The study’s authors, Scott A. Golder and Michael W. Macy, acknowledge such limitations and worked to correct for them. In the study, they collected up to 400 messages from each of 2.4 million Twitter users writing in English, posted from February 2008 through January 2010. They performed text analysis on each message, using a standard computer program that associates certain words, like “awesome” and “agree,” with positive moods and others, like “annoy” and “afraid,” with negative states. They included so-called emoticons, the face symbols like “:)” that punctuate digital missives.

The pair found that about 7 percent of the users qualified as “night owls,” showing peaks in upbeat-sounding messages around midnight and beyond, and about 16 percent were morning people, who showed such peaks very early in the day. After accounting for these differences, the researchers determined that for the average user in each country, positive posts crested around breakfast time, from 6 a.m. to 9 a.m.; they fell off gradually until hitting a trough between 3 p.m. and 4 p.m., then drifted upward, rising more sharply after dinner.