In article <email@example.com>, firstname.lastname@example.org wrote: > On Thu, 02 Nov 2000 17:44:08 GMT, Ross J. Micheals > <email@example.com> wrote: > > > Is there a statistical definition of "representative sampling?" > > No. It is more broadly *logical* than statistical. My notion right > this minute is, it is most clearly defined by its negation. That is, > if you avoid the traps of all potential non-representative-ness, > then you may have representative samples.
Surely the defining property of "representative sampling" is that it be entirely random. Wouldn't any non-representative mistake violate some notion of randomness?
> I expect that if you produce a random assignment > with your chosen 'seed number', you might be unhappy > if one group got the assignment 8 times in a row; and the like. > So, if the program is extreme according to the runs-test, you can try > another seed and get another list. Then you use that one if you like > it better. > > - BUT you should see: A single selection will look 'representative.' > A million selections done like this will be lacking, grossly, in > Runs. Does that matter? - well, it might.
It definitely matters. I would argue that "representativeness" is defined purely by random sampling and the minute we start adding provisos and requirements it isn't random , and it isn't truly representative.
Provided your sampling is random, these extreme relationships you describe should come up in accordance with their probability of occurring. I have also got a program that does runs tests, similar to yours. Its amazing how often, from random sampling, you can violate runs tests. I went to a seminar recently on randomness in which the speaker invited us to guess which three sequences out of 6 binary sequences were randomly generated. Our intuition directs us toward those sequences with the most even "spread" of 1s and 0s (without perfectly alternating), but we are frequently wrong. the moral is that if you decide that a sample is representative by how it looks you are likely to commit error.