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4 Tutorials that teach Sampling With or Without Replacement
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Sampling With or Without Replacement

Sampling With or Without Replacement

Author: Katherine Williams

Determine the population size to treat a sample without replacement as independent.

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Video Transcription

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This tutorial talks about sampling with and without replacement. Now one of the conditions for the most inferenced procedures is that the measurements are independent. And in order to get that independence, ideally we would select members of the population, measure some aspect of that, and then repeat. Now because we are using that process, selecting, measuring, and repeating, we could get somebody that we already measured. Typically, this doesn't happen and we're not looking for that, but it could happen.

So when we're talking about selecting members and creating our samples, we need to be careful to decide whether or not we're talking about sampling with replacement or without replacement. When we're talking about sampling with replacement, just like the name is hinting, when we take out an element from the population, that selected element is returned before we draw again. So repeats are possible.

So for example, if in our population we had two-- oops, three blue balls and one red ball, if I'm selecting samples of two, it is possible on the first draw to get a red and a blue. Then I return everything back in. So on the second draw, it is still possible to get that red and the blue. So the repeats are possible here.

On the other hand, when we're sampling without replacement, when we select an element from the population, that element is not returned before drawing again. So no repeats are possible. So in this example, if we're drawing sample size of two, if on the first draw I get a red and a blue, on the second draw, I cannot get that red again. It's already been taken. And I can't get that specific blue again. It's already been taken and is no longer available to be drawn. Because no repeats are possible, when you're sampling without replacement, the events are no longer independent.

Now if our sample is drawn from a large enough population that we sample 10% of the population or less, then the probabilities don't shift too much. So when we are sampling without replacement, because our population is large and our sample is small, then the probabilities are not going to shift too much from draw to draw. Because the probabilities aren't shifting, then we can act as if those samples are independent. This has been your tutorial on sampling with and without replacement.

Terms to Know
Sampling With Replacement

A sampling plan where each observation that is sampled is replaced after each time it is sampled, resulting in an observation being able to be selected more than once.

Sampling Without Replacement

A sampling plan where each observation that is sampled is kept out of subsequent selections, resulting in a sample where each observation can be selected no more than one time.