House Republicans are looking to today's election to replace Rep. John B. Anderson (R-Ill.) in the number three Republican House leadership post as a test case for 1980.

There is no doubt that whoever succeeds Anderson as conference chairman will be conservative. But what is being tested is the depth of disaffection with the present leadership, and the amount of influence the impatient, hard-charging freshman Republicians have in demanding new faces at the top.

Without the agitation of the freshmen, the election might have been a foregone conclusion. Rep. San Devine (R-Ohio), the present vice chairman of the conference, might simply have moved up in a uncontested election.

As it is, Devine must try to fend off two Illinois Republicans - Rep. Ed Derwinski, an influential veteran, known for his dry, acerbic wit and loud sportscoats, and Rep. Henry Hyde, the successful author of the "Hyde Amendment," which virtually knocks out all federal funding for abortions.

Hyde was "drafted" by the freshman Republicans because he is one of the new generation - he was first elected in 1974 - and thus is unencombuered by the barnacles of seniority.

They are looking, one freshman said, "for someone who will look good on 'Meet the Press,' effectively articulate Republican issues and be a floor leader."

"I had no notion of doing this," said Hyde, who only entered the race last Thursday "but when enough members wanted another option, I decided to run."

Hyde said he first checked to see that more than just the majority of the 37 freshman members would support him, but he admits they are the instigators of his campaign. "They see 1980 as a rare opportunity for the Republican Party to be an active, national success," he said. "In their view, there has to be a change in the status quo and some new leadership ready to carry the banner with energy and conviction."

Derwinski falls somewhere between Devine and Hyde and hopes to pick up support from those who want a fresh face but do not want to repudiate the present leadership.

But, Derwinski has a small problem: he is the foremost Republican trying to help the administration pass the legislation to implement the Panama Canal treaties. That legislation is scheduled for a vote today. "Of all the issues I had to pick to be a statesman on," Derwinski said with a laugh, admitting his support of the Panama Canal legislation is causing some problems in his race. "My timing was atrocious." Still Derwinski can expect support from many moderates.

Devine's campaign was given a boost Monday when conservative Texan James Collins dropped out. The two were competing for the same conservative votes. Still, if Derwinski or Hyde pulls off an upset, it will be seen as a portent of things to come for 1980.

House Minority Leader John Rhodes (R-Ariz.) is a tired man, who has already told his hometown papers he is considering quitting. "You get burned out," Rhodes told the Phoenix Gazette. "I don't think anyone ought to be minority leader for more than seven years." Next year will be Rhodes' seventh year.

Sniping from freshman members and party right-wingers has no doubt added to his burned out feeling. Rhodes has been criticized for not supporting a constitutional amendment to balance the budget, for inaccessibility, and for not formulating a floor strategy on same key issues.

Minority Whip Robert Michel (R-Ill.) has already said he is interested in succeeding Rhodes. But the right wingers and the new members are casting eyes at Rep. Guy Vander Jagt (R-Mich.), who as chairman of the GOP House Campaign Committee, has plenty of younger members grateful for his financial and political aid.

Still he does not have a lock on the freshmen support. If the freshmen who make up more than one-fifth of the Republican contingent win with Hyde, they may feel free to again draft someone of their own choosing. "Give us another freshman class the size or bigger than ours, and the balance of power will have shifted to those who have been here less than six years," one new member said.

Further down the ladder, there is another contested race for secretary of the conference. Here the choice is even clearer, between right wing activist Robert Bauman (R-Md.), a leadership critic, and Clair Burgener (Calif.), a quiet leadership-oriented veteran.

Burgener may have a leg up because he has a large block of western Republicans behind him. A Bauman victory would be a bag sign for the present leadership. CAPTION: Picture, REP. EDWARD J. DERWINSKI . . . "my timing was atrocious"