The income gap between central city residents and suburbanites widened between 1970 and 1978, according to a new Census Bureau study, even though many whites are now moving back into central cities.

For a generation, more affluent families have been moving out to the suburbs, leaving the inner cities increasingly black and low income, but for several years there have been reports of a partial reversal of this trend, in this as in other cities.

The Census Buerau study concluded that despite this so-called "gentrification" movement, inner-city average incomes over the 1970s fell further and further behind those of the suburbs.

Within the District of Columbia for example, median family income at the start of the decade was 69 percent of the figure for its surrounding suburbs.

Eight years later, in a survey taken early in 1978, the D.C. median was $14,382 per family, only 60 percent of the $24,158 median for the surrounding suburbs.

In New York, Baltimore, Cleveland and virtually all the 20 biggest metropolitan areas of the country, the trend was the same. City income as a proportion of suburban income either dropped or made no significant progress.

In Newark, N.J., a heavily black city, median family income of city residents was only two-fifths that of residents of the surrounding suburbs.

Larry Long, one of the authors of the study, said income changes were measured by several different methods, including both family income and per capita income comparisons.

While a few cities showed slight improvements in the ratio of income for inner-city residents by one method or the other, none showed clear improvement by all of the tests. Washington, Baltimore and New York showed a widening gap by both family and per capita income tests.

For the nation as a whole, median family income of central cities dropped from 89 percent of the suburban figure in 1959 to 83 percent in 1970 and 79 percent two years ago. The same trend was evident in per capita figures, too.

The study also noted that in the central cities, family income, measured in constant dollars adjusted for inflation, actually had dropped over the 1970s. The suburbs just about kept up with inflation; the central cities trailed slightly behind it.

Long and coauthor Donald Dahmann concluded from the figures: "Back-to-the-city trends, although highly visible and of significance in individual neighborhoods, do not yet appear to be large enough to clearly establish a new trend toward convergence of city and suburban income levels."

The authors said back-to-city trends were creating what amounted to "affluent islands" of middle-income people within central cities. Outside these "resettlement neighborhoods," they said, the income of the other central city residents was continuing to fall relative to suburban income.

"Middle-income islands in cities will have to grow larger or increase in number before city incomes are raised enough to reduce the city-suburb income gap," they declared.

The authors said the great and continuing disparties between central city and suburban income levels tend to wreck cooperation on issues where a metrowide approach is needed: regional transportation systems, water supply, sewage treatment and the like.

This is because the central cities focus on matters of special interest to their residents, such as welfare, public housing and jobs, whereas affluent suburban residents have "a vastly different set of interests."

The Census Bureau said it is possible that signs of gains by the central cities, reversing the widening income gap, may show up in some cities in the 1980 census, reflecting increased "gentrification" since 1978.

In related study, the Commerce Department's Bureau of Economic Analysis said that the Anchorage, Alaska, metropolitan area had the nation's highest per-capita income in 1978 -- $11,839 -- followed by the Reno, Nev., area, the Bridgeport-Stamford, Conn., metropolitan area; the Midland, Tex., area and the San Francisco-Oakland area.

The District of Columbia area was sixth at $10,259 per person. (All these figures include the city and surrounding suburbs.) The national average was $7,840, so the Washington area was 31 percent above average. Baltimore, at $7,905; was 1 percent over average.

Nine of the lowest 10 metro areas were in the South and Southwest, with McAllen-Pharr-Edinburg, Tex., at the very bottom at $4,323.

Of the nation's big metro areas, only the San Francisco-Oakland metropolitan area trailed Washington.

Interestingly, some of the cities publicly reputed to be poor were in metropolitan areas that ranked high in overall per capita income, because the suburbs brought up the average. Thus, the Detroit metropolitan area ranked 10th in the country at $9,512 and the Newark, N.J., area, with extremely low central-city income, the lowest of any major city, was pulled up to 12th nationwide, at $9,487, by affluent suburbs.