03_DescriptiveAnalysis.ipynb

{
 "cells": [
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    "# Deskriptive Analyse von Daten\n",
    "\n",
    "Jede gute Datenanalyse beinhaltet eine deskriptive Untersuchung der Daten. Dies erfolgt meist eher zu Beginn einer Auswertung, um sich einen ersten Eindruck zu den Merkmalsausprägungen der Daten und potentiellen Zusammenhängen zu machen. Zur deskriptiven Analyse gehört die Interpretation der Verteilung einzelner Merkmale und auch deren Zusammenhänge. Passend für diesen Einsatzbereich sind quantitative Kennzahlen aus der beschreibenden Statistik und graphische Darstellungen. Wir wollen uns in diesem Kapitel einen kleinen Überblick über gängige Kennzahlen und Graphiken verschaffen und diskutieren, welche Schlüsse hieraus gezogen werden können. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Datenerhebung und Datenkollektion\n",
    "\n",
    "Jeder Datenanalyse geht die Erhebung von Daten voraus. Ziel der Analyse ist es möglichst allgemein gültige Zusammenhänge zu identifizieren. Beispielsweise könnten wir uns dafür interessieren, welche Faktoren den Mietpreis von Mietwohungen in Deutschland beeinflussen. Die relevante Einheit unseres Beispiels wären die Wohnungen. Wären wir in der Lage Daten zu allen Wohnungen zu sammeln, so hätten wir den Überblick über die Grundgesamtheit. Dies ist bereits in diesem Beispiel mit offensichtlich hohem Aufwand verbunden bzw. sogar unmmöglich, wenn einige der Immobilieninhaber*innen nicht gewillt sind, die Daten mit uns zu teilen. Zudem stellt sich die Frage, welche Merkmale neben dem Mietpreis gemessen werden sollten, die potentiell Einfluss auf diesen haben. \n",
    "\n",
    "Das einzige was als Lösung bleibt, ist es in der Regel eine Stichprobe der Einheiten (hier Wohnungen) zu ziehen und hierbei möglichst viel sinnvolle Merkmalsausprägungen je Einheit abzufragen. Beziehen wir die Stichprobe bereits von Dritten, müssen wir in der Regel mit dem was zugänglich ist, die Analyse durchführen und zu einem späteren Zeitpunkt entscheiden, ob wir die verschiedenen Merkmale als ausreichend für den Erkenntnisgewinn der Ananlyse betrachten.\n",
    "\n",
    "Eine Stichprobe sollte repräsentativ und zufällig, jedoch nicht willkürlich gewählt werden. In den meisten Fällen macht es am meisten Sinn, wenn jede Einheit mit der gleichen Wahrscheinlichkeit für eine Stichprobe gezogen wird. Ohne näher auf die statistischen Hintergründe einzugehen, kann man festhalten, dass die Erkenntnisse aus den Analysen der Stichprobe nur dann Rückschlüsse auf allgemeine Zusammenhänge zulassen, wenn die Stichprobe in etwa die Zusammenhänge der Daten der Grundgesamtheit widerspiegelt. Dennoch treten leichte unterschiedliche Resultate der Stichprobe bedingt durch die Zufälligkeit der Stichprobenziehung und der damit verbundenen Unvollständigkeit gegenüber der Gesamtpopulation mit Sicherheit auf. Die Quantifizierung dieser Unterschiedlichkeit ist ein zentraler Bestandteil der Statistik, jedoch nicht im zentralen Fokus dieses Kurses. Dennoch sollen die genannten Argumente für einen vorsichtigen Umgang mit den Ergebnissen der Datenanalyse sensibilisieren.\n",
    "\n",
    "## Umgang mit fehlenden Daten\n",
    "\n",
    "In vielen Datensätzen fehlen oft Werte, dies ist meist durch Kürzel wie \"NA, NAN, na, nan\" gekennzeichnet. Wir wollen es im Umgang mit fehlenden Werten in diesem Kurs einfach halten und fokussieren uns daher auf die eher einfachen bestehenden Lösungen. Die beiden einfachsten Möglichkeiten bestehen entweder darin die Zeile (also eine Beobachtung was in der Regel den Ausprägungen einer statistischen Einheit entspricht) zu löschen, in der es zu mindestens einem fehlenden Wert kommt. Dies macht Sinn, wenn der gesamte Datensatz dadurch nicht zu stark reduziert wird. Kommt es vor allem bei einem Merkmal zu häufigen fehlenden Werten, kann auch überlegt werden, nur diese Spalte, also alle Ausprägungen eines Merkmals zu löschen. Alternativ können fehlende Werte durch möglichst repräsentative Werte ersetzt werden. Dies sollte jedoch nicht zu leichtfertig gemacht werden, da auf diese Art eine Verzerrung der Realität bei der Analyse eingeführt wird. Dennoch kann es die bessere Lösung sein, wenn auf anderem Weg die Datengrundlage zu stark eingeschränkt wird. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Merkmalstypen und Skalen\n",
    "\n",
    "Oft sind Datensätze eine Sammlung von Merkmalsausprägungen verschiedener Variablen von Einheiten. Man unterscheidet bei Merkmalen ob diese diskret (mit endlich abzählbar oder unendlich abzählbar vielen möglichen Realisierungen) oder stetig (alle Realisierungen in einem Intervall sind möglich) sind. Zudem ist das Skalenniveu eines Merkmals wichtig für die Datenanalyse. Folgende Skalenniveus werden unterschieden:\n",
    "\n",
    "* nominal: Kategorien, ohne sinnvolle Reihung\n",
    "* ordinal: mögliche Reihung, keine sinnvolle Interpretation der Abstände\n",
    "* kardinal bzw. metrisch: mögliche Reihung und Abstandsinterpretation, zum Teil jedoch ohne sinnvollen Nullpunkt (Intervallskala vs. Verhältnisskala)\n",
    "\n",
    "In der unteren Zelle sehen wir beispielsweise einen Datensatz von Schülern, bei dem es um eine mögliche Analyse zwischen den Zusammenhang zwischen der Prüfungsleistung (G3) und weiteren Merkmalen geht. Die Variable \"sex\" bezieht sich z.B. auf das Geschlecht und ist kategorial, hier ist es durch \"F\" für female und \"M\" wie male abgekürzt. Um die Ausprägungen dieser Variable später analysieren zu können bietet es sich an die Kategorien in Zahlenwerte zu transformieren. Dennoch machen auch nach der Kodierung mathematische Berechnungen wie die Addition inhaltlich keinen Sinn. \"Fedu\" und \"Medu\" sind gemäß der Variablenbeschreibung klar ordinal. Beispielsweise das Alter \"age\" ist metrisch. "
   ]
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       "      <th>sex</th>\n",
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       "      <th>Medu</th>\n",
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       "      <th>studytime</th>\n",
       "      <th>freetime</th>\n",
       "      <th>absences</th>\n",
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       "      <th>3</th>\n",
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       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>10</td>\n",
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      "text/plain": [
       "  sex  age  Medu  Fedu  studytime  freetime  absences  G3\n",
       "0   F   18     4     4          2         3         6   6\n",
       "1   F   17     1     1          2         3         4   6\n",
       "2   F   15     1     1          2         3        10  10\n",
       "3   F   15     4     2          3         2         2  15\n",
       "4   F   16     3     3          2         3         4  10"
      ]
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   ],
   "source": [
    "import pandas as pd\n",
    "\n",
    "\n",
    "# import original data\n",
    "df_math = pd.read_csv(\"../Daten/student/student-mat.csv\", sep = \";\")\n",
    "\n",
    "# variable descriptions\n",
    "# sex - student's sex (binary: \"F\" - female or \"M\" - male)\n",
    "# age - student's age (numeric: from 15 to 22)\n",
    "# Medu - mother's education (numeric: 0 - none,  1 - primary education (4th grade), 2 – 5th to 9th grade, 3 – secondary education or 4 – higher education)\n",
    "# Fedu - father's education (numeric: 0 - none,  1 - primary education (4th grade), 2 – 5th to 9th grade, 3 – secondary education or 4 – higher education)\n",
    "# studytime - weekly study time (numeric: 1 - <2 hours, 2 - 2 to 5 hours, 3 - 5 to 10 hours, or 4 - >10 hours)\n",
    "# freetime - free time after school (numeric: from 1 - very low to 5 - very high)\n",
    "# absences - number of school absences (numeric: from 0 to 93)\n",
    "# G3 - final grade (numeric: from 0 to 20, output target)\n",
    "df_math = df_math.loc[:, [\"sex\", \"age\", \"Medu\", \"Fedu\", \"studytime\", \"freetime\", \"absences\", \"G3\"]]\n",
    "df_math.head()"
   ]
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       "      <th>studytime</th>\n",
       "      <th>freetime</th>\n",
       "      <th>absences</th>\n",
       "      <th>G3</th>\n",
       "      <th>num_sex</th>\n",
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       "      <td>6</td>\n",
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       "      <td>1</td>\n",
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       "      <th>1</th>\n",
       "      <td>17</td>\n",
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       "      <td>4</td>\n",
       "      <td>10</td>\n",
       "      <td>1</td>\n",
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      "text/plain": [
       "   age  Medu  Fedu  studytime  freetime  absences  G3  num_sex\n",
       "0   18     4     4          2         3         6   6        1\n",
       "1   17     1     1          2         3         4   6        1\n",
       "2   15     1     1          2         3        10  10        1\n",
       "3   15     4     2          3         2         2  15        1\n",
       "4   16     3     3          2         3         4  10        1"
      ]
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   ],
   "source": [
    "# numerical transformation of the variable sex\n",
    "df_math.loc[:, \"num_sex\"] = df_math.sex.replace({\"F\": 1, \"M\": 0})\n",
    "df_math.astype({\"num_sex\": \"int32\"})\n",
    "df_math.drop([\"sex\"], axis = 1, inplace = True)\n",
    "df_math.head()"
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "## Quantitative Beschreibung der Merkmale\n",
    "\n",
    "Um einen ersten Überblick über die einzelnen Merkmalsausprägungen zu erhalten, bieten es sich an die Verteilungen dieser näher zu betrachten. Dies kann anhand von beschreibenden Kennzahlen aus der deskriptiven Statistik und anhand von geeigneten Grafiken durchgeführt werden. Gängige Kennzahlen sind das arithmetische Mittel, der Median, Minima, Maxima, Quantile, die Standardabweichung, Schiefe und Wölbung. Zur Wiederholung ein paar Definitionen.\n",
    "\n",
    "Für eine Anzahl von $n$ Beobachtungen eines Merkmals $x_1, ..., x_n$ ist das arithmetische Mittel definiert durch:\n",
    "\n",
    "$$\n",
    "\\bar{x} = \\frac{1}{n} \\sum_{i=1}^n x_i\n",
    "$$\n",
    "\n",
    "Gegeben eine geordnete Liste der Merkmalsausprägungen $x_{(1)}, ..., x_{(n)}$, ist der Median definiert durch:\n",
    "\n",
    "$$\n",
    "x_{med} = \n",
    "\\begin{cases}\n",
    " x_{\\left( \\frac{n+1}{2} \\right)} & \\text{wenn } n \\text{ ungerade}\\\\\n",
    " \\frac{1}{2} \\left(x_{(\\frac{n}{2})} + x_{(\\frac{n}{2}+1)} \\right) & \\text{wenn } n \\text{ gerade}\n",
    "\\end{cases}\n",
    "$$\n",
    "\n",
    "Das $p$ Quantil eines Merkmals ist der Wert für den ein Anteil der Ausprägungen $p$ kleiner oder gleich und mindestens ein Anteil $1-p$ größer oder gleich ist. Minimum und Maximum ist die jeweils kleinste bzw. größte aller Ausprägungen. Um die Schwankung der Ausprägungen untersuchen zu können, wird meist die empirische Standardabweichung verwendet. Die Varianz ist die mittlere quadratische Abweichung der Werte vom Mittelwert.\n",
    "\n",
    "$$\n",
    "s^2 = \\frac{1}{n} \\sum_{i=1}^n \\left( x_i - \\bar{x} \\right)^2\n",
    "$$\n",
    "\n",
    "Die empirische Standardabweichung ist die Wurzel der empirischen Varianz, $s = \\sqrt{s^2}$. Um die Schiefe der Verteilung empirisch zu analysieren wird oft der Momentenkoeffizient der Schiefe verwendet:\n",
    "\n",
    "$$\n",
    "g_m = \\frac{\\frac{1}{n} \\sum_{i - 1}^n \\left( x_i - \\bar{x} \\right)^3}{s^3}\n",
    "$$\n",
    "\n",
    "Ein negativer Wert spricht für eine linksschiefe, ein positiver Wert für eine rechtsschiefe Verteilung. Bei einem Wert von $0$ oder nahe $0$ kann man von einer symmetrischen Verteilung ausgehen. \n",
    "\n",
    "Die Wölbung der Verteilung wird oft mit dem Wölbunsmaß nach Fisher beurteilt:\n",
    "\n",
    "$$\n",
    "\\gamma = \\frac{\\frac{1}{n} \\sum_{i - 1}^n \\left( x_i - \\bar{x} \\right)^4}{s^4} - 3\n",
    "$$\n",
    "\n",
    "Beachten Sie, dass beim letzten Maß der Wert von $3$ abgezogen wird, um die Wölbung mit der einer Normalverteilung zu vergleichen. Bei einem Wert größer $0$ spricht man von einer leptokurtischen, bei einem Wert kleiner $0$ von einer platokurtischen Verteilung. Manche Statistikprogramme ziehen nicht per default den Wert von $3$, dies gilt es zur Sicherheit meist noch zu überprüfen.\n",
    "\n",
    "Wenn wir mit pandas DataFrames arbeiten, ist es relativ einfach diese deskriptiven Maße zu bestimmen. Zum einen besteht die *describe* Funktion, wodurch Anzahl der Beobachtungen, Mittelwert, Standardabweichung, Minimum, Maximum, Median sowie das 25\\% und 75\\% Quantil ausgegeben werden. Darüber hinaus existieren die *skew* und die *kurtosis* Funktion."
   ]
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>age</th>\n",
       "      <th>Medu</th>\n",
       "      <th>Fedu</th>\n",
       "      <th>studytime</th>\n",
       "      <th>freetime</th>\n",
       "      <th>absences</th>\n",
       "      <th>G3</th>\n",
       "      <th>num_sex</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>395.000000</td>\n",
       "      <td>395.000000</td>\n",
       "      <td>395.000000</td>\n",
       "      <td>395.000000</td>\n",
       "      <td>395.000000</td>\n",
       "      <td>395.000000</td>\n",
       "      <td>395.000000</td>\n",
       "      <td>395.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>16.696203</td>\n",
       "      <td>2.749367</td>\n",
       "      <td>2.521519</td>\n",
       "      <td>2.035443</td>\n",
       "      <td>3.235443</td>\n",
       "      <td>5.708861</td>\n",
       "      <td>10.415190</td>\n",
       "      <td>0.526582</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>1.276043</td>\n",
       "      <td>1.094735</td>\n",
       "      <td>1.088201</td>\n",
       "      <td>0.839240</td>\n",
       "      <td>0.998862</td>\n",
       "      <td>8.003096</td>\n",
       "      <td>4.581443</td>\n",
       "      <td>0.499926</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>15.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>16.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>8.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>17.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>11.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>18.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>8.000000</td>\n",
       "      <td>14.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>22.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>75.000000</td>\n",
       "      <td>20.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              age        Medu        Fedu   studytime    freetime    absences  \\\n",
       "count  395.000000  395.000000  395.000000  395.000000  395.000000  395.000000   \n",
       "mean    16.696203    2.749367    2.521519    2.035443    3.235443    5.708861   \n",
       "std      1.276043    1.094735    1.088201    0.839240    0.998862    8.003096   \n",
       "min     15.000000    0.000000    0.000000    1.000000    1.000000    0.000000   \n",
       "25%     16.000000    2.000000    2.000000    1.000000    3.000000    0.000000   \n",
       "50%     17.000000    3.000000    2.000000    2.000000    3.000000    4.000000   \n",
       "75%     18.000000    4.000000    3.000000    2.000000    4.000000    8.000000   \n",
       "max     22.000000    4.000000    4.000000    4.000000    5.000000   75.000000   \n",
       "\n",
       "               G3     num_sex  \n",
       "count  395.000000  395.000000  \n",
       "mean    10.415190    0.526582  \n",
       "std      4.581443    0.499926  \n",
       "min      0.000000    0.000000  \n",
       "25%      8.000000    0.000000  \n",
       "50%     11.000000    1.000000  \n",
       "75%     14.000000    1.000000  \n",
       "max     20.000000    1.000000  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_math.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "age          0.466270\n",
       "Medu        -0.318381\n",
       "Fedu        -0.031672\n",
       "studytime    0.632142\n",
       "freetime    -0.163351\n",
       "absences     3.671579\n",
       "G3          -0.732672\n",
       "num_sex     -0.106886\n",
       "dtype: float64"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_math.skew()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "age          -0.001222\n",
       "Medu         -1.090014\n",
       "Fedu         -1.198539\n",
       "studytime    -0.014432\n",
       "freetime     -0.301807\n",
       "absences     21.719150\n",
       "G3            0.403421\n",
       "num_sex      -1.998721\n",
       "dtype: float64"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_math.kurtosis()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Graphische Darstellung der Daten\n",
    "\n",
    "Es existieren viele anschauliche Möglichkeiten Daten zu visualisieren. Um möglichst erkenntnisreiche Informationen aus den Visualisierungen zu ziehen bedarf es jedoch Erfahrung und Fachkentniss. Wir wollen daher zunächst mit ein paar grundlegenden Grafiktypen beginnen. Die Wahl der passenden Grafik ist auch hier wieder in Teilen mit der Skala eines Merkmals verbunden. Um einen Überblick über die Verteilung von Merkmalsausprägungen zu erhalten bieten sich für nominal oder ordinal skalierte Merkmale Barplots (Stabdiagramme) und für metrisch skalierte Merkmale Histogramme an. \n",
    "\n",
    "\n",
    "### Univariate Verteilungen der Merkmalsausprägungen\n",
    "\n",
    "In der unteren Zelle sehen wir Barplots für die kategorialen bzw. ordinalen Merkmale. Bei den Barplots werden auf der x-Achse die Merkmalsausprägungen und auf der y-Achse die absoluten Häufigkeiten abgetragen. Wir können anhand dieser Darstellungen erkennen, dass die meisten Verteilungen der Merkmalsausprägungen nicht symmetrisch sind und insbesondere bei der \"studytime\" und \"freetime\" meist eine Kategorie deutlich häufiger als alle anderen Kategorien bei den Ausprägungen auftritt. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1400x500 with 5 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pylab as plt\n",
    "\n",
    "\n",
    "non_metric_vars = [\"Medu\", \"Fedu\", \"studytime\", \"freetime\", \"num_sex\"]\n",
    "\n",
    "fig_non_metric, axs_non_metric = plt.subplots(1, 5, figsize = (14, 5))\n",
    "for i, non_m_var in enumerate(non_metric_vars):\n",
    "    nobs_per_cat = df_math.groupby(non_m_var).size()\n",
    "    axs_non_metric[i].bar(nobs_per_cat.index, nobs_per_cat.values)\n",
    "    axs_non_metric[i].set_title(non_m_var)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In der nächsten Zelle sehen wir die Histogramme der metrischen Variablen. Bei einem Histogramm werden die Häufigkeiten der Ausprägungen innerhalb definierter Intervalle gezählt. An Stelle fester Intervallgrenzen wird auch oft eine Anzahl von Internallen (bins) vorgegeben, und die Intervallgrenzen werden entsprchend über die Bandbreite aller Merkmalsausprägungen bestimmt. Alternativ zur absoluten Anzahl der Merkmalsausprägungen innerhalb eines Intervalls, werden auf der y-Achse auch manchmal die empirischen Dichtewerte abgetragen. Hierbei werden die Häufigkeiten so normalsiert, dass die Fläche unterhalb des Histograms den Wert $1$ ergibt. Letzteres wird vor allem dann vorgezogen, wenn die empirische Verteilung mit Dichtefunktionen theoretischer Verteilungen verglichen werden soll."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x500 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pylab as plt\n",
    "\n",
    "\n",
    "metric_vars = [\"age\", \"absences\", \"G3\"]\n",
    "\n",
    "fig_metric, axs_metric = plt.subplots(1, 3, figsize = (12, 5))\n",
    "for i, m_var in enumerate(metric_vars):\n",
    "    axs_metric[i].hist(df_math[m_var], bins = 10, density = True)\n",
    "    axs_metric[i].set_title(m_var)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Eine weitere Möglichkeit eine graphischen Eindruck der Verteilungen zu erhalten, besteht durch die Verwendung von Boxplots, welche sowohl für nicht-metrische wie auch für metrische Variablen eingesetzt werden können. Im Vergleich zu den Barplots und den Histogrammen sind Boxplots besser geeignet, um einen Eindruch von extremen Werten und deren Häufung zu erhalten. Die nächste Zelle visualisiert die Boxplots aller Merkmale im Datensatz. Im Standard, der in der unteren Zelle gezeigt wird, entspricht die untere Kante der Box dem 25\\% und die obere Kante der Box dem 75\\% Quantil, der Strich in der Mitte symbolisiert den Median. Die äußeren Striche sind Abstände in Höhe des $1,5$-fachen des Interquartilsabstands. Als extremeren Ausprägungen werden durch einzelne Punkte dargestellt. Mit Hilfe der Boxplots im Beispiel lässt sich beispielsweise gut erkennen, dass es bei der Abwesenheit deutlich häufiger zu vereinzelt hohen Werten kommt, als bei den übrigen Merkmalen."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "boxplots = df_math.boxplot(figsize = (12, 6))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Darstellung von Zusammenhängen\n",
    "\n",
    "Sehr oft sind Zusammenhänge zwischen den Merkmalsausprägungen einzelner Variablen ebenso von großer Bedeutung für die Datenanalyse. Im ersten Schritt bieten sich Scatterplots an, um paarweise Zusammenhänge zwischen Variablen zu visualisieren. Diese liefern jedoch meist nur Erkenntnisse im Falle von stetigen Variablen. Beispielsweise sehen wir in der unteren Zelle einen Scatterplot zwischen der Abwesenheit und der finalen Note. Hieraus schein durchaus ein Zusammenhang ersichtlich zu sein. Daneben ist ein Scatterplot zwischen der Studien- und der Freizeit. Da beide Variablen in diesem Datensatz diskret sind, kann man aus dieser Ansicht nur erkennen, welche Werte-Kombinationen auftreten, was jedoch wenig erkenntnisreich ist. Als kleinen \"Workaround\" wäre es für solche Fälle möglich, die Größe der Punkte der Grafik proportional zur Häufigkeit der paarweisen Kombinationen darzustellen. Diese Graphik können Sie im dritten Plot betrachten. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x500 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pylab as plt\n",
    "\n",
    "fig, axs = plt.subplots(1, 3, figsize = (12, 5))\n",
    "\n",
    "df_math.plot.scatter(x = \"absences\", y = \"G3\", ax = axs[0])\n",
    "df_math.plot.scatter(x = \"freetime\", y = \"studytime\", ax = axs[1])\n",
    "\n",
    "count_study_free = df_math.groupby([\"freetime\", \"studytime\"]).size()\n",
    "x_levels = count_study_free.index.get_level_values(level = 0)\n",
    "y_levels = count_study_free.index.get_level_values(level = 1)\n",
    "\n",
    "for x in x_levels:\n",
    "    for y in y_levels:\n",
    "        axs[2].scatter(x, y, s = 2 * count_study_free.loc[x, y], color = \"#1f77b4\")\n",
    "\n",
    "axs[2].set_xlabel(\"freetime\")\n",
    "axs[2].set_ylabel(\"studytime\")\n",
    "\n",
    "axs[1].set_title(\"ohne Häufigkeitsinformation\")\n",
    "axs[2].set_title(\"mit Häufigkeitsinformation\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Die Möglichkeit alle paarweisen Abhängigkeiten eines Datensatzes zu visualisieren, besteht durch die Verwendung von Heatmaps der Korrelationsmatrix eines Datensatzes. Auch hier gilt es bei der Berechnung der Korrelationen, die Skalen der Merkmale zu beachten. Solange ein Merkmal mindestens ordinal skaliert ist, kann der Korrelationskoeffizient nach Spearman (Rangkorrelation) verwendet werden. In unserem Beispiel schließen wir daher die Variable des Geschlechts aus. In einer Heatmap werden durch Farben und Zahlen relativ schnell alle paarweisen Abhängigkeiten übersichtilich. Ein Beispiel finden Sie in der folgenden Zelle."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: >"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import seaborn as sns\n",
    "import matplotlib.pylab as plt\n",
    "\n",
    "\n",
    "corr_mat = df_math.drop([\"num_sex\"], axis = 1).corr(method = \"spearman\")\n",
    "mask = np.triu(np.ones_like(corr_mat))\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "sns.heatmap(corr_mat, annot= np.round(corr_mat,2), mask=mask, cmap = \"coolwarm\", ax = ax)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Zuletzt betrachten wir noch ein Beispiel für die Zusammenhangsanalyse, wenn wir an einer Zielvariable und den möglichen Einfluss von einzelnen unabhängigen Merkmalen interessiert sind, die nicht stetig skaliert sind. Es bietet sich hier an, Histogramme nach den Kategorien der unabhängigen Variablen zu generieren. Beispielsweise sehen wir in der Graphik der nächsten Zelle erneut in Histogrammform der finalen Prüfungsergebnisse, jedoch dieses Mal getrennt nach Personen mit hoher und geringerer Lernzeit. Derartige Grafiken lassen sich auch für Merkmale mit mehreren Ausprägungen erstellen. Gleichen sich die Histogramme des Merkmals von Interesse für unterschiedliche Kategorien eines anderen Merkmals, kann eher weniger von einem Einfluss des Merkmals auf die Zielvariable ausgegangen werden. Je unterschiedlicher die Verteilungen in Abhängigkeit der Kategorie, umso stärker ist potentiel der Einfluss des Merkmals."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pylab as plt\n",
    "\n",
    "\n",
    "fig, ax = plt.subplots(figsize = (8, 5))\n",
    "\n",
    "ax.hist(df_math[\"G3\"][df_math.studytime <= 2], alpha = 0.7, label = \"studytime <= 2\")\n",
    "ax.hist(df_math[\"G3\"][df_math.studytime > 2], alpha = 0.7, label = \"studytime > 2\")\n",
    "ax.set_title(\"Final test results\")\n",
    "ax.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hiermit beenden wir den Auszug aus den Möglichkeiten der graphischen Beschreibung von Daten. An dieser Stelle sei angemerkt, dass die Erzeugung erkenntnisreicher Graphiken ein lebenslanger Lernprozess ist, da gute graphische Visualisierungen stark vom jeweiligen Datensatz abhängen."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Vorbereitung der Daten\n",
    "\n",
    "Nach den ersten Erkenntnissen der deskriptiven Analyse, müssen manche Datenpunke vorbereitet werden, um Modelle der Datenanalyse mit diesen Daten zu trainieren. Die relevantesten Aspekte hierbei sind der Umgang mit kategorialen Daten und die Normierung quantitativer Merkmalsausprägungen. Bei nominalen und ordinalen Merkmalen, kann es vorkommen, dass diese im Datensatz als nicht numerische Werte übergebene werden, z.B. \"male\", \"female\" oder \"bad\", \"neutral\", \"good\". Für orinale Merkmale bietet es sich an, den Kategorien Zahlen entsprechend der oridinalen Reihung zuzuordnen, z.B. \"bad\" -> 1, \"neutral\" -> 2, \"good\" -> 3. Es ist übrigens nicht zwingend erforderlich, dass die Zahlen 1,2,3 verwendet werden, solange eine sinnvolle Logik bei der Reihung verwendet wird, können die Ausprägungen beliebig gewählt werden. Ist ein Merkmal nominal skaliert, wird häufig eine 1-0 Kodierung verwendet. Im Englischen spricht man vom One-Hot-Encoding dessen Name impliziert, dass die jeweils zutreffende Kategorie als \"Hot\" durch eine 1 markiert wird. Genauer muss beim One-Hot-Encoding so viele neue Variablen generieren, wie es Kategorien gibt. Bei zwei Kategorien würde beispielsweise die erste Kategorie durch den Vektor $\\begin{pmatrix} 1 & 0 \\end{pmatrix}^T$ und die zweite Kategorie durch den Vektor $\\begin{pmatrix} 0 & 1 \\end{pmatrix}^T$, bei drei Kategorien würde beispielsweise die erste Kategorie durch den Vektor $\\begin{pmatrix} 1 & 0 & 0 \\end{pmatrix}^T$, die zweite Kategorie durch den Vektor $\\begin{pmatrix} 0 & 1 & 0 \\end{pmatrix}^T$ und die dritte Kategorie durch den Vektor $\\begin{pmatrix} 0 & 0 & 1 \\end{pmatrix}^T$ dargestellt werden. Diese Art der Kodierung kann auch für ordinale Merkmale verwendet werden, jedoch geht hiermit die ordinale Information zunächst verloren. Alternativ wird in der Statistik auch die Dummy-Kodierung verwendet, bei der eine Kategorie als Standard festgelegt und die übrigen Ausprägungen durch $K-1$ 1-0 Variablen kodiert werden. \n",
    "\n",
    "Bei numerischen Merkmalen kann es oft sinnvoll und manchmal auch erforderlich sein, die Werte auf einen vergleichbaren Wertebereich zu bringen. Dies erleichtert bei der Analyse die Vergleichbarkeit der Einflussstärke und ist für manche Algorithmen erforderlich um numerische Probleme beim Trainieren der Modelle zu verhindern. Für diesen Zweck, können unterschiedliche Arten der Normierung gewählt werden. Zwei gängie Möglichkeit sind die Standardisierung:\n",
    "\n",
    "$$\n",
    "z = \\frac{x - \\bar{x}}{s}\n",
    "$$\n",
    "\n",
    "und die Min-Max-Skalierung:\n",
    "\n",
    "\n",
    "$$\n",
    "z = \\frac{x - \\min(x)}{\\max(x) - \\min(x)}\n",
    "$$\n",
    "\n",
    "In den unteren Zellen generieren wir einen Beispieldatensatz mit den Merkmalen \"gender\", \"assessment\" und \"score\". Die *info* Methode des pandas-DataFrames zeigt uns, dass es sich bei den ersten beiden Variablen um kategoriale Merkmale handelt, die im Textformat im Datensatz enthalten sind. Dies wird von pandas durch den Typ \"object\" signalisiert. Der Typ \"float64\" beschreibt eine floating point number, was eine Kommatrennzahl entspricht womit wir von einem numerischen Wert ausgehen können. Im ersten Schritt wird das Merkmal \"gender\" auf die Anzahl unterschiedlicher Ausprägungen analysiert und im Anschluss One-Hot-Encoded. Im Anschluss werden den Kategorien der Variable \"assessment\" in aufsteigender Reihenfolge Zahlen zugewiesen. Zuletzt wird die Variable \"score\" standardisiert und Min-Max skaliert. Die Auswirkung der unterschiedlichen Skalierung lässt sich am besten durch den Vergleich der Histogramme oder der Boxplots dieser Variablen visualisieren."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 500 entries, 0 to 499\n",
      "Data columns (total 3 columns):\n",
      " #   Column      Non-Null Count  Dtype  \n",
      "---  ------      --------------  -----  \n",
      " 0   gender      500 non-null    object \n",
      " 1   assessment  500 non-null    object \n",
      " 2   score       500 non-null    float64\n",
      "dtypes: float64(1), object(2)\n",
      "memory usage: 11.8+ KB\n",
      "None\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>gender</th>\n",
       "      <th>assessment</th>\n",
       "      <th>score</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>male</td>\n",
       "      <td>bad</td>\n",
       "      <td>3.086141</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>male</td>\n",
       "      <td>neural</td>\n",
       "      <td>1.538908</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>female</td>\n",
       "      <td>neural</td>\n",
       "      <td>1.024611</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>male</td>\n",
       "      <td>bad</td>\n",
       "      <td>3.094259</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>female</td>\n",
       "      <td>bad</td>\n",
       "      <td>3.540248</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   gender assessment     score\n",
       "0    male        bad  3.086141\n",
       "1    male     neural  1.538908\n",
       "2  female     neural  1.024611\n",
       "3    male        bad  3.094259\n",
       "4  female        bad  3.540248"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import random\n",
    "\n",
    "gender = [\"male\"] * 250 + [\"female\"] * 250\n",
    "random.shuffle(gender)\n",
    "assessment = [\"bad\"] * 150 + [\"neutral\"] * 200 + [\"good\"] * 150\n",
    "random.shuffle(assessment)\n",
    "numerical = np.random.normal(size = 500, loc = 2, scale = 2)\n",
    "\n",
    "df = pd.DataFrame({\"gender\": gender, \"assessment\": assessment, \"score\": numerical})\n",
    "print(df.info())\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The variable gender has the following unique values:\n",
      "['male' 'female']\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "\n",
       "    .dataframe thead th {\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>assessment</th>\n",
       "      <th>score</th>\n",
       "      <th>female</th>\n",
       "      <th>male</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>bad</td>\n",
       "      <td>3.086141</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>neural</td>\n",
       "      <td>1.538908</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>neural</td>\n",
       "      <td>1.024611</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>bad</td>\n",
       "      <td>3.094259</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>bad</td>\n",
       "      <td>3.540248</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  assessment     score  female  male\n",
       "0        bad  3.086141     0.0   1.0\n",
       "1     neural  1.538908     0.0   1.0\n",
       "2     neural  1.024611     1.0   0.0\n",
       "3        bad  3.094259     0.0   1.0\n",
       "4        bad  3.540248     1.0   0.0"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.preprocessing import OneHotEncoder\n",
    "\n",
    "\n",
    "one_hot_encoder = OneHotEncoder()\n",
    "\n",
    "print(\"The variable gender has the following unique values:\")\n",
    "print(df.gender.unique())\n",
    "\n",
    "df.loc[:, [\"female\", \"male\"]] = one_hot_encoder.fit_transform(df.gender.values.reshape(-1, 1)).toarray()\n",
    "df.drop([\"gender\"], axis = 1, inplace = True)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The variable assessment has the following unique values:\n",
      "['bad' 'neural' 'good']\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "\n",
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       "    }\n",
       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>assessment</th>\n",
       "      <th>score</th>\n",
       "      <th>female</th>\n",
       "      <th>male</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>3.086141</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>1.538908</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>1.024611</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>3.094259</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>3.540248</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   assessment     score  female  male\n",
       "0           1  3.086141     0.0   1.0\n",
       "1           2  1.538908     0.0   1.0\n",
       "2           2  1.024611     1.0   0.0\n",
       "3           1  3.094259     0.0   1.0\n",
       "4           1  3.540248     1.0   0.0"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(\"The variable assessment has the following unique values:\")\n",
    "print(df.assessment.unique())\n",
    "\n",
    "df.replace(to_replace = [\"bad\", \"neutral\", \"good\"], value = [1, 2, 3], inplace = True)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\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>assessment</th>\n",
       "      <th>score</th>\n",
       "      <th>female</th>\n",
       "      <th>male</th>\n",
       "      <th>standard_score</th>\n",
       "      <th>minmax_score</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>3.086141</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.505527</td>\n",
       "      <td>0.602140</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>1.538908</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>-0.267140</td>\n",
       "      <td>0.462879</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>1.024611</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-0.523973</td>\n",
       "      <td>0.416589</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>3.094259</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.509581</td>\n",
       "      <td>0.602870</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>3.540248</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.732302</td>\n",
       "      <td>0.643012</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   assessment     score  female  male  standard_score  minmax_score\n",
       "0           1  3.086141     0.0   1.0        0.505527      0.602140\n",
       "1           2  1.538908     0.0   1.0       -0.267140      0.462879\n",
       "2           2  1.024611     1.0   0.0       -0.523973      0.416589\n",
       "3           1  3.094259     0.0   1.0        0.509581      0.602870\n",
       "4           1  3.540248     1.0   0.0        0.732302      0.643012"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.preprocessing import StandardScaler, MinMaxScaler\n",
    "\n",
    "standard_scaler = StandardScaler()\n",
    "minmax_scaler = MinMaxScaler()\n",
    "\n",
    "df.loc[:, \"standard_score\"] = standard_scaler.fit_transform(df.score.values.reshape(-1, 1))\n",
    "df.loc[:, \"minmax_score\"] = minmax_scaler.fit_transform(df.score.values.reshape(-1, 1))\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x500 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pylab as plt\n",
    "\n",
    "fig, axs = plt.subplots(1, 3, figsize = (12, 5))\n",
    "axs[0].hist(df.score)\n",
    "axs[1].hist(df.standard_score)\n",
    "axs[2].hist(df.minmax_score)\n",
    "axs[0].set_title(\"score\")\n",
    "axs[1].set_title(\"standard_score\")\n",
    "axs[2].set_title(\"minmax_score\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: >"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df.loc[:, [\"score\", \"standard_score\", \"minmax_score\"]].boxplot()\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": ".fdavenv",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.16"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}