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Testtheorie und Informationstheorie

In: Grundlagen der erforschenden Statistik

Author

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  • Ernst P. Billeter

    (Universität Freiburg
    Pennsylvania State University)

Abstract

Zusammenfassung Schon im Band über die Grundlagen der Elementarstatistik (7) wurde auf diese Beziehung zwischen Statistik und Informationstheorie hingewiesen [(7), S. 42–57]. Diese Beziehung soll hier wieder aufgenommen und versucht werden, die informationstheoretische Bedeutung der statistischen Testtheorie aufzuzeigen1. Dabei hat es sich ergeben, daß die beiden Begriffe des Informationsgehaltes und dessen Messung sowie der Entropie als eines Ausdruckes der Unbestimmtheit von grundlegender Bedeutung sind. Der Informationsgehalt wird bekanntlich als logarithmische Funktion gekennzeichnet. Der Informationsgehalt eines Versuchsergebnisses über ein Ereignis E, dem die Wahrscheinlichkeit p zukommt, stellt sich nämlich auf $$J(E) = {\log _{2}}\frac{1}{p}Bit $$ .

Suggested Citation

  • Ernst P. Billeter, 1972. "Testtheorie und Informationstheorie," Springer Books, in: Grundlagen der erforschenden Statistik, chapter 3, pages 171-179, Springer.
    • Handle: RePEc:spr:sprchp:978-3-7091-8289-5_3
    DOI: 10.1007/978-3-7091-8289-5_3
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