ExploratoryAnalyses.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#  <span style=\"color:black\">Exploratory Analyses in Python</span>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## <span style=\"color:orange\">ANALYSES AND PYTHON CODE</span>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This script will show how to run exploratory analyses in Python. A [YouTube video](https://www.youtube.com/watch?v=htYV2S1KsnU), a script in the [R programming language](https://rrighart.github.io/RExplor/), and additional materials can be found at my [GitHub](https://rrighart.github.io) page."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "data = {'subject': ['Pierre','Anne','Joyce','Peter','Alan','Camille'], 'age': [20, 16, 19, 99, 23, 18], 'sex': ['M','F','F','M', np.nan, 'F'], 'height': [172, 181, 165, 168, 177, 178], 'speed': [11.20, 3.00, 11.50, 10.35, 10.98, 13.05]}\n",
    "\n",
    "df = pd.DataFrame(data, columns = ['subject','age','sex','height','speed'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>subject</th>\n",
       "      <th>age</th>\n",
       "      <th>sex</th>\n",
       "      <th>height</th>\n",
       "      <th>speed</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Pierre</td>\n",
       "      <td>20</td>\n",
       "      <td>M</td>\n",
       "      <td>172</td>\n",
       "      <td>11.20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Anne</td>\n",
       "      <td>16</td>\n",
       "      <td>F</td>\n",
       "      <td>181</td>\n",
       "      <td>3.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Joyce</td>\n",
       "      <td>19</td>\n",
       "      <td>F</td>\n",
       "      <td>165</td>\n",
       "      <td>11.50</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Peter</td>\n",
       "      <td>99</td>\n",
       "      <td>M</td>\n",
       "      <td>168</td>\n",
       "      <td>10.35</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Alan</td>\n",
       "      <td>23</td>\n",
       "      <td>NaN</td>\n",
       "      <td>177</td>\n",
       "      <td>10.98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Camille</td>\n",
       "      <td>18</td>\n",
       "      <td>F</td>\n",
       "      <td>178</td>\n",
       "      <td>13.05</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   subject  age  sex  height  speed\n",
       "0   Pierre   20    M     172  11.20\n",
       "1     Anne   16    F     181   3.00\n",
       "2    Joyce   19    F     165  11.50\n",
       "3    Peter   99    M     168  10.35\n",
       "4     Alan   23  NaN     177  10.98\n",
       "5  Camille   18    F     178  13.05"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(6, 5)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>subject</th>\n",
       "      <th>age</th>\n",
       "      <th>sex</th>\n",
       "      <th>height</th>\n",
       "      <th>speed</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Pierre</td>\n",
       "      <td>20</td>\n",
       "      <td>M</td>\n",
       "      <td>172</td>\n",
       "      <td>11.20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Anne</td>\n",
       "      <td>16</td>\n",
       "      <td>F</td>\n",
       "      <td>181</td>\n",
       "      <td>3.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Joyce</td>\n",
       "      <td>19</td>\n",
       "      <td>F</td>\n",
       "      <td>165</td>\n",
       "      <td>11.50</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Peter</td>\n",
       "      <td>99</td>\n",
       "      <td>M</td>\n",
       "      <td>168</td>\n",
       "      <td>10.35</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  subject  age sex  height  speed\n",
       "0  Pierre   20   M     172  11.20\n",
       "1    Anne   16   F     181   3.00\n",
       "2   Joyce   19   F     165  11.50\n",
       "3   Peter   99   M     168  10.35"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head(4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "subject     object\n",
       "age          int64\n",
       "sex         object\n",
       "height       int64\n",
       "speed      float64\n",
       "dtype: object"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.dtypes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Some basic statistics can be given by <b><span style=\"background-color:rgba(0, 0, 0, 0.0470588)\"> describe</span></b>. Use <b><span style=\"background-color:rgba(0, 0, 0, 0.0470588)\"> np.round(df.describe(), decimals=2) </span></b> for rounding to two decimals."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>age</th>\n",
       "      <th>height</th>\n",
       "      <th>speed</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>6.000000</td>\n",
       "      <td>6.000000</td>\n",
       "      <td>6.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>32.500000</td>\n",
       "      <td>173.500000</td>\n",
       "      <td>10.013333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>32.660374</td>\n",
       "      <td>6.220932</td>\n",
       "      <td>3.551741</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>16.000000</td>\n",
       "      <td>165.000000</td>\n",
       "      <td>3.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>18.250000</td>\n",
       "      <td>169.000000</td>\n",
       "      <td>10.507500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>19.500000</td>\n",
       "      <td>174.500000</td>\n",
       "      <td>11.090000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>22.250000</td>\n",
       "      <td>177.750000</td>\n",
       "      <td>11.425000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>99.000000</td>\n",
       "      <td>181.000000</td>\n",
       "      <td>13.050000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             age      height      speed\n",
       "count   6.000000    6.000000   6.000000\n",
       "mean   32.500000  173.500000  10.013333\n",
       "std    32.660374    6.220932   3.551741\n",
       "min    16.000000  165.000000   3.000000\n",
       "25%    18.250000  169.000000  10.507500\n",
       "50%    19.500000  174.500000  11.090000\n",
       "75%    22.250000  177.750000  11.425000\n",
       "max    99.000000  181.000000  13.050000"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "##  <span style=\"color:black\">Missing values</span>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To inspect if and where there are missing values (NaN) in the data. The command <b><span style=\"background-color:rgba(0, 0, 0, 0.0470588)\">df.isnull()</span></b> gives the same result."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>subject</th>\n",
       "      <th>age</th>\n",
       "      <th>sex</th>\n",
       "      <th>height</th>\n",
       "      <th>speed</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  subject    age    sex height  speed\n",
       "0   False  False  False  False  False\n",
       "1   False  False  False  False  False\n",
       "2   False  False  False  False  False\n",
       "3   False  False  False  False  False\n",
       "4   False  False   True  False  False\n",
       "5   False  False  False  False  False"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.isnull(df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you want the row and column where NaNs occur. Please remind that Python indexing starts at zero, so the first row and first column are indexed \"0\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([4]), array([2]))"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.where(pd.isnull(df))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##  <span style=\"color:black\">Impossible extreme values</span>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "We can use boxplots to see if there are impossible extreme values in the data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that normally selecting the three variables in a boxplot, using the commands <b><span style=\"background-color:rgba(0, 0, 0, 0.0470588)\">df[['age', 'height', 'speed']].boxplot()</span></b> and <b><span style=\"background-color:rgba(0, 0, 0, 0.0470588)\">plt.show()</span></b>, would have been good solutions. But the problem here is that not the same scaling is used for the three measures. For this reason, one should make boxplots separately, shown side-by-side."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The <b><span style=\"background-color:rgba(0, 0, 0, 0.0470588)\">add_subplot(x,y,z)</span></b> command is used for the positioning of the figures, where the first number denotes that there is one row, the second number denotes that there are three columns, and the third number denotes the position. The command <b><span style=\"background-color:rgba(0, 0, 0, 0.0470588)\">fig.tight_layout()</span></b> is to regulate the spacing between figures."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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nnnlm2iWIJGLPGxtoIse3N0Bj4+jzK01CXx98ZAF0vbFhXPWJVCutF+KlxklE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\nzMysTv8DCdaZmAkZL68AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f37f34b9ed0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "\n",
    "fig.add_subplot(1,3,1)\n",
    "df[['age']].boxplot(sym='.')\n",
    "\n",
    "fig.add_subplot(1,3,2)\n",
    "df[['height']].boxplot(sym='.')\n",
    "\n",
    "fig.add_subplot(1,3,3)\n",
    "df[['speed']].boxplot(sym='.')\n",
    "\n",
    "fig.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##  <span style=\"color:black\">Finding & replacing extreme values manually</span>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compute the mean before the removal of outliers:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "32.5"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['age'].mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Check if there are cases that are older than 40 years:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    False\n",
       "1    False\n",
       "2    False\n",
       "3     True\n",
       "4    False\n",
       "5    False\n",
       "Name: age, dtype: bool"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['age']>40"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Replace the case(s) older than 40 with a missing value (NA)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "df['age'][df['age']>40]=np.nan"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>subject</th>\n",
       "      <th>age</th>\n",
       "      <th>sex</th>\n",
       "      <th>height</th>\n",
       "      <th>speed</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Pierre</td>\n",
       "      <td>20.0</td>\n",
       "      <td>M</td>\n",
       "      <td>172</td>\n",
       "      <td>11.20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Anne</td>\n",
       "      <td>16.0</td>\n",
       "      <td>F</td>\n",
       "      <td>181</td>\n",
       "      <td>3.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Joyce</td>\n",
       "      <td>19.0</td>\n",
       "      <td>F</td>\n",
       "      <td>165</td>\n",
       "      <td>11.50</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Peter</td>\n",
       "      <td>NaN</td>\n",
       "      <td>M</td>\n",
       "      <td>168</td>\n",
       "      <td>10.35</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Alan</td>\n",
       "      <td>23.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>177</td>\n",
       "      <td>10.98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Camille</td>\n",
       "      <td>18.0</td>\n",
       "      <td>F</td>\n",
       "      <td>178</td>\n",
       "      <td>13.05</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   subject   age  sex  height  speed\n",
       "0   Pierre  20.0    M     172  11.20\n",
       "1     Anne  16.0    F     181   3.00\n",
       "2    Joyce  19.0    F     165  11.50\n",
       "3    Peter   NaN    M     168  10.35\n",
       "4     Alan  23.0  NaN     177  10.98\n",
       "5  Camille  18.0    F     178  13.05"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "19.199999999999999"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['age'].mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "##  <span style=\"color:black\">Inspecting mean age for male and female participants</span>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Mean age for male and female participants."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "grpsex = df.groupby('sex')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "sex\n",
       "F    17.666667\n",
       "M    20.000000\n",
       "Name: age, dtype: float64"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grpsex['age'].mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, use <b><span style=\"background-color:rgba(0, 0, 0, 0.0470588)\"> np.round(grpsex['age'].mean(), decimals=2) </span></b> for rounding to two decimals."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##  <span style=\"color:black\">Inspecting relations between variables</span>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use a scatterplot to display the relation between age and speed:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "df.iloc[1,4]=np.nan; # command used to make missing value of 3.00 ms"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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AjsAmwFXAY8Df1NsfaFaBkiSpc4x3xePLVM/s2JJ6taP2b8Ah61uUJEnqTOO9xmM2cEBm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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f37f34b9d10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(df['age'], df['speed'], facecolors='none', edgecolors='b')\n",
    "plt.xlim(15.5,23.5)\n",
    "plt.ylim(10.0, 13.5)\n",
    "plt.xlabel('Age')\n",
    "plt.ylabel('Speed')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that the above figure are the data after the two outliers were replaced by NaN (as discussed in the [YouTube video](https://www.youtube.com/watch?v=htYV2S1KsnU)). So for this reason there are only four datapoints left.\n",
    "Actually, up to now, we only replaced one outlier for Age with a NaN. See the Quiz question below for replacing the outlier in the variable *speed* with NaN."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## <span style=\"color:orange\">QUIZ QUESTIONS AND ANSWERS</span>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##  <span style=\"color:black\">Quiz Question I</span>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Replace the outlier of 3.00 ms in the variable *df$speed* with a NaN."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Answer** There are multiple solutions possible:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df.iloc[1,4]=3.00;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "df['speed'][df['speed']==3.00]=np.nan"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another solution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df.iloc[1,4]=np.nan"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To verify that the value was indeed replaced by NaN use the command <b><span style=\"background-color:rgba(0, 0, 0, 0.0470588)\"> pd.isnull </span></b>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    False\n",
       "1     True\n",
       "2    False\n",
       "3    False\n",
       "4    False\n",
       "5    False\n",
       "Name: speed, dtype: bool"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.isnull(df['speed'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##  <span style=\"color:black\">Quiz Question II</span>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A dataset could erroneously have double records (duplicates). This is bad and should be removed.\n",
    "Seeing the current dataset, what would be a way to discover duplicates in the variable *df$subject*?\n",
    "Check your solution for the following data.frame that contains double data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "data = {'subject': ['Pierre','Anne','Joyce','Peter','Alan','Camille', 'Pierre'], 'age': [20, 16, 19, 99, 23, 18, 20], 'sex': ['M','F','F','M', np.nan, 'F', 'M'], 'height': [172, 181, 165, 168, 177, 178, 172], 'speed': [11.20, 3.00, 11.50, 10.35, 10.98, 13.05, 11.20]}\n",
    "\n",
    "df = pd.DataFrame(data, columns = ['subject','age','sex','height','speed'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Answer**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A way to inspect for double records is to use the <b><span style=\"background-color:rgba(0, 0, 0, 0.0470588)\">value_counts()</span></b> function. For this purpose, we need to transform the variable of interest to a *Pandas Series*."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "dfsubject = pd.Series(df['subject'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pierre     2\n",
       "Joyce      1\n",
       "Alan       1\n",
       "Peter      1\n",
       "Anne       1\n",
       "Camille    1\n",
       "Name: subject, dtype: int64"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dfsubject.value_counts()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But still simpler, using the <b><span style=\"background-color:rgba(0, 0, 0, 0.0470588)\">describe</span></b> function would also show that Pierre has two records:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count          7\n",
       "unique         6\n",
       "top       Pierre\n",
       "freq           2\n",
       "Name: subject, dtype: object"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['subject'].describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##  <span style=\"color:black\">CONTACT</span>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you have any questions, please do not hesitate to contact me: *<span style=\"color:blue\">rrighart@googlemail.com</span>*"
   ]
  }
 ],
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