In practice, it is possible that Public Policy Polling got something like 100 African-American voters on the phone rather than 180, which would be associated with a margin of error of about 10 percent. In addition, all of these African-Americans were reached on landlines, and they may have different demographic characteristics (for instance, being older) than the cellphone voters that the survey missed.

A more robust sample of African-American voters comes from the Gallup poll, which interviews about 3,500 people a week for its national tracking poll and does include cellphones in its sample.

The Gallup poll suggests that Mr. Obama’s ratings among African-American voters may have dropped by a percentage point or two over the past few weeks, but probably not more than that. In the four full weeks of polling since Mr. Obama announced his support for same-sex marriage — which had been unpopular in the African-American community until recently — his approval rating has averaged 86 percent among black voters. That compares with 87 percent for 2012 as a whole…

Furthermore, keep in mind that in addition to the already-high margin of error related to polling demographic subgroups, the margin of error is calculated in such a way that it is supposed to cover 95 percent of all possible cases. But it won’t cover 100 percent. The results from 1 in 20 polls — or 1 in 20 subsamples within polls — will fall outside the margin of error.