“The larger point, which comparisons to the rest of the state obscures, is that these are serious disparities,” said Joseph E. Kennedy, a law professor at University of North Carolina at Chapel Hill and expert in criminal justice racial disparities. “Who cares how bad things are in the rest of the state? A mayor can have a much bigger impact on arrests by his city’s police force than a governor can have in a state where multiple agencies make arrests.”

The South Bend Police Department changed how it reported crime data to the F.B.I. in 2018, using a more detailed reporting system, a Buttigieg campaign spokesman said. Experts agreed that the switch likely accounts for a perceived uptick in drug-related arrests that year. Omitting 2018 from the time frame, though, black residents of South Bend were still 2.7 times more likely than white residents to be arrested on drug charges and 4.1 times more likely for marijuana possession.

What Mr. Buttigieg said

“Poverty rates for black residents decreased by nearly 40 percent since Pete took office and poverty rates for Latino residents decreased by half — far outpacing their counterparts in Indiana and across the country over the same time period.”

— on his campaign website

This is exaggerated. The poverty rates for South Bend’s black and Latino communities did decrease during Mr. Buttigieg’s two terms as mayor, in line with a decade-long trend across the country. But he’s selectively highlighting one set of data to show a greater decline over a more precise data set showing a smaller, but still notable, reduction.

The Census Bureau currently produces two main sets of data through its rolling American Community Survey: one-year estimates, which are more current, and five-year estimates, which have a lower margin of error. The bureau noted that the second set is more reliable for “smaller geographic areas and small population groups.” South Bend has a population of roughly 102,000, including about 27,000 black residents and about 16,000 Latino residents.

As other fact checkers have noted, Mr. Buttigieg is using the one-year estimates for his figures. By this metric, poverty in South Bend declined by 39.3 percent for black residents from 2011 to 2018, and by 49.9 percent for Latino residents. In this same frame, poverty declined in Indiana by 21.6 percent among African-Americans and by 38.3 percent among Latinos, and the reductions were 19.9 percent and 27.1 percent nationwide.

By the five-year estimates, though, black poverty declined by 14.6 percent in South Bend and Latino poverty by 25.9 percent. That still outpaces the rates in the state (2.7 percent and 10.6 percent) and country (6.2 percent and 9.5 percent). A spokesman for Mr. Buttigieg said the five-year estimates did not fully capture the economic investments in the city in recent years.