My scratchbook. :-)<p>I keep meaning to write it up.<p>Mathematically it is similar <a href="http:&#x2F;&#x2F;www.evanmiller.org&#x2F;sequential-ab-testing.html" rel="nofollow">http:&#x2F;&#x2F;www.evanmiller.org&#x2F;sequential-ab-testing.html</a> but with the difference that Evan produced a stopping rule that is a 95% confidence interval, while mine is stopping at 95% confidence that you won&#x27;t come to a different conclusion by the end of the test.  Otherwise the idea of the analysis is the same.<p>(Note, under the null hypothesis reaching sqrt(N) then crossing 0 is exactly as hard as reading 2 sqrt(N) as can be seen by taking any possible sequence that does one, and swapping the values after first reaching sqrt(N) to get a sequence that does the other.)