I have a long list of items with non-random id numbers. I then compute the hashes of the ids (using SHA256 or something similar).
If I now pick all ids where, say, the last digit of the hash is a 3, is that equivalent to a random sample? I know that looking at the hash I can't infer if the id number was odd or even. Does that imply that the collection of all items where the hash ends in a 3 has statistically the same proportion of odd and even id numbers as the entire list? Is there some property of the hash function that guarantees that numeric properties of the hash numbers are uncorrelated to properties of the unhashed data?
