On 6 March 2014 06:45, Gabriel Bodeen <gabebod...@gmail.com> wrote: > Brent was right but the explanation could use some examples to show you > what's happening. The strangeness that you noticed occurs because you're > looking at cases where the proportion is *exactly* 50%. > > binopdf(2,4,0.5)=0.375 > binopdf(3,6,0.5)=0.3125 > binopdf(4,8,0.5)=0.2374 > binopdf(8,16,0.5)=0.1964 > binopdf(1000,2000,0.5)=0.0178 > binopdf(1e6,2e6,0.5)=0.0006 > > Instead let's look at cases which are in some range close to 50%. > > binocdf(5,8,0.5)-binocdf(3,8,0.5)=0.4922 > binocdf(10,16,0.5)-binocdf(6,16,0.5)=0.6677 > binocdf(520,1000,0.5)-binocdf(480,1000,0.5)=0.7939 > binocdf(1001000,2e6,0.5)-binocdf(999000,2e6,0.5)=0.8427 > binocdf(1000050000,2e9,0.5)-binocdf(999950000,2e9,0.5)=0.9747 > > Basically, as you flip a coin more and more times, you get a growing > number of distinct proportions of heads and tails that can come up, so any > exact proportion becomes less likely. But at the same time, as you flip > the coin more and more times, the distribution of proportions starts to > cluster more and more tightly around the expected value. So for tests when > you do two million flips of a fair coin, only about 0.06% of the tests come > up exactly 50% heads and 50% tails, but 84.27% of the tests come up between > 49.95% and 50.05%. >
Thank you, that's exactly what I was attempting to say in my cack-handed way. (And it is almost certainly what Max intended to say.) -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
