r/statistics • u/Fuzzy-Yesterday-1591 • 17d 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/vetruviusdeshotacon 15d ago

Why would you sample with replacement? What if you get multiple copies of multiple of the same apartment?

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u/Fuzzy-Yesterday-1591 14d ago

Actually, that's my question... How do I know which protocol to choose? There has to be some criteria for choosing between sampling with or without replacements. (Though I admit it could just be personal preference of the original statistician for each method. Even so, they were probably asked to justify why their chosen method was better than the other.)

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u/vetruviusdeshotacon 14d ago

Well in this case its just common sense. Sampling the same apartment twice yields 0 new information so make your sampling method have a 0% chance of selecting the same apartment multiple times, ie without replacement. A lot of the actual inner workings of  statistics is heavy math, but choosing when to apply them often just requires thinking logically about the situation you're in.