Definition:Random Sample (Statistics)/Without Replacement

Definition

Let $S$ be a random sample taken from a population $P$ in such a way that each element $x$ may occur once and once only in $S$.

Then the procedure for selecting $x$ is known as sampling without replacement.

That is, once $x$ has been chosen from $P$, it is not "replaced" back into $P$, and so cannot be selected again.

Also see

• Definition:Sampling with Replacement

• Results about random samples in the context of statistics can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): random sample: 1.
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): with or without replacement
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): random sample: 1.
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): with or without replacement