Python_ANOVA/Two_Way_ANOVA_in_Python_Tutorial.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Python ANOVA: 3 Ways to Carry out Two-Way ANOVA \n",
    "This is the Jupyter Notebook for Two-Way ANOVA using Python. This Notebook contains the code for calculating the ANOVA table \"by hand\".\n",
    "\n",
    "Note, it has been updated to use seaborn to create an interaction plot instead of Statsmodels:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Suppress Warnings (not in the blog post)\n",
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")\n",
    "\n",
    "from scipy import stats"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Load the data set from URL\n",
    "Here we load the dataset from an URL, instead of from the harddrive:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>len</th>\n",
       "      <th>supp</th>\n",
       "      <th>dose</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.2</td>\n",
       "      <td>VC</td>\n",
       "      <td>0.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>11.5</td>\n",
       "      <td>VC</td>\n",
       "      <td>0.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>7.3</td>\n",
       "      <td>VC</td>\n",
       "      <td>0.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.8</td>\n",
       "      <td>VC</td>\n",
       "      <td>0.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>6.4</td>\n",
       "      <td>VC</td>\n",
       "      <td>0.5</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    len supp  dose\n",
       "1   4.2   VC   0.5\n",
       "2  11.5   VC   0.5\n",
       "3   7.3   VC   0.5\n",
       "4   5.8   VC   0.5\n",
       "5   6.4   VC   0.5"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = 'https://vincentarelbundock.github.io/Rdatasets/csv/datasets/ToothGrowth.csv'\n",
    "\n",
    "df = pd.read_csv(data, index_col=0)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Interaction plot using Seaborn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = sns.pointplot(x='dose', y='len', hue='supp', data=df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Calculating the Degrees of Freedom"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "N = len(df.len)\n",
    "df_a = len(df.supp.unique()) - 1\n",
    "df_b = len(df.dose.unique()) - 1\n",
    "df_axb = df_a*df_b \n",
    "df_w = N - (len(df.supp.unique())*len(df.dose.unique()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Calculating the Grand Mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "grand_mean = df['len'].mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sum of Squares"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Sum of Squares A\n",
    "ssq_a = sum([(df[df.supp == l].len.mean() - grand_mean)**2 for l in df.supp])\n",
    "# Sum of Squares B\n",
    "ssq_b = sum([(df[df.dose ==l].len.mean() - grand_mean)**2 for l in df.dose])\n",
    "# Sum of Squares T\n",
    "ssq_t = sum((df.len - grand_mean)**2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sum of Squares Within and Interaction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "vc = df[df.supp == 'VC']\n",
    "oj = df[df.supp == 'OJ']\n",
    "vc_dose_means = [vc[vc.dose == d].len.mean() for d in vc.dose]\n",
    "oj_dose_means = [oj[oj.dose == d].len.mean() for d in oj.dose]\n",
    "ssq_w = sum((oj.len - oj_dose_means)**2) +sum((vc.len - vc_dose_means)**2)\n",
    "# Interaction\n",
    "ssq_axb = ssq_t - ssq_a - ssq_b - ssq_w"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Mean Square Errors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "ms_a = ssq_a/df_a\n",
    "ms_b = ssq_b/df_b\n",
    "ms_axb = ssq_axb/df_axb\n",
    "ms_w = ssq_w/df_w"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Calculating F"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "f_a = ms_a/ms_w\n",
    "f_b = ms_b/ms_w\n",
    "f_axb = ms_axb/ms_w"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Obtaining the P-values\n",
    "Here we get the P-values using SciPy:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "p_a = stats.f.sf(f_a, df_a, df_w)\n",
    "p_b = stats.f.sf(f_b, df_b, df_w)\n",
    "p_axb = stats.f.sf(f_axb, df_axb, df_w)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Creating the ANOVA Table"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "results = {'sum_sq':[ssq_a, ssq_b, ssq_axb, ssq_w],\n",
    "           'df':[df_a, df_b, df_axb, df_w],\n",
    "           'F':[f_a, f_b, f_axb, 'NaN'],\n",
    "            'PR(>F)':[p_a, p_b, p_axb, 'NaN']}\n",
    "\n",
    "columns=['sum_sq', 'df', 'F', 'PR(>F)']\n",
    "\n",
    "aov_table1 = pd.DataFrame(results, columns=columns,\n",
    "                          index=['supp', 'dose', \n",
    "                          'supp:dose', 'Residual'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Effect Sizes\n",
    "Here we get the eta squared and omega squared effect sizes and add it to the anova table and print the results:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                sum_sq  df        F       PR(>F)    eta_sq  omega_sq\n",
      "supp        205.350000   1   15.572  0.000231183  0.059484  0.055452\n",
      "dose       2426.434333   2       92  4.04629e-18  0.702864  0.692579\n",
      "supp:dose   108.319000   2  4.10699    0.0218603  0.031377  0.023647\n",
      "Residual    712.106000  54      NaN          NaN       NaN       NaN\n"
     ]
    }
   ],
   "source": [
    "def eta_squared(aov):\n",
    "    aov['eta_sq'] = 'NaN'\n",
    "    aov['eta_sq'] = aov[:-1]['sum_sq']/sum(aov['sum_sq'])\n",
    "    return aov\n",
    "\n",
    "def omega_squared(aov):\n",
    "    mse = aov['sum_sq'][-1]/aov['df'][-1]\n",
    "    aov['omega_sq'] = 'NaN'\n",
    "    aov['omega_sq'] = (aov[:-1]['sum_sq']-(aov[:-1]['df']*mse))/(sum(aov['sum_sq'])+mse)\n",
    "    return aov\n",
    "\n",
    "\n",
    "eta_squared(aov_table1)\n",
    "omega_squared(aov_table1)\n",
    "print(aov_table1)"
   ]
  }
 ],
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    "name": "ipython",
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   "file_extension": ".py",
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