LOS ANGELES — TV’s Asian-American characters are so frequently slighted that even programs set in the biggest, most diverse cities leave them out of the picture, a new study found.

For “Tokens on the Small Screen,” professors and scholars at six California universities looked at 242 broadcast, cable and digital platform shows that aired during the 2015-16 season and tallied the numbers, screen time and portrayals of characters of Asian or Pacific Islander descent among 2,000 TV characters.

The report released Tuesday, a followup to broadcast TV studies done in 2005 and 2006, found increasing opportunities for Asian-American actors but concluded they are still underrepresented and “their characters remain marginalized and tokenized on screen.”

There was a sense of optimism with the emergence of ABC’s “Fresh Off the Boat” and “Dr. Ken” and Netflix’s “Master of None,” all starring and focused on Asian-Americans, said Nancy Wong Yuen, a Biola University associate professor and one of the study’s authors.

“It felt like, ‘Oh, we’re finally making it,’ ” Yuen said in an interview. “But even (“Dr. Ken” star) Ken Jeong said, ‘Of this many shows, we only have three?’

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