Sampling without replacement

Definition

Sampling without replacement is a method of sample selection where each selected unit is not returned to the population before the next draw. This ensures that no unit can be chosen more than once.

5 Must Know Facts For Your Next Test

1. In sampling without replacement, the probability of selecting any particular unit changes after each draw because the population size decreases.
2. This method is commonly used in quality control and auditing to ensure unique samples.
3. The total number of possible samples in sampling without replacement can be calculated using combinations: $C(n, k) = \frac{n!}{k!(n-k)!}$ where $n$ is the population size and $k$ is the sample size.
4. It reduces bias compared to sampling with replacement as it prevents repeated observations of the same units.
5. When analyzing data from this type of sampling, standard deviation and other statistical measures must account for the changing probabilities.

Review Questions

• What changes about the probability of selecting a particular unit in sampling without replacement after each draw?
• How do you calculate the total number of possible samples when using sampling without replacement?
• Why might sampling without replacement reduce bias compared to sampling with replacement?

Related terms

Sampling With Replacement: A method where each selected unit is returned to the population before drawing the next one, allowing for possible repeated selections.

Combination: A selection of items from a larger pool where order does not matter, often used in calculating possible outcomes in sampling scenarios.

Bias:

A systematic error introduced into sampling or testing by selecting or encouraging one outcome over others.