A national survey of more than 2,000 American families has found that the parents most likely to abuse their children are under 30 years of age, live in the Midwest, have a family income of less than $6,000 a year, are high school graduates and are members of minority religions or races.

The "Profile of Violence Towards Children in the United States" prepared by Richard J. Gelles and two associates at the University of Rhode Island indicates that "between 1.4 and 1.9 million children were vulnerable to physical injury from their parents" the year of the study.

It should be noted, the study said, that the Gelles estimate is "at least 1.2 million children higher than previous estimates of the incidence of physical abuse" and includes spanking as a form of violence against children.

"The children who were most vulnerable to physical abuse were the youngest children in our study (3 to 5 years of age) and the oldest (15 to 17 years of age). The oldest children are more likely to face extreme forms of violence (beatings, guns and knives) than other age groups."

The least likely child to be abused, according to the federally financed study, is the single child. Children with one sibling are 50 percent more likely to be physically abused than single children, and parents with five children are the most likely to abuse their children. However, the lowest rate of violence against children occurs in homes with eight or more children.

"The largest families may be the least violent for a number of reasons. Perhaps parents with eight or nine children are simply too exhausted to raise a finger toward their children," the study says, going on to explain that older children may be a "resource" for the parents. They can baby-sit, help with the chores, bring in additional income, and minimize the impact of the last in a parade of children.

The survey found that "there was no significant difference between blacks and whites in terms of abusive violence toward children. Minority racial groups (Orientals, American Indians and others) have the highest rate of violence toward children."

Even there, however, there is not much difference between the groups, with 14 percent of the whites, 15 percent of the blacks, and 18 percent of "other" using physical violence against children during the year of the study.