Spencer Ackerman's excellent article on the Iyad Alawi's "zipless coup" contains a very odd assertion which caught my picky picky eye.

"An ABC News poll from March found that the number of Iraqis who trust Allawi above other leaders was statistically insignificant."

This could only mean statistically insignicantly different from 0. In fact, even one such response rejects the null that the true number is zero at any confidence interval. This is obvious. Since at least one Iraqi who was polled said Allawi, then out of all Iraqis at least one would answer Allawi. The reported result * should be interpreted as more than zero but less that 0.5%.

Pollsters tend to report "sampling standard error" as if it is constant, but, in fact, it depends on the fraction of the population which would respond positively. The sampling error as reported is useful for testing the null that the fraction of the population which would respond positively is 0.5. In general the sampling standard error is proportional to the square root of p*(1-p)/n where n is the number interviewed and p is the fraction of the poopulation. Thus if the true fraction of Iraqis who trusted Allawi most was zero, the sampling standard error would be zero.

In contrast, since the fraction of respondents who report trusting George W. Bush most is exactly 0, the null that the true fraction of Iraqis who trust Bush most is zero can not be rejected.