Varianzanalyse Berechnen Beispiel Essay

Multiples Testen

Obwohl der F-Test zeigt, dass ein Haupteffekt von TrMe auf Feinm besteht, muss anhand von Post-hoc-Tests geklärt werden, zwischen welchen Faktorstufen (Trainingsmethoden) signifikante Unterschiede bezüglich der Feinmotorik bestehen.

Bei der Berechnung von Post-hoc-Tests wird im Prinzip für jede Kombination von zwei Mittelwerten ein t-Test durchgeführt. Im aktuellen Beispiel mit fünf Gruppen sind dies 10 Tests. Multiple Tests sind jedoch problematisch, da der Alpha-Fehler (die fälschliche Ablehnung der Nullhypothese) mit der Anzahl der Vergleiche steigt. Wird nur ein t-Test mit einem Signifikanzlevel von .05 durchgeführt, so beträgt die Wahrscheinlichkeit des Nicht-Eintreffens des Alpha-Fehlers 95%. Werden jedoch zehn solcher Paarvergleiche vorgenommen, so beträgt die Nicht-Eintreffens-Wahrscheinlichkeit des Alpha-Fehlers (.95)10 = .598. Um die Wahrscheinlichkeit des Eintreffens des Alpha-Fehlers zu bestimmen, wird 1 - .598 = .402 gerechnet. Die Wahrscheinlichkeit des Eintreffens des Alpha-Fehlers liegt somit bei 40.2%. Diese Fehlerwahrscheinlichkeit wird als "Familywise Error Rate" bezeichnet.

Um dieses Problem zu beheben kann zum Beispiel die Bonferroni-Korrektur angewendet werden. Hierbei wird α durch die Anzahl der Paarvergleiche dividiert. Im hier aufgeführten Fall ist dies .05/10 = .005. Das heisst, jeder Test wird gegen ein Niveau von .005 geprüft. Die Bonferroni-Korrektur führt zu eher konservativen Tests bezüglich des Alpha-Fehlers, während andere Korrekturen weniger konservativ sind. SPSS bietet eine grosse Auswahl an möglichen Korrekturen (vgl. Klicksequenz in Abbildung 3).

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