Why “sorting” is needed for simple random sampling [closed]

Tutorials demonstrating simple random sampling, first list the full number of population members (i.e., sampling frame) in a column and then assign a random number from 0 to 1 from a uniform distribution to each.

Question: BUT WHY (as shown in this tutorials), before getting a sample (e.g., of n=40) from our sampling frame we must “sort” the sampling frame based on the random numbers for each population member? (What role does sorting etc. play?)

Answer

Sorting a list of objects based on an accompanying set of IID continuous random variables (such as uniform random variables) is equivalent to shuffling those objects into a random order (i.e., by a random permutation). Since the random values are independent continuous random variables, every possible permutation is equally likely, and that is the definition of simple random sampling. This method is used in computer programs that have facilities to create pseudo-random numbers, but do not have an existing sampling function.

Attribution
Source : Link , Question Author : Simon Harmel , Answer Author : Ben

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