The problem in the linked article is an inconsistent use of decimals. They cite the difference between the candidates with one decimal point, but the margin of error with no decimal points. That's just poor reporting. The source at
Citizens for a Strong New Hampshire gives a more consistent picture.
Headline:
CSNH's Latest Poll: Scott Brown leads Senator Jeanne Shaheen by almost 2 points: 45.9% to 44.3%Here they are consistent. This is a large sample and the standard error of the sample is 1.063% and since the sample size (2,214) has four significant figures it is appropriate to keep the same number of figures for the standard error to avoid errors from rounding too early. If they used the standard error based on Brown's percentage the standard error of the sample becomes 1.059%. Either way the 95% margin of error is 1.96 times the standard error or 2.08%. This should be rounded to 2.1% to match the precision of the quoted percentages for the candidates (I'm not sure where they get 2.0%). It is not necessary to round the figures off to the nearest percent, the calculations are perfectly meaningful with one decimal point. Many top scientific papers will quote two significant figures of error.
In this case the extra decimal actually helps to understand the spread. If everything was rounded to the nearest percent the top line would read Brown 46% to Shaheen 44% with a 2% MoE. That makes it look like Brown is ahead at the limits of the MoE or about two times the standard error. Using the given decimal points shows Brown up by 1.6% with a 2.1% MoE. The MoE on the difference is actually somewhat larger that the MoE on the sample, but that doesn't change the conclusion that the difference is well inside the MoE and its 95% confidence level. That makes it look much more like the statistical tie that it is.
Bottom line: Decimals in polls are not necessarily a sign of bad polling or bad statistics.
