“Believe it or not, through all this negative coverage, they did a survey of 600,000 people about how black America views this president. His numbers have actually doubled,” Brian Kilmeade, a “Fox & Friends” host, said during the segment that was broadcast Tuesday morning.

Mr. Kilmeade was almost certainly referring to a distorted finding from SurveyMonkey, an online polling company. Since Mr. Trump’s inauguration, the company has conducted 602,134 interviews with adults of every race group — not just “black America,” as Mr. Kilmeade said.

SurveyMonkey’s results, provided to The New York Times, show that Mr. Trump’s approval ratings among black Americans actually declined from 20 percent in February 2017, his first full month in office, to 15 percent in December. (This is consistent with polling from the Pew Research Center and Reuters.)

How did Mr. Kilmeade and, by extension, Mr. Trump arrive at his approval doubling among black Americans?