notebooks/solutions/SOLN_S2_Inferential_Statistics.ipynb

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    "# Data Science Foundations, Session 2: Inferential Statistics\n",
    "\n",
    "**Instructor**: Wesley Beckner\n",
    "\n",
    "**Contact**: wesleybeckner@gmail.com\n",
    "\n",
    "---\n",
    "\n",
    "<br>\n",
    "\n",
    "In this session we will look at the utility of EDA combined with inferential statistics.\n",
    "\n",
    "<br>\n",
    "\n",
    "---\n"
   ]
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   "source": [
    "<a name='x.0'></a>\n",
    "\n",
    "## 2.0 Preparing Environment and Importing Data\n",
    "\n",
    "[back to top](#top)"
   ]
  },
  {
   "cell_type": "markdown",
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    "id": "biwnU2732lYG"
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   "source": [
    "<a name='x.0.1'></a>\n",
    "\n",
    "### 2.0.1 Import Packages\n",
    "\n",
    "[back to top](#top)"
   ]
  },
  {
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   "source": [
    "# The modules we've seen before\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import plotly.express as px\n",
    "import seaborn as sns\n",
    "\n",
    "# our stats modules\n",
    "import random\n",
    "import scipy.stats as stats\n",
    "import statsmodels.api as sm\n",
    "from statsmodels.formula.api import ols\n",
    "import scipy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "2oNmcaxw2og4"
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   "source": [
    "<a name='x.0.2'></a>\n",
    "\n",
    "### 2.0.2 Load Dataset\n",
    "\n",
    "[back to top](#top)\n",
    "\n",
    "For this session, we will use dummy datasets from sklearn."
   ]
  },
  {
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   "execution_count": 2,
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    "id": "aRWow_s8eSm7"
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   "source": [
    "df = pd.read_csv('https://raw.githubusercontent.com/wesleybeckner/'\\\n",
    "                 'ds_for_engineers/main/data/truffle_margin/truffle_margin_customer.csv')"
   ]
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       "    }\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>Base Cake</th>\n",
       "      <th>Truffle Type</th>\n",
       "      <th>Primary Flavor</th>\n",
       "      <th>Secondary Flavor</th>\n",
       "      <th>Color Group</th>\n",
       "      <th>Customer</th>\n",
       "      <th>Date</th>\n",
       "      <th>KG</th>\n",
       "      <th>EBITDA/KG</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Butter</td>\n",
       "      <td>Candy Outer</td>\n",
       "      <td>Butter Pecan</td>\n",
       "      <td>Toffee</td>\n",
       "      <td>Taupe</td>\n",
       "      <td>Slugworth</td>\n",
       "      <td>1/2020</td>\n",
       "      <td>53770.342593</td>\n",
       "      <td>0.500424</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Butter</td>\n",
       "      <td>Candy Outer</td>\n",
       "      <td>Ginger Lime</td>\n",
       "      <td>Banana</td>\n",
       "      <td>Amethyst</td>\n",
       "      <td>Slugworth</td>\n",
       "      <td>1/2020</td>\n",
       "      <td>466477.578125</td>\n",
       "      <td>0.220395</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Butter</td>\n",
       "      <td>Candy Outer</td>\n",
       "      <td>Ginger Lime</td>\n",
       "      <td>Banana</td>\n",
       "      <td>Burgundy</td>\n",
       "      <td>Perk-a-Cola</td>\n",
       "      <td>1/2020</td>\n",
       "      <td>80801.728070</td>\n",
       "      <td>0.171014</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Butter</td>\n",
       "      <td>Candy Outer</td>\n",
       "      <td>Ginger Lime</td>\n",
       "      <td>Banana</td>\n",
       "      <td>White</td>\n",
       "      <td>Fickelgruber</td>\n",
       "      <td>1/2020</td>\n",
       "      <td>18046.111111</td>\n",
       "      <td>0.233025</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Butter</td>\n",
       "      <td>Candy Outer</td>\n",
       "      <td>Ginger Lime</td>\n",
       "      <td>Rum</td>\n",
       "      <td>Amethyst</td>\n",
       "      <td>Fickelgruber</td>\n",
       "      <td>1/2020</td>\n",
       "      <td>19147.454268</td>\n",
       "      <td>0.480689</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1663</th>\n",
       "      <td>Tiramisu</td>\n",
       "      <td>Chocolate Outer</td>\n",
       "      <td>Doughnut</td>\n",
       "      <td>Pear</td>\n",
       "      <td>Amethyst</td>\n",
       "      <td>Fickelgruber</td>\n",
       "      <td>12/2020</td>\n",
       "      <td>38128.802589</td>\n",
       "      <td>0.420111</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1664</th>\n",
       "      <td>Tiramisu</td>\n",
       "      <td>Chocolate Outer</td>\n",
       "      <td>Doughnut</td>\n",
       "      <td>Pear</td>\n",
       "      <td>Burgundy</td>\n",
       "      <td>Zebrabar</td>\n",
       "      <td>12/2020</td>\n",
       "      <td>108.642857</td>\n",
       "      <td>0.248659</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1665</th>\n",
       "      <td>Tiramisu</td>\n",
       "      <td>Chocolate Outer</td>\n",
       "      <td>Doughnut</td>\n",
       "      <td>Pear</td>\n",
       "      <td>Teal</td>\n",
       "      <td>Zebrabar</td>\n",
       "      <td>12/2020</td>\n",
       "      <td>3517.933333</td>\n",
       "      <td>0.378501</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1666</th>\n",
       "      <td>Tiramisu</td>\n",
       "      <td>Chocolate Outer</td>\n",
       "      <td>Doughnut</td>\n",
       "      <td>Rock and Rye</td>\n",
       "      <td>Amethyst</td>\n",
       "      <td>Slugworth</td>\n",
       "      <td>12/2020</td>\n",
       "      <td>10146.898432</td>\n",
       "      <td>0.213149</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1667</th>\n",
       "      <td>Tiramisu</td>\n",
       "      <td>Chocolate Outer</td>\n",
       "      <td>Doughnut</td>\n",
       "      <td>Rock and Rye</td>\n",
       "      <td>Burgundy</td>\n",
       "      <td>Zebrabar</td>\n",
       "      <td>12/2020</td>\n",
       "      <td>1271.904762</td>\n",
       "      <td>0.431813</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>1668 rows × 9 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     Base Cake     Truffle Type Primary Flavor Secondary Flavor Color Group  \\\n",
       "0       Butter      Candy Outer   Butter Pecan           Toffee       Taupe   \n",
       "1       Butter      Candy Outer    Ginger Lime           Banana    Amethyst   \n",
       "2       Butter      Candy Outer    Ginger Lime           Banana    Burgundy   \n",
       "3       Butter      Candy Outer    Ginger Lime           Banana       White   \n",
       "4       Butter      Candy Outer    Ginger Lime              Rum    Amethyst   \n",
       "...        ...              ...            ...              ...         ...   \n",
       "1663  Tiramisu  Chocolate Outer       Doughnut             Pear    Amethyst   \n",
       "1664  Tiramisu  Chocolate Outer       Doughnut             Pear    Burgundy   \n",
       "1665  Tiramisu  Chocolate Outer       Doughnut             Pear        Teal   \n",
       "1666  Tiramisu  Chocolate Outer       Doughnut     Rock and Rye    Amethyst   \n",
       "1667  Tiramisu  Chocolate Outer       Doughnut     Rock and Rye    Burgundy   \n",
       "\n",
       "          Customer     Date             KG  EBITDA/KG  \n",
       "0        Slugworth   1/2020   53770.342593   0.500424  \n",
       "1        Slugworth   1/2020  466477.578125   0.220395  \n",
       "2      Perk-a-Cola   1/2020   80801.728070   0.171014  \n",
       "3     Fickelgruber   1/2020   18046.111111   0.233025  \n",
       "4     Fickelgruber   1/2020   19147.454268   0.480689  \n",
       "...            ...      ...            ...        ...  \n",
       "1663  Fickelgruber  12/2020   38128.802589   0.420111  \n",
       "1664      Zebrabar  12/2020     108.642857   0.248659  \n",
       "1665      Zebrabar  12/2020    3517.933333   0.378501  \n",
       "1666     Slugworth  12/2020   10146.898432   0.213149  \n",
       "1667      Zebrabar  12/2020    1271.904762   0.431813  \n",
       "\n",
       "[1668 rows x 9 columns]"
      ]
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   "source": [
    "df"
   ]
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   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "id": "I734bGQy10_r"
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   "outputs": [],
   "source": [
    "descriptors = df.columns[:-2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
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    "outputId": "accf4964-c0a0-4b1f-e40d-78a0e51915a9"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Base Cake\n",
      "['Butter' 'Cheese' 'Chiffon' 'Pound' 'Sponge' 'Tiramisu']\n",
      "\n",
      "Truffle Type\n",
      "['Candy Outer' 'Chocolate Outer' 'Jelly Filled']\n",
      "\n",
      "Primary Flavor\n",
      "['Butter Pecan' 'Ginger Lime' 'Margarita' 'Pear' 'Pink Lemonade'\n",
      " 'Raspberry Ginger Ale' 'Sassafras' 'Spice' 'Wild Cherry Cream'\n",
      " 'Cream Soda' 'Horchata' 'Kettle Corn' 'Lemon Bar' 'Orange Pineapple\\tP'\n",
      " 'Plum' 'Orange' 'Butter Toffee' 'Lemon' 'Acai Berry' 'Apricot'\n",
      " 'Birch Beer' 'Cherry Cream Spice' 'Creme de Menthe' 'Fruit Punch'\n",
      " 'Ginger Ale' 'Grand Mariner' 'Orange Brandy' 'Pecan' 'Toasted Coconut'\n",
      " 'Watermelon' 'Wintergreen' 'Vanilla' 'Bavarian Cream' 'Black Licorice'\n",
      " 'Caramel Cream' 'Cheesecake' 'Cherry Cola' 'Coffee' 'Irish Cream'\n",
      " 'Lemon Custard' 'Mango' 'Sour' 'Amaretto' 'Blueberry' 'Butter Milk'\n",
      " 'Chocolate Mint' 'Coconut' 'Dill Pickle' 'Gingersnap' 'Chocolate'\n",
      " 'Doughnut']\n",
      "\n",
      "Secondary Flavor\n",
      "['Toffee' 'Banana' 'Rum' 'Tutti Frutti' 'Vanilla' 'Mixed Berry'\n",
      " 'Whipped Cream' 'Apricot' 'Passion Fruit' 'Peppermint' 'Dill Pickle'\n",
      " 'Black Cherry' 'Wild Cherry Cream' 'Papaya' 'Mango' 'Cucumber' 'Egg Nog'\n",
      " 'Pear' 'Rock and Rye' 'Tangerine' 'Apple' 'Black Currant' 'Kiwi' 'Lemon'\n",
      " 'Hazelnut' 'Butter Rum' 'Fuzzy Navel' 'Mojito' 'Ginger Beer']\n",
      "\n",
      "Color Group\n",
      "['Taupe' 'Amethyst' 'Burgundy' 'White' 'Black' 'Opal' 'Citrine' 'Rose'\n",
      " 'Slate' 'Teal' 'Tiffany' 'Olive']\n",
      "\n",
      "Customer\n",
      "['Slugworth' 'Perk-a-Cola' 'Fickelgruber' 'Zebrabar' \"Dandy's Candies\"]\n",
      "\n",
      "Date\n",
      "['1/2020' '2/2020' '3/2020' '4/2020' '5/2020' '6/2020' '7/2020' '8/2020'\n",
      " '9/2020' '10/2020' '11/2020' '12/2020']\n",
      "\n"
     ]
    }
   ],
   "source": [
    "for col in df.columns[:-2]:\n",
    "  print(col)\n",
    "  print(df[col].unique())\n",
    "  print()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "KKkK88MuiQby"
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   "source": [
    "## 2.1 Many Flavors of Statistical Tests\n",
    "\n",
    "<p align=\"center\">\n",
    "<img src=\"https://luminousmen.com/media/descriptive-and-inferential-statistics.jpeg\" width=400px></img>\n",
    "<br>\n",
    "<small> https://luminousmen.com/post/descriptive-and-inferential-statistics </small>\n",
    "</p>\n",
    "\n",
    "> Descriptive statistics describes data (for example, a chart or graph) and inferential statistics allows you to make predictions (“inferences”) from that data. With inferential statistics, you take data from samples and make generalizations about a population \n",
    "\n",
    "[statshowto](https://www.statisticshowto.com/probability-and-statistics/statistics-definitions/inferential-statistics/)\n",
    "\n",
    "* **Moods Median Test**\n",
    "* [Kruskal-Wallis Test](https://sixsigmastudyguide.com/kruskal-wallis-non-parametric-hypothesis-test/) (Another comparison of Medians test)\n",
    "* T-Test\n",
    "* Analysis of Variance (ANOVA)\n",
    "  * One Way ANOVA\n",
    "  * Two Way ANOVA\n",
    "  * MANOVA\n",
    "  * Factorial ANOVA\n",
    "\n",
    "When do I use each of these? We will talk about this as we proceed through the examples. [This page](https://support.minitab.com/en-us/minitab/20/help-and-how-to/statistics/nonparametrics/supporting-topics/which-test-should-i-use/) from minitab has good rules of thumb on the subject.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "D5evicZ44rAA"
   },
   "source": [
    "### 2.1.1 What is Mood's Median?\n",
    "\n",
    "> You can use Chi-Square to test for a goodness of fit (whether a sample of data represents a distribution) or whether two variables are related (using a contingency table, which we will create below!)\n",
    "\n",
    "**A special case of Pearon's Chi-Squared Test:** We create a table that counts the observations above and below the global median for two different groups. We then perform a *chi-squared test of significance* on this *contingency table* \n",
    "\n",
    "Null hypothesis: the Medians are all equal\n",
    "\n",
    "The chi-square test statistic:\n",
    "\n",
    "$$x^2 = \\sum{\\frac{(O-E)^2}{E}}$$\n",
    "\n",
    "Where \\\\(O\\\\) is the observed frequency and \\\\(E\\\\) is the expected frequency.\n",
    "\n",
    "**Let's take an example**, say we have three shifts with the following production rates:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "id": "_zJS1ehrKi32"
   },
   "outputs": [],
   "source": [
    "np.random.seed(7)\n",
    "shift_one = [round(i) for i in np.random.normal(16, 3, 10)]\n",
    "shift_two = [round(i) for i in np.random.normal(21, 3, 10)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "49AvW9Sq7MKQ",
    "outputId": "bf4f4baa-5d00-49c3-e7eb-5a00d2958a0a"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[21, 15, 16, 17, 14, 16, 16, 11, 19, 18]\n",
      "[19, 20, 23, 20, 20, 17, 23, 21, 22, 16]\n"
     ]
    }
   ],
   "source": [
    "print(shift_one)\n",
    "print(shift_two)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "id": "1zS4K5hL7gON"
   },
   "outputs": [],
   "source": [
    "stat, p, m, table = scipy.stats.median_test(shift_one, shift_two, correction=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "KVzJKeBg9NNu"
   },
   "source": [
    "what is `median_test` returning?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "pLUCH4Rv73Qp",
    "outputId": "784e2590-d32d-4e5d-ef7a-288fed9373b3"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The pearsons chi-square test statistic: 7.20\n",
      "p-value of the test: 0.007\n",
      "the grand median: 18.5\n"
     ]
    }
   ],
   "source": [
    "print(\"The pearsons chi-square test statistic: {:.2f}\".format(stat))\n",
    "print(\"p-value of the test: {:.3f}\".format(p))\n",
    "print(\"the grand median: {}\".format(m))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "_DJLQx0x-hGU"
   },
   "source": [
    "Let's evaluate that test statistic ourselves by taking a look at the contingency table:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "dH_mlqu0762C",
    "outputId": "1a4436a4-0cd8-4ad6-8ae7-c3639267a678"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2, 8],\n",
       "       [8, 2]])"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "table"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "0Ox8X-A4-mnk"
   },
   "source": [
    "This is easier to make sense of if we order the shift times"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "wT4_CjEL-pkg",
    "outputId": "131a432e-d37f-4eba-ae88-c6353d5c7e65"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[11, 14, 15, 16, 16, 16, 17, 18, 19, 21]"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "shift_one.sort()\n",
    "shift_one"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "8QAfysw6-yJR"
   },
   "source": [
    "When we look at shift one, we see that 8 values are at or below the grand median."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "9udymrL9-xxF",
    "outputId": "26618a38-d362-42ac-d0bb-1a795858886d"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[16, 17, 19, 20, 20, 20, 21, 22, 23, 23]"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "shift_two.sort()\n",
    "shift_two"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "jDgDGYlQ-miZ"
   },
   "source": [
    "For shift two, only two are at or below the grand median.\n",
    "\n",
    "Since the sample sizes are the same, the expected value for both groups is the same, 5 above and 5 below the grand median. The chi-square is then:\n",
    "\n",
    "$$X^2 = \\frac{(2-5)^2}{5} + \\frac{(8-5)^2}{5} + \\frac{(8-5)^2}{5} + \\frac{(2-5)^2}{5}$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "F9BEYdaW_m43",
    "outputId": "9c999f6b-7e60-42af-d2f3-b90e86367126"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.2"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(3-5)**2/5 + (7-5)**2/5 + (7-5)**2/5 + (3-5)**2/5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "4X2xYQkuExJ-"
   },
   "source": [
    "Our p-value, or the probability of observing the null-hypothsis, is under 0.05. We can conclude that these shift performances were drawn under seperate distributions.\n",
    "\n",
    "For comparison, let's do this analysis again with shifts of equal performances"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "_bcZqXDmFHBV",
    "outputId": "3b05d986-4ed4-4e07-b809-ddcc26eb8da1"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The pearsons chi-square test statistic: 0.00\n",
      "p-value of the test: 1.000\n",
      "the grand median: 15.5\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(3)\n",
    "shift_three = [round(i) for i in np.random.normal(16, 3, 10)]\n",
    "shift_four = [round(i) for i in np.random.normal(16, 3, 10)]\n",
    "stat, p, m, table = scipy.stats.median_test(shift_three, shift_four,\n",
    "                                            correction=False)\n",
    "print(\"The pearsons chi-square test statistic: {:.2f}\".format(stat))\n",
    "print(\"p-value of the test: {:.3f}\".format(p))\n",
    "print(\"the grand median: {}\".format(m))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "w3CJcRMUFVE3"
   },
   "source": [
    "and the shift raw values:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "crPZoQBMFXYQ",
    "outputId": "69d24210-5420-4e0f-d0c1-ba091967f971"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[10, 14, 15, 15, 15, 16, 16, 16, 17, 21]\n",
      "[11, 12, 13, 14, 15, 16, 19, 19, 19, 21]\n"
     ]
    }
   ],
   "source": [
    "shift_three.sort()\n",
    "shift_four.sort()\n",
    "print(shift_three)\n",
    "print(shift_four)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "etY5ypiYFdxs",
    "outputId": "8e3770d0-1988-457f-85e5-d6f15c5e36a6"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[5, 5],\n",
       "       [5, 5]])"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "table"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "otPGkuW40I_f"
   },
   "source": [
    "### 2.1.2 When to Use Mood's?\n",
    "\n",
    "**Mood's Median Test is highly flexible** but has the following assumptions:\n",
    "\n",
    "* Considers only one categorical factor\n",
    "* Response variable is continuous (our shift rates)\n",
    "* Data does not need to be normally distributed\n",
    "  * But the distributions are similarly shaped\n",
    "* Sample sizes can be unequal and small (less than 20 observations)\n",
    "\n",
    "Other considerations:\n",
    "\n",
    "* Not as powerful as Kruskal-Wallis Test but still useful for small sample sizes or when there are outliers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "NRpmP6jWPHNj"
   },
   "source": [
    "#### 🏋️ Exercise 1: Use Mood's Median Test\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "BNHxgf12nGJs"
   },
   "source": [
    "##### **Part A** Perform moods median test on Base Cake (Categorical Variable) and EBITDA/KG (Continuous Variable) in Truffle data\n",
    "\n",
    "We're also going to get some practice with pandas groupby."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "id": "SaEEogoHjvHj"
   },
   "outputs": [],
   "source": [
    "# what is returned by this groupby?\n",
    "gp = df.groupby('Base Cake')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "0K7e7MGEj5Ht"
   },
   "source": [
    "How do we find out? We could iterate through it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "2LGkJEinj9SK",
    "outputId": "f04a06f1-ccff-4773-cf5d-f7bf7685fc94"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('Butter',      Base Cake     Truffle Type Primary Flavor Secondary Flavor Color Group  \\\n",
      "0       Butter      Candy Outer   Butter Pecan           Toffee       Taupe   \n",
      "1       Butter      Candy Outer    Ginger Lime           Banana    Amethyst   \n",
      "2       Butter      Candy Outer    Ginger Lime           Banana    Burgundy   \n",
      "3       Butter      Candy Outer    Ginger Lime           Banana       White   \n",
      "4       Butter      Candy Outer    Ginger Lime              Rum    Amethyst   \n",
      "...        ...              ...            ...              ...         ...   \n",
      "1562    Butter  Chocolate Outer           Plum     Black Cherry        Opal   \n",
      "1563    Butter  Chocolate Outer           Plum     Black Cherry       White   \n",
      "1564    Butter  Chocolate Outer           Plum            Mango       Black   \n",
      "1565    Butter     Jelly Filled         Orange         Cucumber    Amethyst   \n",
      "1566    Butter     Jelly Filled         Orange         Cucumber    Burgundy   \n",
      "\n",
      "             Customer     Date             KG  EBITDA/KG  \n",
      "0           Slugworth   1/2020   53770.342593   0.500424  \n",
      "1           Slugworth   1/2020  466477.578125   0.220395  \n",
      "2         Perk-a-Cola   1/2020   80801.728070   0.171014  \n",
      "3        Fickelgruber   1/2020   18046.111111   0.233025  \n",
      "4        Fickelgruber   1/2020   19147.454268   0.480689  \n",
      "...               ...      ...            ...        ...  \n",
      "1562     Fickelgruber  12/2020    9772.200521   0.158279  \n",
      "1563      Perk-a-Cola  12/2020   10861.245675  -0.159275  \n",
      "1564        Slugworth  12/2020    3578.592163   0.431328  \n",
      "1565        Slugworth  12/2020   21438.187500   0.105097  \n",
      "1566  Dandy's Candies  12/2020   15617.489115   0.185070  \n",
      "\n",
      "[456 rows x 9 columns])\n"
     ]
    }
   ],
   "source": [
    "# seems to be a tuple of some sort\n",
    "for i in gp:\n",
    "  print(i)\n",
    "  break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "lwMASrDRkTQj",
    "outputId": "489d83aa-697d-4da2-ad3e-d9dffad85749"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Butter\n",
      "     Base Cake     Truffle Type Primary Flavor Secondary Flavor Color Group  \\\n",
      "0       Butter      Candy Outer   Butter Pecan           Toffee       Taupe   \n",
      "1       Butter      Candy Outer    Ginger Lime           Banana    Amethyst   \n",
      "2       Butter      Candy Outer    Ginger Lime           Banana    Burgundy   \n",
      "3       Butter      Candy Outer    Ginger Lime           Banana       White   \n",
      "4       Butter      Candy Outer    Ginger Lime              Rum    Amethyst   \n",
      "...        ...              ...            ...              ...         ...   \n",
      "1562    Butter  Chocolate Outer           Plum     Black Cherry        Opal   \n",
      "1563    Butter  Chocolate Outer           Plum     Black Cherry       White   \n",
      "1564    Butter  Chocolate Outer           Plum            Mango       Black   \n",
      "1565    Butter     Jelly Filled         Orange         Cucumber    Amethyst   \n",
      "1566    Butter     Jelly Filled         Orange         Cucumber    Burgundy   \n",
      "\n",
      "             Customer     Date             KG  EBITDA/KG  \n",
      "0           Slugworth   1/2020   53770.342593   0.500424  \n",
      "1           Slugworth   1/2020  466477.578125   0.220395  \n",
      "2         Perk-a-Cola   1/2020   80801.728070   0.171014  \n",
      "3        Fickelgruber   1/2020   18046.111111   0.233025  \n",
      "4        Fickelgruber   1/2020   19147.454268   0.480689  \n",
      "...               ...      ...            ...        ...  \n",
      "1562     Fickelgruber  12/2020    9772.200521   0.158279  \n",
      "1563      Perk-a-Cola  12/2020   10861.245675  -0.159275  \n",
      "1564        Slugworth  12/2020    3578.592163   0.431328  \n",
      "1565        Slugworth  12/2020   21438.187500   0.105097  \n",
      "1566  Dandy's Candies  12/2020   15617.489115   0.185070  \n",
      "\n",
      "[456 rows x 9 columns]\n"
     ]
    }
   ],
   "source": [
    "# the first object appears to be the group\n",
    "print(i[0])\n",
    "\n",
    "# the second object appears to be the df belonging to that group\n",
    "print(i[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "gFOrTaPoknGx"
   },
   "source": [
    "going back to our diagram from our earlier pandas session. It looks like whenever we split in the groupby method, we create separate dataframes as well as their group label:\n",
    "\n",
    "<img src=\"https://swcarpentry.github.io/r-novice-gapminder/fig/12-plyr-fig1.png\" width=500></img>\n",
    "\n",
    "Ok, so we know `gp` is separate dataframes. How do we turn the 'EBITDA/KG' column of each dataframe into arrays to then pass to `median_test`?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "id": "nVUYH5gFlWFj"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Butter\n",
      "[ 5.00423594e-01  2.20395451e-01  1.71013869e-01  2.33024872e-01\n",
      "  4.80689371e-01  1.64934546e-01  2.03213256e-01  1.78681400e-01\n",
      "  1.25050726e-01  2.17021951e-01  7.95955185e-02  3.25042287e-01\n",
      "  2.17551215e-01  2.48152299e-01 -1.20503094e-02  1.47190567e-01\n",
      "  3.84488948e-01  2.05438764e-01  1.32190256e-01  3.23019144e-01\n",
      " -9.73361477e-03  1.98397692e-01  1.67067902e-01 -2.60063690e-02\n",
      "  1.30365325e-01  2.36337749e-01 -9.70556780e-02  1.59051819e-01\n",
      " -8.76572259e-02 -3.32199843e-02 -5.05704451e-02 -5.56458806e-02\n",
      " -8.86273564e-02  4.32267857e-02 -1.88615579e-01  4.24939227e-01\n",
      "  9.35136847e-02 -3.43605950e-02  1.63823520e-01  2.78522916e-01\n",
      "  1.29207730e-01  1.79194495e-01  1.37419569e-01  1.31372653e-01\n",
      "  2.53275225e-01  2.26761431e-01  1.10173466e-01  1.99338787e-01\n",
      " -2.01250197e-01  1.16567591e-01  1.32324984e-01  4.02912418e-01\n",
      "  9.35051765e-02  1.65865814e-01  2.12269112e-01  2.53461571e-01\n",
      "  1.89055713e-01  1.20416365e-01  3.95276612e-02  2.93121770e-01\n",
      "  1.40947082e-01 -1.21555832e-01  1.56455622e-01 -1.29776953e-02\n",
      " -6.17934014e-02 -8.19904808e-02 -3.14711557e-02 -8.03820228e-02\n",
      "  1.63839981e-01  8.34406336e-02  1.49369698e-01  1.05990633e-01\n",
      "  1.27399979e-01  2.26634255e-01 -2.20801929e-03 -6.92044284e-02\n",
      "  1.74048414e-01  1.30933438e-01  1.27620323e-01  2.78652749e-01\n",
      "  2.14772018e-01  1.40864278e-01  1.23745138e-01  1.66586809e-01\n",
      "  2.91940995e-01  2.49925584e-01  8.65447719e-02  3.80907774e-01\n",
      "  2.70851719e-01  3.32946265e-01  9.00795862e-03  2.00960974e-01\n",
      "  2.72623570e-01  3.35902190e-01  1.27337723e-01  2.36618545e-01\n",
      " -6.82774785e-02  3.13166906e-01  2.15752651e-01  9.29694447e-02\n",
      "  3.60809152e-02  2.32488112e-01  3.38200308e-02  1.70916188e-01\n",
      "  2.81620452e-01 -1.61981289e-01 -4.14570666e-02  1.13465970e-02\n",
      "  2.28733252e-01  9.87516565e-02  3.52732668e-02  6.32598661e-02\n",
      "  2.10300526e-01  1.98761726e-01  1.38832882e-01  2.95465366e-01\n",
      "  2.68022024e-01  3.22389724e-01  4.04867623e-01  2.38086167e-01\n",
      "  1.12586985e-01  1.94010438e-01  1.96757297e-01  1.65215620e-01\n",
      "  1.22730941e-02  1.14415249e-01  3.26252563e-01  1.89080695e-01\n",
      " -5.11830382e-02  2.41661008e-01  2.00063672e-01  3.07633312e-01\n",
      "  4.20740234e-01  1.34764192e-01 -4.75993730e-02  1.52973888e-02\n",
      "  1.87709908e-01  7.20193743e-02  3.48745346e-02  2.77659158e-01\n",
      "  2.73466257e-01  1.32419725e-01  2.85933859e-02  3.99622870e-02\n",
      " -7.46829380e-02  9.03915641e-02 -9.61708181e-02  7.16896946e-02\n",
      "  1.08714611e-01  1.18536709e-01  8.52229628e-02  4.13523715e-01\n",
      "  7.71194281e-01  1.73738798e-01  3.05406909e-01  1.53831064e-01\n",
      "  2.06911408e-01  1.13075512e-01  1.29416734e-01  1.60275533e-01\n",
      "  2.29962628e-01  2.50895646e-01  1.73060658e-01  2.01020670e-01\n",
      "  3.16227457e-01  1.57652647e-01  5.47188384e-02  2.61436808e-01\n",
      "  1.46570523e-01  1.58977569e-01  2.11215119e-01  1.40679855e-01\n",
      " -8.00696326e-02  1.59842103e-01  2.00211820e-01  9.92221921e-02\n",
      " -1.91516176e-02 -5.02510162e-02 -9.15402427e-02  4.28019215e-02\n",
      "  1.06537078e-01 -3.24195486e-01  1.79861627e-02 -1.29900711e-01\n",
      " -1.18627679e-01 -1.26903307e-01 -1.12941251e-01  2.81344485e-01\n",
      " -5.75519167e-02  1.62155727e-02  2.14084866e-01  2.05315240e-01\n",
      "  1.27598359e-01  1.89025252e-01  3.96820478e-01  1.20290515e-01\n",
      "  3.32130996e-01  1.37858897e-01  9.78393589e-02  3.51731323e-01\n",
      "  1.10782088e-01  2.27390210e-01  3.89559348e-01  1.74184808e-01\n",
      "  3.08568571e-01  1.71747215e-01  2.33275587e-01  2.56728635e-01\n",
      "  3.02423314e-01  2.74374851e-01  3.27629705e-02  5.61005655e-02\n",
      "  1.68330538e-01  1.12578506e-01  1.08314409e-02  1.33944964e-01\n",
      " -2.12285231e-01 -1.21224032e-01  1.07819533e-01  3.17613330e-02\n",
      "  2.84300351e-01 -1.58586907e-01  1.36753020e-01  1.26197635e-01\n",
      "  7.40448636e-02  2.35065994e-01 -6.15319415e-02 -7.51966701e-02\n",
      "  4.13427726e-01  1.60539980e-01  1.09901498e-01  1.74329568e-01\n",
      "  1.48135527e-01  1.85728609e-01  2.85476612e-01  2.24898461e-01\n",
      "  1.33343564e-01  1.80618963e-01  2.03080820e-02  2.16728570e-01\n",
      "  1.86566493e-01  1.25929822e-01  1.79317565e-01  3.88162321e-01\n",
      "  2.03009067e-01  2.64872648e-01  4.95978731e-01  1.52347749e-01\n",
      " -7.23596372e-02  1.29552280e-01  6.16496157e-02  1.05956924e-01\n",
      " -2.71699836e-01 -5.64473565e-03 -2.50275527e-02  1.29269950e-01\n",
      " -1.87247727e-01 -3.49347255e-01 -1.93280406e-01  7.87217542e-02\n",
      "  2.21951811e-01  7.10999656e-02  3.49382049e-02  1.48398799e-01\n",
      "  5.65517753e-02  1.05690961e-01  2.55476023e-01  1.28401889e-01\n",
      "  1.33289903e-01  1.14201836e-01  1.43169893e-01  5.69591438e-01\n",
      "  1.54755202e-01  1.55028578e-01  1.64827975e-01  4.67083700e-01\n",
      "  3.31029661e-02  1.62382617e-01  1.54156022e-01  6.55873722e-01\n",
      " -5.31208735e-02  2.37122763e-01  2.71368392e-01  4.69144223e-01\n",
      "  1.62923984e-01  1.22718216e-01  1.68055251e-01  1.35999904e-01\n",
      "  2.04736813e-01  1.27146904e-01 -1.12549423e-01  3.24840692e-03\n",
      "  7.10375441e-02  7.90146006e-03  5.79775663e-02 -1.57867224e-01\n",
      "  1.33194074e-01  1.11364361e-01  1.95665062e-01  5.57144416e-02\n",
      " -6.22623725e-02  2.59366443e-01  1.96512306e-02 -2.47699823e-02\n",
      "  3.37429602e-01  1.84628626e-01  2.42417229e-01  1.88852778e-01\n",
      "  2.10930109e-01  2.10416004e-01  2.81527817e-01  5.45666352e-01\n",
      "  1.85856370e-01  4.88939364e-01  1.29308220e-01  1.30534366e-01\n",
      "  4.31600221e-01  1.42478827e-01  1.11633119e-01  1.45026679e-01\n",
      "  2.79724659e-01  3.33422150e-01  4.92846588e-01  1.88026032e-01\n",
      "  4.35734950e-01  1.29765005e-01  1.36498013e-01  1.27056277e-01\n",
      "  2.39063615e-01 -1.49002763e-01  2.00230923e-02  1.23378339e-01\n",
      "  6.12350194e-02 -1.57952580e-01  5.93742728e-02 -6.88460761e-03\n",
      "  7.48854198e-02  6.45607765e-02  8.47908994e-03  2.15403273e-01\n",
      "  6.38359483e-02 -6.30232436e-04  4.09513551e-01  3.59478228e-01\n",
      "  1.15102395e-01  1.56907967e-01  1.60361237e-01  3.16259692e-01\n",
      "  4.37763243e-01  1.82457530e-01  3.12791208e-01  1.59771151e-01\n",
      " -6.63636501e-02  3.37363422e-01  2.58858115e-01  1.81217734e-01\n",
      "  3.73234115e-02  1.44936318e-01  3.16879135e-01  4.73967251e-01\n",
      "  2.43696316e-01  2.73749525e-01  2.46270449e-02  2.27465471e-01\n",
      "  1.71915626e-01  6.96528119e-02  1.51926333e-01  1.91790172e-01\n",
      " -1.70457889e-01  1.94258861e-02  1.05929285e-01  2.46869777e-01\n",
      " -6.42981449e-03  1.22480623e-01  1.27650832e-01  1.23734951e-01\n",
      "  2.01582021e-01  7.66321281e-02  1.25943788e-01 -5.22321249e-02\n",
      "  2.95908687e-01  3.44925520e-01  1.07812252e-01  1.15365733e-01\n",
      "  2.13185926e-01  1.29626595e-01  4.15526961e-01  1.23294607e-01\n",
      "  1.45059294e-01  1.81411556e-01  1.06561684e-01  1.20626826e-01\n",
      "  2.19538968e-01  3.16034720e-01  9.72365601e-02  1.83261409e-01\n",
      "  1.47228661e-01  1.57946602e-01  3.83712037e-01  1.36031656e-01\n",
      "  3.75214905e-02  1.97768668e-02  3.06073435e-02 -1.01445936e-01\n",
      "  1.41457346e-01  4.89799924e-02  1.35908206e-01  2.95765484e-02\n",
      "  1.34596792e-01 -2.45031560e-01  9.09800159e-02 -2.80465423e-02\n",
      "  4.60956009e-03  4.76391647e-02  9.71343281e-02  6.71838252e-02\n",
      " -1.45994631e-02 -5.39188915e-02  2.79919933e-01  2.31919186e-01\n",
      "  1.12801182e-01  1.13704532e-01  4.26356671e-01  1.90428244e-01\n",
      "  1.10496872e-01  3.31699294e-01  1.36443699e-01  1.97119264e-01\n",
      " -5.57694684e-03  1.11270325e-01  4.61516648e-01  2.68630982e-01\n",
      "  1.00774945e-01  1.41438672e-01  3.97197924e-01  1.92009640e-01\n",
      "  1.34873803e-01  2.20134800e-01  1.11572142e-01  2.04669213e-02\n",
      "  2.21970350e-01 -1.13088611e-01  2.39645009e-01  2.70424952e-01\n",
      "  2.65250470e-01  7.79145265e-02  4.09394578e-03 -2.78502700e-01\n",
      " -1.88647588e-02 -8.11508107e-02  2.05797599e-01  1.58278762e-01\n",
      " -1.59274599e-01  4.31328198e-01  1.05097241e-01  1.85069899e-01]\n"
     ]
    }
   ],
   "source": [
    "# complete this for loop\n",
    "for i, j in gp:\n",
    "  print(i)\n",
    "  print(j['EBITDA/KG'].values)\n",
    "  break\n",
    "  # turn 'EBITDA/KG' of j into an array using the .values attribute\n",
    "  # print this to the screen"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "QlP1VYjSlrOJ"
   },
   "source": [
    "After you've completed the previous step, turn this into a list comprehension and pass the result to a variable called `margins`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "id": "pCr2wjfpP31r"
   },
   "outputs": [],
   "source": [
    "# complete the code below\n",
    "margins = [j['EBITDA/KG'].values for i,j in gp]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "TjN_QppNl4v9"
   },
   "source": [
    "Remember the list unpacking we did for the tic tac toe project? We're going to do the same thing here. Unpack the margins list for `median_test` and run the cell below!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "gJwZFD84PUBP",
    "outputId": "18b008e6-10f2-44da-b46e-6af819873224"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The pearsons chi-square test statistic: 448.81\n",
      "p-value of the test: 8.85e-95\n",
      "the grand median: 2.16e-01\n"
     ]
    }
   ],
   "source": [
    "# complete the following line\n",
    "stat, p, m, table = scipy.stats.median_test(*margins, correction=False)\n",
    "\n",
    "print(\"The pearsons chi-square test statistic: {:.2f}\".format(stat))\n",
    "print(\"p-value of the test: {:.2e}\".format(p))\n",
    "print(\"the grand median: {:.2e}\".format(m))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "-UjWU3c6SV1d"
   },
   "source": [
    "##### **Part B** View the distributions of the data using matplotlib and seaborn\n",
    "\n",
    "What a fantastic statistical result we found! Can we affirm our result with some visualizations? I hope so! Create a boxplot below using pandas. In your call to `df.boxplot()` the `by` parameter should be set to `Base Cake` and the `column` parameter should be set to `EBITDA/KG`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "id": "BwdnbQWYQ4WL"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:title={'center':'EBITDA/KG'}, xlabel='Base Cake'>"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# YOUR BOXPLOT HERE\n",
    "fig, ax = plt.subplots(figsize=(10,5))\n",
    "df.boxplot(by='Base Cake', column='EBITDA/KG', ax=ax)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "AXPBuKkPmZpW"
   },
   "source": [
    "For comparison, I've shown the boxplot below using seaborn!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 442
    },
    "id": "jetbzeP8R6UK",
    "outputId": "d7f0a51c-9b43-4506-fea1-01affdec1c1e"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(10,7))\n",
    "ax = sns.boxplot(x='Base Cake', y='EBITDA/KG', data=df, color='#A0cbe8')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "J2cnPwn8SNq5"
   },
   "source": [
    "##### **Part C** Perform Moods Median on all the other groups"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "EVm8E8XcSmwI",
    "outputId": "6a316d6a-38b2-43f4-f4d8-8d8b678b3979"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['Base Cake', 'Truffle Type', 'Primary Flavor', 'Secondary Flavor',\n",
       "       'Color Group', 'Customer', 'Date'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Recall the other descriptors we have\n",
    "descriptors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "H2ZozFp_SeWx",
    "outputId": "162f2b82-2ebb-41c5-8d8b-6df2ab8569cc"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Base Cake\n",
      "The pearsons chi-square test statistic: 448.81\n",
      "p-value of the test: 8.851450e-95\n",
      "the grand median: 0.21604872880760184\n",
      "\n",
      "Truffle Type\n",
      "The pearsons chi-square test statistic: 22.86\n",
      "p-value of the test: 1.088396e-05\n",
      "the grand median: 0.21604872880760184\n",
      "\n",
      "Primary Flavor\n",
      "The pearsons chi-square test statistic: 638.99\n",
      "p-value of the test: 3.918933e-103\n",
      "the grand median: 0.21604872880760184\n",
      "\n",
      "Secondary Flavor\n",
      "The pearsons chi-square test statistic: 323.13\n",
      "p-value of the test: 6.083210e-52\n",
      "the grand median: 0.21604872880760184\n",
      "\n",
      "Color Group\n",
      "The pearsons chi-square test statistic: 175.18\n",
      "p-value of the test: 1.011412e-31\n",
      "the grand median: 0.21604872880760184\n",
      "\n",
      "Customer\n",
      "The pearsons chi-square test statistic: 5.66\n",
      "p-value of the test: 2.257760e-01\n",
      "the grand median: 0.21604872880760184\n",
      "\n",
      "Date\n",
      "The pearsons chi-square test statistic: 5.27\n",
      "p-value of the test: 9.175929e-01\n",
      "the grand median: 0.21604872880760184\n",
      "\n"
     ]
    }
   ],
   "source": [
    "for desc in descriptors:\n",
    "\n",
    "  # YOUR CODE FORM MARGINS BELOW\n",
    "  gp = df.groupby(desc)\n",
    "  margins = [j['EBITDA/KG'].values for i, j in gp]\n",
    "\n",
    "  # UNPACK MARGINS INTO MEDIAN_TEST\n",
    "  stat, p, m, table = scipy.stats.median_test(*margins, correction=False)\n",
    "  print(desc)\n",
    "  print(\"The pearsons chi-square test statistic: {:.2f}\".format(stat))\n",
    "  print(\"p-value of the test: {:e}\".format(p))\n",
    "  print(\"the grand median: {}\".format(m), end='\\n\\n')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "sYwTWkVCm7jM"
   },
   "source": [
    "##### **Part D** Many boxplots\n",
    "\n",
    "And finally, we will confirm these visually. Complete the Boxplot for each group:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 1000
    },
    "id": "eEFvkzyQZtP2",
    "outputId": "a8470d0d-2368-4284-9d5c-d376e6d80738"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/wbeckner/anaconda3/envs/py39/lib/python3.9/site-packages/IPython/core/pylabtools.py:151: UserWarning: Glyph 9 (\t) missing from current font.\n",
      "  fig.canvas.print_figure(bytes_io, **kw)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for desc in descriptors:\n",
    "  fig, ax = plt.subplots(figsize=(10,5))\n",
    "  sns.boxplot(x=desc, y='EBITDA/KG', data=df, color='#A0cbe8', ax=ax)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "a2hegS_Q2g3K"
   },
   "source": [
    "### 2.1.3 What is a T-test?\n",
    "\n",
    "There are 1-sample and 2-sample T-tests \n",
    "\n",
    "_(note: we would use a 1-sample T-test just to determine if the sample mean is equal to a hypothesized population mean)_\n",
    "\n",
    "Within 2-sample T-tests we have **_independent_** and **_dependent_** T-tests (uncorrelated or correlated samples)\n",
    "\n",
    "For independent, two-sample T-tests:\n",
    "\n",
    "* **_Equal variance_** (or pooled) T-test\n",
    "  * `scipy.stats.ttest_ind(equal_var=True)`\n",
    "* **_Unequal variance_** T-test\n",
    "  * `scipy.stats.ttest_ind(equal_var=False)`\n",
    "  * also called ***Welch's T-test***\n",
    "\n",
    "<br>\n",
    "\n",
    "For dependent T-tests:\n",
    "* Paired (or correlated) T-test\n",
    "  * `scipy.stats.ttest_rel`\n",
    "\n",
    "A full discussion on T-tests is outside the scope of this session, but we can refer to wikipedia for more information, including formulas on how each statistic is computed:\n",
    "* [student's T-test](https://en.wikipedia.org/wiki/Student%27s_t-test#Dependent_t-test_for_paired_samples)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "RUTirNIp0VeC"
   },
   "source": [
    "#### 2.1.3.1 Demonstration of T-tests\n",
    "\n",
    "[back to top](#top)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "fWgpdHu3Mp19"
   },
   "source": [
    "We'll assume our shifts are of **_equal variance_** and proceed with the appropriate **_independent two-sample_** T-test..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "5mxktlT2NB8v",
    "outputId": "5919965b-4314-4838-b257-16967df96272"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[11, 14, 15, 16, 16, 16, 17, 18, 19, 21]\n",
      "[16, 17, 19, 20, 20, 20, 21, 22, 23, 23]\n"
     ]
    }
   ],
   "source": [
    "print(shift_one)\n",
    "print(shift_two)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "NymtMrgQ0FaD"
   },
   "source": [
    "To calculate the T-test, we follow a slightly different statistical formula:\n",
    "\n",
    "$T=\\frac{\\mu_1 - \\mu_2}{s\\sqrt{\\frac{1}{n_1} + \\frac{1}{n_2}}}$\n",
    "\n",
    "where $\\mu$ are the means of the two groups, $n$ are the sample sizes and $s$ is the pooled standard deviation, also known as the cummulative variance (depending on if you square it or not):\n",
    "\n",
    "$s= \\sqrt{\\frac{(n_1-1)\\sigma_1^2 + (n_2-1)\\sigma_2^2}{n_1 + n_2 - 2}}$\n",
    "\n",
    "where $\\sigma$ are the standard deviations. What you'll notice here is we are combining the two variances, we can only do this if we assume the variances are somewhat equal, this is known as the *equal variances* t-test."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "vsol_nFrNXBZ",
    "outputId": "118c737f-518c-4b0a-a051-07bf645c1d4e"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "16.3 20.1\n"
     ]
    }
   ],
   "source": [
    "mean_shift_one = np.mean(shift_one)\n",
    "mean_shift_two = np.mean(shift_two)\n",
    "\n",
    "print(mean_shift_one, mean_shift_two)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "WQpbuu9sQ_Ky",
    "outputId": "5500e04d-5b8d-4886-eed2-3539129d4424"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6.5\n"
     ]
    }
   ],
   "source": [
    "com_var = ((np.sum([(i - mean_shift_one)**2 for i in shift_one]) + \n",
    "            np.sum([(i - mean_shift_two)**2 for i in shift_two])) /\n",
    "            (len(shift_one) + len(shift_two)-2))\n",
    "print(com_var)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "id": "wOqV1VffNhFr"
   },
   "outputs": [],
   "source": [
    "T = (np.abs(mean_shift_one - mean_shift_two) / (\n",
    "     np.sqrt(com_var/len(shift_one) +\n",
    "     com_var/len(shift_two))))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "iGK1cLxvQl6e",
    "outputId": "c44c5339-89c1-493b-e7c6-1fa7fa1fc5d0"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.3328204733667115"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "eX2l-cJbB7fm"
   },
   "source": [
    "We see that this hand-computed result matches that of the `scipy` module:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "rgXWXjqIOPBm",
    "outputId": "267e4179-3c55-445d-aa63-f4a551aaaead"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ttest_indResult(statistic=3.3328204733667115, pvalue=0.0037029158660758575)"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scipy.stats.ttest_ind(shift_two, shift_one, equal_var=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Z5R6Gl9-Kmt_"
   },
   "source": [
    "### 2.1.4 What are F-statistics and the F-test?\n",
    "\n",
    "The F-statistic is simply a ratio of two variances, or the ratio of _mean squares_\n",
    "\n",
    "_mean squares_ is the estimate of population variance that accounts for the degrees of freedom to compute that estimate. \n",
    "\n",
    "We will explore this in the context of ANOVA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "QleTrLDgjYYy"
   },
   "source": [
    "#### 2.1.4.1 What is Analysis of Variance? \n",
    "\n",
    "ANOVA uses the F-test to determine whether the variability between group means is larger than the variability within the groups. If that statistic is large enough, you can conclude that the means of the groups are not equal.\n",
    "\n",
    "**The caveat is that ANOVA tells us whether there is a difference in means but it does not tell us where the difference is.** To find where the difference is between the groups, we have to conduct post-hoc tests.\n",
    "\n",
    "There are two main types:\n",
    "* One-way (one factor) and\n",
    "* Two-way (two factor) where factor is an independent variable\n",
    "\n",
    "<br>\n",
    "\n",
    "| Ind A | Ind B | Dep |\n",
    "|-------|-------|-----|\n",
    "| X     | H     | 10  |\n",
    "| X     | I     | 12  |\n",
    "| Y     | I     | 11  |\n",
    "| Y     | H     | 20  |\n",
    "\n",
    "<br>\n",
    "\n",
    "##### ANOVA Hypotheses\n",
    "\n",
    "* _Null hypothesis_: group means are equal\n",
    "* _Alternative hypothesis_: at least one group mean is different from the other groups\n",
    "\n",
    "##### ANOVA Assumptions\n",
    "\n",
    "* Residuals (experimental error) are normally distributed (test with Shapiro-Wilk)\n",
    "* Homogeneity of variances (variances are equal between groups) (test with Bartlett's)\n",
    "* Observations are sampled independently from each other\n",
    "* _Note: ANOVA assumptions can be checked using test statistics (e.g. Shapiro-Wilk, Bartlett’s, Levene’s test) and the visual approaches such as residual plots (e.g. QQ-plots) and histograms._\n",
    "\n",
    "##### Steps for ANOVA\n",
    "\n",
    "* Check sample sizes: equal observations must be in each group\n",
    "* Calculate Sum of Square between groups and within groups (\\\\(SS_B, SS_E\\\\))\n",
    "* Calculate Mean Square between groups and within groups (\\\\(MS_B, MS_E\\\\))\n",
    "* Calculate F value (\\\\(MS_B/MS_E\\\\))\n",
    "\n",
    "<br>\n",
    "\n",
    "This might be easier to see in a table:\n",
    "\n",
    "<br>\n",
    "\n",
    "| Source of Variation         | degree of freedom (Df) | Sum of squares (SS) | Mean square (MS)   | F value     |\n",
    "|-----------------------------|------------------------|---------------------|--------------------|-------------|\n",
    "| Between Groups             | Df_b = P-1             | SS_B                | MS_B = SS_B / Df_B | MS_B / MS_E |\n",
    "| Within Groups | Df_E = P(N-1)          | SS_E                | MS_E = SS_E / Df_E |             |\n",
    "| total                       | Df_T = PN-1            | SS_T           |                    |             |\n",
    "\n",
    "Where:\n",
    "$$ SS_B = \\sum_{i}^{P}{(\\bar{y}_i-\\bar{y})^2} $$\n",
    "<br>\n",
    "$$ SS_E = \\sum_{ik}^{PN}{(\\bar{y}_{ik}-\\bar{y}_i)^2} $$\n",
    "<br>\n",
    "$$ SS_T = SS_B + SS_E $$\n",
    "\n",
    "Let's go  back to our shift data to take an example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 283
    },
    "id": "NZEL5iUfTeNv",
    "outputId": "e8c37fde-e6b0-43cf-a759-abd0b2b05937"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 89,
     "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": [
    "shifts = pd.DataFrame([shift_one, shift_two, shift_three, shift_four]).T\n",
    "shifts.columns = ['A', 'B', 'C', 'D']\n",
    "shifts.boxplot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "NItJ8vbPWFKo"
   },
   "source": [
    "#### 2.1.4.2 SNS Boxplot\n",
    "\n",
    "this is another great way to view boxplot data. Notice how sns also shows us the raw data alongside the box and whiskers using a _swarmplot_."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 279
    },
    "id": "gBVbCptwUrdN",
    "outputId": "b8acc494-1a9c-4065-ab40-53b700555feb"
   },
   "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": [
    "shift_melt = pd.melt(shifts.reset_index(), id_vars=['index'], \n",
    "                     value_vars=['A', 'B', 'C', 'D'])\n",
    "shift_melt.columns = ['index', 'shift', 'rate']\n",
    "ax = sns.boxplot(x='shift', y='rate', data=shift_melt, color='#A0cbe8')\n",
    "ax = sns.swarmplot(x=\"shift\", y=\"rate\", data=shift_melt, color='#79706e')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "TlgRvZlEGt2l"
   },
   "source": [
    "Anyway back to ANOVA..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "SX5wvWAxV_XC",
    "outputId": "c7b8e464-db2d-48e6-edb7-bacd9b06bb53"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5.599173553719008 0.0029473487978665873\n"
     ]
    }
   ],
   "source": [
    "fvalue, pvalue = stats.f_oneway(shifts['A'], \n",
    "                                shifts['B'],\n",
    "                                shifts['C'],\n",
    "                                shifts['D'])\n",
    "print(fvalue, pvalue)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ywXmwS-aY4YM"
   },
   "source": [
    "We can get this in the format of the table we saw above:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 112
    },
    "id": "sC_-cfKqYnQp",
    "outputId": "42f24caf-2347-473f-da5d-2f575be1b9c0"
   },
   "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(shift)</th>\n",
       "      <td>135.5</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.599174</td>\n",
       "      <td>0.002947</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Residual</th>\n",
       "      <td>290.4</td>\n",
       "      <td>36.0</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(shift)   135.5   3.0  5.599174  0.002947\n",
       "Residual   290.4  36.0       NaN       NaN"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# get ANOVA table \n",
    "import statsmodels.api as sm\n",
    "from statsmodels.formula.api import ols\n",
    "\n",
    "# Ordinary Least Squares (OLS) model\n",
    "model = ols('rate ~ C(shift)', data=shift_melt).fit()\n",
    "anova_table = sm.stats.anova_lm(model, typ=2)\n",
    "anova_table\n",
    "# output (ANOVA F and p value)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "pW5Vx6VWdNxw"
   },
   "source": [
    "The **_Shapiro-Wilk_** test can be used to check the _normal distribution of residuals_. Null hypothesis: data is drawn from normal distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "phB9lnHddQv1",
    "outputId": "57040c36-89eb-4154-9a23-6c7c84150007"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9750654697418213 0.5121709108352661\n"
     ]
    }
   ],
   "source": [
    "w, pvalue = stats.shapiro(model.resid)\n",
    "print(w, pvalue)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "0xRqtKixd1MT"
   },
   "source": [
    "We can use **_Bartlett’s_** test to check the _Homogeneity of variances_. Null hypothesis: samples from populations have equal variances."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "z2sya2JMd2IJ",
    "outputId": "bc968c92-82c0-4497-ac6f-92d80845ca70"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.3763632854696672 0.711084540821183\n"
     ]
    }
   ],
   "source": [
    "w, pvalue = stats.bartlett(shifts['A'], \n",
    "                           shifts['B'], \n",
    "                           shifts['C'], \n",
    "                           shifts['D'])\n",
    "print(w, pvalue)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "mJlzhEk7ar6t"
   },
   "source": [
    "#### 2.1.4.3 ANOVA Interpretation\n",
    "\n",
    "The _p_ value form ANOVA analysis is significant (_p_ < 0.05) and we can conclude there are significant difference between the shifts. But we do not know which shift(s) are different. For this we need to perform a post hoc test. There are a multitude of these that are beyond the scope of this discussion ([Tukey-kramer](https://www.real-statistics.com/one-way-analysis-of-variance-anova/unplanned-comparisons/tukey-kramer-test/) is one such test) \n",
    "\n",
    "<p align=center>\n",
    "<img src=\"https://media.tenor.com/images/4da4d46c8df02570a9a1219cac42bf27/tenor.gif\"></img>\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "_vh_d3ENIImT"
   },
   "source": [
    "### 2.1.5 Putting it all together\n",
    "\n",
    "In summary, there are many statistical tests at our disposal when performing inferential statistical analysis. In times like these, a simple decision tree can be extraordinarily useful!\n",
    "\n",
    "<img src=\"https://cdn.scribbr.com/wp-content/uploads//2020/01/flowchart-for-choosing-a-statistical-test.png\" width=800px></img>\n",
    "\n",
    "<small>source: [scribbr](https://www.scribbr.com/statistics/statistical-tests/)</small>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "uNnqPwXqaAEA"
   },
   "source": [
    "## 🍒 2.2 Enrichment: Evaluate statistical significance of product margin: a snake in the garden"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "X1i4SQ0y2p4Q"
   },
   "source": [
    "### 2.2.1 Mood's Median on product descriptors\n",
    "\n",
    "The first issue we run into with moods is... what? \n",
    "\n",
    "We can only perform moods on two groups at a time. How can we get around this?\n",
    "\n",
    "Let's take a look at the category with the fewest descriptors. If we remember, this was the Truffle Types."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "TqfEEjXbVCTo",
    "outputId": "387a8af8-6296-48be-827e-e5a1cf66e12c"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['Base Cake', 'Truffle Type', 'Primary Flavor', 'Secondary Flavor',\n",
       "       'Color Group', 'Customer', 'Date', 'KG', 'EBITDA/KG'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "iKAlINvT2n2E",
    "outputId": "806bcf2a-5a08-4697-d7ce-e80d1fe21a0d"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['Candy Outer', 'Chocolate Outer', 'Jelly Filled'], dtype=object)"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['Truffle Type'].unique()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "Gsm0QCeywlou",
    "outputId": "617aef39-f7d4-4498-ca9e-fcc0a6b01940"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Candy Outer: N=288\n",
      "Welch's T-Test for Unequal Variances\n",
      "Ttest_indResult(statistic=-2.7615297773427474, pvalue=0.0059110489226580736)\n",
      "\n",
      "Chocolate Outer: N=1356\n",
      "Welch's T-Test for Unequal Variances\n",
      "Ttest_indResult(statistic=4.409449025092911, pvalue=1.1932685612874952e-05)\n",
      "\n",
      "Jelly Filled: N=24\n",
      "Welch's T-Test for Unequal Variances\n",
      "Ttest_indResult(statistic=-8.414252306793504, pvalue=7.929912531660087e-09)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "col = 'Truffle Type'\n",
    "moodsdf = pd.DataFrame()\n",
    "for truff in df[col].unique():\n",
    "  \n",
    "  # for each \n",
    "  group = df.loc[df[col] == truff]['EBITDA/KG']\n",
    "  pop = df.loc[~(df[col] == truff)]['EBITDA/KG']\n",
    "  stat, p, m, table = scipy.stats.median_test(group, pop)\n",
    "  median = np.median(group)\n",
    "  mean = np.mean(group)\n",
    "  size = len(group)\n",
    "  print(\"{}: N={}\".format(truff, size))\n",
    "  print(\"Welch's T-Test for Unequal Variances\")\n",
    "  print(scipy.stats.ttest_ind(group, pop, equal_var=False))\n",
    "  welchp = scipy.stats.ttest_ind(group, pop, equal_var=False).pvalue\n",
    "  print()\n",
    "  moodsdf = pd.concat([moodsdf, \n",
    "                            pd.DataFrame([truff, \n",
    "                                          stat, p, m, mean, median, size,\n",
    "                                          welchp, table]).T])\n",
    "moodsdf.columns = [col, 'pearsons_chi_square', 'p_value', \n",
    "              'grand_median', 'group_mean', 'group_median', 'size', 'welch p',\n",
    "              'table']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "N747uVxhEGEP"
   },
   "source": [
    "### 🙋‍♀️ Question 1: Moods Results on Truffle Type\n",
    "\n",
    "> What do we notice about the resultant table?\n",
    "\n",
    "* **_p-values_** Most are quite small (really low probability of achieving these table results under a single distribution)\n",
    "* group sizes: our Jelly Filled group is relatively small"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 143
    },
    "id": "DGaZNDDSxHeP",
    "outputId": "a1259518-5345-4cb5-aeef-660ec239504d"
   },
   "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>Truffle Type</th>\n",
       "      <th>pearsons_chi_square</th>\n",
       "      <th>p_value</th>\n",
       "      <th>grand_median</th>\n",
       "      <th>group_mean</th>\n",
       "      <th>group_median</th>\n",
       "      <th>size</th>\n",
       "      <th>welch p</th>\n",
       "      <th>table</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Jelly Filled</td>\n",
       "      <td>18.643248</td>\n",
       "      <td>0.000016</td>\n",
       "      <td>0.216049</td>\n",
       "      <td>0.051382</td>\n",
       "      <td>0.017933</td>\n",
       "      <td>24</td>\n",
       "      <td>0.0</td>\n",
       "      <td>[[1, 833], [23, 811]]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Chocolate Outer</td>\n",
       "      <td>6.627496</td>\n",
       "      <td>0.010042</td>\n",
       "      <td>0.216049</td>\n",
       "      <td>0.262601</td>\n",
       "      <td>0.225562</td>\n",
       "      <td>1356</td>\n",
       "      <td>0.000012</td>\n",
       "      <td>[[699, 135], [657, 177]]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Candy Outer</td>\n",
       "      <td>1.515066</td>\n",
       "      <td>0.218368</td>\n",
       "      <td>0.216049</td>\n",
       "      <td>0.230075</td>\n",
       "      <td>0.204264</td>\n",
       "      <td>288</td>\n",
       "      <td>0.005911</td>\n",
       "      <td>[[134, 700], [154, 680]]</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      Truffle Type pearsons_chi_square   p_value grand_median group_mean  \\\n",
       "0     Jelly Filled           18.643248  0.000016     0.216049   0.051382   \n",
       "0  Chocolate Outer            6.627496  0.010042     0.216049   0.262601   \n",
       "0      Candy Outer            1.515066  0.218368     0.216049   0.230075   \n",
       "\n",
       "  group_median  size   welch p                     table  \n",
       "0     0.017933    24       0.0     [[1, 833], [23, 811]]  \n",
       "0     0.225562  1356  0.000012  [[699, 135], [657, 177]]  \n",
       "0     0.204264   288  0.005911  [[134, 700], [154, 680]]  "
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "moodsdf.sort_values('p_value')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "mawPQ2p5xW1O"
   },
   "source": [
    "We can go ahead and repeat this analysis for all of our product categories:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "X7PmQ04oVZRi",
    "outputId": "3be2f506-4fde-4db0-ea91-de4d4c7379f4"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['Base Cake', 'Truffle Type', 'Primary Flavor', 'Secondary Flavor',\n",
       "       'Color Group'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.columns[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "HjTW8SGsvKdF",
    "outputId": "f9629bd3-b47a-4e5d-c64a-6926e867386a"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(101, 10)\n"
     ]
    }
   ],
   "source": [
    "moodsdf = pd.DataFrame()\n",
    "for col in df.columns[:5]:\n",
    "  for truff in df[col].unique():\n",
    "    group = df.loc[df[col] == truff]['EBITDA/KG']\n",
    "    pop = df.loc[~(df[col] == truff)]['EBITDA/KG']\n",
    "    stat, p, m, table = scipy.stats.median_test(group, pop)\n",
    "    median = np.median(group)\n",
    "    mean = np.mean(group)\n",
    "    size = len(group)\n",
    "    welchp = scipy.stats.ttest_ind(group, pop, equal_var=False).pvalue\n",
    "    moodsdf = pd.concat([moodsdf, \n",
    "                              pd.DataFrame([col, truff, \n",
    "                                            stat, p, m, mean, median, size,\n",
    "                                            welchp, table]).T])\n",
    "moodsdf.columns = ['descriptor', 'group', 'pearsons_chi_square', 'p_value', \n",
    "                'grand_median', 'group_mean', 'group_median', 'size', 'welch p',\n",
    "                'table']\n",
    "print(moodsdf.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "h-4GZ5bSvn6f",
    "outputId": "6b7705c5-2468-47cf-ff85-1142630984ac"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(51, 10)\n"
     ]
    }
   ],
   "source": [
    "moodsdf = moodsdf.loc[(moodsdf['welch p'] < 0.005) &\n",
    "            (moodsdf['p_value'] < 0.005)].sort_values('group_median')\n",
    "\n",
    "moodsdf = moodsdf.sort_values('group_median').reset_index(drop=True)\n",
    "print(moodsdf.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 1000
    },
    "id": "V6Rm8Ju82TKd",
    "outputId": "0fe6952f-51b9-4fd9-998f-15fefb5311db"
   },
   "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>descriptor</th>\n",
       "      <th>group</th>\n",
       "      <th>pearsons_chi_square</th>\n",
       "      <th>p_value</th>\n",
       "      <th>grand_median</th>\n",
       "      <th>group_mean</th>\n",
       "      <th>group_median</th>\n",
       "      <th>size</th>\n",
       "      <th>welch p</th>\n",
       "      <th>table</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Secondary Flavor</td>\n",
       "      <td>Papaya</td>\n",
       "      <td>18.643248</td>\n",
       "      <td>0.000016</td>\n",
       "      <td>0.216049</td>\n",
       "      <td>0.016747</td>\n",
       "      <td>0.002458</td>\n",
       "      <td>24</td>\n",
       "      <td>0.0</td>\n",
       "      <td>[[1, 833], [23, 811]]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Primary Flavor</td>\n",
       "      <td>Orange Pineapple\\tP</td>\n",
       "      <td>18.643248</td>\n",
       "      <td>0.000016</td>\n",
       "      <td>0.216049</td>\n",
       "      <td>0.016747</td>\n",
       "      <td>0.002458</td>\n",
       "      <td>24</td>\n",
       "      <td>0.0</td>\n",
       "      <td>[[1, 833], [23, 811]]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Primary Flavor</td>\n",
       "      <td>Cherry Cream Spice</td>\n",
       "      <td>10.156401</td>\n",
       "      <td>0.001438</td>\n",
       "      <td>0.216049</td>\n",
       "      <td>0.018702</td>\n",
       "      <td>0.009701</td>\n",
       "      <td>12</td>\n",
       "      <td>0.000001</td>\n",
       "      <td>[[0, 834], [12, 822]]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Secondary Flavor</td>\n",
       "      <td>Cucumber</td>\n",
       "      <td>18.643248</td>\n",
       "      <td>0.000016</td>\n",
       "      <td>0.216049</td>\n",
       "      <td>0.051382</td>\n",
       "      <td>0.017933</td>\n",
       "      <td>24</td>\n",
       "      <td>0.0</td>\n",
       "      <td>[[1, 833], [23, 811]]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Truffle Type</td>\n",
       "      <td>Jelly Filled</td>\n",
       "      <td>18.643248</td>\n",
       "      <td>0.000016</td>\n",
       "      <td>0.216049</td>\n",
       "      <td>0.051382</td>\n",
       "      <td>0.017933</td>\n",
       "      <td>24</td>\n",
       "      <td>0.0</td>\n",
       "      <td>[[1, 833], [23, 811]]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Primary Flavor</td>\n",
       "      <td>Orange</td>\n",
       "      <td>18.643248</td>\n",
       "      <td>0.000016</td>\n",
       "      <td>0.216049</td>\n",
       "      <td>0.051382</td>\n",
       "      <td>0.017933</td>\n",
       "      <td>24</td>\n",
       "      <td>0.0</td>\n",
       "      <td>[[1, 833], [23, 811]]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>Primary Flavor</td>\n",
       "      <td>Toasted Coconut</td>\n",
       "      <td>15.261253</td>\n",
       "      <td>0.000094</td>\n",
       "      <td>0.216049</td>\n",
       "      <td>0.037002</td>\n",
       "      <td>0.028392</td>\n",
       "      <td>24</td>\n",
       "      <td>0.0</td>\n",
       "      <td>[[2, 832], [22, 812]]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>Secondary Flavor</td>\n",
       "      <td>Apricot</td>\n",
       "      <td>15.261253</td>\n",
       "      <td>0.000094</td>\n",
       "      <td>0.216049</td>\n",
       "      <td>0.060312</td>\n",
       "      <td>0.037422</td>\n",
       "      <td>24</td>\n",
       "      <td>0.0</td>\n",
       "      <td>[[2, 832], [22, 812]]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>Primary Flavor</td>\n",
       "      <td>Kettle Corn</td>\n",
       "      <td>29.062065</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.216049</td>\n",
       "      <td>0.055452</td>\n",
       "      <td>0.045891</td>\n",
       "      <td>60</td>\n",
       "      <td>0.0</td>\n",
       "      <td>[[9, 825], [51, 783]]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>Primary Flavor</td>\n",
       "      <td>Acai Berry</td>\n",
       "      <td>18.643248</td>\n",
       "      <td>0.000016</td>\n",
       "      <td>0.216049</td>\n",
       "      <td>0.036505</td>\n",
       "      <td>0.049466</td>\n",
       "      <td>24</td>\n",
       "      <td>0.0</td>\n",
       "      <td>[[1, 833], [23, 811]]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>Primary Flavor</td>\n",
       "      <td>Pink Lemonade</td>\n",
       "      <td>10.156401</td>\n",
       "      <td>0.001438</td>\n",
       "      <td>0.216049</td>\n",
       "      <td>0.039862</td>\n",
       "      <td>0.056349</td>\n",
       "      <td>12</td>\n",
       "      <td>0.000011</td>\n",
       "      <td>[[0, 834], [12, 822]]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>Secondary Flavor</td>\n",
       "      <td>Black Cherry</td>\n",
       "      <td>58.900366</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.216049</td>\n",
       "      <td>0.055975</td>\n",
       "      <td>0.062898</td>\n",
       "      <td>96</td>\n",
       "      <td>0.0</td>\n",
       "      <td>[[11, 823], [85, 749]]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>Primary Flavor</td>\n",
       "      <td>Watermelon</td>\n",
       "      <td>15.261253</td>\n",
       "      <td>0.000094</td>\n",
       "      <td>0.216049</td>\n",
       "      <td>0.04405</td>\n",
       "      <td>0.067896</td>\n",
       "      <td>24</td>\n",
       "      <td>0.0</td>\n",
       "      <td>[[2, 832], [22, 812]]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>Primary Flavor</td>\n",
       "      <td>Plum</td>\n",
       "      <td>34.851608</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.216049</td>\n",
       "      <td>0.084963</td>\n",
       "      <td>0.079993</td>\n",
       "      <td>72</td>\n",
       "      <td>0.0</td>\n",
       "      <td>[[11, 823], [61, 773]]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>Secondary Flavor</td>\n",
       "      <td>Dill Pickle</td>\n",
       "      <td>10.156401</td>\n",
       "      <td>0.001438</td>\n",
       "      <td>0.216049</td>\n",
       "      <td>0.037042</td>\n",
       "      <td>0.082494</td>\n",
       "      <td>12</td>\n",
       "      <td>0.000007</td>\n",
       "      <td>[[0, 834], [12, 822]]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>Primary Flavor</td>\n",
       "      <td>Horchata</td>\n",
       "      <td>10.156401</td>\n",
       "      <td>0.001438</td>\n",
       "      <td>0.216049</td>\n",
       "      <td>0.037042</td>\n",
       "      <td>0.082494</td>\n",
       "      <td>12</td>\n",
       "      <td>0.000007</td>\n",
       "      <td>[[0, 834], [12, 822]]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>Primary Flavor</td>\n",
       "      <td>Lemon Custard</td>\n",
       "      <td>12.217457</td>\n",
       "      <td>0.000473</td>\n",
       "      <td>0.216049</td>\n",
       "      <td>0.079389</td>\n",
       "      <td>0.087969</td>\n",
       "      <td>24</td>\n",
       "      <td>0.000006</td>\n",
       "      <td>[[3, 831], [21, 813]]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>Primary Flavor</td>\n",
       "      <td>Fruit Punch</td>\n",
       "      <td>10.156401</td>\n",
       "      <td>0.001438</td>\n",
       "      <td>0.216049</td>\n",
       "      <td>0.078935</td>\n",
       "      <td>0.090326</td>\n",
       "      <td>12</td>\n",
       "      <td>0.000076</td>\n",
       "      <td>[[0, 834], [12, 822]]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>Base Cake</td>\n",
       "      <td>Chiffon</td>\n",
       "      <td>117.046226</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.216049</td>\n",
       "      <td>0.127851</td>\n",
       "      <td>0.125775</td>\n",
       "      <td>288</td>\n",
       "      <td>0.0</td>\n",
       "      <td>[[60, 774], [228, 606]]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>Base Cake</td>\n",
       "      <td>Butter</td>\n",
       "      <td>134.36727</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.216049</td>\n",
       "      <td>0.142082</td>\n",
       "      <td>0.139756</td>\n",
       "      <td>456</td>\n",
       "      <td>0.0</td>\n",
       "      <td>[[122, 712], [334, 500]]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>Secondary Flavor</td>\n",
       "      <td>Banana</td>\n",
       "      <td>10.805348</td>\n",
       "      <td>0.001012</td>\n",
       "      <td>0.216049</td>\n",
       "      <td>0.163442</td>\n",
       "      <td>0.15537</td>\n",
       "      <td>60</td>\n",
       "      <td>0.0</td>\n",
       "      <td>[[17, 817], [43, 791]]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>Primary Flavor</td>\n",
       "      <td>Cream Soda</td>\n",
       "      <td>9.511861</td>\n",
       "      <td>0.002041</td>\n",
       "      <td>0.216049</td>\n",
       "      <td>0.150265</td>\n",
       "      <td>0.163455</td>\n",
       "      <td>24</td>\n",
       "      <td>0.000002</td>\n",
       "      <td>[[4, 830], [20, 814]]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>Secondary Flavor</td>\n",
       "      <td>Peppermint</td>\n",
       "      <td>9.511861</td>\n",
       "      <td>0.002041</td>\n",
       "      <td>0.216049</td>\n",
       "      <td>0.150265</td>\n",
       "      <td>0.163455</td>\n",
       "      <td>24</td>\n",
       "      <td>0.000002</td>\n",
       "      <td>[[4, 830], [20, 814]]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>Primary Flavor</td>\n",
       "      <td>Grand Mariner</td>\n",
       "      <td>10.581767</td>\n",
       "      <td>0.001142</td>\n",
       "      <td>0.216049</td>\n",
       "      <td>0.197463</td>\n",
       "      <td>0.165529</td>\n",
       "      <td>72</td>\n",
       "      <td>0.000829</td>\n",
       "      <td>[[22, 812], [50, 784]]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>Color Group</td>\n",
       "      <td>Amethyst</td>\n",
       "      <td>20.488275</td>\n",
       "      <td>0.000006</td>\n",
       "      <td>0.216049</td>\n",
       "      <td>0.195681</td>\n",
       "      <td>0.167321</td>\n",
       "      <td>300</td>\n",
       "      <td>0.0</td>\n",
       "      <td>[[114, 720], [186, 648]]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>Color Group</td>\n",
       "      <td>Burgundy</td>\n",
       "      <td>10.999677</td>\n",
       "      <td>0.000911</td>\n",
       "      <td>0.216049</td>\n",
       "      <td>0.193048</td>\n",
       "      <td>0.171465</td>\n",
       "      <td>120</td>\n",
       "      <td>0.000406</td>\n",
       "      <td>[[42, 792], [78, 756]]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>Color Group</td>\n",
       "      <td>White</td>\n",
       "      <td>35.76526</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.216049</td>\n",
       "      <td>0.19</td>\n",
       "      <td>0.177264</td>\n",
       "      <td>432</td>\n",
       "      <td>0.0</td>\n",
       "      <td>[[162, 672], [270, 564]]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>Color Group</td>\n",
       "      <td>Opal</td>\n",
       "      <td>11.587164</td>\n",
       "      <td>0.000664</td>\n",
       "      <td>0.216049</td>\n",
       "      <td>0.317878</td>\n",
       "      <td>0.259304</td>\n",
       "      <td>324</td>\n",
       "      <td>0.0</td>\n",
       "      <td>[[190, 644], [134, 700]]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>Secondary Flavor</td>\n",
       "      <td>Apple</td>\n",
       "      <td>27.283292</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.216049</td>\n",
       "      <td>0.326167</td>\n",
       "      <td>0.293876</td>\n",
       "      <td>36</td>\n",
       "      <td>0.001176</td>\n",
       "      <td>[[34, 800], [2, 832]]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>Secondary Flavor</td>\n",
       "      <td>Tangerine</td>\n",
       "      <td>32.626389</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.216049</td>\n",
       "      <td>0.342314</td>\n",
       "      <td>0.319273</td>\n",
       "      <td>48</td>\n",
       "      <td>0.000113</td>\n",
       "      <td>[[44, 790], [4, 830]]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>Secondary Flavor</td>\n",
       "      <td>Black Currant</td>\n",
       "      <td>34.778391</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.216049</td>\n",
       "      <td>0.357916</td>\n",
       "      <td>0.332449</td>\n",
       "      <td>36</td>\n",
       "      <td>0.0</td>\n",
       "      <td>[[36, 798], [0, 834]]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>Secondary Flavor</td>\n",
       "      <td>Pear</td>\n",
       "      <td>16.614303</td>\n",
       "      <td>0.000046</td>\n",
       "      <td>0.216049</td>\n",
       "      <td>0.373034</td>\n",
       "      <td>0.33831</td>\n",
       "      <td>60</td>\n",
       "      <td>0.000031</td>\n",
       "      <td>[[46, 788], [14, 820]]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>Primary Flavor</td>\n",
       "      <td>Vanilla</td>\n",
       "      <td>34.778391</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.216049</td>\n",
       "      <td>0.378053</td>\n",
       "      <td>0.341626</td>\n",
       "      <td>36</td>\n",
       "      <td>0.000001</td>\n",
       "      <td>[[36, 798], [0, 834]]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>Color Group</td>\n",
       "      <td>Citrine</td>\n",
       "      <td>10.156401</td>\n",
       "      <td>0.001438</td>\n",
       "      <td>0.216049</td>\n",
       "      <td>0.390728</td>\n",
       "      <td>0.342512</td>\n",
       "      <td>12</td>\n",
       "      <td>0.001925</td>\n",
       "      <td>[[12, 822], [0, 834]]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>Color Group</td>\n",
       "      <td>Teal</td>\n",
       "      <td>13.539679</td>\n",
       "      <td>0.000234</td>\n",
       "      <td>0.216049</td>\n",
       "      <td>0.323955</td>\n",
       "      <td>0.3446</td>\n",
       "      <td>96</td>\n",
       "      <td>0.00121</td>\n",
       "      <td>[[66, 768], [30, 804]]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>Base Cake</td>\n",
       "      <td>Tiramisu</td>\n",
       "      <td>52.360619</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.216049</td>\n",
       "      <td>0.388267</td>\n",
       "      <td>0.362102</td>\n",
       "      <td>144</td>\n",
       "      <td>0.0</td>\n",
       "      <td>[[114, 720], [30, 804]]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>Primary Flavor</td>\n",
       "      <td>Doughnut</td>\n",
       "      <td>74.935256</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.216049</td>\n",
       "      <td>0.439721</td>\n",
       "      <td>0.379361</td>\n",
       "      <td>108</td>\n",
       "      <td>0.0</td>\n",
       "      <td>[[98, 736], [10, 824]]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>Secondary Flavor</td>\n",
       "      <td>Ginger Beer</td>\n",
       "      <td>22.363443</td>\n",
       "      <td>0.000002</td>\n",
       "      <td>0.216049</td>\n",
       "      <td>0.444895</td>\n",
       "      <td>0.382283</td>\n",
       "      <td>24</td>\n",
       "      <td>0.000481</td>\n",
       "      <td>[[24, 810], [0, 834]]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>Color Group</td>\n",
       "      <td>Rose</td>\n",
       "      <td>18.643248</td>\n",
       "      <td>0.000016</td>\n",
       "      <td>0.216049</td>\n",
       "      <td>0.42301</td>\n",
       "      <td>0.407061</td>\n",
       "      <td>24</td>\n",
       "      <td>0.000062</td>\n",
       "      <td>[[23, 811], [1, 833]]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>Base Cake</td>\n",
       "      <td>Cheese</td>\n",
       "      <td>66.804744</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.216049</td>\n",
       "      <td>0.450934</td>\n",
       "      <td>0.435638</td>\n",
       "      <td>84</td>\n",
       "      <td>0.0</td>\n",
       "      <td>[[79, 755], [5, 829]]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>Primary Flavor</td>\n",
       "      <td>Butter Toffee</td>\n",
       "      <td>60.181468</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.216049</td>\n",
       "      <td>0.50366</td>\n",
       "      <td>0.456343</td>\n",
       "      <td>60</td>\n",
       "      <td>0.0</td>\n",
       "      <td>[[60, 774], [0, 834]]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td>Color Group</td>\n",
       "      <td>Slate</td>\n",
       "      <td>10.156401</td>\n",
       "      <td>0.001438</td>\n",
       "      <td>0.216049</td>\n",
       "      <td>0.540214</td>\n",
       "      <td>0.483138</td>\n",
       "      <td>12</td>\n",
       "      <td>0.000017</td>\n",
       "      <td>[[12, 822], [0, 834]]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>Primary Flavor</td>\n",
       "      <td>Gingersnap</td>\n",
       "      <td>22.363443</td>\n",
       "      <td>0.000002</td>\n",
       "      <td>0.216049</td>\n",
       "      <td>0.643218</td>\n",
       "      <td>0.623627</td>\n",
       "      <td>24</td>\n",
       "      <td>0.0</td>\n",
       "      <td>[[24, 810], [0, 834]]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>43</th>\n",
       "      <td>Primary Flavor</td>\n",
       "      <td>Dill Pickle</td>\n",
       "      <td>22.363443</td>\n",
       "      <td>0.000002</td>\n",
       "      <td>0.216049</td>\n",
       "      <td>0.642239</td>\n",
       "      <td>0.655779</td>\n",
       "      <td>24</td>\n",
       "      <td>0.0</td>\n",
       "      <td>[[24, 810], [0, 834]]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>44</th>\n",
       "      <td>Color Group</td>\n",
       "      <td>Olive</td>\n",
       "      <td>44.967537</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.216049</td>\n",
       "      <td>0.637627</td>\n",
       "      <td>0.670186</td>\n",
       "      <td>60</td>\n",
       "      <td>0.0</td>\n",
       "      <td>[[56, 778], [4, 830]]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45</th>\n",
       "      <td>Primary Flavor</td>\n",
       "      <td>Butter Milk</td>\n",
       "      <td>10.156401</td>\n",
       "      <td>0.001438</td>\n",
       "      <td>0.216049</td>\n",
       "      <td>0.699284</td>\n",
       "      <td>0.688601</td>\n",
       "      <td>12</td>\n",
       "      <td>0.0</td>\n",
       "      <td>[[12, 822], [0, 834]]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46</th>\n",
       "      <td>Base Cake</td>\n",
       "      <td>Sponge</td>\n",
       "      <td>127.156266</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.216049</td>\n",
       "      <td>0.698996</td>\n",
       "      <td>0.699355</td>\n",
       "      <td>120</td>\n",
       "      <td>0.0</td>\n",
       "      <td>[[120, 714], [0, 834]]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td>Primary Flavor</td>\n",
       "      <td>Chocolate Mint</td>\n",
       "      <td>10.156401</td>\n",
       "      <td>0.001438</td>\n",
       "      <td>0.216049</td>\n",
       "      <td>0.685546</td>\n",
       "      <td>0.699666</td>\n",
       "      <td>12</td>\n",
       "      <td>0.0</td>\n",
       "      <td>[[12, 822], [0, 834]]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>48</th>\n",
       "      <td>Primary Flavor</td>\n",
       "      <td>Coconut</td>\n",
       "      <td>10.156401</td>\n",
       "      <td>0.001438</td>\n",
       "      <td>0.216049</td>\n",
       "      <td>0.732777</td>\n",
       "      <td>0.717641</td>\n",
       "      <td>12</td>\n",
       "      <td>0.0</td>\n",
       "      <td>[[12, 822], [0, 834]]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>49</th>\n",
       "      <td>Primary Flavor</td>\n",
       "      <td>Blueberry</td>\n",
       "      <td>22.363443</td>\n",
       "      <td>0.000002</td>\n",
       "      <td>0.216049</td>\n",
       "      <td>0.759643</td>\n",
       "      <td>0.72536</td>\n",
       "      <td>24</td>\n",
       "      <td>0.0</td>\n",
       "      <td>[[24, 810], [0, 834]]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50</th>\n",
       "      <td>Primary Flavor</td>\n",
       "      <td>Amaretto</td>\n",
       "      <td>10.156401</td>\n",
       "      <td>0.001438</td>\n",
       "      <td>0.216049</td>\n",
       "      <td>0.782156</td>\n",
       "      <td>0.764845</td>\n",
       "      <td>12</td>\n",
       "      <td>0.0</td>\n",
       "      <td>[[12, 822], [0, 834]]</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          descriptor                group pearsons_chi_square   p_value  \\\n",
       "0   Secondary Flavor               Papaya           18.643248  0.000016   \n",
       "1     Primary Flavor  Orange Pineapple\\tP           18.643248  0.000016   \n",
       "2     Primary Flavor   Cherry Cream Spice           10.156401  0.001438   \n",
       "3   Secondary Flavor             Cucumber           18.643248  0.000016   \n",
       "4       Truffle Type         Jelly Filled           18.643248  0.000016   \n",
       "5     Primary Flavor               Orange           18.643248  0.000016   \n",
       "6     Primary Flavor      Toasted Coconut           15.261253  0.000094   \n",
       "7   Secondary Flavor              Apricot           15.261253  0.000094   \n",
       "8     Primary Flavor          Kettle Corn           29.062065       0.0   \n",
       "9     Primary Flavor           Acai Berry           18.643248  0.000016   \n",
       "10    Primary Flavor        Pink Lemonade           10.156401  0.001438   \n",
       "11  Secondary Flavor         Black Cherry           58.900366       0.0   \n",
       "12    Primary Flavor           Watermelon           15.261253  0.000094   \n",
       "13    Primary Flavor                 Plum           34.851608       0.0   \n",
       "14  Secondary Flavor          Dill Pickle           10.156401  0.001438   \n",
       "15    Primary Flavor             Horchata           10.156401  0.001438   \n",
       "16    Primary Flavor        Lemon Custard           12.217457  0.000473   \n",
       "17    Primary Flavor          Fruit Punch           10.156401  0.001438   \n",
       "18         Base Cake              Chiffon          117.046226       0.0   \n",
       "19         Base Cake               Butter           134.36727       0.0   \n",
       "20  Secondary Flavor               Banana           10.805348  0.001012   \n",
       "21    Primary Flavor           Cream Soda            9.511861  0.002041   \n",
       "22  Secondary Flavor           Peppermint            9.511861  0.002041   \n",
       "23    Primary Flavor        Grand Mariner           10.581767  0.001142   \n",
       "24       Color Group             Amethyst           20.488275  0.000006   \n",
       "25       Color Group             Burgundy           10.999677  0.000911   \n",
       "26       Color Group                White            35.76526       0.0   \n",
       "27       Color Group                 Opal           11.587164  0.000664   \n",
       "28  Secondary Flavor                Apple           27.283292       0.0   \n",
       "29  Secondary Flavor            Tangerine           32.626389       0.0   \n",
       "30  Secondary Flavor        Black Currant           34.778391       0.0   \n",
       "31  Secondary Flavor                 Pear           16.614303  0.000046   \n",
       "32    Primary Flavor              Vanilla           34.778391       0.0   \n",
       "33       Color Group              Citrine           10.156401  0.001438   \n",
       "34       Color Group                 Teal           13.539679  0.000234   \n",
       "35         Base Cake             Tiramisu           52.360619       0.0   \n",
       "36    Primary Flavor             Doughnut           74.935256       0.0   \n",
       "37  Secondary Flavor          Ginger Beer           22.363443  0.000002   \n",
       "38       Color Group                 Rose           18.643248  0.000016   \n",
       "39         Base Cake               Cheese           66.804744       0.0   \n",
       "40    Primary Flavor        Butter Toffee           60.181468       0.0   \n",
       "41       Color Group                Slate           10.156401  0.001438   \n",
       "42    Primary Flavor           Gingersnap           22.363443  0.000002   \n",
       "43    Primary Flavor          Dill Pickle           22.363443  0.000002   \n",
       "44       Color Group                Olive           44.967537       0.0   \n",
       "45    Primary Flavor          Butter Milk           10.156401  0.001438   \n",
       "46         Base Cake               Sponge          127.156266       0.0   \n",
       "47    Primary Flavor       Chocolate Mint           10.156401  0.001438   \n",
       "48    Primary Flavor              Coconut           10.156401  0.001438   \n",
       "49    Primary Flavor            Blueberry           22.363443  0.000002   \n",
       "50    Primary Flavor             Amaretto           10.156401  0.001438   \n",
       "\n",
       "   grand_median group_mean group_median size   welch p  \\\n",
       "0      0.216049   0.016747     0.002458   24       0.0   \n",
       "1      0.216049   0.016747     0.002458   24       0.0   \n",
       "2      0.216049   0.018702     0.009701   12  0.000001   \n",
       "3      0.216049   0.051382     0.017933   24       0.0   \n",
       "4      0.216049   0.051382     0.017933   24       0.0   \n",
       "5      0.216049   0.051382     0.017933   24       0.0   \n",
       "6      0.216049   0.037002     0.028392   24       0.0   \n",
       "7      0.216049   0.060312     0.037422   24       0.0   \n",
       "8      0.216049   0.055452     0.045891   60       0.0   \n",
       "9      0.216049   0.036505     0.049466   24       0.0   \n",
       "10     0.216049   0.039862     0.056349   12  0.000011   \n",
       "11     0.216049   0.055975     0.062898   96       0.0   \n",
       "12     0.216049    0.04405     0.067896   24       0.0   \n",
       "13     0.216049   0.084963     0.079993   72       0.0   \n",
       "14     0.216049   0.037042     0.082494   12  0.000007   \n",
       "15     0.216049   0.037042     0.082494   12  0.000007   \n",
       "16     0.216049   0.079389     0.087969   24  0.000006   \n",
       "17     0.216049   0.078935     0.090326   12  0.000076   \n",
       "18     0.216049   0.127851     0.125775  288       0.0   \n",
       "19     0.216049   0.142082     0.139756  456       0.0   \n",
       "20     0.216049   0.163442      0.15537   60       0.0   \n",
       "21     0.216049   0.150265     0.163455   24  0.000002   \n",
       "22     0.216049   0.150265     0.163455   24  0.000002   \n",
       "23     0.216049   0.197463     0.165529   72  0.000829   \n",
       "24     0.216049   0.195681     0.167321  300       0.0   \n",
       "25     0.216049   0.193048     0.171465  120  0.000406   \n",
       "26     0.216049       0.19     0.177264  432       0.0   \n",
       "27     0.216049   0.317878     0.259304  324       0.0   \n",
       "28     0.216049   0.326167     0.293876   36  0.001176   \n",
       "29     0.216049   0.342314     0.319273   48  0.000113   \n",
       "30     0.216049   0.357916     0.332449   36       0.0   \n",
       "31     0.216049   0.373034      0.33831   60  0.000031   \n",
       "32     0.216049   0.378053     0.341626   36  0.000001   \n",
       "33     0.216049   0.390728     0.342512   12  0.001925   \n",
       "34     0.216049   0.323955       0.3446   96   0.00121   \n",
       "35     0.216049   0.388267     0.362102  144       0.0   \n",
       "36     0.216049   0.439721     0.379361  108       0.0   \n",
       "37     0.216049   0.444895     0.382283   24  0.000481   \n",
       "38     0.216049    0.42301     0.407061   24  0.000062   \n",
       "39     0.216049   0.450934     0.435638   84       0.0   \n",
       "40     0.216049    0.50366     0.456343   60       0.0   \n",
       "41     0.216049   0.540214     0.483138   12  0.000017   \n",
       "42     0.216049   0.643218     0.623627   24       0.0   \n",
       "43     0.216049   0.642239     0.655779   24       0.0   \n",
       "44     0.216049   0.637627     0.670186   60       0.0   \n",
       "45     0.216049   0.699284     0.688601   12       0.0   \n",
       "46     0.216049   0.698996     0.699355  120       0.0   \n",
       "47     0.216049   0.685546     0.699666   12       0.0   \n",
       "48     0.216049   0.732777     0.717641   12       0.0   \n",
       "49     0.216049   0.759643      0.72536   24       0.0   \n",
       "50     0.216049   0.782156     0.764845   12       0.0   \n",
       "\n",
       "                       table  \n",
       "0      [[1, 833], [23, 811]]  \n",
       "1      [[1, 833], [23, 811]]  \n",
       "2      [[0, 834], [12, 822]]  \n",
       "3      [[1, 833], [23, 811]]  \n",
       "4      [[1, 833], [23, 811]]  \n",
       "5      [[1, 833], [23, 811]]  \n",
       "6      [[2, 832], [22, 812]]  \n",
       "7      [[2, 832], [22, 812]]  \n",
       "8      [[9, 825], [51, 783]]  \n",
       "9      [[1, 833], [23, 811]]  \n",
       "10     [[0, 834], [12, 822]]  \n",
       "11    [[11, 823], [85, 749]]  \n",
       "12     [[2, 832], [22, 812]]  \n",
       "13    [[11, 823], [61, 773]]  \n",
       "14     [[0, 834], [12, 822]]  \n",
       "15     [[0, 834], [12, 822]]  \n",
       "16     [[3, 831], [21, 813]]  \n",
       "17     [[0, 834], [12, 822]]  \n",
       "18   [[60, 774], [228, 606]]  \n",
       "19  [[122, 712], [334, 500]]  \n",
       "20    [[17, 817], [43, 791]]  \n",
       "21     [[4, 830], [20, 814]]  \n",
       "22     [[4, 830], [20, 814]]  \n",
       "23    [[22, 812], [50, 784]]  \n",
       "24  [[114, 720], [186, 648]]  \n",
       "25    [[42, 792], [78, 756]]  \n",
       "26  [[162, 672], [270, 564]]  \n",
       "27  [[190, 644], [134, 700]]  \n",
       "28     [[34, 800], [2, 832]]  \n",
       "29     [[44, 790], [4, 830]]  \n",
       "30     [[36, 798], [0, 834]]  \n",
       "31    [[46, 788], [14, 820]]  \n",
       "32     [[36, 798], [0, 834]]  \n",
       "33     [[12, 822], [0, 834]]  \n",
       "34    [[66, 768], [30, 804]]  \n",
       "35   [[114, 720], [30, 804]]  \n",
       "36    [[98, 736], [10, 824]]  \n",
       "37     [[24, 810], [0, 834]]  \n",
       "38     [[23, 811], [1, 833]]  \n",
       "39     [[79, 755], [5, 829]]  \n",
       "40     [[60, 774], [0, 834]]  \n",
       "41     [[12, 822], [0, 834]]  \n",
       "42     [[24, 810], [0, 834]]  \n",
       "43     [[24, 810], [0, 834]]  \n",
       "44     [[56, 778], [4, 830]]  \n",
       "45     [[12, 822], [0, 834]]  \n",
       "46    [[120, 714], [0, 834]]  \n",
       "47     [[12, 822], [0, 834]]  \n",
       "48     [[12, 822], [0, 834]]  \n",
       "49     [[24, 810], [0, 834]]  \n",
       "50     [[12, 822], [0, 834]]  "
      ]
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "moodsdf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "PIiMWCRVGBsB"
   },
   "source": [
    "### 🍒🍒 2.2.2 **Enrichment**: Broad Analysis of Categories: ANOVA\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ytKRGYYWiSFX"
   },
   "source": [
    "Recall our \"melted\" shift data. It will be useful to think of getting our Truffle data in this format:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 206
    },
    "id": "URjZgCMViMiw",
    "outputId": "28621dc6-ee56-4455-c2da-f8360c1ae0a7"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<style scoped>\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>index</th>\n",
       "      <th>shift</th>\n",
       "      <th>rate</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>A</td>\n",
       "      <td>11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>A</td>\n",
       "      <td>14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>A</td>\n",
       "      <td>15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>A</td>\n",
       "      <td>16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>A</td>\n",
       "      <td>16</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   index shift  rate\n",
       "0      0     A    11\n",
       "1      1     A    14\n",
       "2      2     A    15\n",
       "3      3     A    16\n",
       "4      4     A    16"
      ]
     },
     "execution_count": 104,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "shift_melt.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {
    "id": "WYvWTt4YixSw"
   },
   "outputs": [],
   "source": [
    "df.columns = df.columns.str.replace(' ', '_')\n",
    "df.columns = df.columns.str.replace('/', '_')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 112
    },
    "id": "6xBHomXrhqAm",
    "outputId": "cb4b4f26-7085-4c68-906c-37c2b7f6f414"
   },
   "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(Truffle_Type)</th>\n",
       "      <td>1.250464</td>\n",
       "      <td>2.0</td>\n",
       "      <td>12.882509</td>\n",
       "      <td>0.000003</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Residual</th>\n",
       "      <td>80.808138</td>\n",
       "      <td>1665.0</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(Truffle_Type)   1.250464     2.0  12.882509  0.000003\n",
       "Residual         80.808138  1665.0        NaN       NaN"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# get ANOVA table \n",
    "# Ordinary Least Squares (OLS) model\n",
    "model = ols('EBITDA_KG ~ C(Truffle_Type)', data=df).fit()\n",
    "anova_table = sm.stats.anova_lm(model, typ=2)\n",
    "anova_table\n",
    "# output (ANOVA F and p value)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "7A9JQbARjF5B"
   },
   "source": [
    "Recall the **_Shapiro-Wilk_** test can be used to check the _normal distribution of residuals_. Null hypothesis: data is drawn from normal distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "OPiFlR0Ii7RB",
    "outputId": "e47e197c-3da7-43ba-8c56-696d61461118"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9576056599617004 1.2598073820281984e-21\n"
     ]
    }
   ],
   "source": [
    "w, pvalue = stats.shapiro(model.resid)\n",
    "print(w, pvalue)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "f739OA5gjYGZ"
   },
   "source": [
    "And the **_Bartlett’s_** test to check the _Homogeneity of variances_. Null hypothesis: samples from populations have equal variances."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "ozV8i6sLmBst",
    "outputId": "625ab4e6-ab3e-4d8e-980c-ade4fab165f5"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<pandas.core.groupby.generic.SeriesGroupBy object at 0x7fb6940a7370>"
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gb = df.groupby('Truffle_Type')['EBITDA_KG']\n",
    "gb"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "ixHKhdRQjEkh",
    "outputId": "a079e7a8-6ec2-4298-b093-473f86f2b8e0"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "109.93252546442552 1.344173733366234e-24\n"
     ]
    }
   ],
   "source": [
    "w, pvalue = stats.bartlett(*[gb.get_group(x) for x in gb.groups])\n",
    "print(w, pvalue)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "9XIDDKOBmp3L"
   },
   "source": [
    "Wow it looks like our data is not drawn from a normal distribution! Let's check this for other categories...\n",
    "\n",
    "We can wrap these in a for loop:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 847
    },
    "id": "36ctJA_MmrzD",
    "outputId": "fdd9f774-323b-4188-b36e-633fd9add6f9"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Base_Cake\n"
     ]
    },
    {
     "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(Base_Cake)</th>\n",
       "      <td>39.918103</td>\n",
       "      <td>5.0</td>\n",
       "      <td>314.869955</td>\n",
       "      <td>1.889884e-237</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Residual</th>\n",
       "      <td>42.140500</td>\n",
       "      <td>1662.0</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(Base_Cake)  39.918103     5.0  314.869955  1.889884e-237\n",
       "Residual      42.140500  1662.0         NaN            NaN"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shapiro:  0.9634131193161011 4.1681337029688696e-20\n",
      "Bartlett:  69.83288886114286 1.1102218566048873e-13\n",
      "\n",
      "Truffle_Type\n"
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       "      <th>sum_sq</th>\n",
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       "      <th>PR(&gt;F)</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>C(Truffle_Type)</th>\n",
       "      <td>1.250464</td>\n",
       "      <td>2.0</td>\n",
       "      <td>12.882509</td>\n",
       "      <td>0.000003</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Residual</th>\n",
       "      <td>80.808138</td>\n",
       "      <td>1665.0</td>\n",
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      "text/plain": [
       "                    sum_sq      df          F    PR(>F)\n",
       "C(Truffle_Type)   1.250464     2.0  12.882509  0.000003\n",
       "Residual         80.808138  1665.0        NaN       NaN"
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     "text": [
      "Shapiro:  0.9576056599617004 1.2598073820281984e-21\n",
      "Bartlett:  109.93252546442552 1.344173733366234e-24\n",
      "\n",
      "Primary_Flavor\n"
     ]
    },
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       "      <th>C(Primary_Flavor)</th>\n",
       "      <td>50.270639</td>\n",
       "      <td>50.0</td>\n",
       "      <td>51.143649</td>\n",
       "      <td>1.153434e-292</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Residual</th>\n",
       "      <td>31.787964</td>\n",
       "      <td>1617.0</td>\n",
       "      <td>NaN</td>\n",
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      "text/plain": [
       "                      sum_sq      df          F         PR(>F)\n",
       "C(Primary_Flavor)  50.270639    50.0  51.143649  1.153434e-292\n",
       "Residual           31.787964  1617.0        NaN            NaN"
      ]
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     "text": [
      "Shapiro:  0.948470413684845 9.90281706784179e-24\n",
      "Bartlett:  210.15130419114982 1.5872504991225816e-21\n",
      "\n",
      "Secondary_Flavor\n"
     ]
    },
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       "      <th>PR(&gt;F)</th>\n",
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       "  <tbody>\n",
       "    <tr>\n",
       "      <th>C(Secondary_Flavor)</th>\n",
       "      <td>15.088382</td>\n",
       "      <td>28.0</td>\n",
       "      <td>13.188089</td>\n",
       "      <td>1.929302e-54</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Residual</th>\n",
       "      <td>66.970220</td>\n",
       "      <td>1639.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
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       "                        sum_sq      df          F        PR(>F)\n",
       "C(Secondary_Flavor)  15.088382    28.0  13.188089  1.929302e-54\n",
       "Residual             66.970220  1639.0        NaN           NaN"
      ]
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     "metadata": {},
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     "output_type": "stream",
     "text": [
      "Shapiro:  0.9548103213310242 2.649492974953278e-22\n",
      "Bartlett:  420.6274502894812 1.2373007035089195e-71\n",
      "\n",
      "Color_Group\n"
     ]
    },
    {
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       "<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(Color_Group)</th>\n",
       "      <td>16.079685</td>\n",
       "      <td>11.0</td>\n",
       "      <td>36.689347</td>\n",
       "      <td>6.544980e-71</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Residual</th>\n",
       "      <td>65.978918</td>\n",
       "      <td>1656.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
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       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   sum_sq      df          F        PR(>F)\n",
       "C(Color_Group)  16.079685    11.0  36.689347  6.544980e-71\n",
       "Residual        65.978918  1656.0        NaN           NaN"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shapiro:  0.969061017036438 1.8926407335144587e-18\n",
      "Bartlett:  136.55525281340468 8.164787784033709e-24\n",
      "\n"
     ]
    }
   ],
   "source": [
    "for col in df.columns[:5]:\n",
    "  print(col)\n",
    "  model = ols('EBITDA_KG ~ C({})'.format(col), data=df).fit()\n",
    "  anova_table = sm.stats.anova_lm(model, typ=2)\n",
    "  display(anova_table)\n",
    "  w, pvalue = stats.shapiro(model.resid)\n",
    "  print(\"Shapiro: \", w, pvalue)\n",
    "  gb = df.groupby(col)['EBITDA_KG']\n",
    "  w, pvalue = stats.bartlett(*[gb.get_group(x) for x in gb.groups])\n",
    "  print(\"Bartlett: \", w, pvalue)\n",
    "  print()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "2bnum6yeqmy4"
   },
   "source": [
    "### 🍒🍒 2.2.3 **Enrichment**: Visual Analysis of Residuals: QQ-Plots\n",
    "\n",
    "This can be distressing and is often why we want visual methods to see what is going on with our data!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 544
    },
    "id": "M3BHEncwo01Z",
    "outputId": "5d925454-c1c1-4206-8025-ceb80eaa78dc"
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "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": [
    "model = ols('EBITDA_KG ~ C(Truffle_Type)', data=df).fit()\n",
    "\n",
    "#create instance of influence\n",
    "influence = model.get_influence()\n",
    "\n",
    "#obtain standardized residuals\n",
    "standardized_residuals = influence.resid_studentized_internal\n",
    "\n",
    "# res.anova_std_residuals are standardized residuals obtained from ANOVA (check above)\n",
    "sm.qqplot(standardized_residuals, line='45')\n",
    "plt.xlabel(\"Theoretical Quantiles\")\n",
    "plt.ylabel(\"Standardized Residuals\")\n",
    "plt.show()\n",
    "\n",
    "# histogram\n",
    "plt.hist(model.resid, bins='auto', histtype='bar', ec='k') \n",
    "plt.xlabel(\"Residuals\")\n",
    "plt.ylabel('Frequency')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "b5QthjAmqy0k"
   },
   "source": [
    "We see that a lot of our data is swayed by extremely high and low values, so what can we conclude? \n",
    "\n",
    "> You need the right test statistic for the right job, in this case, we are littered with unequal variance in our groupings so we use the moods median and welch (unequal variance t-test) to make conclusions about our data\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "1kO7TDSohI_b"
   },
   "source": [
    "# References\n",
    "\n",
    "* [Renesh Bedre ANOVA](https://www.reneshbedre.com/blog/anova.html)\n",
    "* [Minitab ANOVA](https://blog.minitab.com/en/adventures-in-statistics-2/understanding-analysis-of-variance-anova-and-the-f-test)\n",
    "* [Analytics Vidhya ANOVA](https://www.analyticsvidhya.com/blog/2020/06/introduction-anova-statistics-data-science-covid-python/)\n",
    "* [Renesh Bedre Hypothesis Testing](https://www.reneshbedre.com/blog/hypothesis-testing.html)\n",
    "* [Real Statistics Turkey-kramer](https://www.real-statistics.com/one-way-analysis-of-variance-anova/unplanned-comparisons/tukey-kramer-test/)\n",
    "* [Mutual Information](https://www.kaggle.com/ryanholbrook/mutual-information)"
   ]
  }
 ],
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  "colab": {
   "collapsed_sections": [],
   "include_colab_link": true,
   "name": "S2_Inferential_Statistics.ipynb",
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   "toc_visible": true
  },
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
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}