For me, the most interesting question about child abuse would be about the prevention of abuse or the treatment of those who have been abused. My study would focus on one of those things. If I did the first of these, I would look at various strategies to prevent child abuse and try to determine whether they had any effect on levels of abuse. If I did a study on the second, I would look at various things that were done with abused children. This could include types of psychological therapies or it could include what was done with the child (left in the home, removed to relatives, removed to a foster home, etc). In either case, I would try to determine if those sorts of treatments had an impact in reducing the sorts of problems (poor school performance, depression, etc) faced by abused children.