The plaintiffs claim that the North Carolina law violates Section 2 of the Voting Rights Act, which, as amended in 1982, bans policies that result “in a denial or abridgment” of the right to vote based on race and calls for a judgment “based on the totality of circumstances.”

“What is a practice that results in an abridgment?” asked Edward B. Foley, an expert in election law at Moritz College of Law at Ohio State University.

In the limited number of cases so far, federal appeals courts have sharply diverged, “offering diametrically opposite views of how to understand what is now the most important section of the Voting Rights Act,” Mr. Foley said.

Efforts by civil rights groups to win a preliminary injunction against the North Carolina law before the 2014 election were unsuccessful, so its provisions, except for the voter ID requirement, were in effect then. But the two sides offer contrasting versions of what happened in the election.

The plaintiffs will present numerous witnesses who will testify that the new rules deterred them from voting, as well as expert testimony showing broader discriminatory effects, said Donita Judge, a senior lawyer with the Advancement Project, a civil rights group and co-counsel for the plaintiffs.

That blacks are more likely to use early voting, same-day registration and out-of-precinct voting has been well established in past elections. Many black churches, for example, send busloads of voters to the polls after Sunday services, and often used the extra week that is now eliminated. Poorer and less educated on average, blacks may be more likely to miss the deadline for registration or to be confused by changes in their home precinct and voting spots, according to civil rights groups.

While it is impossible to know how many people did not register or vote in 2014 because of the changes, data does show, as one concrete measure, that 11,000 people who registered in North Carolina less than 25 days before Election Day were unable to vote when they could have under previous rules, said Daniel T. Donovan, a lawyer with Kirkland and Ellis, which is also representing the plaintiffs.