Data_Visualization_and_Repeated_Measures_ANOVA_in_Python.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example Python Jupyter Notebook Online: Binder Tutorial\n",
    "This Jupyter Notebook is an example for the tutorial on [how to use Binder for reproducible research](https://www.marsja.se/how-to-use-binder-python-for-repoducible-research). It contains the code for creating some data visualizations using Python Seaborn. After that is done a repeated measures ANOVA using pingouin.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\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>treatment</th>\n",
       "      <th>gender</th>\n",
       "      <th>pre.1</th>\n",
       "      <th>pre.2</th>\n",
       "      <th>pre.3</th>\n",
       "      <th>pre.4</th>\n",
       "      <th>pre.5</th>\n",
       "      <th>post.1</th>\n",
       "      <th>post.2</th>\n",
       "      <th>post.3</th>\n",
       "      <th>post.4</th>\n",
       "      <th>post.5</th>\n",
       "      <th>fup.1</th>\n",
       "      <th>fup.2</th>\n",
       "      <th>fup.3</th>\n",
       "      <th>fup.4</th>\n",
       "      <th>fup.5</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>control</td>\n",
       "      <td>M</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>5</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>control</td>\n",
       "      <td>M</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>5</td>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "      <td>6</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>control</td>\n",
       "      <td>M</td>\n",
       "      <td>5</td>\n",
       "      <td>6</td>\n",
       "      <td>5</td>\n",
       "      <td>7</td>\n",
       "      <td>7</td>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "      <td>7</td>\n",
       "      <td>5</td>\n",
       "      <td>4</td>\n",
       "      <td>7</td>\n",
       "      <td>6</td>\n",
       "      <td>9</td>\n",
       "      <td>7</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>control</td>\n",
       "      <td>F</td>\n",
       "      <td>5</td>\n",
       "      <td>4</td>\n",
       "      <td>7</td>\n",
       "      <td>5</td>\n",
       "      <td>4</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>5</td>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>control</td>\n",
       "      <td>F</td>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>6</td>\n",
       "      <td>4</td>\n",
       "      <td>3</td>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "      <td>8</td>\n",
       "      <td>6</td>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>3</td>\n",
       "      <td>6</td>\n",
       "      <td>4</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  treatment gender  pre.1  pre.2  pre.3  pre.4  pre.5  post.1  post.2  post.3  \\\n",
       "1   control      M      1      2      4      2      1       3       2       5   \n",
       "2   control      M      4      4      5      3      4       2       2       3   \n",
       "3   control      M      5      6      5      7      7       4       5       7   \n",
       "4   control      F      5      4      7      5      4       2       2       3   \n",
       "5   control      F      3      4      6      4      3       6       7       8   \n",
       "\n",
       "   post.4  post.5  fup.1  fup.2  fup.3  fup.4  fup.5  \n",
       "1       3       2      2      3      2      4      4  \n",
       "2       5       3      4      5      6      4      1  \n",
       "3       5       4      7      6      9      7      6  \n",
       "4       5       3      4      4      5      3      4  \n",
       "5       6       3      4      3      6      4      3  "
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import pandas as pd\n",
    "\n",
    "\n",
    "# Suppress warnings\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "\n",
    "# Getting the data\n",
    "data = \"https://vincentarelbundock.github.io/Rdatasets/csv/carData/OBrienKaiser.csv\"\n",
    "\n",
    "# Loading the data into a Pandas dataframe\n",
    "df = pd.read_csv(data, index_col=0)\n",
    "\n",
    "# Using Pandas head to check the first 5 rows of the dataframe\n",
    "df.head()"
   ]
  },
  {
   "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>id</th>\n",
       "      <th>gender</th>\n",
       "      <th>treatment</th>\n",
       "      <th>hour</th>\n",
       "      <th>phase</th>\n",
       "      <th>value</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>M</td>\n",
       "      <td>control</td>\n",
       "      <td>1</td>\n",
       "      <td>pre</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>M</td>\n",
       "      <td>control</td>\n",
       "      <td>2</td>\n",
       "      <td>pre</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>M</td>\n",
       "      <td>control</td>\n",
       "      <td>3</td>\n",
       "      <td>pre</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>M</td>\n",
       "      <td>control</td>\n",
       "      <td>4</td>\n",
       "      <td>pre</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>M</td>\n",
       "      <td>control</td>\n",
       "      <td>5</td>\n",
       "      <td>pre</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   id gender treatment  hour phase  value\n",
       "0   1      M   control     1   pre      1\n",
       "1   1      M   control     2   pre      2\n",
       "2   1      M   control     3   pre      4\n",
       "3   1      M   control     4   pre      2\n",
       "4   1      M   control     5   pre      1"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[\"id\"] = df.index\n",
    "df_long = pd.wide_to_long(df, [\"pre\", \"post\", \"fup\"], \n",
    "                i=[\"id\", \"gender\", \"treatment\"], \n",
    "                j='hour', sep=\".\").reset_index()\n",
    "\n",
    "df_long = pd.melt(df_long,id_vars=[\"id\", \"gender\", \"treatment\", \"hour\"], \n",
    "                  var_name='phase', value_name='value')\n",
    "\n",
    "df_long.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Box Plots in Python using Seaborn\n",
    "Time for some data visualization and we start by creating a box plot using Seaborn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 864x864 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 447.27x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "\n",
    "# Change the size of the font\n",
    "sns.set(font_scale=1.2)\n",
    "\n",
    "g = sns.catplot(x=\"phase\", y=\"value\", kind=\"box\",\n",
    "                hue=\"treatment\", data=df_long)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Line Plots using Seaborn\n",
    "Next, we create some simple lineplots."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Two-Way Mixed ANOVA in Python\n",
    "Lets analyze the data using a Two-Way Mixed ANOVA using the Python package Pingouin"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "        Source     SS  DF1  DF2      MS       F     p-unc    np2    eps\n",
      "0    treatment  37.35    2   13  18.675   2.914  0.090042  0.310      -\n",
      "1        phase  33.50    2   26  16.750  23.626  0.000001  0.645  0.772\n",
      "2  Interaction  15.40    4   26   3.850   5.430  0.002578  0.455      -\n"
     ]
    }
   ],
   "source": [
    "from pingouin import mixed_anova\n",
    "\n",
    "aov = mixed_anova(dv='value', between='treatment',\n",
    "                  within='phase', subject='id', data=df_long)\n",
    "\n",
    "print(aov)"
   ]
  }
 ],
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