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dbr:Principle_of_transformation_groups
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dbr:Sampling_probability
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Sampling probability Auswahlsatz
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In statistics, in the theory relating to sampling from finite populations, the sampling probability (also known as inclusion probability) of an element or member of the population, is its probability of becoming part of the sample during the drawing of a single sample. For example, in simple random sampling the probability of a particular unit to be selected into the sample is where is the sample size and is the population size. Der Auswahlsatz einer Stichprobe, auch Auswahl-, Inklusions-, Ziehungs- oder Einschlusswahrscheinlichkeit, selten Stichprobengewichte (engl. inclusion probability), gibt an, mit welcher Wahrscheinlichkeit eine oder mehrere Elemente einer Grundgesamtheit in eine Zufallsstichprobe gelangen. Inklusionswahrscheinlichkeiten lassen sich nur für Zufallsstichproben berechnen.
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Der Auswahlsatz einer Stichprobe, auch Auswahl-, Inklusions-, Ziehungs- oder Einschlusswahrscheinlichkeit, selten Stichprobengewichte (engl. inclusion probability), gibt an, mit welcher Wahrscheinlichkeit eine oder mehrere Elemente einer Grundgesamtheit in eine Zufallsstichprobe gelangen. Inklusionswahrscheinlichkeiten lassen sich nur für Zufallsstichproben berechnen. Als Inklusionswahrscheinlichkeit 1. Ordnung wird die Wahrscheinlichkeit bezeichnet, dass das i-te Element der Grundgesamtheit in einer Stichprobe vom Umfang enthalten ist. Analog ist die Inklusionswahrscheinlichkeit 2. Ordnung (mit ) die Wahrscheinlichkeit mit der das i-te und j-te Element in eine Stichprobe vom Umfang gelangen. Bei einer uneingeschränkten oder einfachen Zufallstichprobe lassen sich die Inklusionswahrscheinlichkeiten direkt angeben. Bei treten Designeffekte auf. Hier hat auch nicht jedes Element die gleiche Wahrscheinlichkeit, in die Stichprobe zu gelangen. In statistics, in the theory relating to sampling from finite populations, the sampling probability (also known as inclusion probability) of an element or member of the population, is its probability of becoming part of the sample during the drawing of a single sample. For example, in simple random sampling the probability of a particular unit to be selected into the sample is where is the sample size and is the population size. Each element of the population may have a different probability of being included in the sample. The inclusion probability is also termed the "first-order inclusion probability" to distinguish it from the "second-order inclusion probability", i.e. the probability of including a pair of elements. Generally, the first-order inclusion probability of the ith element of the population is denoted by the symbol πi and the second-order inclusion probability that a pair consisting of the ith and jth element of the population that is sampled is included in a sample during the drawing of a single sample is denoted by πij.
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