two-way-anova-with-python.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# a couple of ways to do two-way ANOVA with Python\n",
    "Here is my version of [this article](https://www.marsja.se/three-ways-to-carry-out-2-way-anova-with-python/)\n",
    "There are a lot of errors, and so, I'd fixed it"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import statsmodels.api as sm\n",
    "from statsmodels.formula.api import ols\n",
    "from statsmodels.stats.anova import anova_lm\n",
    "from statsmodels.graphics.factorplots import interaction_plot\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy import stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "datafile = \"ToothGrowth.csv\"\n",
    "data = pd.read_csv(datafile)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\monika201103\\Anaconda3\\lib\\site-packages\\statsmodels\\graphics\\factorplots.py:131: FutureWarning: In a future version of pandas, a length 1 tuple will be returned when iterating over a groupby with a grouper equal to a list of length 1. Don't supply a list with a single grouper to avoid this warning.\n",
      "  for i, (values, group) in enumerate(plot_data.groupby(['trace'])):\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = interaction_plot(data.dose, data.supp, data.len,\n",
    "             colors=['red','blue'], markers=['D','^'], ms=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Calculation of Sum of Squares\n",
    "The calculations of the sum of squares (the variance in the data) are quite simple using Python. \n",
    "First, we start with getting the sample size (N) and the degree of freedoms needed. \n",
    "We will use them later to calculate the mean square. \n",
    "After we have the degree of freedom we continue with the calculation of the sum of squares."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Degrees of Freedom"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "N = len(data.len)\n",
    "df_a = len(data.supp.unique()) - 1\n",
    "df_b = len(data.dose.unique()) - 1\n",
    "df_axb = df_a*df_b \n",
    "df_w = N - (len(data.supp.unique())*len(data.dose.unique()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Sum of Squares\n",
    "For the calculation of the sum of squares A, B and Total we will need to have the grand mean. Using Pandas DataFrame method mean on the dependent variable only will give us the grand mean:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "grand_mean = data['len'].mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Sum of Squares A – supp\n",
    "We start with calculation of Sum of Squares for the factor A (supp)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "ssq_a = sum([(data[data.supp ==l].len.mean()-grand_mean)**2 for l in data.supp])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Sum of Squares B – dose\n",
    "Calculation of the second Sum of Square, B (dose), is pretty much the same but over the levels of that factor."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "ssq_b = sum([(data[data.dose ==l].len.mean()-grand_mean)**2 for l in data.dose])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Sum of Squares Total"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "ssq_t = sum((data.len - grand_mean)**2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Sum of Squares Within (error/residual)\n",
    "Next, we need to calculate the Sum of Squares Within which is sometimes referred to as error or residual."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "vc = data[data.supp == 'VC']\n",
    "oj = data[data.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]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "ssq_w = sum(((oj.len - oj_dose_means)**2) + sum((vc.len - vc_dose_means)**2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Sum of Squares interaction\n",
    "Since we have a two-way design we need to calculate the Sum of Squares for the interaction of A and B."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "ssq_axb = ssq_t-ssq_a-ssq_b-ssq_w"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Mean Squares\n",
    "We continue with the calculation of the mean square for each factor, the interaction of the factors, and within."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Mean Square A\n",
    "ms_a = ssq_a/df_a\n",
    "\n",
    "# Mean Square B\n",
    "ms_b = ssq_b/df_b\n",
    "\n",
    "# Mean Square AxB\n",
    "ms_axb = ssq_axb/df_axb\n",
    "\n",
    "# Mean Square Within/Error/Residual\n",
    "ms_w = ssq_w/df_w"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# F-ratio\n",
    "The F-statistic is simply the mean square for each effect and the interaction \n",
    "divided by the mean square for within (error/residual)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# F-ratio A\n",
    "f_a = ms_a/ms_w\n",
    "# F-ratio B\n",
    "f_b = ms_b/ms_w\n",
    "# F-ratio AxB\n",
    "f_axb = ms_axb/ms_w"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Obtaining p-values\n",
    "We can use the scipy.stats method f.sf to check if our obtained F-ratios is above the critical value. Doing that we need to use our F-value for each effect and interaction as well as the degrees of freedom for them, and the degree of freedom within."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "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": [
    "The results are, right now, stored in a lot of variables. To obtain a more readable result we can create a DataFrame that will contain our ANOVA table."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "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(&gt;F)':[p_a, p_b, p_axb, 'NaN']}\n",
    "columns=['sum_sq', 'df', 'F', 'PR(&gt;F)']\n",
    "aov_table1 = pd.DataFrame(results, columns=columns,\n",
    "                          index=['supp', 'dose', \n",
    "                          'supp:dose', 'Residual'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So, common software, such as SPSS has eta squared as output. However, eta squared is an overestimation of the effect. To get a less biased effect size measure we can use omega squared. The following two functions add eta squared and omega squared to the above DataFrame that contains the ANOVA table."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sum_sq</th>\n",
       "      <th>df</th>\n",
       "      <th>F</th>\n",
       "      <th>PR(&amp;gt;F)</th>\n",
       "      <th>eta_sq</th>\n",
       "      <th>omega_sq</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>supp</th>\n",
       "      <td>205.350000</td>\n",
       "      <td>1</td>\n",
       "      <td>1.072413</td>\n",
       "      <td>0.305016</td>\n",
       "      <td>0.059484</td>\n",
       "      <td>0.003805</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>dose</th>\n",
       "      <td>2426.434333</td>\n",
       "      <td>2</td>\n",
       "      <td>6.335868</td>\n",
       "      <td>0.003374</td>\n",
       "      <td>0.702864</td>\n",
       "      <td>0.560823</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>supp:dose</th>\n",
       "      <td>-9519.710000</td>\n",
       "      <td>2</td>\n",
       "      <td>-24.857719</td>\n",
       "      <td>1.0</td>\n",
       "      <td>-2.757570</td>\n",
       "      <td>-2.717758</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Residual</th>\n",
       "      <td>10340.135000</td>\n",
       "      <td>54</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 sum_sq  df          F PR(&gt;F)    eta_sq  omega_sq\n",
       "supp         205.350000   1   1.072413  0.305016  0.059484  0.003805\n",
       "dose        2426.434333   2   6.335868  0.003374  0.702864  0.560823\n",
       "supp:dose  -9519.710000   2 -24.857719       1.0 -2.757570 -2.717758\n",
       "Residual   10340.135000  54        NaN       NaN       NaN       NaN"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "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",
    "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",
    "eta_squared(aov_table1)\n",
    "omega_squared(aov_table1)\n",
    "aov_table1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "\n",
    "# Two-way ANOVA using Statsmodels\n",
    "There is, of course, a much easier way to do Two-way ANOVA with Python. We can use Statsmodels which have a similar model notation as many R-packages (e.g., lm). We start with the formulation of the model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "formula = 'len ~ C(supp) + C(dose) + C(supp):C(dose)'\n",
    "model = ols(formula, data).fit()\n",
    "aov_table = anova_lm(model, typ=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Statsmodels does not calculate effect sizes for us. My functions above can, again, be used and will add omega and eta squared effect sizes to the ANOVA table. Actually, I created these two functions to enable calculation of omega and eta squared effect sizes on the output of Statsmodels anova_lm method. Note, statsmodels can be installed with e.g. pip or conda."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sum_sq</th>\n",
       "      <th>df</th>\n",
       "      <th>F</th>\n",
       "      <th>PR(&gt;F)</th>\n",
       "      <th>eta_sq</th>\n",
       "      <th>omega_sq</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>C(supp)</th>\n",
       "      <td>205.350</td>\n",
       "      <td>1.0</td>\n",
       "      <td>15.572</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.059</td>\n",
       "      <td>0.055</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C(dose)</th>\n",
       "      <td>2426.434</td>\n",
       "      <td>2.0</td>\n",
       "      <td>92.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.703</td>\n",
       "      <td>0.693</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C(supp):C(dose)</th>\n",
       "      <td>108.319</td>\n",
       "      <td>2.0</td>\n",
       "      <td>4.107</td>\n",
       "      <td>0.022</td>\n",
       "      <td>0.031</td>\n",
       "      <td>0.024</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Residual</th>\n",
       "      <td>712.106</td>\n",
       "      <td>54.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   sum_sq    df       F  PR(>F)  eta_sq  omega_sq\n",
       "C(supp)           205.350   1.0  15.572   0.000   0.059     0.055\n",
       "C(dose)          2426.434   2.0  92.000   0.000   0.703     0.693\n",
       "C(supp):C(dose)   108.319   2.0   4.107   0.022   0.031     0.024\n",
       "Residual          712.106  54.0     NaN     NaN     NaN       NaN"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eta_squared(aov_table)\n",
    "omega_squared(aov_table)\n",
    "aov_table.round(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What is neat with using statsmodels is that we can also do some diagnostics. It is, for instance, very easy to take our model fit (the linear model fitted with the OLS method) and get a Quantile-Quantile (QQplot):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "res = model.resid \n",
    "fig = sm.qqplot(res, stats.t, fit=True, line=\"45\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Two-Way ANOVA using Pingouin\n",
    "Here, Pingouin offers a very easy way to for ANOVA in Python.\n",
    "Unfortunatelly, it doesn't work on the Kaggle site (in reason of this library, which i use), but you can copy these few lines of code..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "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>Unnamed: 0</th>\n",
       "      <th>len</th>\n",
       "      <th>supp</th>\n",
       "      <th>dose</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>4.2</td>\n",
       "      <td>VC</td>\n",
       "      <td>0.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>11.5</td>\n",
       "      <td>VC</td>\n",
       "      <td>0.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>7.3</td>\n",
       "      <td>VC</td>\n",
       "      <td>0.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>5.8</td>\n",
       "      <td>VC</td>\n",
       "      <td>0.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>6.4</td>\n",
       "      <td>VC</td>\n",
       "      <td>0.5</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Unnamed: 0   len supp  dose\n",
       "0           1   4.2   VC   0.5\n",
       "1           2  11.5   VC   0.5\n",
       "2           3   7.3   VC   0.5\n",
       "3           4   5.8   VC   0.5\n",
       "4           5   6.4   VC   0.5"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pingouin as pg\n",
    "data = pd.read_csv(datafile)\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "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>Source</th>\n",
       "      <th>SS</th>\n",
       "      <th>DF</th>\n",
       "      <th>MS</th>\n",
       "      <th>F</th>\n",
       "      <th>p-unc</th>\n",
       "      <th>np2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>supp</td>\n",
       "      <td>205.350000</td>\n",
       "      <td>1</td>\n",
       "      <td>205.350000</td>\n",
       "      <td>15.571979</td>\n",
       "      <td>2.311828e-04</td>\n",
       "      <td>0.223825</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>dose</td>\n",
       "      <td>2426.434333</td>\n",
       "      <td>2</td>\n",
       "      <td>1213.217167</td>\n",
       "      <td>91.999965</td>\n",
       "      <td>4.046291e-18</td>\n",
       "      <td>0.773109</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>supp * dose</td>\n",
       "      <td>108.319000</td>\n",
       "      <td>2</td>\n",
       "      <td>54.159500</td>\n",
       "      <td>4.106991</td>\n",
       "      <td>2.186027e-02</td>\n",
       "      <td>0.132028</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Residual</td>\n",
       "      <td>712.106000</td>\n",
       "      <td>54</td>\n",
       "      <td>13.187148</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        Source           SS  DF           MS          F         p-unc  \\\n",
       "0         supp   205.350000   1   205.350000  15.571979  2.311828e-04   \n",
       "1         dose  2426.434333   2  1213.217167  91.999965  4.046291e-18   \n",
       "2  supp * dose   108.319000   2    54.159500   4.106991  2.186027e-02   \n",
       "3     Residual   712.106000  54    13.187148        NaN           NaN   \n",
       "\n",
       "        np2  \n",
       "0  0.223825  \n",
       "1  0.773109  \n",
       "2  0.132028  \n",
       "3       NaN  "
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "aov = pg.anova(data, dv='len', between=['supp', 'dose'], detailed=True)\n",
    "aov"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Thank you!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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