# sampling distributions - composed of permutations or combinations?

#### bruin

##### Member
This seems like a very basic question, but I'm having a hard time answering it by googling.

If a sampling distribution is composed of all the values of a given statistic derived from all possible samples of a given sample size, then does "all possible samples" refer to nPr or nCr?

My guess is combinations - because for any statistic I can think of (sample mean, variance, etc.) the *order* of the scores in the calculation certainly wouldn't affect the value of the statistic for that sample - but it's bothering me that I can't find something authoritative that confirms my guess.

Or is it possible that it doesn’t even matter? E.g., if [X]% of all permutation-samples would have a sample mean above or below a given value, would that exact same [X]% of combination-samples have a sample mean above or below that same threshold?

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#### bruin

##### Member
Or is it possible that it doesn’t even matter? E.g., if [X]% of all permutation-samples would have a sample mean above or below a given value, would that exact same [X]% of combination-samples have a sample mean above or below that same threshold?
Below is an example of what I mean. After writing it out this way, I’m thinking that I answered my own question, and that the answer is: permutations vs combinations doesn’t matter insofar as it has no bearing on any probabilities derived from the sampling distribution. But I’m interested to hear whether others agree. Last edited: