We’d still have the effect even if there were plenty of points at all values.
Are you talking about relative sample sizes, or absolute? The effect requires that as you go from +4sd to +3sd to +2sd, your population increases sufficiently fast. As long as that holds, it doesn’t go away if the total population grows. (But that’s because if you get lots of points at +4sd, then you have a smaller number at +5sd. So you don’t have “plenty of points at all values”.)
If you have equal numbers at +4 and +3 and +2, then most of the +4 still may not be the best, but the best is likely to be +4.
I don’t believe we disagree on anything. For example, I agree with this:
If you have equal numbers at +4 and +3 and +2, then most of the +4 still may not be the best, but the best is likely to be +4.
Are you talking about relative sample sizes, or absolute?
By ‘plenty of points’… I was imagining that we are taking a finite sample from a theoretically infinite population. A person decides on a density that represents ‘plenty of points’ and then keeps adding to the sample until they have that density up to a certain specified sd.
Are you talking about relative sample sizes, or absolute? The effect requires that as you go from +4sd to +3sd to +2sd, your population increases sufficiently fast. As long as that holds, it doesn’t go away if the total population grows. (But that’s because if you get lots of points at +4sd, then you have a smaller number at +5sd. So you don’t have “plenty of points at all values”.)
If you have equal numbers at +4 and +3 and +2, then most of the +4 still may not be the best, but the best is likely to be +4.
(Warning: I did not actually do the math.)
I don’t believe we disagree on anything. For example, I agree with this:
If you have equal numbers at +4 and +3 and +2, then most of the +4 still may not be the best, but the best is likely to be +4.
By ‘plenty of points’… I was imagining that we are taking a finite sample from a theoretically infinite population. A person decides on a density that represents ‘plenty of points’ and then keeps adding to the sample until they have that density up to a certain specified sd.