The nation's big chain stores added up their Christmas sales yesterday and discovered that consumers spent more money than most retailers and retail stock analysts had expected.

Sales for December ran 8 to 20 percent ahead of last year at most big chains, although Sears, Roebuck & Co., the biggest retailer of all, reported its volume was down two percent.

Sears downturn reflected that chain's decision to reduce its advertising and promotional price cuts, while the gains at the other chains apparently resulted from more aggressive advertising and pre-Christmas sales.

"It was a promotional environment." said Stuart Robbins, retail anlyst for Paine Webber Mitchell Hutchins. Because fall sales were slower than anticipated, most stores went into the Christmas season with larger inventories than they wanted and had to push harder to clean out their wares.

Whether this will mean lower profits for the critical period -- the fourth quarter when most retailers make their money for the year -- is not clear, Robbins said.

Heavy markdowns were taken by many chains in order to boost sales, he noted, but some big companies including K mart Corp. and Dayton Hudson Corp. were able to avoid cutting prices.

Some chains had raised their initial markups this fall, so the cuts will still give them better gross margins than last year, Rollins added.

He also pointed out that Christmas sales were very strong on "big ticket" items -- expensive clothing, electronic games, etc -- on which profits are generally greater than on cheaper goods.

Rollins said the figures released yesterday were "in general better in sales growth than either retailers oranalysts expected."

Even discounting the effect of inflation -- about 4 to 5 percent on most retail goods -- and factoring out the increases that came from opening additional stores, most major chains showed improvements over Christmas, 1977, which was the biggest ever.

Leading the major chains was Dayton Hudson Corp., which operates department stores in Minneapolis and Detroit, a midwestern discount chain and the B. Dalton book stores. Dayton Hudson December sales were up 20.1 percent to $564.6 million from $470.1 million a year ago.

At Sears, where sales have been declining for several months because of the new corporate strategy, December business declined to $2.68 billion from $2.74 billion in December 1977. For the first 4, weeks of its fiscal year, Sears sales increased 3.8 percent to a record $18.5 billion from $17.8 billion.

In the race to be the second largest retailer, Kmart stayed ahead of J.C. Penney for December and the year to date.

Kmart's Christmas-month volume rose 18 percent to just over $2 billion from $1.73 billion last year. For the 48 weeks, sales jumped 16 percent to $10.87 billion from $9.38 billion.

Penney's sales increased 11.5 percent over December 1977 to $1.90 billion from $1.71 billion and were 18.1 percent ahead of the first 11 months of 1977, at $10.22 billion compared with $8.66 billion.

The May Department Stores of St. Louis, the company that owns Hecht's, reported a 6 percent increase in December sales, to $501 million from $432 million. Year-to-date sales were up 12.3 percent to $2.4/ billion from $2.14 billion.

The May company said sales on a "same store" basis -- the same stores in operation a year ago -- were up 6.9 percent. with the company's department stores posing a 7.3 percent "same store" increase and its discount store up 5.1 percent.

Montgomery Ward reported an 8.8 percent increase, to $767 million from $705 million for December, and a 10.4 gain for the year, to $4.7 billion from $4.3 billion.

F. W. Woolworth said sales of its stores increased 12.1 percent in December and 9.3 percent for the first 48 weeks of fiscal 1978. December volume was $1.12 billion.

Carter Hawey Hale Stores, the company that owns Neiman Marcus here and several other chains, reported an 11.2 percent gain for the month, to $415 million from $373 million. Saes for the first 11 months of its year increased 11.2 percent to $2.2 billion from $1.82 billion.

G.C. Murphy Co. reported a 16.6 percent increase to $133 million from $114 million for December; year-to-date volume was up 6.4 percent to $674 million from $634 million.