There is no scientific evidence to support the common belief that children's homework done while watching television is of poorer quality than homework done with the box turned off, two psychologists say.

The surprising findings are contained in a paper, "The Impact on Children's Education: Influence on Cognitive Development," distributed by the U.S. Department of Education's Office of Educational Research and Improvement.The authors, University of Massachusetts psychology professor Daniel R. Anderson and graduate student Patricia A. Collins, did not conduct original research or studies with children. They said the research literature behind many common assertions about television's impact on children is "sparse."

But their reading of the available studies led them to the following conclusions:

- "There is no evidence that television has a mesmerizing effect on children's attention caused by color, movement and visual changes."

- "Contrary to popular assertions, children are cognitively active during television viewing and attempt to form a coherent, connected understanding of television programs."

- "There is no evidence that children generally get overstimulated by television."

- Television viewing generally displaces not reading but "movie attendance, radio listening, comic book reading and participation in organized sports."

- "There is no evidence that homework done during television viewing is of lower quality than homework done in silence."

- There is little evidence to show that television viewing reduces children's attention span, and some indicates it may actually increase their ability to focus attention.

- "There is no evidence that television makes children cognitively `passive.' "

- "There is some weak evidence that television availability reduces reading achievement," but if so, this "appears to occur during the early elementary school years and is probably temporary."

In sum, the authors said, "The research literature provides little support for most of the common beliefs about the influence of television."

American children send an average of 12 to 25 hours a week watching television.

Lest parents despair of ever weaning their offspring from the tube, they can point to tests that show those who spent the most hours each day in front of the television generally performed well below average.

According to a National Assessment of Educational Progress reading test given in 1984, 9-year-olds who watched six hours or more of television a day scored sharply lower than those who watched less. But there was little difference between those who watched less than two hours of television per day and those who watched three to five hours.

Among 13- and 17-year-olds tested, reading scores went up as television watching went down, with those who watched two hours or less scoring higher than those who watched three to five hours, and the latter outscoring those who watched six hours or more.

Chester E. Finn Jr., until recently the assistant secretary of education for research and improvement, said in an interview: "We've known for a long time that some TV is good for some kids. For the most disadvantaged kids, some TV actually appears to increase their cultural literacy."