海角大神

As the political pundits parse the Republican debate 鈥� a topic I will tackle later 鈥� I want to return to a story that attracted quite a bit of media play last week. On Aug. 4, New Hampshire television station WMUR in conjunction with CNN听听that showed Hillary Clinton and Bernie Sanders in a 鈥渟tatistical tie鈥� in New Hampshire. Not surprisingly, the poll generated quite a bit of media coverage, with听The New York Times听headline for its story on the poll proclaiming that Clinton and Sanders were听听 Other news outlets, citing the same poll,听听. In fact, the survey, which was in the field during the last week of July, showed 42% percent of likely Democratic primary voters saying they will vote for Clinton, with 36% saying they are backing Sanders. How can the New Hampshire race be a 鈥渢ied鈥� when the poll shows Clinton with a 6% lead? The answer is that because the two candidates鈥� numbers fall within the poll鈥檚 sampling margin of error (a measure of how confident pollsters are in their results), one can鈥檛 discount the possibility that Sanders is actually tied, or perhaps even ahead, of Clinton. Remember, surveys are simply estimates of the sentiments of an underlying population 鈥� in this instance, likely Democratic primary voters in New Hampshire 鈥� and one鈥檚 confidence in the results depends in part on how many people are surveyed and what confidence level we are willing to accept in evaluating the results. In this case, the WMUR听听at the 95% confidence level for the Democratic nominating race is +/-5.9%. In describing the race as a 鈥渟tatistical tie鈥�, then, the WMUR pollsters are acknowledging the possibility that despite Clinton鈥檚 6% lead, Sanders鈥檚 actual support might be at the upper end of the margin of error, and Clinton鈥檚 at the lower end. (Of course, it鈥檚 possible their support lies outside the margin of error, but this is even more unlikely.) Hence, WMUR鈥檚 decision to label the race a 鈥渟tatistical tie.鈥�

At the risk of nitpicking, however, I would argue that a 鈥渟tatistical tie鈥� is not the equivalent of a 鈥渄ead heat,"听the Times鈥檚听headline notwithstanding. To understand why, one should also ask: What is the probability that a purely random sample of 274 likely Democratic voters (the size of the WMUR poll on the Democratic side) would show Clinton ahead by 6%, if in fact there is no difference in polling support between Clinton and Sanders in the underlying population 鈥� that is, that they really are tied? It turns out that it is not very likely 鈥� in fact, a simple test of the difference in survey sample results suggests there is a less than 10% probability that the race is actually tied, given the survey findings showing Clinton ahead by 6% (and making certain other assumptions about how the WMUR poll was conducted.) So, it is true that we can鈥檛 be sure that Clinton is ahead, at least not using the conventional 95% uncertainty level. But it is much more likely, given these poll鈥檚 parameters, that she is leading Sanders than that they are in a true dead heat. My quibble with most of the media stories reporting the WMUR poll is that they don鈥檛 make the difference between a 鈥渟tatistical tie鈥� and an actual tie very clear.

鈥淔ine,鈥� you respond. 鈥淎t least I can take comfort in knowing that Bernie is closing the gap with Hillary.鈥� And, in fact, the first line of the Times听story notes that 鈥淪enator Bernie Sanders of Vermont continues to tighten the race with Hillary Rodham Clinton in New Hampshire, according to a poll released on Tuesday.鈥� As evidence, the author notes that a previous WMUR/CNN poll of likely Democratic voters that was in the field from June 18 to 24 found Clinton leading Sanders by 43%-35% (with a margin of error of +/- 5.2%).听 Based on these two polls, then, it appears that Sanders has gained 2% on Clinton 鈥� evidence that, according to the Times, 鈥淢r. Sanders continues to gain momentum after months of negative publicity about Mrs. Clinton鈥檚 use of a private email server as secretary of state.鈥�

Well, maybe. Again, it is useful to put this claim in proper context too. If you parse the polling numbers, the one-month change from a 43%-35% Clinton lead in early July to 42%-36% margin this week comes out to approximately a handful of respondents expressing a preference for Sanders rather than Clinton this month compared to last month. Now, this might reflect an actual change in the sentiments of the underlying population. Or, it might just be the result of picking up a couple more Bernie supporters in the random sampling process, even though there鈥檚 been no actual change in voter preferences. The bottom line is that we should be cautious about extrapolating that Sanders is gaining on Clinton based solely on a 2% change in the WMUR polling results across a one-month period.

This doesn鈥檛 mean Bernie hasn鈥檛 gained ground on Hillary in New Hampshire. As this shows, if we widen our time horizon it鈥檚 clear that Bernie has closed the polling gap, particularly when Elizabeth Warren鈥檚 name was dropped from the survey options.

But there hasn鈥檛 been a lot of recent polls in New Hampshire. A NBC poll in late July had Clinton up by a larger margin, 47%-34%, while a recently released Gravis poll has it 43%-39% in Clinton鈥檚 favor. (I haven鈥檛 looked closely at the internals of either poll.) The aggregate Pollster polling has Clinton up 43.3%-38.8%.听, which uses a slightly different aggregating algorithm, has Clinton with a more substantial lead over Bernie, at 44.8%-31.6%.

The bottom line is that rather than a 鈥渄ead heat," Clinton is probably leading Bernie in New Hampshire, and that it is not even clear, despite an abundance of recent negative news coverage for Clinton and Bernie鈥檚 well-attended campaign events, that he has gained all that much ground over the last month. Alas, for a media with a vested interest in seeing a competitive race for the Democratic nomination, that narrative is probably a lot less interesting, even if it is likely to be a bit more accurate.

Matthew Dickinson publishes his Presidential Power blog at听.