There is sometimes a temptation to lump Iowa and New Hampshire together as a kind of opening chapter to the nominating process. After all, both are heavily white states and nonrepresentative of the country’s population at large. And indeed, the results this year could end up being quite similar in both states.

But the two contests differ significantly. Iowa’s consists of caucuses — which favor candidates with younger and more activist supporters — and includes only Democrats. New Hampshire’s election is a simple primary, and is also open to political independents.

In 2016, when Mr. Sanders beat Hillary Clinton in the primary there, he relied largely on the support of independent voters. He is himself a political independent, and he still does well among this group. But the 26 percent support he is now earning from non-Democrats in the Monmouth poll is still far less than the nearly three-quarters of independent voters he got in 2016.

This reflects the complications of a more crowded field this year, and the fact that the independent voters who participate on Tuesday may skew slightly more conservative than they did in 2016. That is because there was a competitive Republican primary that year. With Mr. Trump’s nomination all but guaranteed among Republicans this year, a broader cross-section of independents may consider weighing in on the Democratic race.

Mr. Buttigieg, who is the only other candidate to break 20 percent among non-Democrats in the Monmouth poll, could stand to gain.

Ms. Warren — whose poll numbers in New Hampshire crested in the fall, but who still stands a chance at a strong showing — is far less popular among independents. She pulls the vast majority of her backing from Democrats, and from liberals.

The divide between her liberal supporters and Mr. Sanders’s falls strikingly along gender lines. He is nearly twice as popular among New Hampshire men than he is among women there, according to the Monmouth poll. For Ms. Warren, the inverse is true.