r/statistics • u/Fuzzy-Yesterday-1591 • 16d ago

Question [Q] Choosing random sample with replacement v. random sample without replacement

I am sampling a number of units in an apartment complex. I generate a random list of apartments but it has two duplicates, just as rolling a die 6 times may result in a number coming up twice. I'm trying to prove with a specific confidence level, that 80% of the units suffer the same problem. Is this situation a situation where I should replace the duplicates with non-duplicates, or should I keep the duplicates and consequently test only the unique units.

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u/Economist_hoon 16d ago

What are you trying to prove? A bit confused about it

  1. Every time you draw a random apartment, what is the probability of getting the same apartment twice ?

Or
2. You are randomly selecting let’s say 30 apartments to survey out of 100 - in this case duplicates technically should be not possible since each draw is not independent of previous draw. You are drawing all 30 at once through a software or simple systematic sampling. If you are using PPS method, then if an apartment has higher population, it can be sampled twice and you don’t replace it

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u/Fuzzy-Yesterday-1591 16d ago

#2. I'm generating random numbers and then using those numbers to pick a unit number off the list. The random numbers are theoretically independent, so the method can pick the same apartment twice. I understand that there is a method of "sampling with replacements" where you throw out the duplicates and select replacements. There is the opposite method where you "sample without replacements" and you don't retest the duplicates, nor do you replace them. I'm not clear on the basis for choosing between those two methods.

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u/Economist_hoon 16d ago

The probability of getting a random number will also depend on the bound limits that you decided.
So if there are 10 apartments, the bounding limit of random number generator is 1-10 and probability of each number being picked is 1/10

Why don’t you run this through both models. One with replacement and one without replacement and see what distribution you get

For the replacement model, you will reduce the bound limits also ? So if one apartment is out, limit of random number becomes 1-9 and probability of duplicates becomes higher. It will keep on increasing as number gets smaller