Sampling without replacement

Definition

Sampling without replacement refers to a sampling method where an item is selected from a population and then not returned to the population before the next selection. This approach ensures that each selected item is unique, which affects the probability of subsequent selections. It's crucial in scenarios where the same item cannot be chosen more than once, influencing various statistical calculations and outcomes.

5 Must Know Facts For Your Next Test

1. In sampling without replacement, the total number of items in the population decreases with each selection, affecting probabilities.
2. This method contrasts with sampling with replacement, where selected items are returned to the population, keeping the sample size constant.
3. When using sampling without replacement, the hypergeometric distribution is often used to model the probabilities of different outcomes.
4. The probability of selecting a specific item changes after each draw, as the composition of the remaining population is altered.
5. Sampling without replacement is commonly used in quality control and surveys, where selecting the same individual or item multiple times is impractical.

Review Questions

• How does sampling without replacement influence the probability calculations in statistical studies?
  • Sampling without replacement changes the probability calculations because each time an item is selected, it reduces the total number of items left in the population. This means that subsequent selections are dependent on previous ones, altering their probabilities. For instance, if an item is chosen successfully, it can't be picked again, which increases the likelihood of selecting other items in future draws.
• Discuss how sampling without replacement relates to hypergeometric distribution and provide an example.
  • Sampling without replacement is directly linked to hypergeometric distribution as this distribution describes scenarios where items are drawn from a finite population without returning them. For example, if you have a box containing 10 red and 5 blue balls and you draw 3 balls without replacing them, hypergeometric distribution helps calculate the probabilities of drawing various combinations of red and blue balls. This illustrates how sampling affects outcome probabilities based on prior selections.
• Evaluate the advantages and disadvantages of using sampling without replacement compared to sampling with replacement in research design.
  • Using sampling without replacement has its advantages and disadvantages when compared to sampling with replacement. One advantage is that it prevents over-representation of certain items or individuals, leading to potentially more accurate representations of the population. However, a disadvantage is that it can lead to decreased variability in samples as fewer options remain after each draw. In contrast, sampling with replacement allows for constant population size and greater variability but may over-represent some cases. Evaluating these methods depends on research goals and desired outcomes.

Related terms

Probability Distribution:

A function that describes the likelihood of obtaining the possible values that a random variable can take.

Population:

The complete set of items or individuals from which a sample can be drawn for a statistical study.

Hypergeometric Distribution:

A probability distribution that describes the number of successes in a sequence of draws from a finite population without replacement.