Zusammenfassung
Bevor in den kommenden Kapiteln Funktionen zur inferenzstatistischen Datenanalyse besprochen werden, ist es notwendig Hilfsmittel vorzustellen, auf die viele dieser Funktionen zurückgreifen.
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Notes
- 1.
- 2.
Handelt es sich um eine zusammengesetzte H0 – etwa bei gerichteter H1, ist hier immer die H0 gemeint, die am dichtesten an der H1 liegt.
- 3.
In dieser Darstellung werden die unterschiedlichen Ansätze von Fisher sowie von Neyman und Pearson vermischt. Während für Fisher der p-Wert entsprechend des Likelihood-Prinzips ein Maß für die lokale Evidenz vorliegender Daten gegen die H0 ist, begrenzen Neyman und Pearson die langfristige Fehlerrate erster Art der häufig angewendeten Entscheidungsregel für die Wahl zwischen H0 und H1 auf α.
- 4.
Modellformeln verwenden die Wilkinson-Rogers-Notation (G. N. Wilkinson & Rogers, 1973; für Details vgl. ?formula). Im Sinne des allgemeinen linearen Modells beschreibt die rechte Seite einer Modellformel die spaltenweise Zusammensetzung der Designmatrix, die model.matrix(〈Modellformel〉) für ein konkretes Modell ausgibt (Abschn. 12.9 und Venables & Ripley, 2002, p. 144 ff.). Bei einem multivariaten Modell können auch mehrere AVn vorhanden sein.
- 5.
Orthogonale Polynome eines numerischen Prädiktors erzeugt poly() . Für splines s. das im Basisumfang von R enthaltene Paket splines mit den Funktionen ns() und und bs() .
- 6.
Für weitere Verteilungen vgl. ?Distributions sowie den Abschnitt Probability Distributions der CRAN Task Views (Dutang, 2016).
- 7.
- 8.
Im Fall diskreter (z. B. binomialverteilter) Variablen die Wahrscheinlichkeitsfunktion. Zusätzlich existiert mit pbirthday() eine Funktion zur Berechnung der Wahrscheinlichkeit, dass in einer Menge mit n Elementen coincident viele denselben Wert auf einer kategorialen Variable mit classes vielen, gleich wahrscheinlichen Stufen haben. Mit classes=365 und coincident=2 ist dies die Wahrscheinlichkeit, dass zwei Personen am selben Tag Geburtstag haben.
- 9.
Bei der Verwendung von Verteilungsfunktionen diskreter (z. B. binomialverteilter) Variablen ist zu beachten, dass die Funktion die Wahrscheinlichkeit dafür berechnet, dass die zugehörige Zufallsvariable Werte ≤ q annimmt – die Grenze q also mit eingeschlossen ist. Für die Berechnung der Wahrscheinlichkeit, dass die Variable Werte ≥ q annimmt, ist als erstes Argument deshalb q − 1 zu übergeben, andernfalls würde nur die Wahrscheinlichkeit für Werte > q bestimmt.
- 10.
Bei diskreten Verteilungen (z. B. Binomialverteilung) ist das Ergebnis bei lower.tail=TRUE der kleinste Wert, der in der zugehörigen Wahrscheinlichkeitsfunktion mindestens p links abschneidet. Bei lower.tail=FALSE ist das Ergebnis entsprechend der größte Wert, der mindestens p rechts abschneidet.
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Wollschläger, D. (2017). Hilfsmittel für die Inferenzstatistik. In: Grundlagen der Datenanalyse mit R. Statistik und ihre Anwendungen. Springer Spektrum, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53670-4_5
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