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 the population, it is not put back, so it cannot be chosen again in the same sampling process.
Quick Scoop
Plain-language meaning
Think of a bowl with 10 distinct marbles.
If you draw one marble, keep it out, then draw another, you are sampling
without replacement.
Each marble can appear at most once in your sample, and the total number of marbles left to pick from shrinks after each draw.
Key points at a glance
- Once chosen, an item is removed from the pool and cannot be selected again.
- The population size decreases after each selection (10 items, then 9, then 8, etc.).
- Probabilities change from one draw to the next, because the composition of what’s left has changed (events are dependent).
- Common in “real life” surveys, lotteries, and samples where you don’t want duplicates, like picking unique households for a survey.
Tiny example
Suppose you have cards numbered 1, 2, 3, 4, 5.
You draw two cards without replacement :
- First draw: probability of drawing a 1 is 1/51/51/5.
- If you did draw a 1, then for the second draw there are only 4 cards left (2, 3, 4, 5), so the probability of drawing, say, a 2 is now 1/41/41/4.
The second probability depends on what happened first, which is exactly what “without replacement” captures.
Quick contrast (with vs. without)
| Aspect | With replacement | Without replacement |
|---|---|---|
| Can you pick the same item twice? | Yes, items go back into the pool. | [5][1]No, each item can appear only once. | [9][1][3]
| Population size while sampling | Stays the same. | [1]Decreases after each draw. | [7][1]
| Relationship between draws | Usually treated as independent. | [3]Dependent: each draw changes the next probabilities. | [5][3]
| Typical uses | Bootstrapping, some simulations. | [1]Surveys, lotteries, choosing unique people/items. | [5][1][3]
In short, “sampling without replacement” = pick unique items, don’t put them back, and remember that each pick changes the odds for the next one.
Information gathered from public forums or data available on the internet and portrayed here.