PALO ALTO, CALIF. — A STUDY of homeless families released last month by Stanford University sociologists shows the public has a number of wrong perceptions about who is homeless and why.The general public thinks of the homeless as mainly substance abusers, mentally ill, and/or lazy, notes researcher Sandy Dornbush, the study's author. "The reality is quite different," he says. The Stanford Center for the Study of Families, Children, and Youth conducted the study in two San Francisco Bay Area counties; 2,741 children and adults were surveyed over a two-year period. The study found that among the parents of homeless families: * Only 5 percent had been treated for mental illness or emotional problems. * Only 34 percent reported any history of alcohol or drug abuse. Substance abuse among African-Americans and Mexican-Americans lower than among whites, the study found. Professor Dornbush says ethnic minorities are more likely to become homeless as a result of poverty, whereas whites' substance abuse may drive them into homelessness. * Homeless parents are eager to find work but generally have a low level of education and job skills. The study shows that most families become homeless because of poverty and the high cost of housing, rather than because of personal shortcomings. Dornbush says earning the minimum wage used to mean a worker could survive economically. But today, he says, if "two parents are working for minimum wage in this area where housing costs are high, they still are at risk of homelessness." Although the study itself makes no recommendations, Dornbush suggests a number of ways to fight homelessness. He says the government should provide more low-income housing and better vocational education, and revamp welfare rules so people can get more assistance before they become homeless. Many homeless, he says, complained they couldn't get rent subsidies or other government help until they had lost everything. "We let them become homeless and then thousands of dollars become available," he says, "where hundreds weren't available just a few days earlier." The Stanford researcher also recommends establishing one-stop assistance centers where the homeless can apply for services such as welfare, food stamps, rent subsidies, and job retraining.