The South, for all the lore of the Sun Belt and all the real progress it has made, is still by far the poorest part of the country, according to the first major report on the 1980 census.

The poverty rate in the South fell by nearly a fourth from 1970 to 1980, from 20.3 to 15.3 percent of the population. The five states with the greatest declines in poverty in those 10 years were all in the South--Mississippi, Arkansas, South Carolina, West Virginia and Alabama--while the five with the greatest increases were all in the North--New York, Michigan, New Jersey, Connecticut and Illinois.

Yet the poverty rate in the states the Census Bureau calls southern was still more than a fifth higher than the rate--12.5 percent--for the nation as a whole in 1980. In one state, Mississippi, a fourth of the population continued to live below the official poverty threshold, and in four others--Louisiana, Arkansas, Kentucky and Alabama--more than a sixth did.

The South progressed but still lagged; that is the lesson from the Provisional Estimates of Social Economic and Housing Characteristics published this week.

Conservatives have complained for some time that the Census Bureau exaggerates poverty by the way it measures it. It takes only cash income into account and not non-cash benefits--Medicare and Medicaid, food stamps, housing assistance--which have been the fastest-growing forms of federal aid in recent years. The bureau itself recently reported that the poverty rate would be cut about 40 percent if these in-kind benefits were counted.

When the census was taken, the poverty line was an income of about $7,400 for an urban family of four. It was higher for larger families, lower for smaller and rural ones. The poverty line is adjusted each year to keep pace with inflation.

The Northeast's poverty rate was 11.3 percent, up from 10.1 in the 1970 census. The North Central states were at 10.7 percent, down a fraction from 10.8 percent 10 years ago, and the West was at 11.3 percent, down from 11.7.

The bureau counts as southern the District of Columbia and 16 states: Texas, Oklahoma, Louisiana, Arkansas, Mississippi, Alabama, Tennessee, Kentucky, Florida, Georgia, South Carolina, North Carolina, Virginia, West Virginia, Maryland and Delaware. All except Virginia, Maryland and Delaware had median family income below the national average of $19,908 in the 1980 census, and the same 14 all had higher poverty percentages than the national average.

Two other often-used indices of progress also rate the South behind the nation.

In 12 southern states, a smaller percentage of the population had completed four years of high school than the 66.3 percent in the country as a whole; and in 10 of the southern states the percentage of dwelling units without adequate plumbing was higher than the 3.3 percent for the nation as a whole.

All five of the nation's top poverty states were in the South. In Mississippi, 24.5 percent of all people and 46 percent of the blacks were living in poverty; in Louisiana, 18.9 percent overall and 37.2 percent of the blacks; in Arkansas, 18.7 percent and 41.1 percent; in Kentucky, 18.4 and 38.3, and in Alabama, 17.9 and 36.8.

The five states having the least poverty, with rates from 8 to 8.7 percent, were Wyoming, Wisconsin, Nevada, Connecticut and New Hampshire.

Similarly, of the five metropolitan areas with the highest poverty rates--New Orleans, San Antonio, New York, Miami and Los Angeles-Long Beach, with figures ranging from 18.7 percent to 13.1 percent--three were in the South. The six with the lowest rates, ranging from 5.5 to 8 percent, were Nassau-Suffolk counties (N.Y.), Minneapolis-St. Paul, Anaheim-Santa Ana (Calif.), Seattle, Pittsburgh and San Jose.

The improvement in southern conditions is shown by the fact that the six metropolitan areas with the biggest decreases in the poverty rate since the 1970 census were Tampa-St. Petersburg, Houston, Phoenix, New Orleans, Fort Lauderdale-Hollywood (Fla.) and San Antonio. The biggest metropolitan-area increases were in New York, Newark, Chicago, Detroit and Los Angeles-Long Beach.