Definition:Sampling Error

Definition

Let $E$ be an estimate of a population parameter based on a sample.

Let $P$ be the true value of the population parameter.

The sampling error is the difference between $E$ and $P$.

Examples

Normal Distribution

Let $S = \set {x_1, x_2, \ldots, x_n}$ be a random sample of size $n$ from a normal distribution $\Gaussian \lambda {\rho^2}$ whose mean is $\lambda$ and whose standard deviation is $\rho$.

Then the mean $m$ of $S$ has a normal distribution whose mean is $\lambda$ and a standard deviation is $\dfrac \rho {\sqrt n}$.

If $\rho$ is unknown, then $\dfrac \rho {\sqrt n}$ is estimated by $\dfrac s {\sqrt n}$, where:

$s^2 = \ds \sum_i \dfrac {\paren {x - m}^2} {n - 1}$

Also see

• Definition:Standard Error

• Results about sampling errors can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): sampling error
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): sampling error