Zufallsstichprobe Beispiel Essay

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Die einfache Zufallsstichprobe ist eine probabilistische Stichprobe. Die Entscheidung darüber, welche Elemente der Population in eine einfache Zufallsstichprobe einbezogen werden, hängt ausschließlich vom Zufall ab.

Voraussetzung ist, dass jedes Untersuchungsobjekt der zu untersuchenden Population identifizierbar ist. Alle diese Objekte werden in einer Liste vollständig und erschöpfend aufgezählt. Aus dieser Liste wird im nächsten Schritt eine Stichprobe nach dem Zufallsprinzip ausgewählt.

Dies ist mittels verschiedener Strategien realisierbar:

  • Auswahl nach dem Lottoprinzip: Für jedes Element der Population wird ein Los angefertigt und nach dem Durchmischen werden mehrere Lose gezogen, die eine Stichprobe bilden.
  • Auswahl mittels Zufallszahlen: Elemente der Population werden durchnummeriert und mittels Tafeln mit Zufallszahlen wird die Stichprobe gezogen.
  • Systematische Auswahl: Aus der zufällig geordneten Reihenfolge der Objekte der Population wird jedes K-te Element ausgewählt. Hat die Population N Elemente, erhält man bei einem Stichprobenumfang n für: K=N/n. Das Element der Population, das den Startpunkt bildet, wird dabei zufällig ausgewählt. Ab diesem Startpunkt wird jedes K-te Element in die Stichprobe aufgenommen.

Beispiel:
Für die Auswahl einer einfachen Zufallsstichprobe wird als Erhebungsrahmen ein Telefonbuch verwendet. Es wird davon ausgegangen, dass ein Telefonbuch alle Untersuchungsobjekte (in diesem Fall Personen) der zu untersuchenden Population enthält. Die Personen werden anhand der Nutzung des Zufallsprinzips für die Stichprobe ausgewählt. So entsteht eine einfache, weitgehend repräsentative Zufallsstichprobe.
Allerdings gehört eine Telefonnummer normalerweise zu einem Haushalt und nicht zu einer Person. Es ist also möglich, dass in Mehrpersonenhaushalten manche Personen eher ans Telefon gehen als andere. Somit würde die Stichprobe verzerrt. Um sicherzustellen, dass die Probanden tatsächlich zufällig ausgewählt werden, verwendet man die Geburtstagsmethode. Der Interviewer fragt im telefonischen Gespräch, ob er mit demjenigen im Haushalt sprechen darf, der zuletzt Geburtstag hatte. So wird ein zusätzliches Zufallselement in die Auswahl des Befragten eingebracht.

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