Talk Business polled 446 voters in the second congressional district, and the results were a little surprising, at least on the surface.

21% Joyce Elliott

16% Robbie Wills

11% Patrick Kennedy

7% David Boling

4% John Adams

41% Undecided

A few thoughts on these numbers:

First, while everyone knew Elliott was a strong candidate, I don’t think anyone planned on her pacing the field at this point.Â Perhaps this is a sign that Robbie Wills’ “campaign like I’m already anointed as the candidate” approach isn’t really resonating outside of his home county.

Second, and despite Patrick Kennedy’s Facebook crowing about being in third, if these numbers tell us anything, it is that Kennedy, Boling, and Adams are in trouble.Â Allow me to explain.

The margin of error in a poll generally refers to the confidence interval of the results, and the margin of error in this poll is +/- 4.6%.Â Most of the time, as in this poll, the confidence interval is set to 95% and is calculated byÂ (meanÂ +/- (1.96 * Standard Deviation)).Â Side note: if the confidence interval were 90% or 99%, the 1.96 number would be different.

In English, this means that, if there is no bias in your collection methods, the results represent the general population +/- 4.6%.Â So far, so good?Â Good.

Now that we’re on the same page, let’s look at the implications of our result.Â While the poll says that 21% of the sampled voters selected Joyce Elliott, the true percentage is really somewhere between 16.4% and 25.6%.Â This goes for the other candidates as well: Robbie Wills’ 18% is really 13.4% to 22.6%; Kennedy’s 11% is 6.4% to 15.6%; Boling’s 7% is 2.4% to 11.6%; and Adams’ 4% is somewhere between 0 and 8.6%.

The 95% confidence interval part that we mentioned a moment agao essentially means that there is a 95% probability that the true feelings of the total population are within each of those ranges.Â Correspondingly, there is only a 5% probability that the true percentage is outside of the given range.Â Another way to think of this is that if you were to take the poll again, there is a 95% chance that your result for any given candidate will fall within the ranges above.

With all that said, the obvious conclusion is that you can *not* statistically say that people truly prefer Elliott over Wills because the intervals overlap if you take Elliott’s low (16.4%) and Wills’ high (22.6%).Â Likewise, we cannot say for certain that voters prefer Kennedy over Boling or Adams, as all three candidates’ intervals overlap to some degree.Â And, though the overlap is small, we cannot be sure that people prefer Wills over Kennedy (Wills’ low: 13.4%; Kennedy’s high: 15.6%)

You *could*, however, say that people prefer Elliot over Kennedy (and, by extension, Boling and Adams) because those intervals do not overlap (16.4% to 15.6%, respectively).Â Now there is a caveat, of course.Â There is a 2.5% chance (half of the 5% I mentioned above — the other 2.5% would be above the range) that the true percentage in favor of Elliott is below 16.4% and a 2.5% chance that the true percentage in favor of Kennedy is higher than 15.6%.Â However, that percentage drops quickly as you move further away from the interval, so I would be pretty confident in saying people truly prefer Elliott over Kennedy (and Boling and Adams).

So, that being the case, it is highly unlikely that any of those three will beat Elliott to get into a run-off, meaning that their only real shot is to beat Wills and hope that they compare better head-to-head with Elliott when the voters who preferred any candidate not in the run-off are back in play.Â However, when we look at the intervals, only Kennedy is close enough to Wills to say that people don’t necessarily prefer Wills over Kennedy.Â Boling and Adams are not.Â All things being equal, one would think that Kennedy had a shot to beat Wills that Boling and Adams lacked.

Of course, all things are NOT equal; Wills and Boling have a lot more money to spend than does Kennedy.Â I would speculate further and say that there is little reason to think Kennedy beat Adams’ $50,000 in 1Q fundraising, given that Kennedy did not immediately try to trump the surprise of Adams’ announcement by releasing his own numbers.Â Wills almost certainly has Faulkner County sewn up, and none of the other candidates should count on winning much of the 29% undecided there.Â In fact, it was only in White County where Kennedy polled appreciably better than Wills, and, while 51% of that county is still undecided, White only comprises about 8% of the Democratic voters in the district.

In the counties that “matter” (relatively speaking, of course) — Pulaski, Faulkner, Saline — Wills is trouncing Kennedy (and everyone else) in Faulkner, is in a dead heat with Kennedy in Pulaski (though both trail Elliott by a large margin), and polled better (though in a very small sample size) in Saline.Â Combine that with Wills’ monetary edge and it becomes highly improbable that Kennedy, Adams, or Boling will beat Wills in the primary.Â This becomes all the more apparent when you throw in that Boling, Adams, and Kennedy, in spending campaign money to reach voters, are more likely to take votes from each other, as the three are fungible to a large degree, than from Wills, who by all accounts is the more conservative Blue Dog candidate.

Long story short, if these poll numbers mean anything, it is that your run-off is very likely to be Elliott and Wills.Â To the extent that one of the other three candidates might shock us and get in to the run-off, my money would be on Boling because poll numbers can certainly change in a hurry in a five-person race, but the thing that will change them the most is money, and Boling has a lot more than Adams or Kennedy.Â So, Facebook bragging notwithstanding, the math would suggest that Kennedy’s third-place finish portends far more problems than possibilities.