I am new on this website, and thus don’t feel experienced enough to give global remarks on your post. For the same reason, please correct me if I am going against guidelines or acting in a way which is unusual on LessWrong.
I think I might have an explanation for your note:
4. In fact, the RMD looks like it might vary as a power law of sample size
Your samplings can probably be modeled through a random 1D symmetric motion, as suggested by your coin tossing example. This one is known to present a standard deviation proportional to the square-root of the sample size. The RMD should behave in a similar way, namely:
RMD∼σn∼n−12
This is perfectly consistent with your graph: a factor 10000 on the x-axis gives a factor 1⁄100 on the y-axis.
I am new on this website, and thus don’t feel experienced enough to give global remarks on your post. For the same reason, please correct me if I am going against guidelines or acting in a way which is unusual on LessWrong.
I think I might have an explanation for your note:
Your samplings can probably be modeled through a random 1D symmetric motion, as suggested by your coin tossing example. This one is known to present a standard deviation proportional to the square-root of the sample size. The RMD should behave in a similar way, namely:
This is perfectly consistent with your graph: a factor 10000 on the x-axis gives a factor 1⁄100 on the y-axis.
Nice.
Edited to add:
This is a great comment and I upvoted it.