On 6 March 2014 06:45, Gabriel Bodeen <[email protected]> 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 [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
