What is what does it mean when sampling is done without replacement?

When sampling is done without replacement, it means that once an item is selected from a population for inclusion in a sample, it is not returned to the population. Consequently, the item cannot be selected again in the same sample. This method is in contrast to sampling with replacement, where an item is returned to the population after being selected, allowing for the possibility of its re-selection.

Key characteristics of sampling without replacement:

• Population size decreases: After each selection, the size of the population from which samples are drawn reduces.
• Observations are independent: Each element is unique.
• Probability changes: The probability of selecting a particular item changes with each draw, as the population size decreases.
• Used When: In cases where duplicate selections are not desired or when dealing with finite populations where removing elements affects subsequent probabilities.
• Formulas for Probability: When computing the probability of selecting particular items, formulas must account for the decreasing population size. For instance, the hypergeometric distribution is commonly used in such scenarios.