According to the Certified Flight Instructor (CFI), prior to takeoff and during the engine performance check, the left and right magnetos checked out okay, but the engine ran rough. He applied carburetor heat for a while and the engine smoothed out. He taxied out onto runway 05. During takeoff the engine continued to run rough and the stall warning horn was heard. He stated that he had planned to abort the takeoff but the airplane started to lift off the runway and he was at a point of no return. As the pilot continued to climb out the engine started loosing power and the stall warning horn was getting louder. The pilot immediately pulled the carburetor heat lever and the engine rpm dropped. The pilot made a forced landing in a field north of the airport. During landing the nose wheel stuck in the mud and the airplane flipped over and landed inverted. The pilot had not submitted an NTSB Form 6120.1 pilot operator report at the time of this report. Examination of the airplane by an FAA inspector found substantial damage to the vertical stabilizer, and buckling of the cockpit and fuselage. There were no mechanical or engine problems discovered during the post-accident examination of the airplane.