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zA22@PA9O$<A|8LxAyQKSK}YxxW(1HIVK_lAfEo5LoB8;mf7pqT%ggh}+8|*3zw7${ z+5`jvc_4qR5rXbtd4Z@Z;D6Q{-qH)e{nH2_VvFEI+<^Wm9L)QB3;zSg^Dl=%K*;Z1 z^ba}+6tPA80|tfi^Zy+z*ni3up%@XFKL|l!KE6LAjbQ$l5-2|u{3kDzANYH3`a>}y zFaH690TJZ``ZK+Oyof;k8BVAG^v^U!@bUuxr9|Mbt@s~`5%T_BBK-VdFzg@J06_wL z5S~8;@&ZB7Kf{Vp3;okTUJxJfUobET^hcfpc@Z1(e{vP}_eP2U^6~tceEbkZX#Qy+ zVk-mwX$)c$=l?U*2(6%h6&M7{%ln5TFvPMWO#G)35U&83?+?WY7?k&)Yxg@^z(1pa zsA7JBKN1)L6X5;BImDfVUjR&lSbxOvpCkk$>InKr!XaSb-_LV@&_RAb%=`i4{e7GL z1NOg}{{M6!RR2GR|8pM$1Ak9l`6n|N#LEj87z9wjpoq~c8qUs$N3h@i{(c0Lcd~Xy zTp=Rz*OfGlfiOfs3Mk9RBL$J-=K(?`q`?9_AZY<0A0lxjKs>TQQJVjM5+fSK1G1aD anX9{(tCckt;uZ~ofUwXR8D&&uvHm|Ti-qL? diff --git a/Bericht/bericht.tex b/Bericht/bericht.tex index 7407825..f79de21 100644 --- a/Bericht/bericht.tex +++ b/Bericht/bericht.tex @@ -41,7 +41,7 @@ Die Daten sind zufällig generiert und enthalten Informationen zu Studenten: Ges Für die Lösung der Frage ob Studenten, die den Vorbereitungskurs abgeschlossen haben bessere Leistungen erzielen, werden die Leistungen der Studenten mit abgeschlossenem Vorbereitungskurs den Leistungen der Studenten ohne abgeschlossenem Vorbereitungskurs in einem QQ-Plot gegenübergestellt, aus dem ablesbar sein wird, dass die Studenten mit abgeschlossenem Vorbereitungskurs bessere Leistungen erzielen. -In der zweiten Visualisierung wird die Frage beantwortet, ob die Leistung der Studenten vom Bildungsgrad der Eltern abhängt. Dazu werden analog der ersten Visualisierung die Studenten nach Bildungsgrad der Eltern aufgeteilt und es werden jeweils die Quantile für die Durchschnittliche Leistung für jeden Bildungsgrad berechnet. Es gibt insgesamt 6 Bildungsgrade: Associateabschluss, Bachelorabschluss, Masterabschluss, Oberschulabschluss, irgendein Collageabschluss, irgendein Oberschulabschluss. Daher kann der QQ-Plot nicht 2-Dimensional erfolgen, stattdessen wird dieser QQ-Plot mehrdimensional gezeichnet. Zusätzlich gibt es die Interaktion bei der Mehrdimensionalen Darstellung 2 Dimensionen auszuwählen und dann einen 2D-Plot anzeigen zu lassen wie in der 1. Visualisierung. +In der zweiten Visualisierung wird die Frage beantwortet, ob die Leistung der Studenten vom Bildungsgrad der Eltern abhängt. Dazu werden analog der ersten Visualisierung die Studenten nach Bildungsgrad der Eltern aufgeteilt und es werden jeweils die Quantile für die Durchschnittliche Leistung für jeden Bildungsgrad berechnet. Es gibt insgesamt 6 Bildungsgrade: Associateabschluss, Bachelorabschluss, Masterabschluss, Oberschulabschluss, irgendein Collageabschluss, irgendein Oberschulabschluss. Daher kann der QQ-Plot nicht 2-Dimensional erfolgen, stattdessen wird dieser QQ-Plot mehrdimensional gezeichnet. Zusätzlich gibt es die Interaktionsmöglichkeit bei der Mehrdimensionalen Darstellung 2 Dimensionen auszuwählen und dann einen 2D-Plot anzeigen zu lassen wie in der 1. Visualisierung. %-Visualisierung 2- Gesamtpunktzahl splitten nach Bildungsgrad der Eltern -> Daraus Quantile berechnen -> Mehrdimensionalen QQ-Plot -Visualisierung 3- wie Vis1 nur mit sowas wie Chernoff-Gesichtern? @@ -104,6 +104,24 @@ Durch die Entfernung der Punkte von der Geraden erkennt man gut ob und in welche %Weiterhin müssen sie begründen, warum die gewählte visuelle Kodierung der Daten für das zulösenden Problem passend ist. Alternativ zum Quantil-Quantil-Plot könnte man in einem Boxplot 2 Boxen zeichnen: eine für die Studenten, die am Vorbereitungskurs teilgenommen haben und eine für die Studenten, die am Vorbereitungskurs nicht teilgenommen haben. Jede Box stellt dann die Verteilung der Leistungen der entsprechenden Studenten dar. Vorteil des Boxplots wäre, dass man die Mediane sowie die Quantile, die den Rand der Box darstellen, der beiden Verteilungen leichter vergleichen kann, da diese durch die Horizontale Position verglichen werden können und diese explizit durch Linien markiert sind, sodass der Vergleich leichter wahrzunehmen ist als beim Quantil-Quantil-Plot, bei dem man die Quantile selbst nicht direkt ablesen kann. Nachteil des Boxplots ist aber, dass nur wenige Quantile miteinander verglichen werden können, nämlich nur die, die durch die Linien eingezeichnet wurden, während im QQ-Plot zu jedem einzelnen eingetragenen zum Quantil zugehörigen Wert der entsprechende Wert des selben Quantils der anderen Verteilung abgelesen und so verglichen werden kann. Auf die Weise bekommt man ein schärferes Bild des Vergleichs. Durch die zusätzlich eingetragene Linie bei x=y kann man außerdem sehen welche Quantile näher am Gleich-sein sind und welche einen größeren Unterschied aufweisen. Diese Linie erlaubt einen Vergleich, bei dem man lediglich eindimensionale Abstände wahrnehmen muss. Eindimensionale, parallele Abstände lassen sich sehr einfach wahrnehmen. Dadurch überbringt diese Visualisierung ihre Hauptinformation, dessen Wahrnehmung den Betrachtern leicht fällt. Durch dieses schärfere Bild kann man somit nicht nur erkennen welche der Studentengruppen (mit abgeschlossenem Vorbereitungskurs, ohne abgeschlossenem Vorbereitungskurs) bessere Leistungen abscheidet, sondern auch die Studentengruppen aufzeigt, auf die sich der Vorbereitungskurs unterschiedlich stark auswirkt. So sieht man, dass die Wahrscheinlichkeit, dass Studenten, die den Vorbereitungskurs abgeschlossen haben eine sehr schlechte Leitung in der Prüfung aufzeigen deutlich geringer ist als die Wahrscheinlichkeit, dass Studenten, die den Vorbereitungskurs nicht abgeschlossen haben eine sehr schlechte Leistung in der Prüfung aufzeigen. Wohingegen die Wahrscheinlichkeit, dass Studenten, die den Vorbereitungskurs abgeschlossen haben eine sehr gute Leistung vollbringen ähnlich der Wahrscheinlichkeit, dass Studenten, die den Vorbereitungskurs nicht abgeschlossen haben und trotzdem eine sehr gute Leistung vollbringen, ist. \subsubsection{Visualisierung Zwei} +%Präsentieren sie die visuelle Abbildungen und Kodierungen der Daten und Interaktionsmöglichkeiten. +In der zweiten Visualisierung wird die Frage beantwortet, ob die Leistung der Studenten vom Bildungsgrad der Eltern abhängt. Dazu werden analog der ersten Visualisierung die Studenten nach Bildungsgrad der Eltern aufgeteilt und es werden jeweils die Quantile für die Durchschnittliche Leistung für jeden Bildungsgrad berechnet. Es gibt insgesamt 6 Bildungsgrade: Associateabschluss, Bachelorabschluss, Masterabschluss, Oberschulabschluss, irgendein Collageabschluss, irgendein Oberschulabschluss. Somit gibt es insgesamt 6 Dimensionen. Diese Daten werden in parallelen Koordinaten visualisiert. Jede Dimension wird hier auf einer senkrechten Achse dargestellt. Alle Achsen sind parallel zu einander. Ein Vergleichspunkt auf dieser Visualisierung ist ein Pfad, der über alle Dimensionen geht und somit die Werte aller Dimensionen miteinander verbindet. Über jeder Achse ist deren Beschriftung. Wenn man auf eines der schwarzen Dreiecke klickt, dann werden 2 benachbarte Achsen miteinander vertauscht. So kann man sich die Anordnung der Achsen so zurechtlegen, wie man daraus am besten die Information, nach der man sucht ablesen kann. Üblicherweise hat jede Achse seine eigene Skalierung, da unterschiedliche Dimensionen im Allgemeinen unterschiedliche Wertebereiche haben können. Bei dieser Visualisierung werden aber alle Achsen gleich skaliert. Das wird dadurch ermöglicht, dass jeder Wertebereich ein Teilbereich von 0 bis 100 ist. Die gleiche Skalierung der Achsen ermöglicht es die Dimensionen anhand des Höhenunterschiedes eines Pfads miteinander zu vergleichen. So sieht man leicht, dass der Wert des untersten Quantils beim Masterabschluss wesentlich besser ist als der Wert des selben Quantils beim Bachelorabschluss, da diese Gerade in Richtung der Bachelor-Achse nach unten geneigt ist. So kann man anhand der Neigungen der Geraden zwischen 2 Dimensionen erkennen welche der beiden Studentengruppen bessere Leistungen erreicht. +\begin{figure}[h] +\centering +\includegraphics[scale=0.365]{Bilder/Visualisierung2.jpg} +\end{figure} +Allerdings sieht man ebenso, dass zwischen 2 Dimensionen es oft sowohl steigende als auch fallende Geraden gibt, wodurch es schwieriger wird eine Aussage für die 2 gesamten Gruppen zu treffen. Daher wurde noch die Interaktionsmöglichkeit hinzugefügt, die erlaubt bis zu 2 Achsen auszuwählen. Diese beiden Achsen werden dann in einem 2-dimensionalen QQ-Plot gegenübergestellt (analog Visualisierung 1). Da der 1-dimensionale Abstand in der 1. Visualisierung viel leichter wahrgenommen werden kann als geringe Anstiegsunterschiede von Geraden, lässt es sich mit der 2-dimensionalen Darstellung leichter ermitteln welche der beiden Studentengruppen dann doch besser ist und wenn deren Leistung dann durchschnittlich doch auf das gleiche hinauskommt, kann man trotzdem mit der 2-dimensionalen Darstellung konkretere Aussagen treffen. Außerdem gibt es noch die Interaktionsmöglichkeit mit der Maus über eine der Achsen zu fahren und damit die Beschriftung der Werte der Achse ablesen zu können. + +\begin{figure}[h] +\centering +\includegraphics[scale=0.365]{Bilder/Visualisierung2-1.jpg} +\end{figure} + +%Sie müssen begründen, warum und wiegut ihre Designentscheidungen die erstellten Anforderungen erfüllen. +Diese Visualisierung zeigt gut wie die Leistung der Studenten vom Bildungsgrad der Eltern abhängt: Man hat sowohl einen Überblick über alle Bildungsgrade durch die Mehrdimensionale Darstellung als auch ist man in der Lage 2 Dimensionen miteinander optisch zu vergleichen anhand der Neigungen der Geraden zwischen den 2 Dimensionen. Durch die Interaktionsmöglichkeit die Achsen beliebig anzuordnen, kann man so 2 beliebige Dimensionen miteinander vergleichen. Für einen detailreicheren Vergleich hilft die Auswahl der zu vergleichenden Achsen und deren Gegenüberstellung in einem QQ-Plot der gleichen Art wie der ersten Visualisierung. Die Interaktionsmöglichkeit mit der Maus über eine Achse zu fahren und dabei dann die Beschriftung der Werte dieser Achse zu sehen ermöglicht es sowohl alle Pfade vollständig sehen zu können, während die Maus nicht auf einer dieser Achsen ist, als auch den Wert dieser Dimension dieses Mehrdimensionalen Punktes näherungsweise ablesen zu können, während die Maus auf einer dieser Achsen ist. Insgesamt kann man die Leistungen der verschiedenen Studentengruppen, die nach dem Bildungsgrad der Eltern gebildet wurden, sehr einfach und übersichtlich miteinander vergleichen. + +%Weiterhin müssen sie begründen, warum die gewählte visuelle Kodierung der Daten für das zulösenden Problem passend ist. +Es gibt auch Alternativen wie man Mehrdimensionale Daten darstellen kann: beispielsweise Chernoff-Gesichter, Sternkoordinaten oder Sternförmige Koordinaten. Aber keine dieser Alternativen ermöglicht es so einfach die Dimensionen miteinander zu vergleichen wie die Parallelen Koordinaten: Chernoff-Gesichter bilden Elemente auf einer Fläche. Aufgrund der Kompliziertheit jedes Gesichts ist es schwierig den Vergleich wahrzunehmen. Außerdem ist es schwierig bei ihnen konkrete Werte abzulesen. Eignet sich also nicht so gut für Vergleiche. Sternkoordinaten platzieren Punkte auf einer Fläche, deren Werte der verschiedenen Dimensionen nicht mehr eindeutig ablesbar sind, daher eignet sich das auch nicht für Vergleiche. Sternförmige Koordinaten sind da etwas näher dran: Die Punkte in Sternförmigen Koordinaten werden genauso dargestellt wie in parallelen Koordinaten mit dem einzigen Unterschied, dass alle Achsen sich in einem Punkt treffen und sternförmig voneinander gehen. Bei diesen Koordinaten wäre ein Vergleich machbar, da man 2 Werte von 2 Dimensionen anhand der Entfernung zum Mittelpunkt vergleichen könnte. Allerdings ist es schwieriger die Längen von 2 nichtparallelen Linien, die sich in einem Endpunkt treffen zu vergleichen, als den Anstieg einer geraden Linie wahrzunehmen. Daher sind parallele Koordinaten die beste Wahl. \subsubsection{Visualisierung Drei} \subsection{Interaktion} -- GitLab