In statistics, a sampling distribution is the probability distribution of a given statistic based on a random sample of certain size n. It may be considered as the distribution of the statistic for all possible samples of a given size. The sampling distribution depends on the underlying distribution of the population, the statistic being considered, and the sample size used.

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  • In statistics, a sampling distribution is the probability distribution of a given statistic based on a random sample of certain size n. It may be considered as the distribution of the statistic for all possible samples of a given size. The sampling distribution depends on the underlying distribution of the population, the statistic being considered, and the sample size used. The sampling distribution is frequently opposed to the asymptotic distribution, which corresponds to the limit case n = ∞. For example, consider a normal population with mean μ and variance σ². Assume we repeatedly take samples of a given size from this population and calculate the arithmetic mean <math>\scriptstyle \bar x</math> for each sample — this statistic is called the sample mean. Each sample will have its own average value, and the distribution of these averages will be called the “sampling distribution of the sample mean”. This distribution will be normal <math>\scriptstyle \mathcal{N}(\mu,\, \sigma^2/n)</math> since the underlying population is normal. This was an example of a simple statistic taken from one of the simplest statistical populations. For other statistics and other populations the formulas are frequently more complicated, and oftentimes they don’t even exist in closed-form. In such cases the sampling distributions may be approximated through Monte-Carlo simulations, bootstrap method, or asymptotic distribution theory. The standard deviation of the sampling distribution of the statistic is referred to as the standard error of that quantity. For the case where the statistic is the sample mean, the standard error is: <math>\sigma_{\bar x} = \frac{\sigma}{\sqrt{n}}</math> where <math>\sigma</math> is the standard deviation of the population distribution of that quantity and n is the size (number of items) in the sample. A very important implication of this formula is that you must quadruple the sample size (4×) to achieve half (1/2) the measurement error. When designing statistical studies where cost is a factor, this may have a factor in understanding cost-benefit tradeoffs. Alternatively, consider the sample median from the same population. It has a different sampling distribution which is generally not normal (but may be close under certain circumstances).
  • Unter Stichprobenverteilung versteht man die Verteilung einer Stichprobenfunktion <math>\theta(X_1, ... , X_n)</math> über alle möglichen Stichproben aus der Grundgesamtheit. Die Stichprobenfunktion <math>\theta</math> sind in der Regel Schätzgrößen oder Teststatistiken, daher spricht man statt von Stichprobenverteilung auch einfach von der Verteilung einer Schätzgröße oder (Test-)Statistik. Die Verteilung der Stichprobenfunktion dient der Gewinnung von Aussagen über die Ermittlung dieser Schätzgrößen in der Grundgesamtheit aufgrund von einer Stichprobe. Die Stichprobenverteilung ist ein frequentistisches Konzept. Das Bayesianische Pendant ist die A-posteriori-Verteilung.
  • En estadística, la distribución muestral es lo que resulta de considerar todas las muestras posibles que pueden ser tomadas de una población. Su estudio permite calcular la probabilidad que se tiene, dada una sola muestra, de acercarse al parámetro de la población. Mediante la distribución muestral se puede estimar el error para un tamaño de muestra dado. La fórmula para la distribución muestral dependerá de la distribución de la población, del estadístico y del tamaño de la muestra.
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  • In statistics, a sampling distribution is the probability distribution of a given statistic based on a random sample of certain size n. It may be considered as the distribution of the statistic for all possible samples of a given size. The sampling distribution depends on the underlying distribution of the population, the statistic being considered, and the sample size used.
  • Unter Stichprobenverteilung versteht man die Verteilung einer Stichprobenfunktion <math>\theta(X_1, ... , X_n)</math> über alle möglichen Stichproben aus der Grundgesamtheit. Die Stichprobenfunktion <math>\theta</math> sind in der Regel Schätzgrößen oder Teststatistiken, daher spricht man statt von Stichprobenverteilung auch einfach von der Verteilung einer Schätzgröße oder (Test-)Statistik.
  • En estadística, la distribución muestral es lo que resulta de considerar todas las muestras posibles que pueden ser tomadas de una población. Su estudio permite calcular la probabilidad que se tiene, dada una sola muestra, de acercarse al parámetro de la población. Mediante la distribución muestral se puede estimar el error para un tamaño de muestra dado.
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  • Sampling distribution
  • Stichprobenverteilung
  • Distribución muestral
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