AFTER A GATE DELAY TO LOAD LATE PASSENGERS, THE FLIGHT WAS CLEARED FOR TAKEOFF ON RUNWAY 28L. ABOUT 4 SECONDS AFTER ROTATION SPEED WAS CALLED, THE STICKSHAKER ACTIVATED AND THE TAKEOFF WAS ABORTED. A READOUT OF THE CVR INDICATED THAT THE THRUST REVERSERS WERE DEPLOYED 11 SECONDS LATER. THE AIRCRAFT WAS BROUGHT TO A STOP IN THE DIRT OVERRUN ABOUT 50' PAST THE END OF THE RUNWAY. ONLY MINOR DAMAGE WAS SUSTAINED BY THE AIRCRAFT AND THERE WERE NO INJURIES. THE AIRCRAFT HAD BEEN PLACARDED FOR AN INOPERATIVE ANTI-SKID SYSTEM PRIOR TO ITS DEPARTURE FROM SEATTLE, WA. INVESTIGATION REVEALED THAT THE RIGHT FLAP POSITION TRANSMITTER HAD MALFUNCTIONED DUE TO CORROSION. A MALFUNCTION OF EITHER FLAP POSITION TRANSMITTER CAN SEND AN ERRONEOUS FLAP SETTING SIGNAL TO THE STALL WARNING COMPUTER WHICH, IN TURN, WILL ACTIVATE THE STICKSHAKER/STALL WARNING SYSTEM AT INCORRECT AIRSPEEDS.