaN\n",
       "47  3.534260       NaN       NaN  4.178580       NaN\n",
       "48  4.286656       NaN       NaN  4.429376       NaN\n",
       "49  4.011833       NaN       NaN  4.431810       NaN\n",
       "50  3.744583       NaN       NaN  4.111228       NaN\n",
       "51  3.606908       NaN       NaN  3.823645       NaN\n",
       "52       NaN       NaN       NaN  4.048533       NaN"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "895ff314",
   "metadata": {},
   "outputs": [],
   "source": [
    "data = data.melt(value_name=\"RecoveryTime\",var_name=\"Drug\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "bb20773b",
   "metadata": {},
   "outputs": [],
   "source": [
    "data = data.dropna()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "0a8cd2c1",
   "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>Drug</th>\n",
       "      <th>RecoveryTime</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>drug1</td>\n",
       "      <td>3.764755</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>drug1</td>\n",
       "      <td>3.840444</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>drug1</td>\n",
       "      <td>3.745722</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>drug1</td>\n",
       "      <td>3.916050</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>drug1</td>\n",
       "      <td>3.804726</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>247</th>\n",
       "      <td>drug5</td>\n",
       "      <td>4.461538</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>248</th>\n",
       "      <td>drug5</td>\n",
       "      <td>4.065747</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>249</th>\n",
       "      <td>drug5</td>\n",
       "      <td>3.763537</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>250</th>\n",
       "      <td>drug5</td>\n",
       "      <td>4.258112</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>251</th>\n",
       "      <td>drug5</td>\n",
       "      <td>3.754918</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>228 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      Drug  RecoveryTime\n",
       "0    drug1      3.764755\n",
       "1    drug1      3.840444\n",
       "2    drug1      3.745722\n",
       "3    drug1      3.916050\n",
       "4    drug1      3.804726\n",
       "..     ...           ...\n",
       "247  drug5      4.461538\n",
       "248  drug5      4.065747\n",
       "249  drug5      3.763537\n",
       "250  drug5      4.258112\n",
       "251  drug5      3.754918\n",
       "\n",
       "[228 rows x 2 columns]"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "54deec22",
   "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>sum_sq</th>\n",
       "      <th>df</th>\n",
       "      <th>F</th>\n",
       "      <th>PR(&gt;F)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>C(Drug)</th>\n",
       "      <td>30.192801</td>\n",
       "      <td>4.0</td>\n",
       "      <td>163.938021</td>\n",
       "      <td>3.313057e-65</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Residual</th>\n",
       "      <td>10.267592</td>\n",
       "      <td>223.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             sum_sq     df           F        PR(>F)\n",
       "C(Drug)   30.192801    4.0  163.938021  3.313057e-65\n",
       "Residual  10.267592  223.0         NaN           NaN"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = ols('RecoveryTime ~ C(Drug)', data=data).fit()\n",
    "aov_table = sm.stats.anova_lm(model, typ=2)\n",
    "aov_table"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "6d9c7287",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "\n",
       "        if (window._pyforest_update_imports_cell) { window._pyforest_update_imports_cell('from scipy import stats'); }\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>Test Multiple Comparison ttest_ind \n",
       "FWER=0.05 method=bonf\n",
       "alphacSidak=0.01, alphacBonf=0.005</caption>\n",
       "<tr>\n",
       "  <th>group1</th> <th>group2</th>   <th>stat</th>    <th>pval</th>  <th>pval_corr</th> <th>reject</th>\n",
       "</tr>\n",
       "<tr>\n",
       "   <td>drug1</td>  <td>drug2</td>  <td>-0.6918</td> <td>0.4908</td>    <td>1.0</td>     <td>False</td>\n",
       "</tr>\n",
       "<tr>\n",
       "   <td>drug1</td>  <td>drug3</td>  <td>20.9581</td>   <td>0.0</td>     <td>0.0</td>     <td>True</td> \n",
       "</tr>\n",
       "<tr>\n",
       "   <td>drug1</td>  <td>drug4</td>  <td>-1.7393</td>  <td>0.085</td>  <td>0.8498</td>    <td>False</td>\n",
       "</tr>\n",
       "<tr>\n",
       "   <td>drug1</td>  <td>drug5</td>  <td>-0.7517</td> <td>0.4542</td>    <td>1.0</td>     <td>False</td>\n",
       "</tr>\n",
       "<tr>\n",
       "   <td>drug2</td>  <td>drug3</td>  <td>19.0045</td>   <td>0.0</td>     <td>0.0</td>     <td>True</td> \n",
       "</tr>\n",
       "<tr>\n",
       "   <td>drug2</td>  <td>drug4</td>  <td>-0.843</td>  <td>0.4013</td>    <td>1.0</td>     <td>False</td>\n",
       "</tr>\n",
       "<tr>\n",
       "   <td>drug2</td>  <td>drug5</td>  <td>-0.0595</td> <td>0.9527</td>    <td>1.0</td>     <td>False</td>\n",
       "</tr>\n",
       "<tr>\n",
       "   <td>drug3</td>  <td>drug4</td> <td>-22.2435</td>   <td>0.0</td>     <td>0.0</td>     <td>True</td> \n",
       "</tr>\n",
       "<tr>\n",
       "   <td>drug3</td>  <td>drug5</td> <td>-18.8176</td>   <td>0.0</td>     <td>0.0</td>     <td>True</td> \n",
       "</tr>\n",
       "<tr>\n",
       "   <td>drug4</td>  <td>drug5</td>  <td>0.7649</td>  <td>0.4463</td>    <td>1.0</td>     <td>False</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.table.SimpleTable'>"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "comp = mc.MultiComparison(data['RecoveryTime'], data[\"Drug\"])\n",
    "tbl, a1, a2 = comp.allpairtest(stats.ttest_ind, method= \"bonf\")\n",
    "\n",
    "tbl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "c4b4391c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>Multiple Comparison of Means - Tukey HSD, FWER=0.05</caption>\n",
       "<tr>\n",
       "  <th>group1</th> <th>group2</th> <th>meandiff</th>  <th>p-adj</th>  <th>lower</th>   <th>upper</th>  <th>reject</th>\n",
       "</tr>\n",
       "<tr>\n",
       "   <td>drug1</td>  <td>drug2</td>  <td>0.0298</td>    <td>0.9</td>  <td>-0.0904</td>  <td>0.15</td>    <td>False</td>\n",
       "</tr>\n",
       "<tr>\n",
       "   <td>drug1</td>  <td>drug3</td>  <td>-0.9421</td>  <td>0.001</td> <td>-1.0681</td> <td>-0.8162</td>  <td>True</td> \n",
       "</tr>\n",
       "<tr>\n",
       "   <td>drug1</td>  <td>drug4</td>  <td>0.0664</td>  <td>0.5074</td> <td>-0.0488</td> <td>0.1816</td>   <td>False</td>\n",
       "</tr>\n",
       "<tr>\n",
       "   <td>drug1</td>  <td>drug5</td>  <td>0.0328</td>    <td>0.9</td>  <td>-0.0914</td> <td>0.1569</td>   <td>False</td>\n",
       "</tr>\n",
       "<tr>\n",
       "   <td>drug2</td>  <td>drug3</td>  <td>-0.9719</td>  <td>0.001</td> <td>-1.1019</td> <td>-0.8419</td>  <td>True</td> \n",
       "</tr>\n",
       "<tr>\n",
       "   <td>drug2</td>  <td>drug4</td>  <td>0.0366</td>    <td>0.9</td>  <td>-0.0831</td> <td>0.1562</td>   <td>False</td>\n",
       "</tr>\n",
       "<tr>\n",
       "   <td>drug2</td>  <td>drug5</td>   <td>0.003</td>    <td>0.9</td>  <td>-0.1253</td> <td>0.1312</td>   <td>False</td>\n",
       "</tr>\n",
       "<tr>\n",
       "   <td>drug3</td>  <td>drug4</td>  <td>1.0085</td>   <td>0.001</td>  <td>0.883</td>  <td>1.1339</td>   <td>True</td> \n",
       "</tr>\n",
       "<tr>\n",
       "   <td>drug3</td>  <td>drug5</td>  <td>0.9749</td>   <td>0.001</td> <td>0.8412</td>  <td>1.1085</td>   <td>True</td> \n",
       "</tr>\n",
       "<tr>\n",
       "   <td>drug4</td>  <td>drug5</td>  <td>-0.0336</td>   <td>0.9</td>  <td>-0.1572</td>  <td>0.09</td>    <td>False</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.table.SimpleTable'>"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import statsmodels.stats.multicomp as mc\n",
    "\n",
    "comp = mc.MultiComparison(data['RecoveryTime'], data[\"Drug\"])\n",
    "post_hoc_res = comp.tukeyhsd()\n",
    "post_hoc_res.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "e302d50c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "post_hoc_res.plot_simultaneous(ylabel= \"Drug\", xlabel= \"Score Difference\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fabd35c6",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a2a83366",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6c2450bc",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7f0b02f7",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "05f60cc9",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d95c3bf2",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "ceb49085",
   "metadata": {},
   "source": [
    "# QQplot Implementation  : "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "32db175a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "\n",
       "        if (window._pyforest_update_imports_cell) { window._pyforest_update_imports_cell('from scipy import stats'); }\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df = pd.DataFrame(stats.norm.rvs(75,10,50),columns=[\"Weights\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "d79ebc16",
   "metadata": {},
   "outputs": [],
   "source": [
    "df.sort_values(by=\"Weights\",inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "4ab1f477",
   "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>Weights</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>59.241995</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>59.922607</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>44</th>\n",
       "      <td>60.317630</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>61.220444</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>61.272364</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>62.472159</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>43</th>\n",
       "      <td>64.054462</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>64.897276</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>64.960099</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>66.082806</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>67.093995</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>67.162970</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>49</th>\n",
       "      <td>67.552164</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46</th>\n",
       "      <td>67.709763</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>67.900086</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>69.096582</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>70.274869</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>70.474554</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>71.020417</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td>71.190105</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>71.675880</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>71.986170</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>73.140168</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>73.165817</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>48</th>\n",
       "      <td>73.343850</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>73.882829</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>74.576124</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>75.666389</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>76.314274</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>78.675975</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>78.922815</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>79.016181</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>79.723979</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>81.073759</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>81.477996</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>82.566257</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>85.307392</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>85.349826</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>86.468381</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45</th>\n",
       "      <td>86.888637</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>87.117803</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>87.975112</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>88.848108</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>90.451729</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>91.439467</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td>92.727667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>94.148789</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>94.168698</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>94.696472</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>97.057544</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      Weights\n",
       "37  59.241995\n",
       "18  59.922607\n",
       "44  60.317630\n",
       "17  61.220444\n",
       "30  61.272364\n",
       "36  62.472159\n",
       "43  64.054462\n",
       "3   64.897276\n",
       "14  64.960099\n",
       "34  66.082806\n",
       "22  67.093995\n",
       "24  67.162970\n",
       "49  67.552164\n",
       "46  67.709763\n",
       "25  67.900086\n",
       "6   69.096582\n",
       "12  70.274869\n",
       "15  70.474554\n",
       "8   71.020417\n",
       "41  71.190105\n",
       "19  71.675880\n",
       "39  71.986170\n",
       "9   73.140168\n",
       "21  73.165817\n",
       "48  73.343850\n",
       "11  73.882829\n",
       "7   74.576124\n",
       "2   75.666389\n",
       "31  76.314274\n",
       "29  78.675975\n",
       "42  78.922815\n",
       "26  79.016181\n",
       "32  79.723979\n",
       "28  81.073759\n",
       "1   81.477996\n",
       "35  82.566257\n",
       "5   85.307392\n",
       "20  85.349826\n",
       "13  86.468381\n",
       "45  86.888637\n",
       "16  87.117803\n",
       "10  87.975112\n",
       "27  88.848108\n",
       "33  90.451729\n",
       "4   91.439467\n",
       "47  92.727667\n",
       "38  94.148789\n",
       "23  94.168698\n",
       "0   94.696472\n",
       "40  97.057544"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "bb121c9a",
   "metadata": {},
   "outputs": [],
   "source": [
    "df[\"Count\"] = np.arange(1,51)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "8d307ad0",
   "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>Weights</th>\n",
       "      <th>Count</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>59.241995</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>59.922607</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>44</th>\n",
       "      <td>60.317630</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>61.220444</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>61.272364</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      Weights  Count\n",
       "37  59.241995      1\n",
       "18  59.922607      2\n",
       "44  60.317630      3\n",
       "17  61.220444      4\n",
       "30  61.272364      5"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "9f1d24fb",
   "metadata": {},
   "outputs": [],
   "source": [
    "df[\"percentiles\"] = df[\"Count\"]/50"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "23aa9fea",
   "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>Weights</th>\n",
       "      <th>Count</th>\n",
       "      <th>percentiles</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>59.241995</td>\n",
       "      <td>1</td>\n",
       "      <td>0.02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>59.922607</td>\n",
       "      <td>2</td>\n",
       "      <td>0.04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>44</th>\n",
       "      <td>60.317630</td>\n",
       "      <td>3</td>\n",
       "      <td>0.06</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>61.220444</td>\n",
       "      <td>4</td>\n",
       "      <td>0.08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>61.272364</td>\n",
       "      <td>5</td>\n",
       "      <td>0.10</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      Weights  Count  percentiles\n",
       "37  59.241995      1         0.02\n",
       "18  59.922607      2         0.04\n",
       "44  60.317630      3         0.06\n",
       "17  61.220444      4         0.08\n",
       "30  61.272364      5         0.10"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "4fba0833",
   "metadata": {},
   "outputs": [],
   "source": [
    "df[\"Z_emperical\"] = (df[\"Weights\"]-df[\"Weights\"].mean())/df[\"Weights\"].std()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "8e7f25b2",
   "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>Weights</th>\n",
       "      <th>Count</th>\n",
       "      <th>percentiles</th>\n",
       "      <th>Z_emperical</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>59.241995</td>\n",
       "      <td>1</td>\n",
       "      <td>0.02</td>\n",
       "      <td>-1.566991</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>59.922607</td>\n",
       "      <td>2</td>\n",
       "      <td>0.04</td>\n",
       "      <td>-1.503483</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>44</th>\n",
       "      <td>60.317630</td>\n",
       "      <td>3</td>\n",
       "      <td>0.06</td>\n",
       "      <td>-1.466623</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>61.220444</td>\n",
       "      <td>4</td>\n",
       "      <td>0.08</td>\n",
       "      <td>-1.382382</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>61.272364</td>\n",
       "      <td>5</td>\n",
       "      <td>0.10</td>\n",
       "      <td>-1.377538</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      Weights  Count  percentiles  Z_emperical\n",
       "37  59.241995      1         0.02    -1.566991\n",
       "18  59.922607      2         0.04    -1.503483\n",
       "44  60.317630      3         0.06    -1.466623\n",
       "17  61.220444      4         0.08    -1.382382\n",
       "30  61.272364      5         0.10    -1.377538"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "1b86d9ba",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "\n",
       "        if (window._pyforest_update_imports_cell) { window._pyforest_update_imports_cell('from scipy import stats'); }\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df[\"Z_theoretical\"] = stats.norm.ppf(df[\"percentiles\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "61af11b5",
   "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>Weights</th>\n",
       "      <th>Count</th>\n",
       "      <th>percentiles</th>\n",
       "      <th>Z_emperical</th>\n",
       "      <th>Z_theoretical</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>59.241995</td>\n",
       "      <td>1</td>\n",
       "      <td>0.02</td>\n",
       "      <td>-1.566991</td>\n",
       "      <td>-2.053749</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>59.922607</td>\n",
       "      <td>2</td>\n",
       "      <td>0.04</td>\n",
       "      <td>-1.503483</td>\n",
       "      <td>-1.750686</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>44</th>\n",
       "      <td>60.317630</td>\n",
       "      <td>3</td>\n",
       "      <td>0.06</td>\n",
       "      <td>-1.466623</td>\n",
       "      <td>-1.554774</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>61.220444</td>\n",
       "      <td>4</td>\n",
       "      <td>0.08</td>\n",
       "      <td>-1.382382</td>\n",
       "      <td>-1.405072</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>61.272364</td>\n",
       "      <td>5</td>\n",
       "      <td>0.10</td>\n",
       "      <td>-1.377538</td>\n",
       "      <td>-1.281552</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      Weights  Count  percentiles  Z_emperical  Z_theoretical\n",
       "37  59.241995      1         0.02    -1.566991      -2.053749\n",
       "18  59.922607      2         0.04    -1.503483      -1.750686\n",
       "44  60.317630      3         0.06    -1.466623      -1.554774\n",
       "17  61.220444      4         0.08    -1.382382      -1.405072\n",
       "30  61.272364      5         0.10    -1.377538      -1.281552"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "cbe83205",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x28465f79d00>]"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "sns.scatterplot(y=df[\"Z_emperical\"],\n",
    "               x = df[\"Z_theoretical\"])\n",
    "plt.plot([-2,-1,0,1,2],[-2,-1,0,1,2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "24f27a36",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAX4AAAEGCAYAAABiq/5QAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/MnkTPAAAACXBIWXMAAAsTAAALEwEAmpwYAAAgGUlEQVR4nO3de7wcdZnn8c+XQAaiKCQEjEpyABEVRyMeGUCHUQHXyTgC7nibs3oGXI6KKLCOKy+z42WUFRR1XsoIE24T3DOMXHRgERliRpFVw3iCAYKgiCQRiOFwFQmakDz7R1WbTqe6u/pSff2+X69+dXd1VfVzCvKcOr/fU08pIjAzs+GxU7cDMDOzznLiNzMbMk78ZmZDxonfzGzIOPGbmQ2ZnbsdQB577bVXjIyMdDsMM7O+snLlyociYm7l8r5I/CMjI0xNTXU7DDOzviJpbdZyD/WYmQ0ZJ34zsyHjxG9mNmSc+M3MhowTv5nZkHHiNzPrQ5OTMDICO+2UPE9O5t+2L8o5zcxsm8lJmJiAjRuT92vXJu8Bxsbqb+8zfjOzPrN48bakX7JxY7I8Dyd+M7M+s25dY8srOfGbmfWZ+fMbW17Jid/MrM+ceSbMmrX9slmzkuV5OPGbmfWZsTFYsgQWLAApeV6yJN/ELriqx8ysL42N5U/0lXzGb2Y2ZJz4zcyGjBO/mdmQKTTxSzpV0mpJd0g6LV32SUn3S1qVPhYVGYOZmW2vsMldSS8FTgIOBTYB10v6VvrxlyLinKK+28zMqivyjP/FwIqI2BgRTwM3AscX+H1mZj2llUZqRSoy8a8GjpQ0R9IsYBGwb/rZKZJuk3SxpD2zNpY0IWlK0tT09HSBYZqZtV+pkdratRCxrZFaLyT/whJ/RNwJnA0sA64HbgWeBs4DDgAWAuuBL1TZfklEjEbE6Ny5O9wk3sysKY2chbdyxt5qI7UiFTq5GxEXRcQhEXEk8Ahwd0RsiIgtEbEVuIBkDsDMrHCNnIW3esbeaiO1IhVd1bN3+jwfeAtwmaR5ZascTzIkZGZWuEbOwls9Y2+1kVqRim7ZcJWkOcBm4AMR8aikr0laCASwBnhvwTGYmQGNnYW3esZ+5pnb3ywFGmukVqRCE39E/GnGsncV+Z1mZtXMn58M2WQtb2XdLKU+OosXJ78s5s9Pkn6z/XXayVfumtnQaKSdcautjyFJ8mvWwNatyXMvJH1w4jezIdJIO+NWWx/3MkVEt2Ooa3R0NKamprodhplZX5G0MiJGK5f7jN/MBkKvXiXbi3wjFjPre6Wa+1IFTanmHgZjaKbdfMZvZn2vl6+S7UVO/GbW93r5Ktle5MRvZn2vl6+S7UVO/GbW99pRcz9MnPjNrO8Ncs19EZz4zawv1CvX7NWrZHuRyznNrOe5XLO9fMZvZj3P5Zrt5cRvZj3P5Zrt5cRvZj3P5Zrt5cRvZj2j2gSuyzXby5O7ZtYT8kzg9uJNTfpRoW2ZJZ0KnAQIuCAi/kHSbODrwAjJrRffFhGP1tqP2zKbDb6Rkew7Xi1YkJRnWuM63pZZ0ktJkv6hwMuBN0k6EDgDWB4RBwLL0/dmNuQ8gds5RY7xvxhYEREbI+Jp4EbgeOBYYGm6zlLguAJjMLM+4Qncziky8a8GjpQ0R9IsYBGwL7BPRKwHSJ/3ztpY0oSkKUlT09PTBYZpZr3AE7idU1jij4g7gbOBZcD1wK3A0w1svyQiRiNidO7cuQVFaWa9wv12OqfQqp6IuAi4CEDS/wbuAzZImhcR6yXNAx4sMgYz6x9jY070nVBoHb+kvdPn+cBbgMuAa4DxdJVx4OoiYzCz3uJ743Zf0XX8V0maA2wGPhARj0o6C7hc0nuAdcBbC47BzHqEm631hkLr+NvFdfxmg8G1+p3V8Tp+M7NKrtXvDU78ZtYxrtXvDU78ZlaIrElc1+r3Bid+M2u70iTu2rUQsf0krmv1u8+Tu2bWdp7E7Q2e3DWzjvEkbm9z4jezlmSN5XsSt7c58ZtZbpVJ/uSTs8fyFy3yJG4vc+I3s1yyJmzPP3/bVbglGzfCddd5EreXeXLXzHKpNmGbRYKtWwsNx3Lw5K6ZNaRyWCdv0geP5fc632zdzHaQ1UxNSoZ4KlUu91h+7/MZv5ntYPHiHcfuI5IkX27WLHjf+zyW3298xm9mO6hWbx+RJPd165LhnDPPdJLvR3UTv6QDgPsi4veSXgu8DLg0Ih4rNjQz65b5833l7SDLM9RzFbBF0gtIbqO4H/AvhUZlZh1VOZHrOvzBlifxb42Ip4HjgX+IiNOBecWGZWZFyXMR1tKlMD7usftBlWeMf7Okd5LcH/cv02W75Nm5pNOB/w4EcDtwAnAGcBIwna72sYi4rpGgzaw5WdU655+/Y7VO6SIsD+sMpjxn/CcAhwNnRsS9kvYD/k+9jSQ9D/gQMBoRLwVmAO9IP/5SRCxMH076Zh1SrVonixuqDa66iT8ifgp8FLglfX9vRJyVc/87A7tJ2hmYBTzQbKBm1rpGkrkvwhpcdRO/pL8EVgHXp+8XSrqm3nYRcT9wDrAOWA88HhE3pB+fIuk2SRdL2rPK905ImpI0NT09nbWKmTWoWjLPqs/3RO7gyjPU80ngUOAxgIhYRVLZU1Oa0I9N130u8AxJ/w04DzgAWEjyC+ELWdtHxJKIGI2I0blz5+YI08zqqXbrQ1+ENVzyTO4+HRGPa/tTgjyd3Y4G7o2IaQBJ3wCOiIg/zA9IugC4toF4zawFpWS+eLEvwhpmeRL/akl/DcyQdCDJhO0Pc2y3DjhM0izgKeAoYErSvIhYn65zPLC6ibjNrEljY070wy7PUM8HgYOB3wOXAb8BTqu3UUTcDFxJMil8e/pdS4DPSbpd0m3A64DTm4rczMya4n78ZmYDqlo//qpDPZL+LzXG8iPizW2KzczMOqjWGP85HYvCzMw6pmrij4gbOxmImZl1Rq2hnssj4m2SbidjyCciXlZoZGZmVohaVT2nps9vImnOVvkwsz5Q2Y1zcrLbEVm3VU38ZbX2J0fE2vIHcHJnwjOzVpS6cZa3XJ6YcPIfdnnq+I/JWPbn7Q7EzNovqxvnxo3Jchtetcb4309yZr9/erFVye7AD4oOzMxaV60bp1suD7da5Zz/Anwb+CzJzVNKnoiIRwqNyszaotq9c91yebjVGuN/PCLWRMQ7gfuAzSTVPc+U5P9tzPpAtW6cbrk83PL04z8F2AAsA76VPtxR06wHVVbwQNJi2S2XrVye7pynAQdFxMMFx2JmLci6n+7ERJLofe9cK5enqudXwONFB2JmjSs/wx8fdwWP5ZPnjP+XwPckfYukNTMAEfHFwqIys7oqz/C3bMlezxU8VilP4l+XPmamDzPrAVk1+llcwWOV6ib+iPhUJwIxs8bkOZN3BY9lqZv4Jc0F/ifJXbh2LS2PiNcXGJeZ1VGtRn/GDNi61ffTteryTO5OAncB+wGfAtYAP86zc0mnS7pD0mpJl0naVdJsScsk3Z0+79l09GZDrFqN/tKlSeJfs8ZJ37LlSfxzIuIiYHNE3BgRJwKH1dtI0vNIbsw+GhEvBWYA7yC5Cnh5RBwILGf7q4LNLKexMdfoW3PyJP7N6fN6SX8h6RXA83Puf2dgN0k7A7OAB4BjgaXp50uB4/KHazbcsi7QWrPGZ/jWmDxVPZ+R9Gzgw8BXgGcBp9fbKCLul3QOSUXQU8ANEXGDpH1KLZ8jYr2kvbO2lzQBTADMd1mCWdULtMAJ3xqjiKr3U29tx8nY/VXA24HHgCuAK4FzI2KPsvUejYia4/yjo6MxNTVVSJxm/WJkJHsyd8ECX5lr2SStjIjRyuV5qnouIfvWiyfW2fRo4N6ImE738w3gCGCDpHnp2f484ME8P4DZsHOLZWuXPGP817KtOdtykqGe3+bYbh1wmKRZkgQcBdwJXAOMp+uMA1c3GrTZoKocwz/55G3vd6ryr9UjodaoPBdwXVX+XtJlwHdybHezpCuBW4CngZ8AS4BnApdLeg/JL4e3NhG32UCYnEyuwF23DmbPhieegE2bks/WroXzztu2blZLBl+gZc3IM7lb6UAg1zlGRHwC+ETF4t+TnP2bDbXKydqHc/a/9QVa1qo8Y/xPkIzxK33+NfDRguMyG3h5e+1U2ro1eZg1K89Qz+6dCMRs2DQ7KesxfWtVzcQvaTdgDHhJumgKuDIiNhUdmNmgq9ZrpxaP6Vs7VK3qkfTHJFU4f0rSn2ct8F+AH0jaQ9JnOhKh2YDK6rWzyy4wZ862Fgzvf79bMlj71Trj/zJwUkQsK18o6WhgNXBHkYGZDbpSAi9V9Xiy1jql6pW7ku6KiBdV+exe4OCIaGJqqnG+ctfMrHHVrtytdQHXTpL+KGNHu5J06uxI0jczs/aqlfgvBa6SNFJakL6+HPhasWGZmVlRqo7xR8RnJJ0CfF9SaQrqSeCciPhKR6IzM7O2q1nOGRHnAudK2j19/0RHojIzs8LkatnghG9mNjjydOc0szap7L45OdntiGwYNdOkzcya4DtoWa+oe8af9tP/O0kXpO8PlPSm4kMzGyxZTdk2bkyWm3VSnqGeS0haKR+evr8PcLsGsxzKh3aq9eXxHbSs0/Ik/gMi4nPAZoCIeIqkRbOZ1VAa2lm7Fmrd2trdNq3T8iT+TWmXzgCQdADJXwBmVkOefvvutmndkGdy9xPA9cC+kiaBVwN/U28jSQcBXy9btD/wcWAP4CRgOl3+sYi4Ln/IZv2h1hCO5KZs1j15bsSyTNItwGEkQzynRsRDObb7GbAQQNIM4H7gm8AJwJci4pwW4jbredX67S9YAGvWdDwcsz+o1Y//kNIDWACsBx4A5qfLGnEUcE9ENHjbCbP+ldVv30M71gtqnfF/ocZnAby+ge95B3BZ2ftTJL2b5I5eH46IRxvYl1nPmpzcvr/++Dhcd5377VtvqdqPv21fIM0k+Uvh4IjYIGkf4CGSXx6fBuZFxIkZ200AEwDz589/5dpG71Fn1mGVF2hBcobvu2ZZt1Trx1838af9908GXkOSrG8Czo+I3+X84mOBD0TEGzI+GwGujYiX1tqHb8Ri/WBkxGP61luauRFLyaXAwcBXgHNJbrzeSD/+d1I2zCNpXtlnx5PcxtGsL/kCLetHeco5D4qIl5e9/66kW/PsPO3jfwzw3rLFn5O0kOSvhzUVn5n1jayhnSy+QMt6TZ7E/xNJh0XECgBJfwL8IM/O09szzqlY9q6GozTrQb5Ay/pVnqGePwF+KGmNpDXAj4A/k3S7pNsKjc6sx+QZ2oHkAq0FCzyxa70pzxn/GwuPwqyHVJZkLlqUlGSuXZsk9HqFcJ7MtV6X58rdtZL2BPYtXz8ibikyMLNuyOqZf9552z6vl/Q9tGP9oG7il/Rpkt4895A2aqPxC7jM+kKecfss7r1j/STPUM/bSFozbyo6GLNua6b00kM71m/yTO6uJumoaTbwGi299NCO9aM8if+zJCWd/y7pmtKj6MDMuiGrsVolpbchctWO9as8Qz1LgbOB24GtxYZj1nn1GquVqnrcaM0GRZ7E/1BEfLnwSMy6IKuKZ+lSn8nbYMsz1LNS0mclHV7Ro9+sL5VfhDU+vmMVz8aNyV8AZoMqzxn/K9Lnw8qWuZzT+lLlGf6WLdnrubGaDbI8F3C9rhOBmBWlfAx/p52qJ/tybqxmgyzPGT+S/oKkNfOupWUR8fdFBWXWivJEP3s2PPEEbEqvQsmT9F2iaYMuz5W75wOzgNcBFwJ/BfxnwXGZNaVyKOfhh/NtN2MGbN3qqh0bDnkmd4+IiHcDj0bEp4DDSfr2mPWcZlouzJqVVPJs3Zpcgeukb4MuT+J/Kn3eKOm5wGZgv+JCMmtM3lbJ5WbMcOtkG155xvivlbQH8HngFpKKnguKDMqsllpj+Hn4Bug27PJU9Xw6fXmVpGuBXSPi8WLDMsvWzBj+LrvAs54FjzziMXwzqDHUI+lVkp5T9v7dwOXApyXNrrdjSQdJWlX2+I2k0yTNlrRM0t3p857t+VFsGDQyhl8ayrnkEnjoIY/hm5XUGuP/J2ATgKQjgbOAS4HHgSX1dhwRP4uIhRGxEHglsBH4JnAGsDwiDgSWp+/Ncsl7YdWCBU70ZtXUSvwzIuKR9PXbgSURcVVE/B3wgga/5yjgnohYCxxL0viN9Pm4BvdlQyzPhVWuwzerrWbil1SaAzgK+I+yz3Jd+FXmHcBl6et9ImI9QPq8d9YGkiYkTUmamp6ebvDrbFBltU3eZReYM8dVOmZ51Ur8lwE3SrqapKTzJgBJLyAZ7slF0kzgzcAVjQQWEUsiYjQiRufOndvIpjZAyks1R0aSZUuWJAneY/hmzal65h4RZ0paDswDboj4w22mdwI+2MB3/DlwS0RsSN9vkDQvItZLmgc82EzgNviyWiZPTCSJ37c6NGtezQu4ImJFRHwzIp4sW/bziLilge94J9uGeQCuAcbT1+PA1Q3sy4ZIVgWPWyabtS7PlbtNkzQLOAb4Rtnis4BjJN2dfnZWkTFY/6pWweOWyWataXSStiERsRGYU7HsYZLJYrOa5s/PbsHglslmrSn0jN+sFVkVPC7VNGudE7/1rLGxHSt4XKpp1jonfuspWeWba9a4VNOsnZz4rWMqk/rk5PbL9toLTjwxGdeP2Fa+OTnZ5cDNBoy2lef3rtHR0Ziamup2GNaCypp8SK64leq3VF6wwHX7Zs2QtDIiRiuXF1rVY1aSVZO/eXO+bV2+adZeHuqxltUbwhkZyX9nrCwu3zRrL5/xW0uy2iqccML2Qzhr1ybvmxlVdPmmWfv5jN9aUm0Ip3LcPiJJ/uV22QVmztxxmTttmhXLid9a0sj4e8SOXTUvvtidNs06zUM91pJqbRWyVKvOcXI36yyf8VtDKidtFy3KvjFK5RCOx+rNeocTv+VWmsgtv8Bq6VIYH68/hOOxerPe4Qu4LLdqZZm+wMqsN1W7gMtn/Jab++ObDQYnfsut2oVUvsDKrL848Vtu7o9vNhiKvvXiHpKulHSXpDslHS7pk5Lul7QqfSwqMgarLavdQrXl7o9vNhgKndyVtBS4KSIulDQTmAWcBvw2Is7Jux9P7hYjq2PmrFlJlc7SpTsud5I36y8dn9yV9CzgSOAigIjYFBGPFfV91risdgsbNyYJPmv54sWdi83MilPkUM/+wDRwiaSfSLpQ0jPSz06RdJukiyXtmbWxpAlJU5KmpqenCwxzeFWrxtmypbH1zay/FJn4dwYOAc6LiFcATwJnAOcBBwALgfXAF7I2joglETEaEaNz584tMMzhVa0aZ8aMxtY3s/5SZOK/D7gvIm5O318JHBIRGyJiS0RsBS4ADi0wBqP6BG61Kp2JCVfvmA2ywhJ/RPwa+JWkg9JFRwE/lTSvbLXjgdVFxWDZbRZK97GtVqXz1a+6esdskBVd1bMQuBCYCfwSOAH4MskwTwBrgPdGxPpa+3FVT/PcZsFseHXlnrsRsQqo/NJ3Ffmdtj23WTCzSr5yd8C5zYKZVXLiH3Bus2BmlZz4B5zbLJhZJd96cQiMjTnRm9k2PuMfENVq9c3MKvmMfwBUNlsr1eqDz/TNbEc+4x8A1ZqtuamamWVx4h8ArtU3s0Y48Q8A1+qbWSOc+AeAa/XNrBFO/H2gXsWOa/XNrBFO/F1WL6nX6q5Zbmwsabq2dWvy7KRvZtU48XdRnqTuih0zazcn/i7Kk9RdsWNm7ebE30V5krordsys3Zz426yR1gl5krordsys3Zz42yjvRGxJnqTuih0za7dCE7+kPSRdKekuSXdKOlzSbEnLJN2dPu9ZZAzNaLbhWaMTsXmTuit2zKydir7n7lLgpoi4UNJMYBbwMeCRiDhL0hnAnhHx0Vr76eQ9dysbnkFyFp7nLHunnZIz/UpSkrTNzDqp2j13Czvjl/Qs4EjgIoCI2BQRjwHHAkvT1ZYCxxUVQzNaKZ/0RKyZ9YMih3r2B6aBSyT9RNKFkp4B7BMR6wHS572zNpY0IWlK0tT09HSBYW6vlfJJT8SaWT8oMvHvDBwCnBcRrwCeBM7Iu3FELImI0YgYnTt37nafFXnTkVbO2j0Ra2b9oMjEfx9wX0TcnL6/kuQXwQZJ8wDS5wcb2WmjlTONavWs3ROxZtbrCkv8EfFr4FeSDkoXHQX8FLgGGE+XjQNXN7LfolsY+KzdzAZd0VU9C4ELgZnAL4ETSH7ZXA7MB9YBb42IR2rtp7yqx5UzZmb5VKvqKfSeuxGxCtjhS0nO/psyf34yvJO13MzM6uu7K3ddOWNm1pq+S/wegzcza02hQz1FGRtzojcza1bfnfGbmVlrnPjNzIaME7+Z2ZBx4jczGzJO/GZmQ6bQK3fbRdI0kHHZVqa9gIcKDKcVjq05jq05jq05gxTbgoiYW7mwLxJ/IyRNZV2i3AscW3McW3McW3OGITYP9ZiZDRknfjOzITOIiX9JtwOowbE1x7E1x7E1Z+BjG7gxfjMzq20Qz/jNzKwGJ34zsyHT94lf0ucl3SXpNknflLRHlfXeKOlnkn4hKfdN31uM7a2S7pC0VVLVEixJayTdLmmVpKkei60bx222pGWS7k6f96yyXseOW73joMSX089vk3RIkfE0GNtrJT2eHqdVkj7ewdgulvSgpNVVPu/mcasXW1eOm6R9JX1X0p3pv9FTM9Zp7bhFRF8/gDcAO6evzwbOzlhnBnAPsD/JbSBvBV7SgdheDBwEfA8YrbHeGmCvDh+3urF18bh9DjgjfX1G1n/TTh63PMcBWAR8GxBwGHBzh/475onttcC1nfz/q+y7jwQOAVZX+bwrxy1nbF05bsA84JD09e7Az9v9/1vfn/FHxA0R8XT6dgXw/IzVDgV+ERG/jIhNwL8Cx3Ygtjsj4mdFf08zcsbWleOWfsfS9PVS4LgOfGcteY7DscClkVgB7CFpXo/E1jUR8X2g1j21u3Xc8sTWFRGxPiJuSV8/AdwJPK9itZaOW98n/gonkvwWrPQ84Fdl7+9jxwPZTQHcIGmlpIluB1OmW8dtn4hYD8k/AmDvKut16rjlOQ7dOlZ5v/dwSbdK+rakgzsQV169/m+zq8dN0gjwCuDmio9aOm59cQcuSd8BnpPx0eKIuDpdZzHwNDCZtYuMZW2pY80TWw6vjogHJO0NLJN0V3o20u3YunLcGthNIcctQ57jUNixqiPP995C0rPlt5IWAf8GHFh0YDl167jl0dXjJumZwFXAaRHxm8qPMzbJfdz6IvFHxNG1Ppc0DrwJOCrSAbAK9wH7lr1/PvBAJ2LLuY8H0ucHJX2T5M/3lhNYG2LrynGTtEHSvIhYn/75+mCVfRRy3DLkOQ6FHas66n5vedKIiOskfVXSXhHRC43IunXc6urmcZO0C0nSn4yIb2Ss0tJx6/uhHklvBD4KvDkiNlZZ7cfAgZL2kzQTeAdwTadirEXSMyTtXnpNMlmdWWXQBd06btcA4+nrcWCHv046fNzyHIdrgHen1RaHAY+XhqsKVjc2Sc+RpPT1oST/7h/uQGx5dOu41dWt45Z+50XAnRHxxSqrtXbcOj1j3e4H8AuSsa5V6eP8dPlzgevK1ltEMjt+D8lQRydiO57kN/PvgQ3Av1fGRlKNcWv6uKOXYuvicZsDLAfuTp9nd/u4ZR0H4H3A+9LXAv4x/fx2alRxdSG2U9JjdCtJAcQRHYztMmA9sDn9/+09PXTc6sXWleMGvIZk2Oa2sry2qJ3HzS0bzMyGTN8P9ZiZWWOc+M3MhowTv5nZkHHiNzMbMk78ZmZDxonfOkbSnLJOh7+WdH/6+jFJP+1wLMdJeknZ+7+X1PAFb5JGanR3PFjSf0j6uaR7JH1KUtv/zdX6WSR9TzW6r9pwcuK3jomIhyNiYUQsBM4HvpS+Xghsbff3Sap1ZfpxwB+SZUR8PCK+08bv3o3kIpuzIuKFwB+TXFm8Q4vdNjiOAn8WGzxO/NYrZki6IO0/fkOaOJF0gKTr00ZsN0l6Ubp8gaTlaS/y5ZLmp8v/WdIXJX0XODtre0lHAG8GPp/+xXFAut1fpft4laQfKmnO9Z+Sdk/P7G+SdEv6OKLOz/PXwA8i4gaASK4qPwX4SPodn5T0t6WVJa1W0pALSf+WxnuHyprPSfqtpDPTuFZI2qfez1JO0hsk/SiN/wolvWCQdJakn6bH8pzG/9NZv3Hit15xIPCPEXEw8BjwX9PlS4APRsQrgb8FvpouP5ekLe3LSBrzfblsXy8Ejo6ID2dtHxE/JDkb/0j6F8g9pQ3TtgdfB06NiJcDRwNPkfQLOiYiDgHeXvF9WQ4GVpYvSL9nN1W5WVCZE9N4R4EPSZqTLn8GsCKN6/vASbV+lnKS9gL+V3pcDgGmgP8haTbJVdwHp8fyM3ViswHQF03abCjcGxGr0tcrgZH0jPQI4Iq0ZQrAH6XPhwNvSV9/jeTmLSVXRMSWOttXcxCwPiJ+DNsadSnpB3SupIXAFpJfLrWI7G6JWV0VK31I0vHp631Jfik+DGwCrk2XrwSOybGvksNIhoN+kB6LmcCPgN8AvwMulPStsv3bAHPit17x+7LXW4DdSP4ifSydB6inPMk+mT43sn1JtYR9OklPo5en+/1dnf3cQXKHp207lvYHHoqIxyQ9zfZ/ce+arvNakr8yDo+IjZK+V/oM2BzbeqxsobF/vwKWRcQ7d/ggaUB2FEmDt1OA1zewX+tDHuqxnpWebd8r6a3wh/uMvjz9+IckiQpgDPh/DW7/BMlt7SrdBTxX0qvSbXZPJ4mfTfKXwFbgXSS3PKxlEnhNWXXNbiTDQ59IP19Dcts/lNwvdb90+bOBR9Ok/yKSM/V6qv0s5VYAr5b0gvQ7Z0l6YfpX0bMj4jrgNJKJdhtwTvzW68aA90gqdeEs3VbwQ8AJkm4jScTVqmWqbf+vwEck/UTSAaWVI7l94duBr6TbLCM54/4qMC5pBckwz5PUEBFPkUy6Lpb0c+Ahksne0o2CrgJmS1oFvJ+kuybA9cDO6c/1aZKEXU/mz1IRzzTwN8Bl6b5XAC8i+YVxbbrsRpK/bGzAuTunWQdIOg74IvC6iFjb5XBsyDnxm5kNGQ/1mJkNGSd+M7Mh48RvZjZknPjNzIaME7+Z2ZBx4jczGzL/H3bDFX8OyfAhAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "sm.qqplot(df[\"Weights\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8f2985ca",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "cf82f77d",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}